test no 1 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_SerialOver calling smultin_MultinomialOver test no 1 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 2 0 0 0 0 > 0.99999 || = 0.64 503 493 533 470 464 | 500 < 0.00002 1 1 0 0 0 | 0.5 | 1 0 1 0 1 > 0.99998 || = 0.63 523 524 523 468 466 | 500 < 0.00003 0 0 1 0 2 | 0.5 | 0 1 0 0 0 > 0.99997 || = 0.62 477 516 489 492 515 | 500 < 0.00004 1 0 0 0 1 | 0.5 | 0 1 0 0 1 > 0.99996 || = 0.61 487 529 480 523 482 | 500 < 0.00005 0 1 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99995 || = 0.60 453 550 523 546 506 | 500 < 0.00006 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 495 462 485 501 498 | 500 < 0.00007 2 1 0 0 2 | 0.5 | 1 1 3 1 0 > 0.99993 || = 0.58 484 481 487 529 515 | 500 < 0.00008 1 1 1 0 2 | 0.5 | 0 1 1 0 0 > 0.99992 || = 0.57 485 469 494 494 496 | 500 < 0.00009 1 1 0 0 1 | 0.5 | 0 1 0 1 1 > 0.99991 || = 0.56 505 500 503 481 500 | 500 < 0.0001 0 0 1 0 1 | 0.5 | 1 0 2 1 2 > 0.9999 || = 0.55 510 514 461 515 509 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 491 472 496 479 499 | 500 < 0.0001 7 5 3 0 9 | 5 | 6 5 7 3 5 > 0.9999 || = 0.53 507 526 478 474 528 | 500 < 0.0002 6 4 8 3 13 | 5 | 2 1 4 2 3 > 0.9998 || = 0.52 522 467 507 486 461 | 500 < 0.0003 6 2 6 6 5 | 5 | 10 5 2 5 4 > 0.9997 || = 0.51 530 483 494 494 496 | 500 < 0.0004 7 6 5 6 8 | 5 | 3 4 2 2 5 > 0.9996 || = 0.50 451 510 511 451 514 | 500 < 0.0005 7 5 5 4 5 | 5 | 5 5 2 6 6 > 0.9995 || = 0.49 512 513 504 507 535 | 500 < 0.0006 5 4 3 4 1 | 5 | 4 4 9 6 3 > 0.9994 || = 0.48 444 513 497 527 498 | 500 < 0.0007 7 6 6 4 6 | 5 | 5 6 8 5 4 > 0.9993 || = 0.47 486 542 542 520 542 | 500 < 0.0008 5 1 4 4 6 | 5 | 1 3 4 5 9 > 0.9992 || = 0.46 487 516 515 529 492 | 500 < 0.0009 2 9 9 6 6 | 5 | 6 3 5 3 10 > 0.9991 || = 0.45 504 495 508 526 498 | 500 < 0.001 9 4 7 3 5 | 5 | 4 2 4 5 4 > 0.999 || = 0.44 509 512 488 489 494 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 496 503 492 469 513 | 500 < 0.001 61 46 56 40 64 | 50 | 46 38 47 42 53 > 0.999 || = 0.42 519 513 517 504 474 | 500 < 0.002 57 45 51 61 57 | 50 | 47 58 49 49 46 > 0.998 || = 0.41 553 476 531 485 531 | 500 < 0.003 41 55 64 41 49 | 50 | 57 56 44 42 62 > 0.997 || = 0.40 521 509 493 517 491 | 500 < 0.004 54 59 52 54 41 | 50 | 41 48 56 42 51 > 0.996 || = 0.39 467 474 527 500 500 | 500 < 0.005 49 42 45 47 37 | 50 | 55 56 47 44 59 > 0.995 || = 0.38 456 510 508 471 472 | 500 < 0.006 45 48 53 37 55 | 50 | 56 45 57 49 51 > 0.994 || = 0.37 541 499 491 518 524 | 500 < 0.007 47 58 52 54 51 | 50 | 55 59 54 52 49 > 0.993 || = 0.36 543 501 501 519 506 | 500 < 0.008 47 55 50 48 50 | 50 | 60 50 41 44 40 > 0.992 || = 0.35 496 482 532 508 481 | 500 < 0.009 33 53 47 53 56 | 50 | 46 49 41 54 54 > 0.991 || = 0.34 510 495 511 506 521 | 500 < 0.01 44 47 51 40 44 | 50 | 49 41 40 53 50 > 0.99 || = 0.33 525 500 491 526 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 481 485 461 514 492 | 500 < 0.01 478 508 521 475 504 | 497.5 | 512 500 476 471 515 > 0.99 || = 0.31 504 486 496 502 495 | 500 = 0.01 252 270 258 241 237 | 252.5 | 235 260 262 229 242 = 0.99 || = 0.30 504 534 489 483 492 | 500 = 0.02 474 496 490 456 509 | 500 | 471 489 493 537 508 = 0.98 || = 0.29 488 525 516 479 487 | 500 =================================================================| 500 | 486 521 518 487 485 = 0.97 || = 0.28 558 466 504 520 486 | 500 Test smarsa_SerialOver calling smultin_MultinomialOver | 500 | 501 484 494 505 532 = 0.96 || = 0.27 537 497 483 547 469 | 500 smultin_MultinomialOver test: | 500 | 517 470 534 510 469 = 0.95 || = 0.26 521 485 475 498 523 | 500 ----------------------------------------------- | 500 | 488 508 517 504 455 = 0.94 || = 0.25 520 500 490 507 557 | 500 N = 1, n = 1000000000, r = 0, d = 256, t = 3, | 500 | 492 477 493 486 495 = 0.93 || = 0.24 479 527 463 490 504 | 500 | 500 | 538 471 494 503 499 = 0.92 || = 0.23 488 509 516 492 496 | 500 =================================================================| 500 | 528 518 471 545 466 = 0.91 || = 0.22 474 527 495 504 500 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 484 484 520 532 486 = 0.90 || = 0.21 517 474 464 522 515 | 500 -----------------------------------------------------------------| 500 | 511 512 520 469 512 = 0.89 || = 0.20 511 459 534 491 477 | 500 SD Bern.: d 1.07078 1.12838 0.84658 | 500 | 512 474 473 494 504 = 0.88 || = 0.19 483 494 519 506 486 | 500 s 0.90779 0.80289 0.97206 | 500 | 523 465 570 483 454 = 0.87 || = 0.18 520 513 485 474 505 | 500 t 0.97371 0.75535 0.91477 | 500 | 526 527 498 498 524 = 0.86 || = 0.17 505 512 516 463 518 | 500 m 1.00059 1.11858 0.76848 | 500 | 526 497 518 474 516 = 0.85 || = 0.16 473 505 486 530 492 | 500 x 0.95646 1.09049 0.85948 | 500 | 501 518 472 504 507 = 0.84 || = 0.15 516 508 481 512 524 | 500 | 500 | 488 494 466 518 499 = 0.83 || = 0.14 526 510 483 494 501 | 500 Changes: d 49 3 4 | 500 | 501 489 508 518 470 = 0.82 || = 0.13 510 456 509 492 485 | 500 s 48 4 6 | 500 | 499 498 504 497 508 = 0.81 || = 0.12 524 490 501 526 488 | 500 t 51 4 4 | 500 | 494 539 464 469 485 = 0.80 || = 0.11 471 506 512 473 506 | 500 m 46 8 3 | 500 | 512 509 464 491 472 = 0.79 || = 0.10 539 507 539 486 544 | 500 x 58 5 5 | 500 | 497 514 498 515 496 = 0.78 || = 0.09 516 466 493 483 471 | 500 -----------------------------------------------------------------| 500 | 478 524 479 546 534 = 0.77 || = 0.08 527 493 492 502 495 | 500 Aver./ d 0.49886 501 > 500: 4 7 6 6 6 5 4 3 7 5 | 500 | 439 481 511 537 494 = 0.76 || = 0.07 479 524 504 480 521 | 500 median s 0.49940 502 ----- 6 7 4 3 8 3 5 7 3 5 | 500 | 524 503 485 483 473 = 0.75 || = 0.06 475 531 488 486 525 | 500 t 0.50050 497 4 6 4 5 6 3 4 4 6 4 | 500 | 511 492 478 500 522 = 0.74 || = 0.05 509 503 462 510 517 | 500 m 0.50065 500 3 4 5 7 7 4 5 4 4 6 | 500 | 469 468 526 473 492 = 0.73 || = 0.04 499 502 498 490 464 | 500 x 0.49812 498 6 6 4 4 4 4 3 3 6 3 | 500 | 487 503 567 480 495 = 0.72 || = 0.03 503 497 506 559 540 | 500 -----------------------------------------------------------------| 500 | 453 519 516 501 520 = 0.71 || = 0.02 474 496 490 456 509 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 519 519 513 520 476 = 0.70 || = 0.01 252 270 258 241 237 | 252.5 d 0 0 5 12 66 16 2 0 0 | 500 | 494 499 524 521 542 = 0.69 || < 0.01 478 508 521 475 504 | 497.5 s 0 0 0 18 68 14 1 0 0 | 500 | 490 467 490 489 495 = 0.68 ||========================================================================= t 0 0 0 12 74 13 0 2 0 | 500 | 503 497 482 510 485 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 16 68 11 5 0 0 | 500 | 457 489 483 479 496 = 0.66 ||========================================================================= x 0 0 2 15 69 14 1 0 0 | 500 | 481 507 478 511 521 = 0.65 || Test smarsa_SerialOver calling smultin_MultinomialOver no 1 test no 2 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_SerialOver calling smultin_MultinomialOver test no 2 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 2 1 0 2 | 0.5 | 0 0 2 1 1 > 0.99999 || = 0.64 445 493 487 508 487 | 500 < 0.00002 1 1 1 0 0 | 0.5 | 0 0 5 0 1 > 0.99998 || = 0.63 473 490 515 497 500 | 500 < 0.00003 0 1 0 0 0 | 0.5 | 1 0 0 0 1 > 0.99997 || = 0.62 445 485 449 551 496 | 500 < 0.00004 0 0 0 0 2 | 0.5 | 1 0 0 1 0 > 0.99996 || = 0.61 481 508 498 500 529 | 500 < 0.00005 0 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 484 495 532 474 499 | 500 < 0.00006 1 1 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99994 || = 0.59 537 525 466 492 495 | 500 < 0.00007 0 1 0 0 1 | 0.5 | 0 1 1 1 0 > 0.99993 || = 0.58 489 516 495 476 519 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 530 542 476 507 486 | 500 < 0.00009 1 1 0 1 0 | 0.5 | 1 1 0 0 0 > 0.99991 || = 0.56 466 501 506 524 548 | 500 < 0.0001 0 0 0 1 0 | 0.5 | 0 1 0 1 1 > 0.9999 || = 0.55 521 508 507 486 473 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 484 528 489 508 514 | 500 < 0.0001 4 8 3 3 6 | 5 | 3 3 8 4 5 > 0.9999 || = 0.53 540 478 463 507 476 | 500 < 0.0002 2 4 4 4 1 | 5 | 1 0 1 3 2 > 0.9998 || = 0.52 516 446 500 498 522 | 500 < 0.0003 4 4 4 5 5 | 5 | 1 5 7 11 2 > 0.9997 || = 0.51 492 458 506 513 493 | 500 < 0.0004 7 6 6 2 3 | 5 | 5 4 8 4 2 > 0.9996 || = 0.50 489 513 522 485 508 | 500 < 0.0005 3 5 3 4 3 | 5 | 1 4 2 10 5 > 0.9995 || = 0.49 507 488 489 494 516 | 500 < 0.0006 4 6 8 3 2 | 5 | 3 4 7 8 8 > 0.9994 || = 0.48 491 546 487 479 486 | 500 < 0.0007 8 6 3 0 3 | 5 | 4 3 4 10 8 > 0.9993 || = 0.47 519 502 535 543 498 | 500 < 0.0008 7 6 1 5 6 | 5 | 5 9 6 3 3 > 0.9992 || = 0.46 488 525 506 520 527 | 500 < 0.0009 6 6 3 5 2 | 5 | 3 5 4 2 5 > 0.9991 || = 0.45 479 500 538 490 520 | 500 < 0.001 3 3 5 2 4 | 5 | 8 4 8 3 3 > 0.999 || = 0.44 539 566 520 518 497 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 506 497 541 488 494 | 500 < 0.001 48 54 40 33 35 | 50 | 34 41 55 58 43 > 0.999 || = 0.42 534 511 490 514 517 | 500 < 0.002 57 35 63 55 52 | 50 | 44 59 40 57 50 > 0.998 || = 0.41 513 474 498 515 458 | 500 < 0.003 41 57 47 38 41 | 50 | 50 49 58 53 39 > 0.997 || = 0.40 507 531 527 482 513 | 500 < 0.004 45 47 47 56 49 | 50 | 47 58 45 48 52 > 0.996 || = 0.39 493 496 566 503 489 | 500 < 0.005 42 52 51 48 32 | 50 | 40 44 56 36 56 > 0.995 || = 0.38 495 495 511 520 517 | 500 < 0.006 55 51 35 59 43 | 50 | 43 43 44 66 73 > 0.994 || = 0.37 496 509 484 509 499 | 500 < 0.007 49 56 52 58 39 | 50 | 60 47 49 51 49 > 0.993 || = 0.36 509 496 498 526 550 | 500 < 0.008 62 46 52 42 47 | 50 | 56 44 56 47 61 > 0.992 || = 0.35 504 515 514 468 482 | 500 < 0.009 44 51 46 46 61 | 50 | 50 32 36 57 46 > 0.991 || = 0.34 489 503 462 497 528 | 500 < 0.01 46 43 50 43 55 | 50 | 41 46 45 48 47 > 0.99 || = 0.33 500 518 468 506 507 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 475 492 527 517 534 | 500 < 0.01 489 492 483 478 454 | 497.5 | 465 463 484 521 516 > 0.99 || = 0.31 494 499 490 488 540 | 500 = 0.01 253 289 245 222 254 | 252.5 | 253 262 257 229 240 = 0.99 || = 0.30 533 538 497 481 462 | 500 = 0.02 470 434 521 535 541 | 500 | 494 479 484 490 498 = 0.98 || = 0.29 484 482 460 497 465 | 500 =================================================================| 500 | 539 486 481 453 494 = 0.97 || = 0.28 506 494 488 490 523 | 500 Test smarsa_SerialOver calling smultin_MultinomialOver | 500 | 486 496 493 507 462 = 0.96 || = 0.27 499 494 504 488 514 | 500 smultin_MultinomialOver test: | 500 | 529 493 510 520 475 = 0.95 || = 0.26 476 489 504 474 471 | 500 ----------------------------------------------- | 500 | 503 499 491 505 475 = 0.94 || = 0.25 505 506 489 479 478 | 500 N = 1, n = 1000000000, r = 22, d = 256, t = 3, | 500 | 526 514 456 516 521 = 0.93 || = 0.24 497 508 533 470 525 | 500 | 500 | 506 494 528 546 527 = 0.92 || = 0.23 499 508 504 489 521 | 500 =================================================================| 500 | 514 543 520 518 489 = 0.91 || = 0.22 463 483 524 467 507 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 506 524 489 477 515 = 0.90 || = 0.21 547 509 520 526 449 | 500 -----------------------------------------------------------------| 500 | 521 499 574 501 500 = 0.89 || = 0.20 487 494 470 500 449 | 500 SD Bern.: d 1.06711 0.94386 1.15556 | 500 | 506 493 494 521 466 = 0.88 || = 0.19 485 501 495 500 491 | 500 s 1.05341 0.90155 1.18125 | 500 | 515 507 500 500 502 = 0.87 || = 0.18 457 516 531 519 498 | 500 t 1.12228 1.03685 1.04358 | 500 | 506 516 535 535 499 = 0.86 || = 0.17 506 529 482 506 494 | 500 m 0.92988 1.24319 1.13281 | 500 | 520 506 514 522 536 = 0.85 || = 0.16 459 522 494 517 420 | 500 x 1.19435 1.38632 1.33182 | 500 | 492 474 491 478 504 = 0.84 || = 0.15 472 499 514 527 508 | 500 | 500 | 518 526 477 498 462 = 0.83 || = 0.14 471 515 482 510 531 | 500 Changes: d 50 6 2 | 500 | 506 473 506 462 548 = 0.82 || = 0.13 514 477 480 481 478 | 500 s 52 7 4 | 500 | 498 485 510 524 506 = 0.81 || = 0.12 468 522 515 496 493 | 500 t 48 6 7 | 500 | 486 522 540 484 505 = 0.80 || = 0.11 468 523 474 489 470 | 500 m 47 6 5 | 500 | 521 514 463 495 522 = 0.79 || = 0.10 494 456 497 461 508 | 500 x 53 3 4 | 500 | 516 451 481 479 569 = 0.78 || = 0.09 500 474 539 508 498 | 500 -----------------------------------------------------------------| 500 | 506 481 482 479 467 = 0.77 || = 0.08 510 438 464 495 454 | 500 Aver./ d 0.50282 500 > 500: 6 2 3 3 7 5 4 6 8 7 | 500 | 504 505 540 504 499 = 0.76 || = 0.07 512 465 497 510 518 | 500 median s 0.50012 500 ----- 4 7 4 5 6 6 3 6 5 3 | 500 | 484 509 518 473 496 = 0.75 || = 0.06 511 487 538 497 488 | 500 t 0.49888 497 5 3 6 4 6 4 2 4 5 4 | 500 | 511 513 506 532 486 = 0.74 || = 0.05 460 517 470 501 556 | 500 m 0.50079 500 6 5 1 6 5 5 4 3 5 7 | 500 | 496 463 468 495 460 = 0.73 || = 0.04 511 509 519 504 487 | 500 x 0.50083 499 5 3 5 6 5 4 5 3 6 3 | 500 | 438 496 496 531 474 = 0.72 || = 0.03 536 512 557 513 508 | 500 -----------------------------------------------------------------| 500 | 502 522 482 488 485 = 0.71 || = 0.02 470 434 521 535 541 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 520 518 501 509 522 = 0.70 || = 0.01 253 289 245 222 254 | 252.5 d 0 0 3 14 71 10 2 1 0 | 500 | 567 479 446 498 492 = 0.69 || < 0.01 489 492 483 478 454 | 497.5 s 0 0 4 11 72 11 3 0 0 | 500 | 562 469 475 478 471 = 0.68 ||========================================================================= t 0 0 2 16 65 15 2 1 0 | 500 | 495 495 492 490 517 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 13 73 12 2 0 0 | 500 | 519 514 474 471 517 = 0.66 ||========================================================================= x 0 1 3 17 63 11 5 1 0 | 500 | 498 486 490 538 553 = 0.65 || Test smarsa_SerialOver calling smultin_MultinomialOver no 2 test no 3 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_CollisionOver calling smultin_MultinomialOver test no 3 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 2 | 0.5 | 1 0 0 0 0 > 0.99999 || = 0.64 494 490 498 493 540 | 500 < 0.00002 0 0 1 0 0 | 0.5 | 0 0 0 2 2 > 0.99998 || = 0.63 498 520 490 518 498 | 500 < 0.00003 1 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99997 || = 0.62 478 497 512 497 543 | 500 < 0.00004 3 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 504 508 501 515 510 | 500 < 0.00005 0 1 1 1 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 563 544 489 525 555 | 500 < 0.00006 0 0 1 0 0 | 0.5 | 0 1 0 0 0 > 0.99994 || = 0.59 531 503 500 562 564 | 500 < 0.00007 1 1 0 0 1 | 0.5 | 0 1 0 1 2 > 0.99993 || = 0.58 522 520 503 573 546 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 1 2 0 1 2 > 0.99992 || = 0.57 526 560 572 533 533 | 500 < 0.00009 1 0 2 0 1 | 0.5 | 0 0 1 1 1 > 0.99991 || = 0.56 505 550 552 492 576 | 500 < 0.0001 0 0 0 1 1 | 0.5 | 2 1 0 1 1 > 0.9999 || = 0.55 528 553 517 495 554 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 568 528 545 530 537 | 500 < 0.0001 7 3 5 2 7 | 5 | 4 5 1 6 9 > 0.9999 || = 0.53 552 514 592 570 542 | 500 < 0.0002 11 4 8 8 5 | 5 | 3 3 1 3 1 > 0.9998 || = 0.52 531 516 542 590 542 | 500 < 0.0003 5 5 4 5 7 | 5 | 8 5 2 6 7 > 0.9997 || = 0.51 530 551 519 538 551 | 500 < 0.0004 3 8 5 5 5 | 5 | 6 5 2 1 4 > 0.9996 || = 0.50 1065 1075 1072 1046 1070 | 500 < 0.0005 2 3 5 5 5 | 5 | 3 5 1 4 1 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 3 1 3 4 5 | 5 | 6 2 7 3 8 > 0.9994 || = 0.48 535 536 522 549 527 | 500 < 0.0007 3 5 7 6 5 | 5 | 6 14 10 12 4 > 0.9993 || = 0.47 542 554 526 528 583 | 500 < 0.0008 4 4 9 14 6 | 5 | 9 5 9 9 4 > 0.9992 || = 0.46 530 557 488 532 533 | 500 < 0.0009 2 1 7 1 4 | 5 | 5 5 1 5 3 > 0.9991 || = 0.45 546 528 511 497 509 | 500 < 0.001 3 6 4 6 6 | 5 | 6 6 3 6 5 > 0.999 || = 0.44 507 563 539 495 530 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 510 545 536 528 515 | 500 < 0.001 43 40 57 56 55 | 50 | 56 55 37 55 46 > 0.999 || = 0.42 543 509 580 511 521 | 500 < 0.002 60 50 53 46 47 | 50 | 48 48 47 48 58 > 0.998 || = 0.41 546 542 523 507 503 | 500 < 0.003 52 49 49 47 49 | 50 | 58 60 51 63 40 > 0.997 || = 0.40 534 513 520 550 542 | 500 < 0.004 53 39 42 55 44 | 50 | 43 41 34 37 48 > 0.996 || = 0.39 491 484 582 526 468 | 500 < 0.005 57 62 44 49 51 | 50 | 50 54 50 45 57 > 0.995 || = 0.38 525 544 501 528 517 | 500 < 0.006 40 38 37 42 30 | 50 | 53 33 49 33 33 > 0.994 || = 0.37 469 537 479 515 521 | 500 < 0.007 48 37 37 48 41 | 50 | 46 49 28 49 54 > 0.993 || = 0.36 499 508 520 522 500 | 500 < 0.008 58 38 55 38 52 | 50 | 48 58 68 50 54 > 0.992 || = 0.35 465 510 470 487 490 | 500 < 0.009 68 70 78 53 59 | 50 | 61 60 72 65 56 > 0.991 || = 0.34 452 473 482 487 480 | 500 < 0.01 37 34 26 29 28 | 50 | 41 27 25 31 26 > 0.99 || = 0.33 520 452 449 484 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 469 479 499 505 490 | 500 < 0.01 516 457 478 463 456 | 497.5 | 504 485 461 476 472 > 0.99 || = 0.31 450 467 460 478 470 | 500 = 0.01 245 248 245 241 222 | 252.5 | 270 254 248 241 275 = 0.99 || = 0.30 484 470 424 453 458 | 500 = 0.02 508 498 495 509 487 | 500 | 450 421 475 403 437 = 0.98 || = 0.29 454 475 430 473 455 | 500 =================================================================| 500 | 527 525 533 550 575 = 0.97 || = 0.28 431 511 441 463 443 | 500 Test smarsa_CollisionOver calling smultin_MultinomialOver | 500 | 453 464 504 436 434 = 0.96 || = 0.27 424 440 446 400 411 | 500 smultin_MultinomialOver test: | 500 | 413 393 429 401 406 = 0.95 || = 0.26 449 466 441 410 442 | 500 ----------------------------------------------- | 500 | 673 581 637 638 610 = 0.94 || = 0.25 839 901 857 891 853 | 500 N = 30, n = 20000000, r = 0, d = 2097152, t = 2, | 500 | 374 343 351 345 356 = 0.93 || = 0.24 416 395 426 430 404 | 500 | 500 | 620 607 617 623 647 = 0.92 || = 0.23 400 407 400 432 353 | 500 =================================================================| 500 | 449 465 447 441 459 = 0.91 || = 0.22 381 392 378 386 406 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 497 489 507 478 467 = 0.90 || = 0.21 791 760 755 803 772 | 500 -----------------------------------------------------------------| 500 | 503 524 480 510 501 = 0.89 || = 0.20 402 368 365 386 388 | 500 SD Bern.: d 5.57963 1.32126 0.87678 | 500 | 542 567 529 502 523 = 0.88 || = 0.19 366 359 357 368 349 | 500 s 5.69138 1.72074 1.55576 | 500 | 539 572 576 555 608 = 0.87 || = 0.18 715 683 693 703 682 | 500 t 5.52861 1.94107 2.17041 | 500 | 305 287 315 297 280 = 0.86 || = 0.17 308 339 362 318 353 | 500 m 5.78606 1.22453 1.59327 | 500 | 599 607 640 644 597 = 0.85 || = 0.16 633 622 617 689 611 | 500 x 5.59379 1.49874 1.52784 | 500 | 339 324 315 303 346 = 0.84 || = 0.15 299 299 310 314 334 | 500 | 500 | 724 675 698 719 682 = 0.83 || = 0.14 544 571 597 621 588 | 500 Changes: d 46 4 7 | 500 | 347 370 366 358 354 = 0.82 || = 0.13 578 550 591 546 506 | 500 s 48 4 7 | 500 | 359 399 368 352 314 = 0.81 || = 0.12 539 509 526 538 507 | 500 t 46 3 4 | 500 | 743 751 724 718 707 = 0.80 || = 0.11 475 492 468 469 492 | 500 m 48 5 5 | 500 | 409 355 403 382 402 = 0.79 || = 0.10 464 443 464 479 456 | 500 x 44 5 6 | 500 | 375 401 415 401 427 = 0.78 || = 0.09 407 404 435 465 432 | 500 -----------------------------------------------------------------| 500 | 392 378 392 429 418 = 0.77 || = 0.08 569 611 583 584 573 | 500 Aver./ d 0.50113 497 > 500: 5 5 2 2 9 10 2 2 5 5 | 500 | 827 875 844 872 853 = 0.76 || = 0.07 341 334 357 344 333 | 500 median s 0.49964 498 ----- 3 5 3 4 9 10 4 2 5 4 | 500 | 454 455 414 420 406 = 0.75 || = 0.06 612 598 540 629 615 | 500 t 0.50079 491 3 5 2 3 8 8 4 2 5 4 | 500 | 462 436 432 415 453 = 0.74 || = 0.05 403 376 408 390 402 | 500 m 0.49710 493 4 5 2 5 7 8 3 2 5 3 | 500 | 473 452 475 473 427 = 0.73 || = 0.04 542 562 564 563 554 | 500 x 0.50126 501 3 5 2 3 9 10 7 2 5 4 | 500 | 494 470 484 433 449 = 0.72 || = 0.03 442 444 480 404 462 | 500 -----------------------------------------------------------------| 500 | 466 451 466 444 459 = 0.71 || = 0.02 508 498 495 509 487 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 485 428 470 445 483 = 0.70 || = 0.01 245 248 245 241 222 | 252.5 d 18 4 9 11 21 19 4 3 12 | 500 | 473 506 467 451 442 = 0.69 || < 0.01 516 457 478 463 456 | 497.5 s 20 2 8 10 26 9 10 4 12 | 500 | 471 476 470 458 513 = 0.68 ||========================================================================= t 16 7 6 11 29 10 3 5 14 | 500 | 523 497 525 491 511 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 20 6 6 7 27 11 7 3 14 | 500 | 494 488 504 497 517 = 0.66 ||========================================================================= x 19 4 8 11 23 12 6 5 13 | 500 | 467 515 495 529 514 = 0.65 || Test smarsa_CollisionOver calling smultin_MultinomialOver no 3 test no 4 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_CollisionOver calling smultin_MultinomialOver test no 4 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 2 0 0 0 | 0.5 | 0 0 1 1 0 > 0.99999 || = 0.64 521 500 503 554 500 | 500 < 0.00002 0 0 0 1 1 | 0.5 | 0 0 3 1 0 > 0.99998 || = 0.63 475 489 516 496 519 | 500 < 0.00003 2 0 0 0 0 | 0.5 | 0 0 2 0 0 > 0.99997 || = 0.62 526 510 514 492 503 | 500 < 0.00004 0 2 0 1 4 | 0.5 | 0 0 0 0 2 > 0.99996 || = 0.61 499 497 539 514 545 | 500 < 0.00005 1 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 518 509 549 592 539 | 500 < 0.00006 0 0 1 0 0 | 0.5 | 0 1 0 0 1 > 0.99994 || = 0.59 476 543 563 513 501 | 500 < 0.00007 0 1 0 0 1 | 0.5 | 0 0 0 1 1 > 0.99993 || = 0.58 556 546 520 546 514 | 500 < 0.00008 0 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 556 550 513 518 511 | 500 < 0.00009 0 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 522 500 503 522 542 | 500 < 0.0001 0 1 0 0 1 | 0.5 | 1 0 0 0 1 > 0.9999 || = 0.55 561 560 531 532 556 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 524 534 563 534 532 | 500 < 0.0001 4 8 2 3 7 | 5 | 1 1 7 3 5 > 0.9999 || = 0.53 527 559 526 486 561 | 500 < 0.0002 4 9 3 3 5 | 5 | 3 3 1 3 3 > 0.9998 || = 0.52 533 583 541 584 520 | 500 < 0.0003 4 2 4 5 5 | 5 | 5 7 4 5 6 > 0.9997 || = 0.51 535 560 571 535 527 | 500 < 0.0004 5 2 7 4 3 | 5 | 2 4 4 2 5 > 0.9996 || = 0.50 1055 1129 1072 1083 1036 | 500 < 0.0005 9 3 4 4 2 | 5 | 2 5 2 4 5 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 4 5 6 4 3 | 5 | 4 8 2 4 5 > 0.9994 || = 0.48 553 525 520 534 561 | 500 < 0.0007 3 2 7 5 4 | 5 | 8 9 6 6 6 > 0.9993 || = 0.47 547 559 555 545 551 | 500 < 0.0008 5 6 7 5 6 | 5 | 3 4 5 5 8 > 0.9992 || = 0.46 566 548 552 562 546 | 500 < 0.0009 7 3 3 7 3 | 5 | 1 2 2 5 6 > 0.9991 || = 0.45 553 559 548 521 586 | 500 < 0.001 2 4 7 3 5 | 5 | 6 4 1 2 4 > 0.999 || = 0.44 535 548 509 500 547 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 521 519 545 517 583 | 500 < 0.001 47 44 50 43 43 | 50 | 35 47 34 39 53 > 0.999 || = 0.42 534 498 540 550 523 | 500 < 0.002 42 44 40 53 50 | 50 | 56 56 56 62 52 > 0.998 || = 0.41 512 478 558 559 472 | 500 < 0.003 59 58 34 45 47 | 50 | 43 37 42 51 51 > 0.997 || = 0.40 508 544 500 537 511 | 500 < 0.004 48 52 51 58 53 | 50 | 44 47 39 32 54 > 0.996 || = 0.39 525 492 520 485 524 | 500 < 0.005 51 63 45 48 56 | 50 | 48 50 55 51 58 > 0.995 || = 0.38 547 511 493 507 487 | 500 < 0.006 35 35 41 40 33 | 50 | 37 50 26 50 36 > 0.994 || = 0.37 465 506 547 545 497 | 500 < 0.007 45 53 44 55 39 | 50 | 50 48 50 45 62 > 0.993 || = 0.36 509 527 539 531 466 | 500 < 0.008 52 51 44 52 57 | 50 | 54 50 41 49 53 > 0.992 || = 0.35 508 506 503 513 479 | 500 < 0.009 53 40 45 71 53 | 50 | 58 54 68 58 60 > 0.991 || = 0.34 477 449 482 510 530 | 500 < 0.01 31 36 30 31 32 | 50 | 25 27 40 37 35 > 0.99 || = 0.33 468 487 501 490 529 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 490 481 435 480 433 | 500 < 0.01 463 476 424 496 463 | 497.5 | 450 466 451 474 514 > 0.99 || = 0.31 467 493 424 511 451 | 500 = 0.01 260 247 244 253 273 | 252.5 | 259 276 252 259 249 = 0.99 || = 0.30 446 449 456 459 441 | 500 = 0.02 506 488 495 462 510 | 500 | 456 430 443 440 459 = 0.98 || = 0.29 470 442 445 488 472 | 500 =================================================================| 500 | 554 528 528 516 537 = 0.97 || = 0.28 456 483 448 426 391 | 500 Test smarsa_CollisionOver calling smultin_MultinomialOver | 500 | 477 458 433 452 521 = 0.96 || = 0.27 428 446 453 449 444 | 500 smultin_MultinomialOver test: | 500 | 416 421 428 421 399 = 0.95 || = 0.26 448 411 431 446 449 | 500 ----------------------------------------------- | 500 | 634 682 617 628 629 = 0.94 || = 0.25 813 878 828 869 885 | 500 N = 30, n = 20000000, r = 9, d = 2097152, t = 2, | 500 | 404 341 370 363 356 = 0.93 || = 0.24 400 394 395 434 407 | 500 | 500 | 605 603 627 599 586 = 0.92 || = 0.23 379 400 380 417 415 | 500 =================================================================| 500 | 473 420 417 445 442 = 0.91 || = 0.22 412 423 393 381 386 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 468 486 475 498 476 = 0.90 || = 0.21 728 733 728 754 785 | 500 -----------------------------------------------------------------| 500 | 504 538 523 501 514 = 0.89 || = 0.20 356 371 387 381 353 | 500 SD Bern.: d 5.47418 1.25202 1.56538 | 500 | 548 537 541 548 562 = 0.88 || = 0.19 367 343 364 359 343 | 500 s 5.75950 1.29679 1.24319 | 500 | 540 566 552 583 562 = 0.87 || = 0.18 678 661 671 691 672 | 500 t 5.73908 1.38632 1.78021 | 500 | 301 312 285 280 295 = 0.86 || = 0.17 343 333 352 336 334 | 500 m 5.58154 1.47178 1.30448 | 500 | 672 645 699 614 622 = 0.85 || = 0.16 649 641 686 619 662 | 500 x 5.60378 1.33857 1.23996 | 500 | 335 328 323 298 338 = 0.84 || = 0.15 296 310 339 317 319 | 500 | 500 | 722 665 672 694 656 = 0.83 || = 0.14 570 600 597 566 624 | 500 Changes: d 52 6 4 | 500 | 384 401 365 368 338 = 0.82 || = 0.13 528 578 547 584 558 | 500 s 46 4 4 | 500 | 378 362 345 368 357 = 0.81 || = 0.12 552 529 548 522 499 | 500 t 42 2 6 | 500 | 732 725 767 689 771 = 0.80 || = 0.11 450 517 444 500 490 | 500 m 50 6 6 | 500 | 388 413 362 342 380 = 0.79 || = 0.10 431 413 457 457 471 | 500 x 43 4 3 | 500 | 400 409 369 384 394 = 0.78 || = 0.09 422 452 395 389 410 | 500 -----------------------------------------------------------------| 500 | 413 385 404 433 427 = 0.77 || = 0.08 573 610 642 583 598 | 500 Aver./ d 0.50123 501 > 500: 5 5 2 4 9 9 5 2 5 4 | 500 | 842 828 874 832 787 = 0.76 || = 0.07 362 335 347 342 353 | 500 median s 0.49935 489 ----- 3 6 2 4 7 9 1 2 5 4 | 500 | 411 410 419 447 453 = 0.75 || = 0.06 637 613 641 614 621 | 500 t 0.49966 498 3 5 2 5 8 10 5 2 5 3 | 500 | 389 441 464 464 431 = 0.74 || = 0.05 415 361 397 415 385 | 500 m 0.49875 498 4 5 2 6 8 9 2 2 5 4 | 500 | 437 452 415 457 438 = 0.73 || = 0.04 581 616 574 535 601 | 500 x 0.49941 499 5 4 2 3 8 10 3 2 5 5 | 500 | 466 421 441 435 429 = 0.72 || = 0.03 452 434 423 415 421 | 500 -----------------------------------------------------------------| 500 | 466 476 494 448 445 = 0.71 || = 0.02 506 488 495 462 510 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 463 426 471 470 494 = 0.70 || = 0.01 260 247 244 253 273 | 252.5 d 17 7 7 16 18 10 11 3 12 | 500 | 506 468 497 473 473 = 0.69 || < 0.01 463 476 424 496 463 | 497.5 s 18 8 9 4 25 10 10 2 15 | 500 | 451 479 457 454 475 = 0.68 ||========================================================================= t 19 9 8 6 21 10 12 2 14 | 500 | 501 449 489 477 495 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 15 6 10 9 28 7 9 4 13 | 500 | 494 483 478 495 479 = 0.66 ||========================================================================= x 19 6 8 9 22 10 10 3 14 | 500 | 521 484 527 494 500 = 0.65 || Test smarsa_CollisionOver calling smultin_MultinomialOver no 4 test no 5 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_CollisionOver calling smultin_MultinomialOver test no 5 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 1 0 0 | 0.5 | 1 0 1 2 0 > 0.99999 || = 0.64 485 514 506 522 501 | 500 < 0.00002 1 0 1 0 1 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 493 517 509 526 502 | 500 < 0.00003 0 0 0 0 1 | 0.5 | 0 1 2 0 1 > 0.99997 || = 0.62 503 553 529 488 506 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 0 1 0 1 0 > 0.99996 || = 0.61 540 526 495 550 503 | 500 < 0.00005 0 2 0 1 1 | 0.5 | 1 0 1 0 0 > 0.99995 || = 0.60 516 542 525 522 564 | 500 < 0.00006 0 0 1 0 1 | 0.5 | 1 0 0 1 1 > 0.99994 || = 0.59 515 537 502 520 555 | 500 < 0.00007 0 0 1 1 1 | 0.5 | 1 0 1 0 1 > 0.99993 || = 0.58 527 517 527 510 533 | 500 < 0.00008 1 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99992 || = 0.57 549 530 553 559 536 | 500 < 0.00009 1 0 0 1 2 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 536 560 510 539 564 | 500 < 0.0001 0 1 1 2 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 502 558 523 549 556 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 569 477 564 563 537 | 500 < 0.0001 5 3 6 6 8 | 5 | 5 3 6 4 3 > 0.9999 || = 0.53 560 600 540 534 520 | 500 < 0.0002 7 2 3 4 9 | 5 | 5 3 2 4 3 > 0.9998 || = 0.52 537 541 576 545 545 | 500 < 0.0003 3 4 5 0 2 | 5 | 8 3 5 2 5 > 0.9997 || = 0.51 530 508 546 517 544 | 500 < 0.0004 6 3 4 7 3 | 5 | 5 2 3 2 4 > 0.9996 || = 0.50 1057 1072 1132 1076 1088 | 500 < 0.0005 5 6 5 7 3 | 5 | 3 4 5 2 3 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 5 8 2 7 4 | 5 | 2 16 2 2 6 > 0.9994 || = 0.48 545 527 502 529 581 | 500 < 0.0007 4 7 3 4 3 | 5 | 3 7 9 6 6 > 0.9993 || = 0.47 519 576 581 539 541 | 500 < 0.0008 13 8 6 8 4 | 5 | 3 4 7 8 11 > 0.9992 || = 0.46 521 551 521 533 544 | 500 < 0.0009 6 1 6 6 4 | 5 | 4 3 5 5 2 > 0.9991 || = 0.45 540 524 511 508 551 | 500 < 0.001 4 10 4 4 2 | 5 | 2 2 4 10 6 > 0.999 || = 0.44 538 568 500 525 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 549 498 514 529 499 | 500 < 0.001 58 52 44 53 42 | 50 | 40 47 48 45 49 > 0.999 || = 0.42 560 530 501 528 526 | 500 < 0.002 55 51 48 38 38 | 50 | 46 46 48 57 47 > 0.998 || = 0.41 496 496 533 508 532 | 500 < 0.003 42 49 45 48 45 | 50 | 56 41 48 49 51 > 0.997 || = 0.40 558 520 548 559 541 | 500 < 0.004 63 56 63 58 37 | 50 | 49 42 39 36 37 > 0.996 || = 0.39 477 552 556 537 491 | 500 < 0.005 48 48 46 54 62 | 50 | 60 54 51 46 65 > 0.995 || = 0.38 501 515 553 530 500 | 500 < 0.006 42 38 34 50 34 | 50 | 35 59 40 38 49 > 0.994 || = 0.37 512 495 511 530 503 | 500 < 0.007 59 49 48 55 48 | 50 | 53 41 50 40 57 > 0.993 || = 0.36 505 481 464 532 444 | 500 < 0.008 55 47 41 66 55 | 50 | 46 55 67 47 50 > 0.992 || = 0.35 509 483 492 498 468 | 500 < 0.009 68 61 70 58 59 | 50 | 69 68 64 59 56 > 0.991 || = 0.34 480 492 484 492 456 | 500 < 0.01 30 27 36 28 37 | 50 | 40 30 34 42 27 > 0.99 || = 0.33 477 509 479 485 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 496 461 483 459 496 | 500 < 0.01 520 478 475 508 457 | 497.5 | 494 483 489 459 488 > 0.99 || = 0.31 420 490 502 465 487 | 500 = 0.01 226 266 251 226 250 | 252.5 | 265 283 292 246 256 = 0.99 || = 0.30 454 449 441 459 499 | 500 = 0.02 471 509 499 490 475 | 500 | 491 433 435 458 464 = 0.98 || = 0.29 443 443 484 458 436 | 500 =================================================================| 500 | 542 510 554 553 590 = 0.97 || = 0.28 462 462 455 440 437 | 500 Test smarsa_CollisionOver calling smultin_MultinomialOver | 500 | 475 484 488 452 472 = 0.96 || = 0.27 427 442 459 486 442 | 500 smultin_MultinomialOver test: | 500 | 449 395 418 405 411 = 0.95 || = 0.26 464 435 447 409 456 | 500 ----------------------------------------------- | 500 | 636 637 663 649 617 = 0.94 || = 0.25 848 792 868 892 831 | 500 N = 30, n = 20000000, r = 0, d = 16384, t = 3, | 500 | 387 353 340 372 366 = 0.93 || = 0.24 366 411 425 409 390 | 500 | 500 | 632 589 585 597 597 = 0.92 || = 0.23 374 414 418 387 407 | 500 =================================================================| 500 | 453 440 424 471 443 = 0.91 || = 0.22 399 421 361 396 450 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 476 470 466 481 444 = 0.90 || = 0.21 782 783 782 783 695 | 500 -----------------------------------------------------------------| 500 | 506 499 536 460 478 = 0.89 || = 0.20 374 369 390 384 397 | 500 SD Bern.: d 5.47907 1.56282 1.38921 | 500 | 564 501 548 525 513 = 0.88 || = 0.19 379 375 368 339 356 | 500 s 5.53041 1.30448 1.48194 | 500 | 598 602 571 568 592 = 0.87 || = 0.18 681 680 667 671 669 | 500 t 5.75848 1.54154 1.39711 | 500 | 302 279 298 315 288 = 0.86 || = 0.17 332 314 340 351 327 | 500 m 5.62275 1.46086 1.17104 | 500 | 587 656 622 568 616 = 0.85 || = 0.16 598 654 671 626 598 | 500 x 5.47160 1.47110 1.42899 | 500 | 345 339 307 313 358 = 0.84 || = 0.15 314 302 330 297 302 | 500 | 500 | 681 670 704 712 665 = 0.83 || = 0.14 612 612 559 573 586 | 500 Changes: d 43 5 8 | 500 | 357 334 367 355 323 = 0.82 || = 0.13 569 563 525 548 593 | 500 s 52 5 4 | 500 | 395 380 352 366 358 = 0.81 || = 0.12 511 554 478 486 529 | 500 t 44 4 4 | 500 | 757 745 758 727 737 = 0.80 || = 0.11 485 458 481 487 478 | 500 m 43 5 4 | 500 | 379 431 367 367 393 = 0.79 || = 0.10 450 452 457 463 456 | 500 x 44 4 8 | 500 | 418 362 390 407 378 = 0.78 || = 0.09 402 396 431 409 439 | 500 -----------------------------------------------------------------| 500 | 435 380 396 425 393 = 0.77 || = 0.08 584 566 599 580 596 | 500 Aver./ d 0.50266 493 > 500: 4 5 2 4 8 10 2 2 5 4 | 500 | 799 810 792 831 831 = 0.76 || = 0.07 353 373 343 340 373 | 500 median s 0.49918 496 ----- 5 5 2 3 7 9 6 2 4 4 | 500 | 448 420 463 396 480 = 0.75 || = 0.06 608 578 624 633 616 | 500 t 0.49898 495 3 4 2 4 8 10 3 2 5 4 | 500 | 472 412 416 436 433 = 0.74 || = 0.05 367 426 384 413 387 | 500 m 0.49974 492 4 4 2 4 9 10 5 3 4 3 | 500 | 442 492 417 503 472 = 0.73 || = 0.04 577 540 589 558 547 | 500 x 0.50060 496 3 5 2 1 8 10 7 2 4 4 | 500 | 440 445 455 453 432 = 0.72 || = 0.03 429 452 449 419 450 | 500 -----------------------------------------------------------------| 500 | 490 480 439 465 489 = 0.71 || = 0.02 471 509 499 490 475 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 457 503 466 450 470 = 0.70 || = 0.01 226 266 251 226 250 | 252.5 d 17 4 10 12 24 9 7 5 13 | 500 | 464 447 473 515 472 = 0.69 || < 0.01 520 478 475 508 457 | 497.5 s 16 7 9 6 28 10 8 3 14 | 500 | 485 493 455 471 545 = 0.68 ||========================================================================= t 16 7 8 10 25 8 10 4 13 | 500 | 480 462 476 490 507 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 20 3 5 12 22 15 9 4 11 | 500 | 455 511 458 489 464 = 0.66 ||========================================================================= x 18 2 9 12 24 10 8 2 16 | 500 | 461 481 498 524 518 = 0.65 || Test smarsa_CollisionOver calling smultin_MultinomialOver no 5 test no 6 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_CollisionOver calling smultin_MultinomialOver test no 6 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 1 | 0.5 | 3 1 0 0 0 > 0.99999 || = 0.64 498 507 500 483 539 | 500 < 0.00002 2 0 0 0 0 | 0.5 | 0 1 1 0 0 > 0.99998 || = 0.63 502 516 494 511 527 | 500 < 0.00003 0 0 1 3 1 | 0.5 | 0 1 1 0 0 > 0.99997 || = 0.62 499 546 482 521 538 | 500 < 0.00004 0 0 0 0 1 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 516 528 527 476 545 | 500 < 0.00005 0 2 0 0 1 | 0.5 | 0 0 0 1 0 > 0.99995 || = 0.60 549 544 510 521 527 | 500 < 0.00006 1 0 0 1 1 | 0.5 | 0 1 0 0 0 > 0.99994 || = 0.59 521 517 556 552 540 | 500 < 0.00007 2 0 1 0 0 | 0.5 | 1 0 0 0 1 > 0.99993 || = 0.58 545 540 501 517 545 | 500 < 0.00008 0 0 1 0 0 | 0.5 | 1 0 1 0 0 > 0.99992 || = 0.57 543 516 536 512 522 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 2 1 2 0 0 > 0.99991 || = 0.56 556 541 571 540 541 | 500 < 0.0001 0 2 0 0 0 | 0.5 | 1 1 1 1 3 > 0.9999 || = 0.55 533 513 561 572 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 534 566 559 519 590 | 500 < 0.0001 5 4 3 5 5 | 5 | 9 6 6 2 4 > 0.9999 || = 0.53 521 519 536 558 577 | 500 < 0.0002 6 4 8 4 6 | 5 | 3 2 1 2 3 > 0.9998 || = 0.52 522 551 513 536 545 | 500 < 0.0003 4 4 4 6 4 | 5 | 7 3 4 6 2 > 0.9997 || = 0.51 537 531 531 550 531 | 500 < 0.0004 4 6 1 5 6 | 5 | 8 5 4 6 9 > 0.9996 || = 0.50 1116 1162 1053 1059 1081 | 500 < 0.0005 6 0 5 4 5 | 5 | 4 2 4 4 1 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 5 4 3 3 0 | 5 | 1 3 7 8 10 > 0.9994 || = 0.48 541 567 565 533 527 | 500 < 0.0007 11 5 7 6 4 | 5 | 5 3 9 3 5 > 0.9993 || = 0.47 554 549 522 573 521 | 500 < 0.0008 6 5 2 5 3 | 5 | 8 4 9 8 4 > 0.9992 || = 0.46 534 550 509 545 556 | 500 < 0.0009 5 3 7 2 4 | 5 | 2 5 2 5 3 > 0.9991 || = 0.45 557 554 531 488 535 | 500 < 0.001 2 6 5 3 3 | 5 | 5 3 6 2 6 > 0.999 || = 0.44 523 534 548 557 575 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 535 514 531 555 523 | 500 < 0.001 54 41 45 43 40 | 50 | 52 36 52 46 47 > 0.999 || = 0.42 529 542 506 537 537 | 500 < 0.002 48 55 61 52 47 | 50 | 61 59 49 50 41 > 0.998 || = 0.41 496 527 562 482 541 | 500 < 0.003 60 53 49 53 45 | 50 | 54 43 44 65 46 > 0.997 || = 0.40 526 539 518 502 533 | 500 < 0.004 48 48 45 47 56 | 50 | 45 39 37 43 47 > 0.996 || = 0.39 509 490 511 546 494 | 500 < 0.005 41 40 48 58 45 | 50 | 59 50 60 38 64 > 0.995 || = 0.38 515 526 538 519 532 | 500 < 0.006 48 39 36 44 35 | 50 | 46 42 46 37 41 > 0.994 || = 0.37 515 512 508 509 522 | 500 < 0.007 49 52 44 48 50 | 50 | 39 43 59 49 61 > 0.993 || = 0.36 513 490 493 496 490 | 500 < 0.008 47 60 48 64 58 | 50 | 67 62 61 46 53 > 0.992 || = 0.35 504 511 507 478 518 | 500 < 0.009 52 58 61 65 55 | 50 | 72 59 68 61 55 > 0.991 || = 0.34 511 513 494 468 482 | 500 < 0.01 48 28 40 38 49 | 50 | 42 24 34 38 38 > 0.99 || = 0.33 485 524 445 483 478 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 510 488 507 473 480 | 500 < 0.01 495 474 477 512 480 | 497.5 | 537 457 510 473 493 > 0.99 || = 0.31 488 438 492 436 424 | 500 = 0.01 250 255 244 279 250 | 252.5 | 284 240 257 253 274 = 0.99 || = 0.30 436 450 501 469 485 | 500 = 0.02 500 459 477 494 463 | 500 | 452 427 466 420 418 = 0.98 || = 0.29 453 452 512 430 452 | 500 =================================================================| 500 | 533 522 514 603 546 = 0.97 || = 0.28 452 426 427 441 454 | 500 Test smarsa_CollisionOver calling smultin_MultinomialOver | 500 | 427 461 443 443 471 = 0.96 || = 0.27 448 452 460 421 454 | 500 smultin_MultinomialOver test: | 500 | 402 382 411 422 420 = 0.95 || = 0.26 438 418 435 457 414 | 500 ----------------------------------------------- | 500 | 632 649 628 642 658 = 0.94 || = 0.25 893 862 837 861 789 | 500 N = 30, n = 20000000, r = 16, d = 16384, t = 3, | 500 | 339 341 356 325 350 = 0.93 || = 0.24 429 448 441 416 439 | 500 | 500 | 594 603 579 550 593 = 0.92 || = 0.23 404 433 406 406 377 | 500 =================================================================| 500 | 435 394 423 435 438 = 0.91 || = 0.22 397 374 395 365 397 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 476 472 457 458 517 = 0.90 || = 0.21 766 766 790 790 720 | 500 -----------------------------------------------------------------| 500 | 536 489 497 521 515 = 0.89 || = 0.20 375 362 324 406 364 | 500 SD Bern.: d 5.83025 0.67412 1.56346 | 500 | 509 527 549 545 513 = 0.88 || = 0.19 323 351 393 351 358 | 500 s 5.91708 1.40924 1.71023 | 500 | 572 618 566 586 561 = 0.87 || = 0.18 708 676 686 745 730 | 500 t 5.59156 1.12572 1.48935 | 500 | 299 278 320 289 288 = 0.86 || = 0.17 333 296 346 311 324 | 500 m 5.63623 1.21715 1.33107 | 500 | 633 625 655 609 619 = 0.85 || = 0.16 616 641 672 651 606 | 500 x 5.51940 1.01045 1.17616 | 500 | 323 328 333 344 341 = 0.84 || = 0.15 308 295 314 314 300 | 500 | 500 | 660 688 704 697 644 = 0.83 || = 0.14 602 576 572 558 570 | 500 Changes: d 47 5 5 | 500 | 322 350 348 364 374 = 0.82 || = 0.13 553 549 613 543 545 | 500 s 46 4 4 | 500 | 352 303 341 389 360 = 0.81 || = 0.12 521 516 529 575 482 | 500 t 45 4 5 | 500 | 785 782 720 736 769 = 0.80 || = 0.11 456 499 495 483 503 | 500 m 47 6 4 | 500 | 391 389 389 406 384 = 0.79 || = 0.10 410 457 470 503 469 | 500 x 44 4 4 | 500 | 403 393 382 383 377 = 0.78 || = 0.09 402 447 415 424 418 | 500 -----------------------------------------------------------------| 500 | 434 389 403 421 411 = 0.77 || = 0.08 594 629 573 568 580 | 500 Aver./ d 0.50031 503 > 500: 3 5 2 7 8 10 4 2 5 5 | 500 | 847 817 831 834 811 = 0.76 || = 0.07 341 374 361 359 341 | 500 median s 0.49741 504 ----- 4 5 2 5 9 10 6 2 4 3 | 500 | 457 445 433 417 398 = 0.75 || = 0.06 625 616 660 610 644 | 500 t 0.49827 500 3 5 3 6 9 10 2 2 4 5 | 500 | 445 452 431 441 453 = 0.74 || = 0.05 378 434 346 419 410 | 500 m 0.49840 485 5 6 2 3 7 10 2 2 5 4 | 500 | 409 455 436 476 431 = 0.73 || = 0.04 540 532 532 546 547 | 500 x 0.50077 495 3 5 2 3 9 10 4 2 6 4 | 500 | 443 448 473 474 473 = 0.72 || = 0.03 428 468 409 414 467 | 500 -----------------------------------------------------------------| 500 | 453 447 446 471 471 = 0.71 || = 0.02 500 459 477 494 463 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 503 455 475 461 467 = 0.70 || = 0.01 250 255 244 279 250 | 252.5 d 20 3 11 6 25 15 6 1 14 | 500 | 495 504 474 477 460 = 0.69 || < 0.01 495 474 477 512 480 | 497.5 s 17 4 14 8 22 13 7 2 14 | 500 | 471 453 451 474 485 = 0.68 ||========================================================================= t 19 5 7 9 28 9 8 4 12 | 500 | 507 510 467 479 491 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 15 10 5 14 23 6 11 5 12 | 500 | 466 477 505 469 484 = 0.66 ||========================================================================= x 18 6 6 9 21 16 8 4 13 | 500 | 463 478 498 485 466 = 0.65 || Test smarsa_CollisionOver calling smultin_MultinomialOver no 6 test no 7 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_CollisionOver calling smultin_MultinomialOver test no 7 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 1 2 0 > 0.99999 || = 0.64 533 514 531 476 459 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 1 0 1 1 > 0.99998 || = 0.63 464 503 502 551 478 | 500 < 0.00003 1 1 0 0 0 | 0.5 | 0 2 0 0 1 > 0.99997 || = 0.62 471 483 459 525 491 | 500 < 0.00004 0 1 0 0 3 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 535 461 504 520 522 | 500 < 0.00005 2 0 2 1 2 | 0.5 | 1 3 0 1 0 > 0.99995 || = 0.60 551 486 489 488 534 | 500 < 0.00006 0 0 0 0 2 | 0.5 | 1 0 1 1 0 > 0.99994 || = 0.59 528 518 523 584 510 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 1 0 1 1 1 > 0.99993 || = 0.58 556 507 516 564 504 | 500 < 0.00008 2 0 0 3 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 570 551 540 541 521 | 500 < 0.00009 0 2 1 0 0 | 0.5 | 1 1 2 0 1 > 0.99991 || = 0.56 552 518 566 507 505 | 500 < 0.0001 1 0 0 1 0 | 0.5 | 0 1 1 0 1 > 0.9999 || = 0.55 518 528 506 522 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 533 524 499 525 563 | 500 < 0.0001 6 4 3 6 7 | 5 | 4 8 6 6 5 > 0.9999 || = 0.53 538 507 480 535 521 | 500 < 0.0002 7 11 7 4 2 | 5 | 1 4 2 5 4 > 0.9998 || = 0.52 537 575 536 506 537 | 500 < 0.0003 4 4 7 3 6 | 5 | 5 11 4 2 8 > 0.9997 || = 0.51 522 571 560 528 550 | 500 < 0.0004 5 7 1 4 8 | 5 | 6 6 3 6 5 > 0.9996 || = 0.50 1048 1021 1033 1031 1098 | 500 < 0.0005 3 6 6 7 5 | 5 | 6 8 7 7 2 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 5 3 6 4 5 | 5 | 9 4 5 4 8 > 0.9994 || = 0.48 483 505 558 531 522 | 500 < 0.0007 2 7 3 4 4 | 5 | 8 4 4 9 4 > 0.9993 || = 0.47 470 547 466 526 552 | 500 < 0.0008 7 10 5 8 8 | 5 | 3 10 8 8 5 > 0.9992 || = 0.46 533 516 521 511 537 | 500 < 0.0009 5 3 1 5 3 | 5 | 3 5 6 3 5 > 0.9991 || = 0.45 550 534 531 530 522 | 500 < 0.001 9 0 7 5 4 | 5 | 8 1 4 5 5 > 0.999 || = 0.44 520 503 502 492 520 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 520 544 547 517 517 | 500 < 0.001 53 55 46 50 52 | 50 | 53 61 49 55 51 > 0.999 || = 0.42 497 527 538 518 553 | 500 < 0.002 56 39 71 53 52 | 50 | 49 43 49 48 67 > 0.998 || = 0.41 551 447 500 523 538 | 500 < 0.003 40 56 61 52 60 | 50 | 64 57 52 55 40 > 0.997 || = 0.40 469 509 529 505 475 | 500 < 0.004 63 49 60 60 63 | 50 | 53 39 41 55 55 > 0.996 || = 0.39 516 477 514 536 494 | 500 < 0.005 57 67 57 50 52 | 50 | 53 53 64 48 53 > 0.995 || = 0.38 507 491 492 521 469 | 500 < 0.006 32 37 46 49 50 | 50 | 40 50 48 53 50 > 0.994 || = 0.37 516 497 482 477 511 | 500 < 0.007 44 46 47 49 57 | 50 | 47 56 55 49 43 > 0.993 || = 0.36 504 500 490 475 485 | 500 < 0.008 54 69 53 54 48 | 50 | 49 48 60 62 69 > 0.992 || = 0.35 485 520 468 474 470 | 500 < 0.009 80 72 61 68 61 | 50 | 79 59 44 69 90 > 0.991 || = 0.34 481 479 480 512 459 | 500 < 0.01 39 41 38 28 28 | 50 | 34 37 43 32 42 > 0.99 || = 0.33 449 468 504 462 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 457 506 448 457 472 | 500 < 0.01 518 531 540 513 523 | 497.5 | 521 503 505 526 560 > 0.99 || = 0.31 486 456 449 486 491 | 500 = 0.01 259 281 255 255 246 | 252.5 | 266 295 289 279 286 = 0.99 || = 0.30 457 459 476 474 466 | 500 = 0.02 510 545 538 543 510 | 500 | 496 474 456 456 459 = 0.98 || = 0.29 496 478 439 470 464 | 500 =================================================================| 500 | 550 541 595 593 529 = 0.97 || = 0.28 467 499 423 429 450 | 500 Test smarsa_CollisionOver calling smultin_MultinomialOver | 500 | 519 473 492 452 485 = 0.96 || = 0.27 434 397 456 455 449 | 500 smultin_MultinomialOver test: | 500 | 401 393 443 421 430 = 0.95 || = 0.26 438 448 426 425 404 | 500 ----------------------------------------------- | 500 | 732 648 684 690 654 = 0.94 || = 0.25 837 840 877 828 844 | 500 N = 30, n = 20000000, r = 0, d = 64, t = 7, | 500 | 350 377 387 356 383 = 0.93 || = 0.24 415 409 372 388 400 | 500 | 500 | 625 661 628 673 625 = 0.92 || = 0.23 390 432 416 417 431 | 500 =================================================================| 500 | 461 437 451 447 447 = 0.91 || = 0.22 392 397 413 421 392 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 479 476 484 444 475 = 0.90 || = 0.21 794 752 785 771 715 | 500 -----------------------------------------------------------------| 500 | 519 496 512 495 475 = 0.89 || = 0.20 380 334 370 338 375 | 500 SD Bern.: d 5.66405 1.87710 1.69258 | 500 | 541 527 590 555 554 = 0.88 || = 0.19 346 352 348 350 341 | 500 s 5.49897 1.78021 1.13104 | 500 | 598 599 564 542 578 = 0.87 || = 0.18 700 693 726 701 713 | 500 t 5.54416 1.43319 0.99748 | 500 | 302 300 294 316 333 = 0.86 || = 0.17 320 312 353 372 339 | 500 m 5.57235 1.37108 1.35860 | 500 | 598 676 606 577 632 = 0.85 || = 0.16 666 640 650 602 623 | 500 x 5.65539 1.37108 2.23628 | 500 | 321 321 338 320 302 = 0.84 || = 0.15 314 300 278 309 315 | 500 | 500 | 704 701 679 678 721 = 0.83 || = 0.14 619 581 596 582 611 | 500 Changes: d 48 5 5 | 500 | 347 348 390 341 380 = 0.82 || = 0.13 543 568 566 548 569 | 500 s 48 7 9 | 500 | 356 355 363 355 364 = 0.81 || = 0.12 526 517 525 512 551 | 500 t 52 4 6 | 500 | 778 714 747 768 737 = 0.80 || = 0.11 506 444 496 502 484 | 500 m 44 4 7 | 500 | 357 399 380 372 363 = 0.79 || = 0.10 431 480 447 461 463 | 500 x 48 5 5 | 500 | 369 397 395 399 364 = 0.78 || = 0.09 450 437 426 454 467 | 500 -----------------------------------------------------------------| 500 | 370 419 411 423 396 = 0.77 || = 0.08 590 543 574 598 598 | 500 Aver./ d 0.49949 503 > 500: 6 6 2 4 5 10 4 2 5 6 | 500 | 778 823 799 862 820 = 0.76 || = 0.07 376 342 360 352 322 | 500 median s 0.50020 496 ----- 6 5 2 2 8 9 3 2 4 5 | 500 | 415 450 428 428 423 = 0.75 || = 0.06 567 627 607 638 653 | 500 t 0.50160 492 6 5 2 2 7 7 4 2 5 5 | 500 | 422 494 478 452 443 = 0.74 || = 0.05 419 423 417 407 380 | 500 m 0.49972 495 6 6 2 3 8 9 3 2 4 5 | 500 | 437 470 464 421 480 = 0.73 || = 0.04 593 605 538 592 614 | 500 x 0.50012 487 5 5 2 1 8 9 3 2 4 5 | 500 | 429 461 463 422 453 = 0.72 || = 0.03 477 470 430 448 425 | 500 -----------------------------------------------------------------| 500 | 402 474 462 500 422 = 0.71 || = 0.02 510 545 538 543 510 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 503 457 455 467 470 = 0.70 || = 0.01 259 281 255 255 246 | 252.5 d 18 6 5 13 25 11 6 2 15 | 500 | 472 467 459 460 503 = 0.69 || < 0.01 518 531 540 513 523 | 497.5 s 17 3 7 14 27 11 4 4 14 | 500 | 461 435 463 488 477 = 0.68 ||========================================================================= t 15 8 7 12 25 11 7 1 15 | 500 | 460 493 512 451 504 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 15 9 8 13 21 14 4 3 14 | 500 | 517 526 469 485 498 = 0.66 ||========================================================================= x 18 5 5 16 26 6 8 2 15 | 500 | 464 491 479 475 474 = 0.65 || Test smarsa_CollisionOver calling smultin_MultinomialOver no 7 test no 8 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_CollisionOver calling smultin_MultinomialOver test no 8 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 1 0 0 | 0.5 | 0 0 2 1 1 > 0.99999 || = 0.64 496 501 480 534 483 | 500 < 0.00002 1 0 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99998 || = 0.63 465 510 455 513 476 | 500 < 0.00003 1 1 0 0 1 | 0.5 | 1 2 1 2 0 > 0.99997 || = 0.62 495 471 477 555 462 | 500 < 0.00004 0 0 2 0 0 | 0.5 | 1 0 0 0 2 > 0.99996 || = 0.61 537 497 471 495 546 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 549 505 499 475 541 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99994 || = 0.59 491 497 485 516 499 | 500 < 0.00007 0 2 2 1 0 | 0.5 | 0 2 0 0 0 > 0.99993 || = 0.58 517 501 553 526 502 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99992 || = 0.57 507 503 550 542 528 | 500 < 0.00009 1 1 0 0 1 | 0.5 | 1 0 0 4 3 > 0.99991 || = 0.56 535 529 516 510 491 | 500 < 0.0001 1 2 1 0 0 | 0.5 | 0 0 0 1 1 > 0.9999 || = 0.55 482 528 505 515 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 527 503 578 519 529 | 500 < 0.0001 4 8 6 2 4 | 5 | 4 5 5 8 8 > 0.9999 || = 0.53 520 555 534 520 480 | 500 < 0.0002 5 1 7 9 7 | 5 | 9 4 3 4 3 > 0.9998 || = 0.52 554 540 530 522 558 | 500 < 0.0003 5 2 4 4 4 | 5 | 10 6 3 5 6 > 0.9997 || = 0.51 538 503 555 522 554 | 500 < 0.0004 7 5 7 12 9 | 5 | 4 3 4 4 6 > 0.9996 || = 0.50 1108 1118 1088 1014 1111 | 500 < 0.0005 6 8 4 3 7 | 5 | 5 8 2 7 7 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 6 3 5 3 5 | 5 | 8 7 5 3 3 > 0.9994 || = 0.48 568 481 515 550 543 | 500 < 0.0007 5 3 4 10 9 | 5 | 6 7 7 5 7 > 0.9993 || = 0.47 585 562 513 538 542 | 500 < 0.0008 7 9 11 5 8 | 5 | 5 6 10 7 8 > 0.9992 || = 0.46 492 513 516 522 530 | 500 < 0.0009 5 5 2 5 4 | 5 | 3 7 5 2 4 > 0.9991 || = 0.45 523 502 511 553 527 | 500 < 0.001 5 3 2 5 1 | 5 | 5 7 9 7 6 > 0.999 || = 0.44 527 494 513 561 519 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 555 507 562 492 500 | 500 < 0.001 55 47 52 58 58 | 50 | 59 60 53 52 58 > 0.999 || = 0.42 509 560 513 554 479 | 500 < 0.002 55 62 59 38 53 | 50 | 52 51 50 65 69 > 0.998 || = 0.41 466 507 497 512 507 | 500 < 0.003 57 66 53 50 55 | 50 | 62 48 66 54 49 > 0.997 || = 0.40 517 506 577 499 531 | 500 < 0.004 53 60 68 46 61 | 50 | 38 48 54 53 29 > 0.996 || = 0.39 517 501 521 478 533 | 500 < 0.005 55 58 55 39 62 | 50 | 61 70 60 81 59 > 0.995 || = 0.38 526 513 561 510 486 | 500 < 0.006 41 44 46 44 59 | 50 | 33 47 41 42 49 > 0.994 || = 0.37 500 500 512 470 524 | 500 < 0.007 54 46 48 50 45 | 50 | 56 52 37 45 49 > 0.993 || = 0.36 491 447 493 483 508 | 500 < 0.008 53 50 49 58 53 | 50 | 54 57 54 63 56 > 0.992 || = 0.35 495 506 483 518 502 | 500 < 0.009 62 48 61 56 64 | 50 | 69 82 60 61 69 > 0.991 || = 0.34 449 487 499 471 492 | 500 < 0.01 32 42 34 34 43 | 50 | 41 30 44 37 32 > 0.99 || = 0.33 501 477 459 468 490 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 461 478 465 454 475 | 500 < 0.01 517 523 525 473 553 | 497.5 | 525 545 519 553 519 > 0.99 || = 0.31 446 480 518 469 456 | 500 = 0.01 267 284 279 246 249 | 252.5 | 310 296 279 273 270 = 0.99 || = 0.30 458 434 467 418 470 | 500 = 0.02 527 533 549 525 526 | 500 | 460 485 450 457 500 = 0.98 || = 0.29 437 448 435 475 454 | 500 =================================================================| 500 | 551 595 543 614 575 = 0.97 || = 0.28 467 447 477 457 429 | 500 Test smarsa_CollisionOver calling smultin_MultinomialOver | 500 | 496 489 501 476 459 = 0.96 || = 0.27 435 412 452 473 429 | 500 smultin_MultinomialOver test: | 500 | 458 421 424 414 410 = 0.95 || = 0.26 425 415 428 415 453 | 500 ----------------------------------------------- | 500 | 644 628 639 606 660 = 0.94 || = 0.25 813 828 811 809 788 | 500 N = 30, n = 20000000, r = 24, d = 64, t = 7, | 500 | 388 399 385 365 382 = 0.93 || = 0.24 429 444 416 410 414 | 500 | 500 | 670 573 595 618 636 = 0.92 || = 0.23 410 382 362 421 368 | 500 =================================================================| 500 | 450 467 426 455 425 = 0.91 || = 0.22 383 422 377 398 430 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 490 470 466 478 507 = 0.90 || = 0.21 751 768 788 785 730 | 500 -----------------------------------------------------------------| 500 | 513 484 517 485 507 = 0.89 || = 0.20 392 356 408 354 373 | 500 SD Bern.: d 5.58521 1.18971 1.59891 | 500 | 568 593 530 556 526 = 0.88 || = 0.19 341 364 370 340 340 | 500 s 5.71317 1.17787 1.99849 | 500 | 592 586 584 620 610 = 0.87 || = 0.18 675 679 742 684 691 | 500 t 5.72853 1.29756 1.25201 | 500 | 310 276 295 308 301 = 0.86 || = 0.17 335 314 309 349 337 | 500 m 5.62104 1.21468 1.87869 | 500 | 607 671 610 593 633 = 0.85 || = 0.16 595 571 640 701 625 | 500 x 5.68950 1.20309 1.82901 | 500 | 306 316 344 303 355 = 0.84 || = 0.15 336 318 331 297 290 | 500 | 500 | 659 657 716 685 644 = 0.83 || = 0.14 619 610 562 605 617 | 500 Changes: d 48 3 5 | 500 | 347 317 338 328 333 = 0.82 || = 0.13 545 578 571 527 518 | 500 s 48 2 5 | 500 | 364 386 383 368 366 = 0.81 || = 0.12 497 552 550 546 532 | 500 t 44 3 5 | 500 | 773 795 784 776 735 = 0.80 || = 0.11 477 455 518 448 514 | 500 m 49 3 3 | 500 | 404 355 363 415 356 = 0.79 || = 0.10 453 457 431 397 428 | 500 x 54 3 5 | 500 | 419 387 388 413 421 = 0.78 || = 0.09 418 410 385 441 406 | 500 -----------------------------------------------------------------| 500 | 409 402 388 407 396 = 0.77 || = 0.08 600 587 575 595 594 | 500 Aver./ d 0.50195 495 > 500: 6 4 2 3 7 8 1 2 5 5 | 500 | 812 846 854 890 902 = 0.76 || = 0.07 348 388 374 364 355 | 500 median s 0.50130 497 ----- 6 5 2 3 7 9 4 2 4 5 | 500 | 388 443 435 409 434 = 0.75 || = 0.06 644 655 597 612 665 | 500 t 0.49819 499 6 6 2 4 8 8 1 2 5 6 | 500 | 472 448 410 455 431 = 0.74 || = 0.05 386 418 380 402 424 | 500 m 0.50166 487 4 5 2 2 7 9 4 3 4 5 | 500 | 436 445 428 443 452 = 0.73 || = 0.04 552 522 589 628 604 | 500 x 0.50045 499 5 6 2 4 7 7 3 2 6 5 | 500 | 450 460 436 478 478 = 0.72 || = 0.03 468 476 462 447 437 | 500 -----------------------------------------------------------------| 500 | 451 459 448 509 429 = 0.71 || = 0.02 527 533 549 525 526 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 442 480 445 471 472 = 0.70 || = 0.01 267 284 279 246 249 | 252.5 d 17 4 10 13 23 9 6 4 15 | 500 | 490 486 462 455 472 = 0.69 || < 0.01 517 523 525 473 553 | 497.5 s 16 5 9 8 32 7 6 5 13 | 500 | 463 495 464 460 473 = 0.68 ||========================================================================= t 19 6 8 10 25 7 8 5 13 | 500 | 495 505 504 440 503 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 17 6 9 13 24 7 8 0 17 | 500 | 467 485 484 494 470 = 0.66 ||========================================================================= x 16 10 5 10 25 14 4 1 16 | 500 | 472 523 499 508 501 = 0.65 || Test smarsa_CollisionOver calling smultin_MultinomialOver no 8 test no 9 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_CollisionOver calling smultin_MultinomialOver test no 9 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 4 3 7 5 2 | 0.5 | 1 4 4 3 1 > 0.99999 || = 0.64 432 509 508 428 453 | 500 < 0.00002 4 2 2 6 4 | 0.5 | 2 6 1 2 6 > 0.99998 || = 0.63 434 489 445 424 499 | 500 < 0.00003 4 3 5 6 1 | 0.5 | 3 3 0 1 1 > 0.99997 || = 0.62 482 469 423 462 425 | 500 < 0.00004 8 0 4 4 3 | 0.5 | 0 2 6 2 4 > 0.99996 || = 0.61 489 449 465 501 484 | 500 < 0.00005 2 2 4 3 2 | 0.5 | 1 3 5 4 2 > 0.99995 || = 0.60 427 433 506 469 481 | 500 < 0.00006 1 1 1 2 0 | 0.5 | 0 2 4 0 2 > 0.99994 || = 0.59 457 474 468 447 478 | 500 < 0.00007 2 2 3 3 3 | 0.5 | 3 2 1 6 3 > 0.99993 || = 0.58 452 459 462 472 445 | 500 < 0.00008 0 2 2 1 1 | 0.5 | 3 0 1 1 2 > 0.99992 || = 0.57 454 437 464 477 501 | 500 < 0.00009 2 2 2 1 1 | 0.5 | 3 8 4 0 3 > 0.99991 || = 0.56 474 485 470 441 425 | 500 < 0.0001 1 4 3 2 3 | 0.5 | 2 3 2 0 2 > 0.9999 || = 0.55 432 466 488 489 511 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 484 450 471 475 478 | 500 < 0.0001 28 21 33 33 20 | 5 | 18 33 28 19 26 > 0.9999 || = 0.53 498 485 466 474 477 | 500 < 0.0002 20 20 12 18 20 | 5 | 2 15 14 12 9 > 0.9998 || = 0.52 493 446 505 451 474 | 500 < 0.0003 15 20 21 16 19 | 5 | 12 30 20 21 15 > 0.9997 || = 0.51 463 490 444 468 469 | 500 < 0.0004 10 13 13 19 22 | 5 | 15 14 16 11 11 > 0.9996 || = 0.50 959 954 950 969 945 | 500 < 0.0005 11 5 18 17 8 | 5 | 8 10 12 11 12 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 18 13 13 16 9 | 5 | 17 11 9 10 6 > 0.9994 || = 0.48 490 451 467 471 497 | 500 < 0.0007 19 19 15 11 9 | 5 | 16 18 11 14 15 > 0.9993 || = 0.47 460 488 449 479 464 | 500 < 0.0008 16 23 14 25 26 | 5 | 21 18 16 19 24 > 0.9992 || = 0.46 475 457 488 466 446 | 500 < 0.0009 6 9 15 12 7 | 5 | 10 17 3 10 9 > 0.9991 || = 0.45 469 502 455 469 484 | 500 < 0.001 9 8 11 14 9 | 5 | 7 17 13 15 7 > 0.999 || = 0.44 476 481 421 435 446 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 439 475 452 482 503 | 500 < 0.001 152 151 165 181 149 | 50 | 126 183 142 142 134 > 0.999 || = 0.42 471 483 436 473 417 | 500 < 0.002 112 114 109 98 105 | 50 | 119 131 126 120 118 > 0.998 || = 0.41 493 455 450 458 496 | 500 < 0.003 139 108 97 110 106 | 50 | 116 112 113 114 129 > 0.997 || = 0.40 461 417 456 464 409 | 500 < 0.004 115 122 124 93 100 | 50 | 93 95 67 82 82 > 0.996 || = 0.39 478 482 494 449 455 | 500 < 0.005 98 103 86 100 93 | 50 | 122 95 113 81 116 > 0.995 || = 0.38 489 468 443 467 442 | 500 < 0.006 67 90 73 77 66 | 50 | 79 70 70 78 57 > 0.994 || = 0.37 429 436 448 442 417 | 500 < 0.007 60 90 78 76 90 | 50 | 84 85 89 87 78 > 0.993 || = 0.36 442 489 445 488 415 | 500 < 0.008 87 97 97 83 84 | 50 | 100 99 83 108 97 > 0.992 || = 0.35 455 492 460 435 411 | 500 < 0.009 97 91 108 85 98 | 50 | 103 107 111 98 115 > 0.991 || = 0.34 423 466 447 468 421 | 500 < 0.01 47 65 41 55 55 | 50 | 70 52 53 59 45 > 0.99 || = 0.33 435 427 431 434 434 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 467 459 477 413 412 | 500 < 0.01 974 1031 978 958 946 | 497.5 | 1012 1029 967 969 971 > 0.99 || = 0.31 459 450 416 443 399 | 500 = 0.01 386 386 390 393 374 | 252.5 | 402 426 415 432 431 = 0.99 || = 0.30 447 444 422 423 431 | 500 = 0.02 663 668 699 718 725 | 500 | 613 639 641 660 683 = 0.98 || = 0.29 449 409 379 427 414 | 500 =================================================================| 500 | 738 685 728 681 711 = 0.97 || = 0.28 414 421 382 424 414 | 500 Test smarsa_CollisionOver calling smultin_MultinomialOver | 500 | 604 597 579 557 590 = 0.96 || = 0.27 407 376 457 394 433 | 500 smultin_MultinomialOver test: | 500 | 492 541 524 464 516 = 0.95 || = 0.26 389 423 402 399 363 | 500 ----------------------------------------------- | 500 | 808 752 707 775 741 = 0.94 || = 0.25 766 757 766 779 782 | 500 N = 30, n = 20000000, r = 0, d = 8, t = 14, | 500 | 370 403 385 397 393 = 0.93 || = 0.24 399 354 373 358 402 | 500 | 500 | 625 666 638 664 636 = 0.92 || = 0.23 377 361 369 433 392 | 500 =================================================================| 500 | 444 478 481 455 478 = 0.91 || = 0.22 418 390 401 377 362 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 479 471 497 475 530 = 0.90 || = 0.21 729 737 728 704 679 | 500 -----------------------------------------------------------------| 500 | 530 568 478 568 556 = 0.89 || = 0.20 387 320 345 338 355 | 500 SD Bern.: d 6.74036 8.08785 7.70215 | 500 | 555 521 545 537 565 = 0.88 || = 0.19 390 340 344 337 343 | 500 s 6.73229 8.12428 8.88396 | 500 | 566 605 565 613 569 = 0.87 || = 0.18 684 666 696 666 707 | 500 t 6.64553 8.08538 7.64672 | 500 | 290 291 286 300 300 = 0.86 || = 0.17 302 309 311 320 330 | 500 m 6.76918 7.89799 7.39923 | 500 | 642 620 611 661 654 = 0.85 || = 0.16 635 626 660 609 639 | 500 x 6.80505 7.16626 7.82605 | 500 | 306 345 320 343 286 = 0.84 || = 0.15 284 294 320 292 270 | 500 | 500 | 700 667 664 695 733 = 0.83 || = 0.14 575 565 593 552 603 | 500 Changes: d 30 1 0 | 500 | 348 354 337 331 360 = 0.82 || = 0.13 570 543 563 590 531 | 500 s 34 0 0 | 500 | 361 325 375 328 358 = 0.81 || = 0.12 550 516 573 535 566 | 500 t 36 1 0 | 500 | 721 682 776 750 755 = 0.80 || = 0.11 473 484 524 526 489 | 500 m 34 0 0 | 500 | 361 377 371 379 381 = 0.79 || = 0.10 484 460 488 513 506 | 500 x 38 0 1 | 500 | 367 411 375 381 383 = 0.78 || = 0.09 454 473 468 439 458 | 500 -----------------------------------------------------------------| 500 | 367 397 371 401 399 = 0.77 || = 0.08 637 641 610 620 653 | 500 Aver./ d 0.49924 463 > 500: 8 5 2 0 0 0 0 2 5 7 | 500 | 776 735 790 818 829 = 0.76 || = 0.07 397 406 433 384 346 | 500 median s 0.50149 468 ----- 7 5 2 0 1 0 1 2 5 8 | 500 | 393 396 439 426 413 = 0.75 || = 0.06 725 703 739 730 707 | 500 t 0.49910 462 7 6 2 0 0 2 1 2 4 8 | 500 | 437 417 413 418 446 = 0.74 || = 0.05 506 478 483 481 472 | 500 m 0.50065 464 7 7 2 0 0 0 1 2 5 7 | 500 | 420 381 450 441 361 = 0.73 || = 0.04 701 718 677 709 681 | 500 x 0.50407 469 7 6 2 0 1 2 0 2 6 8 | 500 | 380 416 402 424 410 = 0.72 || = 0.03 557 581 565 599 575 | 500 -----------------------------------------------------------------| 500 | 460 458 452 419 415 = 0.71 || = 0.02 663 668 699 718 725 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 379 396 424 422 441 = 0.70 || = 0.01 386 386 390 393 374 | 252.5 d 21 10 14 14 13 1 4 2 22 | 500 | 437 442 407 448 426 = 0.69 || < 0.01 974 1031 978 958 946 | 497.5 s 22 8 13 13 17 2 1 2 23 | 500 | 418 416 449 412 437 = 0.68 ||========================================================================= t 21 8 17 14 11 2 4 2 22 | 500 | 437 442 436 417 483 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 18 16 13 17 7 3 2 1 24 | 500 | 428 444 458 415 469 = 0.66 ||========================================================================= x 23 15 10 7 16 2 3 2 23 | 500 | 464 454 436 414 430 = 0.65 || Test smarsa_CollisionOver calling smultin_MultinomialOver no 9 test no 10 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_CollisionOver calling smultin_MultinomialOver test no 10 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 4 1 2 4 9 | 0.5 | 4 6 3 1 3 > 0.99999 || = 0.64 462 447 439 423 481 | 500 < 0.00002 4 2 3 1 6 | 0.5 | 0 2 4 6 1 > 0.99998 || = 0.63 426 443 465 467 457 | 500 < 0.00003 3 3 3 1 7 | 0.5 | 1 1 2 5 6 > 0.99997 || = 0.62 440 470 460 463 492 | 500 < 0.00004 2 6 3 5 1 | 0.5 | 2 2 2 2 7 > 0.99996 || = 0.61 466 472 462 472 447 | 500 < 0.00005 3 0 2 2 5 | 0.5 | 4 1 0 4 1 > 0.99995 || = 0.60 483 464 500 436 415 | 500 < 0.00006 1 0 1 1 2 | 0.5 | 4 1 3 3 1 > 0.99994 || = 0.59 454 452 446 470 415 | 500 < 0.00007 5 2 2 4 1 | 0.5 | 2 1 5 4 6 > 0.99993 || = 0.58 433 433 477 472 495 | 500 < 0.00008 3 2 2 3 3 | 0.5 | 2 1 0 1 3 > 0.99992 || = 0.57 429 414 460 471 470 | 500 < 0.00009 0 1 1 2 2 | 0.5 | 3 3 2 0 3 > 0.99991 || = 0.56 481 449 457 480 479 | 500 < 0.0001 1 0 1 1 0 | 0.5 | 2 1 1 3 3 > 0.9999 || = 0.55 480 479 487 480 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 472 487 440 454 513 | 500 < 0.0001 26 17 20 24 36 | 5 | 24 19 22 29 34 > 0.9999 || = 0.53 482 457 459 442 515 | 500 < 0.0002 19 18 20 20 12 | 5 | 7 16 8 9 4 > 0.9998 || = 0.52 462 499 479 490 490 | 500 < 0.0003 20 16 21 12 14 | 5 | 15 12 22 10 18 > 0.9997 || = 0.51 477 491 472 440 483 | 500 < 0.0004 23 17 23 22 16 | 5 | 17 14 11 15 14 > 0.9996 || = 0.50 1023 955 957 933 966 | 500 < 0.0005 9 10 10 11 7 | 5 | 8 12 5 10 12 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 20 13 8 17 17 | 5 | 9 12 17 14 16 > 0.9994 || = 0.48 459 477 446 478 461 | 500 < 0.0007 9 12 11 15 14 | 5 | 17 12 11 13 7 > 0.9993 || = 0.47 494 474 458 517 459 | 500 < 0.0008 14 22 22 22 11 | 5 | 16 17 22 12 18 > 0.9992 || = 0.46 464 481 455 500 475 | 500 < 0.0009 9 10 8 5 6 | 5 | 5 10 9 8 8 > 0.9991 || = 0.45 484 484 498 456 487 | 500 < 0.001 14 7 9 18 14 | 5 | 9 11 12 13 13 > 0.999 || = 0.44 498 476 441 460 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 484 487 489 433 506 | 500 < 0.001 163 142 152 166 147 | 50 | 127 135 139 133 144 > 0.999 || = 0.42 449 432 482 497 456 | 500 < 0.002 108 100 114 110 120 | 50 | 111 99 128 104 103 > 0.998 || = 0.41 479 424 459 453 448 | 500 < 0.003 114 88 115 112 105 | 50 | 115 122 113 113 125 > 0.997 || = 0.40 462 457 477 469 485 | 500 < 0.004 101 113 123 112 99 | 50 | 94 76 76 76 76 > 0.996 || = 0.39 450 432 468 426 468 | 500 < 0.005 115 83 94 107 130 | 50 | 95 85 97 105 80 > 0.995 || = 0.38 493 446 440 475 465 | 500 < 0.006 68 71 77 61 72 | 50 | 72 86 81 68 67 > 0.994 || = 0.37 465 467 479 452 481 | 500 < 0.007 76 74 70 88 73 | 50 | 98 79 89 83 86 > 0.993 || = 0.36 410 448 480 474 440 | 500 < 0.008 76 80 85 90 91 | 50 | 72 105 103 88 103 > 0.992 || = 0.35 447 441 482 444 435 | 500 < 0.009 102 97 102 119 100 | 50 | 117 122 109 106 91 > 0.991 || = 0.34 479 477 446 411 432 | 500 < 0.01 62 42 64 53 57 | 50 | 59 65 56 55 54 > 0.99 || = 0.33 447 437 407 436 415 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 422 409 454 401 422 | 500 < 0.01 985 890 996 1018 994 | 497.5 | 960 974 991 931 929 > 0.99 || = 0.31 480 384 395 433 460 | 500 = 0.01 368 400 379 385 355 | 252.5 | 400 443 419 406 402 = 0.99 || = 0.30 429 423 430 416 437 | 500 = 0.02 690 696 730 733 706 | 500 | 615 656 675 661 642 = 0.98 || = 0.29 416 423 410 436 431 | 500 =================================================================| 500 | 683 724 730 701 708 = 0.97 || = 0.28 379 392 422 391 424 | 500 Test smarsa_CollisionOver calling smultin_MultinomialOver | 500 | 585 605 538 600 565 = 0.96 || = 0.27 431 399 397 376 406 | 500 smultin_MultinomialOver test: | 500 | 488 468 503 498 479 = 0.95 || = 0.26 401 372 372 378 414 | 500 ----------------------------------------------- | 500 | 725 731 724 753 703 = 0.94 || = 0.25 719 771 797 733 809 | 500 N = 30, n = 20000000, r = 27, d = 8, t = 14, | 500 | 382 434 398 436 415 = 0.93 || = 0.24 379 405 379 381 380 | 500 | 500 | 690 663 652 691 647 = 0.92 || = 0.23 426 334 400 393 361 | 500 =================================================================| 500 | 457 500 481 478 465 = 0.91 || = 0.22 351 385 363 331 357 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 486 471 485 490 501 = 0.90 || = 0.21 723 719 755 717 683 | 500 -----------------------------------------------------------------| 500 | 516 561 542 469 551 = 0.89 || = 0.20 343 353 325 385 344 | 500 SD Bern.: d 6.65129 7.95117 7.16989 | 500 | 539 604 545 554 549 = 0.88 || = 0.19 334 362 353 320 363 | 500 s 6.66849 6.58447 7.39043 | 500 | 640 665 571 574 581 = 0.87 || = 0.18 678 718 649 703 599 | 500 t 6.77354 7.90889 7.70670 | 500 | 318 311 279 297 322 = 0.86 || = 0.17 336 339 336 328 296 | 500 m 6.68956 8.48103 6.85805 | 500 | 654 577 610 626 640 = 0.85 || = 0.16 621 555 654 639 620 | 500 x 6.51156 7.92583 7.06568 | 500 | 351 336 333 341 320 = 0.84 || = 0.15 308 261 299 308 310 | 500 | 500 | 643 647 666 638 668 = 0.83 || = 0.14 600 596 597 638 582 | 500 Changes: d 32 0 0 | 500 | 304 350 335 352 340 = 0.82 || = 0.13 543 560 555 552 588 | 500 s 30 1 0 | 500 | 323 370 364 381 374 = 0.81 || = 0.12 538 534 537 562 514 | 500 t 28 0 0 | 500 | 722 775 747 801 702 = 0.80 || = 0.11 514 524 561 480 481 | 500 m 34 0 0 | 500 | 372 370 418 398 373 = 0.79 || = 0.10 499 466 460 451 431 | 500 x 36 0 0 | 500 | 383 395 369 372 367 = 0.78 || = 0.09 460 466 433 474 435 | 500 -----------------------------------------------------------------| 500 | 369 379 370 365 408 = 0.77 || = 0.08 615 651 609 569 630 | 500 Aver./ d 0.49954 465 > 500: 7 6 2 0 0 0 0 2 5 7 | 500 | 807 820 784 782 792 = 0.76 || = 0.07 394 402 403 396 390 | 500 median s 0.50409 464 ----- 8 6 2 0 0 0 0 2 5 7 | 500 | 412 394 365 415 372 = 0.75 || = 0.06 700 700 698 752 752 | 500 t 0.49936 460 8 6 2 0 0 0 0 2 5 8 | 500 | 412 452 425 435 399 = 0.74 || = 0.05 475 502 510 478 468 | 500 m 0.50105 469 7 5 2 0 1 0 0 2 4 7 | 500 | 406 411 372 427 409 = 0.73 || = 0.04 722 685 685 688 676 | 500 x 0.50115 468 7 5 2 0 1 3 0 2 6 7 | 500 | 440 439 430 400 441 = 0.72 || = 0.03 585 594 606 583 614 | 500 -----------------------------------------------------------------| 500 | 422 415 429 423 447 = 0.71 || = 0.02 690 696 730 733 706 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 439 453 442 405 452 = 0.70 || = 0.01 368 400 379 385 355 | 252.5 d 20 11 11 13 18 3 0 2 23 | 500 | 436 426 410 430 488 = 0.69 || < 0.01 985 890 996 1018 994 | 497.5 s 23 9 16 14 9 2 3 1 24 | 500 | 465 445 405 460 432 = 0.68 ||========================================================================= t 25 7 11 15 13 3 3 1 23 | 500 | 479 434 447 475 478 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 23 9 12 17 12 0 3 3 22 | 500 | 444 438 473 477 442 = 0.66 ||========================================================================= x 20 11 11 11 20 0 3 3 22 | 500 | 435 442 457 456 434 = 0.65 || Test smarsa_CollisionOver calling smultin_MultinomialOver no 10 test no 11 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_CollisionOver calling smultin_MultinomialOver test no 11 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 23 34 26 32 31 | 0.5 | 27 11 23 20 26 > 0.99999 || = 0.64 392 396 418 377 416 | 500 < 0.00002 5 16 20 11 14 | 0.5 | 13 14 10 10 7 > 0.99998 || = 0.63 411 402 427 408 408 | 500 < 0.00003 8 3 8 9 15 | 0.5 | 8 12 9 9 7 > 0.99997 || = 0.62 413 416 416 403 392 | 500 < 0.00004 5 10 15 14 11 | 0.5 | 16 12 9 9 11 > 0.99996 || = 0.61 388 440 412 432 439 | 500 < 0.00005 13 2 4 4 7 | 0.5 | 6 9 9 9 9 > 0.99995 || = 0.60 386 405 365 411 445 | 500 < 0.00006 4 4 2 6 6 | 0.5 | 7 4 2 3 1 > 0.99994 || = 0.59 404 427 411 412 434 | 500 < 0.00007 11 11 6 14 8 | 0.5 | 13 8 7 12 5 > 0.99993 || = 0.58 403 367 422 418 391 | 500 < 0.00008 6 2 1 6 4 | 0.5 | 4 6 8 9 6 > 0.99992 || = 0.57 409 394 439 423 426 | 500 < 0.00009 10 4 1 2 5 | 0.5 | 0 6 5 1 3 > 0.99991 || = 0.56 423 398 412 417 439 | 500 < 0.0001 7 7 7 11 4 | 0.5 | 11 9 5 15 3 > 0.9999 || = 0.55 415 403 412 396 417 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 406 440 411 394 403 | 500 < 0.0001 92 93 90 109 105 | 5 | 105 91 87 97 78 > 0.9999 || = 0.53 400 434 410 402 427 | 500 < 0.0002 53 60 61 62 58 | 5 | 33 37 36 28 30 > 0.9998 || = 0.52 409 447 414 417 435 | 500 < 0.0003 45 51 37 36 38 | 5 | 56 34 42 59 42 > 0.9997 || = 0.51 444 401 427 414 442 | 500 < 0.0004 35 23 31 33 49 | 5 | 39 44 44 45 46 > 0.9996 || = 0.50 876 871 801 848 839 | 500 < 0.0005 18 23 31 28 33 | 5 | 28 28 41 42 23 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 26 28 41 37 20 | 5 | 28 25 27 26 33 > 0.9994 || = 0.48 387 383 398 404 441 | 500 < 0.0007 31 46 32 39 28 | 5 | 42 43 41 26 44 > 0.9993 || = 0.47 418 442 422 422 417 | 500 < 0.0008 39 42 36 34 43 | 5 | 45 46 35 39 22 > 0.9992 || = 0.46 450 377 424 391 411 | 500 < 0.0009 19 15 20 24 32 | 5 | 20 20 23 21 22 > 0.9991 || = 0.45 404 389 445 397 401 | 500 < 0.001 23 24 19 28 18 | 5 | 23 21 10 20 18 > 0.999 || = 0.44 424 409 431 381 444 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 423 424 343 390 419 | 500 < 0.001 381 405 398 430 424 | 50 | 419 389 386 403 358 > 0.999 || = 0.42 409 400 411 434 456 | 500 < 0.002 224 232 233 239 228 | 50 | 217 251 230 235 231 > 0.998 || = 0.41 402 405 426 417 447 | 500 < 0.003 173 173 183 177 165 | 50 | 207 202 184 183 211 > 0.997 || = 0.40 418 441 374 437 429 | 500 < 0.004 182 164 175 164 192 | 50 | 141 138 122 134 122 > 0.996 || = 0.39 410 379 414 417 428 | 500 < 0.005 147 158 145 155 159 | 50 | 155 166 160 179 147 > 0.995 || = 0.38 407 372 420 432 385 | 500 < 0.006 121 124 151 115 118 | 50 | 146 126 115 124 101 > 0.994 || = 0.37 442 380 411 433 396 | 500 < 0.007 146 108 117 137 98 | 50 | 133 108 132 121 119 > 0.993 || = 0.36 377 402 411 427 394 | 500 < 0.008 138 125 163 139 153 | 50 | 149 176 135 154 147 > 0.992 || = 0.35 421 379 430 394 386 | 500 < 0.009 139 146 135 118 150 | 50 | 137 158 132 122 143 > 0.991 || = 0.34 414 416 395 387 371 | 500 < 0.01 75 78 58 90 70 | 50 | 86 76 82 96 82 > 0.99 || = 0.33 415 385 390 377 399 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 374 391 367 408 347 | 500 < 0.01 1726 1713 1758 1764 1757 | 497.5 | 1790 1790 1678 1751 1661 > 0.99 || = 0.31 365 389 353 393 390 | 500 = 0.01 520 560 534 509 518 | 252.5 | 595 552 565 533 586 = 0.99 || = 0.30 363 399 410 365 374 | 500 = 0.02 918 897 886 920 862 | 500 | 784 794 808 828 796 = 0.98 || = 0.29 375 352 398 348 374 | 500 =================================================================| 500 | 873 882 900 910 829 = 0.97 || = 0.28 351 389 402 377 393 | 500 Test smarsa_CollisionOver calling smultin_MultinomialOver | 500 | 683 691 663 682 652 = 0.96 || = 0.27 374 389 350 384 376 | 500 smultin_MultinomialOver test: | 500 | 605 574 572 560 530 = 0.95 || = 0.26 380 370 369 371 356 | 500 ----------------------------------------------- | 500 | 798 808 796 841 801 = 0.94 || = 0.25 723 737 702 712 703 | 500 N = 30, n = 20000000, r = 0, d = 4, t = 21, | 500 | 457 437 483 433 392 = 0.93 || = 0.24 354 408 363 367 321 | 500 | 500 | 715 702 697 739 770 = 0.92 || = 0.23 340 358 327 347 368 | 500 =================================================================| 500 | 499 508 488 485 510 = 0.91 || = 0.22 357 352 336 331 329 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 502 499 505 552 557 = 0.90 || = 0.21 651 708 677 688 643 | 500 -----------------------------------------------------------------| 500 | 539 547 520 525 565 = 0.89 || = 0.20 319 323 311 368 337 | 500 SD Bern.: d 10.95055 20.61836 22.04626 | 500 | 585 577 556 567 569 = 0.88 || = 0.19 323 302 288 329 322 | 500 s 10.82950 21.14836 21.78160 | 500 | 595 579 605 584 567 = 0.87 || = 0.18 620 610 641 644 654 | 500 t 10.59996 21.53656 20.33049 | 500 | 307 306 309 282 290 = 0.86 || = 0.17 283 291 321 300 300 | 500 m 10.87838 22.20164 21.40476 | 500 | 645 586 585 589 627 = 0.85 || = 0.16 600 599 628 595 561 | 500 x 10.61398 22.13648 19.73715 | 500 | 304 317 298 301 297 = 0.84 || = 0.15 287 273 298 312 288 | 500 | 500 | 635 638 639 610 654 = 0.83 || = 0.14 543 578 586 592 557 | 500 Changes: d 28 0 0 | 500 | 351 340 341 299 328 = 0.82 || = 0.13 560 538 530 562 548 | 500 s 28 0 0 | 500 | 303 330 333 349 332 = 0.81 || = 0.12 543 526 549 528 510 | 500 t 28 0 0 | 500 | 710 662 693 663 657 = 0.80 || = 0.11 501 501 530 537 538 | 500 m 28 0 0 | 500 | 321 321 335 348 360 = 0.79 || = 0.10 465 485 501 449 514 | 500 x 26 0 0 | 500 | 347 356 357 363 362 = 0.78 || = 0.09 493 451 488 521 413 | 500 -----------------------------------------------------------------| 500 | 318 383 347 336 392 = 0.77 || = 0.08 649 654 706 655 666 | 500 Aver./ d 0.50365 413 > 500: 8 6 2 0 0 0 0 2 6 8 | 500 | 758 742 736 720 738 = 0.76 || = 0.07 437 428 444 405 407 | 500 median s 0.50338 408 ----- 8 6 2 0 0 0 0 2 5 9 | 500 | 382 403 379 366 365 = 0.75 || = 0.06 789 721 720 772 779 | 500 t 0.50131 418 8 7 2 0 0 0 0 2 6 8 | 500 | 381 373 370 373 354 = 0.74 || = 0.05 530 538 544 535 527 | 500 m 0.50050 414 9 6 2 0 0 0 0 2 6 8 | 500 | 360 381 406 372 379 = 0.73 || = 0.04 776 789 765 783 835 | 500 x 0.50159 417 8 7 2 0 0 0 0 2 6 9 | 500 | 360 393 351 362 397 = 0.72 || = 0.03 676 699 664 696 734 | 500 -----------------------------------------------------------------| 500 | 387 393 384 379 350 = 0.71 || = 0.02 918 897 886 920 862 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 371 406 431 360 367 = 0.70 || = 0.01 520 560 534 509 518 | 252.5 d 50 10 4 2 4 4 1 1 25 | 500 | 403 402 403 384 404 = 0.69 || < 0.01 1726 1713 1758 1764 1757 | 497.5 s 52 6 8 0 4 3 1 5 22 | 500 | 373 425 388 389 410 = 0.68 ||========================================================================= t 44 17 3 0 6 3 2 3 23 | 500 | 400 374 411 409 375 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 49 14 3 0 2 4 3 2 24 | 500 | 401 388 388 386 391 = 0.66 ||========================================================================= x 47 9 9 1 3 3 5 2 22 | 500 | 398 399 392 391 408 = 0.65 || Test smarsa_CollisionOver calling smultin_MultinomialOver no 11 test no 12 TestU01 250000 runs BigCrush Test smarsa_S Test smarsa_CollisionOver calling smultin_MultinomialOver test no 12 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 21 22 29 21 21 | 0.5 | 31 17 25 31 23 > 0.99999 || = 0.64 433 358 403 402 431 | 500 < 0.00002 19 11 15 12 15 | 0.5 | 5 16 7 10 8 > 0.99998 || = 0.63 425 388 403 430 388 | 500 < 0.00003 8 14 13 15 23 | 0.5 | 13 7 12 6 13 > 0.99997 || = 0.62 397 410 393 398 398 | 500 < 0.00004 7 10 9 10 15 | 0.5 | 3 11 13 13 8 > 0.99996 || = 0.61 382 405 420 399 385 | 500 < 0.00005 9 8 12 10 7 | 0.5 | 8 9 9 9 6 > 0.99995 || = 0.60 449 406 377 430 392 | 500 < 0.00006 6 5 3 6 6 | 0.5 | 2 8 5 5 3 > 0.99994 || = 0.59 416 401 382 437 414 | 500 < 0.00007 3 15 10 7 9 | 0.5 | 11 10 8 15 4 > 0.99993 || = 0.58 418 429 415 434 397 | 500 < 0.00008 5 3 7 3 6 | 0.5 | 5 7 9 7 9 > 0.99992 || = 0.57 388 395 434 418 413 | 500 < 0.00009 6 8 8 6 3 | 0.5 | 4 8 7 3 5 > 0.99991 || = 0.56 415 444 431 420 397 | 500 < 0.0001 10 6 4 4 10 | 0.5 | 9 7 6 11 4 > 0.9999 || = 0.55 436 393 458 395 390 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 434 421 423 432 436 | 500 < 0.0001 94 102 110 94 115 | 5 | 91 100 101 110 83 > 0.9999 || = 0.53 408 433 459 445 423 | 500 < 0.0002 49 51 62 56 70 | 5 | 31 19 24 30 27 > 0.9998 || = 0.52 462 429 400 400 413 | 500 < 0.0003 48 39 37 50 35 | 5 | 44 40 43 54 65 > 0.9997 || = 0.51 403 399 433 393 422 | 500 < 0.0004 27 30 36 47 41 | 5 | 38 37 42 28 29 > 0.9996 || = 0.50 813 846 832 882 851 | 500 < 0.0005 31 36 19 31 35 | 5 | 28 24 32 39 23 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 30 27 29 38 43 | 5 | 33 24 38 28 29 > 0.9994 || = 0.48 439 429 432 431 406 | 500 < 0.0007 32 42 51 30 34 | 5 | 29 34 29 27 36 > 0.9993 || = 0.47 408 420 419 391 399 | 500 < 0.0008 28 45 32 44 48 | 5 | 34 44 44 35 49 > 0.9992 || = 0.46 425 417 390 425 418 | 500 < 0.0009 21 19 31 17 24 | 5 | 22 20 28 20 27 > 0.9991 || = 0.45 434 421 409 421 415 | 500 < 0.001 21 22 21 20 30 | 5 | 21 24 24 27 16 > 0.999 || = 0.44 418 384 388 404 380 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 381 394 402 356 465 | 500 < 0.001 381 413 428 427 475 | 50 | 371 366 405 398 384 > 0.999 || = 0.42 393 388 419 428 396 | 500 < 0.002 242 206 251 231 216 | 50 | 241 233 234 231 214 > 0.998 || = 0.41 419 425 393 405 410 | 500 < 0.003 204 198 184 201 191 | 50 | 175 190 178 178 192 > 0.997 || = 0.40 425 405 373 435 419 | 500 < 0.004 159 185 174 181 174 | 50 | 136 134 135 154 150 > 0.996 || = 0.39 397 377 400 410 443 | 500 < 0.005 145 169 155 150 150 | 50 | 179 151 167 167 163 > 0.995 || = 0.38 389 425 407 400 407 | 500 < 0.006 113 104 95 112 112 | 50 | 110 123 108 139 123 > 0.994 || = 0.37 393 388 350 387 402 | 500 < 0.007 121 105 116 118 114 | 50 | 127 137 145 123 124 > 0.993 || = 0.36 393 369 404 375 362 | 500 < 0.008 153 120 118 119 128 | 50 | 151 161 150 156 134 > 0.992 || = 0.35 418 376 414 406 386 | 500 < 0.009 164 140 157 142 138 | 50 | 123 156 145 141 155 > 0.991 || = 0.34 385 433 392 378 361 | 500 < 0.01 87 71 78 77 62 | 50 | 84 94 75 87 84 > 0.99 || = 0.33 381 379 438 413 401 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 382 406 380 383 404 | 500 < 0.01 1769 1711 1756 1758 1760 | 497.5 | 1697 1745 1742 1774 1723 > 0.99 || = 0.31 381 361 362 374 377 | 500 = 0.01 524 550 513 530 563 | 252.5 | 562 587 546 570 552 = 0.99 || = 0.30 341 390 349 383 392 | 500 = 0.02 928 913 935 854 903 | 500 | 788 800 829 788 840 = 0.98 || = 0.29 377 383 390 382 375 | 500 =================================================================| 500 | 898 872 892 906 877 = 0.97 || = 0.28 392 370 343 392 396 | 500 Test smarsa_CollisionOver calling smultin_MultinomialOver | 500 | 629 692 701 667 684 = 0.96 || = 0.27 400 348 339 352 347 | 500 smultin_MultinomialOver test: | 500 | 513 565 594 603 572 = 0.95 || = 0.26 373 366 377 355 355 | 500 ----------------------------------------------- | 500 | 822 832 843 828 797 = 0.94 || = 0.25 738 719 720 739 711 | 500 N = 30, n = 20000000, r = 28, d = 4, t = 21, | 500 | 450 456 414 411 416 = 0.93 || = 0.24 384 364 372 383 373 | 500 | 500 | 731 741 693 739 686 = 0.92 || = 0.23 326 372 350 318 390 | 500 =================================================================| 500 | 467 505 454 481 470 = 0.91 || = 0.22 362 350 339 343 339 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 517 523 520 497 510 = 0.90 || = 0.21 679 688 638 658 653 | 500 -----------------------------------------------------------------| 500 | 523 546 544 515 512 = 0.89 || = 0.20 337 345 314 336 343 | 500 SD Bern.: d 10.74699 21.22527 20.27829 | 500 | 570 568 560 568 627 = 0.88 || = 0.19 313 275 337 344 322 | 500 s 10.81234 21.44793 20.43534 | 500 | 554 591 640 596 611 = 0.87 || = 0.18 613 627 665 634 635 | 500 t 10.92673 22.41120 21.42182 | 500 | 326 318 302 285 310 = 0.86 || = 0.17 324 294 302 297 325 | 500 m 10.94130 22.24956 21.40649 | 500 | 597 562 618 641 646 = 0.85 || = 0.16 605 581 648 636 622 | 500 x 10.86095 23.47874 20.57369 | 500 | 303 342 323 317 302 = 0.84 || = 0.15 292 287 314 315 285 | 500 | 500 | 631 653 637 681 640 = 0.83 || = 0.14 603 609 588 538 561 | 500 Changes: d 28 0 0 | 500 | 331 321 327 316 351 = 0.82 || = 0.13 543 574 529 573 561 | 500 s 26 0 0 | 500 | 314 351 319 283 327 = 0.81 || = 0.12 528 519 545 557 464 | 500 t 28 0 0 | 500 | 734 637 654 658 648 = 0.80 || = 0.11 526 515 498 541 552 | 500 m 28 0 0 | 500 | 342 348 313 329 336 = 0.79 || = 0.10 481 497 497 464 497 | 500 x 30 0 0 | 500 | 336 341 347 332 336 = 0.78 || = 0.09 463 459 490 492 479 | 500 -----------------------------------------------------------------| 500 | 362 349 353 371 340 = 0.77 || = 0.08 651 649 706 646 649 | 500 Aver./ d 0.49922 418 > 500: 8 6 2 0 0 0 0 2 6 8 | 500 | 734 747 772 710 724 = 0.76 || = 0.07 439 419 393 398 416 | 500 median s 0.50287 417 ----- 8 6 2 0 0 0 0 2 6 9 | 500 | 357 393 344 350 381 = 0.75 || = 0.06 754 793 749 749 764 | 500 t 0.50148 414 8 5 2 0 0 0 0 2 6 8 | 500 | 368 393 395 373 377 = 0.74 || = 0.05 571 541 578 539 527 | 500 m 0.50275 413 8 6 2 0 0 0 0 2 5 8 | 500 | 380 370 353 403 394 = 0.73 || = 0.04 822 773 763 800 862 | 500 x 0.50024 410 8 5 2 0 0 0 0 2 6 8 | 500 | 380 373 376 408 395 = 0.72 || = 0.03 680 709 703 640 703 | 500 -----------------------------------------------------------------| 500 | 383 380 347 356 397 = 0.71 || = 0.02 928 913 935 854 903 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 356 395 373 365 353 = 0.70 || = 0.01 524 550 513 530 563 | 252.5 d 45 12 7 3 3 4 1 2 24 | 500 | 397 378 414 400 358 = 0.69 || < 0.01 1769 1711 1756 1758 1760 | 497.5 s 50 13 1 2 4 2 3 3 23 | 500 | 418 426 383 400 404 = 0.68 ||========================================================================= t 49 12 3 2 4 2 2 2 25 | 500 | 414 399 394 384 397 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 50 11 4 1 4 3 1 2 25 | 500 | 343 384 391 399 392 = 0.66 ||========================================================================= x 51 11 2 3 4 1 3 1 25 | 500 | 395 373 418 413 390 = 0.65 || Test smarsa_CollisionOver calling smultin_MultinomialOver no 12 test no 13 TestU01 250000 runs BigCrush Test smarsa_S smarsa_BirthdaySpacings test: test no 13 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 3 1 0 0 0 | 0.5 | 0 0 1 2 1 > 0.99999 || = 0.64 523 486 505 534 525 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 2 2 1 0 > 0.99998 || = 0.63 553 518 487 504 515 | 500 < 0.00003 0 0 1 1 0 | 0.5 | 1 0 1 1 0 > 0.99997 || = 0.62 526 507 519 472 494 | 500 < 0.00004 0 2 1 0 1 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 541 504 526 540 527 | 500 < 0.00005 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 524 501 558 530 506 | 500 < 0.00006 1 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 562 520 494 496 588 | 500 < 0.00007 0 1 0 1 0 | 0.5 | 2 0 0 0 0 > 0.99993 || = 0.58 531 501 541 545 523 | 500 < 0.00008 3 1 4 1 2 | 0.5 | 0 0 0 1 0 > 0.99992 || = 0.57 530 573 536 538 552 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 2 0 0 1 1 > 0.99991 || = 0.56 545 510 516 540 530 | 500 < 0.0001 0 0 1 0 0 | 0.5 | 0 2 1 0 1 > 0.9999 || = 0.55 544 514 542 563 547 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 275 312 249 272 284 | 500 < 0.0001 8 5 7 3 3 | 5 | 6 4 6 6 3 > 0.9999 || = 0.53 550 514 553 533 542 | 500 < 0.0002 10 3 6 3 1 | 5 | 4 6 3 2 1 > 0.9998 || = 0.52 558 504 540 571 579 | 500 < 0.0003 5 6 0 8 3 | 5 | 6 5 3 4 5 > 0.9997 || = 0.51 559 536 549 524 528 | 500 < 0.0004 3 5 2 2 6 | 5 | 3 3 3 6 2 > 0.9996 || = 0.50 816 763 793 795 787 | 500 < 0.0005 10 5 1 6 8 | 5 | 10 3 3 5 5 > 0.9995 || = 0.49 540 500 532 555 549 | 500 < 0.0006 4 3 3 4 3 | 5 | 3 5 4 6 1 > 0.9994 || = 0.48 261 287 282 266 283 | 500 < 0.0007 4 9 7 7 4 | 5 | 5 8 13 9 7 > 0.9993 || = 0.47 548 557 576 534 524 | 500 < 0.0008 5 6 6 4 3 | 5 | 6 9 6 5 2 > 0.9992 || = 0.46 529 533 550 538 496 | 500 < 0.0009 3 3 4 10 7 | 5 | 6 4 0 5 1 > 0.9991 || = 0.45 586 543 565 539 532 | 500 < 0.001 2 5 6 3 5 | 5 | 3 4 7 8 7 > 0.999 || = 0.44 526 545 524 557 541 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 546 530 526 535 531 | 500 < 0.001 54 50 42 50 43 | 50 | 52 51 48 56 34 > 0.999 || = 0.42 523 503 501 524 521 | 500 < 0.002 50 62 50 41 41 | 50 | 42 52 52 49 54 > 0.998 || = 0.41 520 558 504 527 490 | 500 < 0.003 57 51 62 48 46 | 50 | 40 35 43 40 46 > 0.997 || = 0.40 239 257 281 272 263 | 500 < 0.004 46 36 51 47 48 | 50 | 63 38 47 58 57 > 0.996 || = 0.39 540 537 526 535 499 | 500 < 0.005 45 51 55 47 53 | 50 | 50 53 47 58 58 > 0.995 || = 0.38 546 536 514 494 534 | 500 < 0.006 58 50 50 61 43 | 50 | 48 49 47 46 42 > 0.994 || = 0.37 517 505 499 543 497 | 500 < 0.007 45 46 48 49 45 | 50 | 53 44 49 57 60 > 0.993 || = 0.36 506 531 492 548 485 | 500 < 0.008 61 51 54 56 60 | 50 | 38 46 38 37 41 > 0.992 || = 0.35 470 475 516 509 479 | 500 < 0.009 35 46 38 41 43 | 50 | 57 49 45 50 41 > 0.991 || = 0.34 496 542 489 535 538 | 500 < 0.01 54 52 59 54 53 | 50 | 50 52 40 47 49 > 0.99 || = 0.33 494 535 492 540 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 471 534 461 505 479 | 500 < 0.01 505 495 509 494 475 | 497.5 | 493 469 456 498 482 > 0.99 || = 0.31 481 459 487 438 473 | 500 = 0.01 261 253 248 245 233 | 252.5 | 241 277 251 275 264 = 0.99 || = 0.30 715 692 656 673 710 | 500 = 0.02 482 497 439 468 488 | 500 | 474 471 513 438 532 = 0.98 || = 0.29 410 471 471 460 454 | 500 =================================================================| 500 | 480 540 546 485 503 = 0.97 || = 0.28 448 464 445 442 456 | 500 smarsa_BirthdaySpacings test: | 500 | 460 467 440 444 445 = 0.96 || = 0.27 430 457 436 418 457 | 500 ----------------------------------------------- | 500 | 519 517 545 530 556 = 0.95 || = 0.26 471 479 418 453 430 | 500 N = 100, n = 10000000, r = 0, d = 2147483648, t = 2, p = 1 | 500 | 459 446 500 462 500 = 0.94 || = 0.25 602 614 681 652 626 | 500 | 500 | 448 432 472 446 451 = 0.93 || = 0.24 443 392 416 417 396 | 500 | 500 | 508 490 474 505 505 = 0.92 || = 0.23 571 582 641 629 655 | 500 =================================================================| 500 | 560 555 561 544 523 = 0.91 || = 0.22 376 367 395 346 417 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 479 452 473 466 442 = 0.90 || = 0.21 593 571 624 609 621 | 500 -----------------------------------------------------------------| 500 | 494 513 539 516 494 = 0.89 || = 0.20 368 357 389 393 399 | 500 SD Bern.: d 3.96913 1.05598 1.04262 | 500 | 418 411 400 386 407 = 0.88 || = 0.19 532 586 554 554 523 | 500 s 3.71268 0.87106 0.93961 | 500 | 589 667 569 570 583 = 0.87 || = 0.18 512 504 520 527 573 | 500 t 3.76797 0.97925 0.84183 | 500 | 440 433 449 485 475 = 0.86 || = 0.17 507 495 482 471 529 | 500 m 3.75003 0.84658 1.00846 | 500 | 456 511 475 487 497 = 0.85 || = 0.16 490 507 496 474 522 | 500 x 3.73927 0.88474 1.20724 | 500 | 483 518 490 486 441 = 0.84 || = 0.15 462 497 434 458 460 | 500 | 500 | 519 534 529 524 484 = 0.83 || = 0.14 408 449 456 422 450 | 500 Changes: d 43 8 7 | 500 | 547 509 513 538 504 = 0.82 || = 0.13 594 568 571 574 575 | 500 s 56 7 4 | 500 | 581 536 603 575 556 = 0.81 || = 0.12 406 388 420 440 398 | 500 t 53 5 2 | 500 | 361 350 367 375 346 = 0.80 || = 0.11 492 506 508 512 530 | 500 m 52 5 5 | 500 | 627 613 557 577 620 = 0.79 || = 0.10 599 593 585 577 597 | 500 x 52 5 6 | 500 | 404 383 410 403 397 = 0.78 || = 0.09 429 407 419 447 406 | 500 -----------------------------------------------------------------| 500 | 617 655 655 627 578 = 0.77 || = 0.08 453 517 501 478 485 | 500 Aver./ d 0.50076 506 > 500: 4 5 3 5 8 9 6 3 4 3 | 500 | 407 425 418 418 442 = 0.76 || = 0.07 524 517 536 518 557 | 500 median s 0.49984 504 ----- 4 6 3 8 7 9 5 3 7 4 | 500 | 429 454 403 475 431 = 0.75 || = 0.06 475 460 489 483 475 | 500 t 0.50037 499 4 5 3 4 8 8 4 3 5 4 | 500 | 702 666 640 682 649 = 0.74 || = 0.05 478 494 488 478 475 | 500 m 0.50011 504 1 5 3 8 8 8 5 3 5 5 | 500 | 408 439 446 469 450 = 0.73 || = 0.04 520 486 520 492 481 | 500 x 0.49937 497 1 7 3 3 6 9 6 3 3 6 | 500 | 433 443 481 453 430 = 0.72 || = 0.03 482 509 472 461 477 | 500 -----------------------------------------------------------------| 500 | 483 474 462 440 490 = 0.71 || = 0.02 482 497 439 468 488 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 488 499 460 459 505 = 0.70 || = 0.01 261 253 248 245 233 | 252.5 d 13 5 5 9 29 14 12 3 11 | 500 | 481 472 459 520 481 = 0.69 || < 0.01 505 495 509 494 475 | 497.5 s 12 3 7 11 36 14 4 5 9 | 500 | 478 509 499 454 525 = 0.68 ||========================================================================= t 10 5 7 12 32 12 10 4 9 | 500 | 555 450 490 470 489 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 9 4 11 13 21 23 6 6 8 | 500 | 728 737 738 721 717 = 0.66 ||========================================================================= x 11 4 8 10 29 18 6 6 9 | 500 | 237 279 273 281 252 = 0.65 || smarsa_BirthdaySpacings test: no 13 test no 14 TestU01 250000 runs BigCrush Test smarsa_S smarsa_BirthdaySpacings test: test no 14 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 0 | 0.5 | 0 1 3 0 0 > 0.99999 || = 0.64 537 564 568 594 548 | 500 < 0.00002 0 1 1 0 1 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 581 551 528 549 635 | 500 < 0.00003 1 0 0 0 2 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 275 296 308 287 323 | 500 < 0.00004 1 1 1 1 0 | 0.5 | 1 0 1 2 0 > 0.99996 || = 0.61 616 614 602 577 571 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 2 0 0 0 0 > 0.99995 || = 0.60 613 580 571 576 589 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 0 1 0 1 0 > 0.99994 || = 0.59 594 567 568 548 568 | 500 < 0.00007 1 0 2 2 0 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 333 313 308 302 315 | 500 < 0.00008 0 0 0 1 3 | 0.5 | 1 1 2 1 0 > 0.99992 || = 0.57 584 618 540 637 618 | 500 < 0.00009 1 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 607 605 572 597 590 | 500 < 0.0001 0 1 1 1 0 | 0.5 | 1 0 1 0 1 > 0.9999 || = 0.55 275 300 288 298 276 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 566 606 577 605 586 | 500 < 0.0001 4 3 6 5 8 | 5 | 7 5 7 4 1 > 0.9999 || = 0.53 601 559 573 592 581 | 500 < 0.0002 2 4 5 1 4 | 5 | 3 1 1 0 1 > 0.9998 || = 0.52 310 296 299 321 294 | 500 < 0.0003 1 5 4 4 3 | 5 | 4 5 2 4 6 > 0.9997 || = 0.51 596 651 604 606 617 | 500 < 0.0004 4 2 4 5 9 | 5 | 9 7 4 4 4 > 0.9996 || = 0.50 585 634 605 586 622 | 500 < 0.0005 5 3 3 5 5 | 5 | 5 2 8 7 2 > 0.9995 || = 0.49 557 593 614 606 556 | 500 < 0.0006 1 1 6 5 2 | 5 | 4 3 4 2 5 > 0.9994 || = 0.48 620 618 571 616 575 | 500 < 0.0007 7 5 2 3 6 | 5 | 4 1 6 2 7 > 0.9993 || = 0.47 310 297 279 305 322 | 500 < 0.0008 5 9 5 5 10 | 5 | 4 2 6 2 5 > 0.9992 || = 0.46 620 608 596 615 584 | 500 < 0.0009 5 6 3 2 3 | 5 | 11 7 6 9 4 > 0.9991 || = 0.45 630 607 617 646 597 | 500 < 0.001 7 1 5 2 2 | 5 | 6 7 4 4 4 > 0.999 || = 0.44 284 299 268 291 319 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 583 653 625 583 590 | 500 < 0.001 41 39 43 37 52 | 50 | 57 40 48 38 39 > 0.999 || = 0.42 577 569 603 608 610 | 500 < 0.002 46 55 53 53 59 | 50 | 46 38 59 42 49 > 0.998 || = 0.41 293 296 297 290 299 | 500 < 0.003 49 60 45 46 44 | 50 | 48 47 48 46 50 > 0.997 || = 0.40 563 583 558 522 546 | 500 < 0.004 46 53 43 41 50 | 50 | 42 45 39 53 44 > 0.996 || = 0.39 608 557 581 605 577 | 500 < 0.005 51 39 44 48 50 | 50 | 47 38 40 53 53 > 0.995 || = 0.38 584 599 558 600 559 | 500 < 0.006 61 52 70 53 67 | 50 | 60 29 43 64 58 > 0.994 || = 0.37 297 277 288 284 281 | 500 < 0.007 42 39 37 50 33 | 50 | 53 53 58 53 51 > 0.993 || = 0.36 567 553 593 598 562 | 500 < 0.008 63 56 56 49 69 | 50 | 53 43 48 49 57 > 0.992 || = 0.35 550 522 592 587 583 | 500 < 0.009 57 49 53 53 56 | 50 | 65 43 64 56 54 > 0.991 || = 0.34 521 556 564 542 570 | 500 < 0.01 43 33 26 36 34 | 50 | 41 34 33 40 37 > 0.99 || = 0.33 551 514 512 546 542 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 268 257 260 269 253 | 500 < 0.01 499 475 470 466 514 | 497.5 | 512 410 480 494 492 > 0.99 || = 0.31 547 503 528 522 518 | 500 = 0.01 256 264 260 255 262 | 252.5 | 272 256 270 244 268 = 0.99 || = 0.30 543 541 561 508 537 | 500 = 0.02 494 457 495 508 527 | 500 | 454 488 516 466 462 = 0.98 || = 0.29 489 481 555 486 500 | 500 =================================================================| 500 | 517 484 495 484 544 = 0.97 || = 0.28 510 529 497 535 466 | 500 smarsa_BirthdaySpacings test: | 500 | 474 452 439 464 430 = 0.96 || = 0.27 478 454 497 514 536 | 500 ----------------------------------------------- | 500 | 561 588 547 530 540 = 0.95 || = 0.26 463 518 474 466 458 | 500 N = 20, n = 20000000, r = 0, d = 2097152, t = 3, p = 1 | 500 | 438 445 449 494 444 = 0.94 || = 0.25 495 488 464 473 507 | 500 | 500 | 471 515 485 516 489 = 0.93 || = 0.24 496 487 498 450 448 | 500 | 500 | 579 608 607 558 563 = 0.92 || = 0.23 480 485 460 414 449 | 500 =================================================================| 500 | 493 477 515 491 489 = 0.91 || = 0.22 673 710 649 651 659 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 377 401 398 372 425 = 0.90 || = 0.21 455 443 468 377 429 | 500 -----------------------------------------------------------------| 500 | 556 573 572 549 517 = 0.89 || = 0.20 393 422 424 422 448 | 500 SD Bern.: d 4.17451 1.06542 1.06447 | 500 | 476 426 426 458 469 = 0.88 || = 0.19 617 671 577 670 633 | 500 s 4.35606 1.28671 1.56666 | 500 | 458 493 508 465 473 = 0.87 || = 0.18 432 409 403 409 356 | 500 t 4.17012 1.64885 1.35122 | 500 | 475 499 489 522 484 = 0.86 || = 0.17 624 587 621 581 553 | 500 m 4.30097 0.99447 1.08127 | 500 | 497 517 602 527 527 = 0.85 || = 0.16 511 564 567 579 535 | 500 x 4.18765 1.64520 0.96587 | 500 | 551 561 567 541 550 = 0.84 || = 0.15 546 514 530 518 536 | 500 | 500 | 404 390 405 365 370 = 0.83 || = 0.14 331 348 343 340 324 | 500 Changes: d 56 4 3 | 500 | 607 553 549 596 624 = 0.82 || = 0.13 587 654 645 611 609 | 500 s 56 6 2 | 500 | 440 408 423 397 384 = 0.81 || = 0.12 454 426 492 450 446 | 500 t 56 6 6 | 500 | 405 424 441 425 429 = 0.80 || = 0.11 444 426 457 445 466 | 500 m 54 6 4 | 500 | 668 626 643 672 693 = 0.79 || = 0.10 518 500 505 510 555 | 500 x 57 5 2 | 500 | 447 464 444 458 476 = 0.78 || = 0.09 479 540 483 534 489 | 500 -----------------------------------------------------------------| 500 | 444 457 425 499 470 = 0.77 || = 0.08 558 591 548 555 562 | 500 Aver./ d 0.49891 507 > 500: 5 6 2 8 7 7 7 4 3 5 | 500 | 445 467 463 485 462 = 0.76 || = 0.07 475 468 500 508 490 | 500 median s 0.49823 506 ----- 5 5 3 8 7 7 8 3 4 4 | 500 | 498 475 498 507 498 = 0.75 || = 0.06 459 411 460 445 466 | 500 t 0.49963 512 3 6 2 8 7 7 8 2 5 5 | 500 | 482 505 495 510 477 = 0.74 || = 0.05 531 515 502 527 486 | 500 m 0.49931 510 6 6 3 8 7 7 8 4 5 3 | 500 | 503 487 542 493 498 = 0.73 || = 0.04 507 503 476 491 535 | 500 x 0.49973 524 5 6 3 8 7 7 8 3 4 4 | 500 | 522 464 497 507 542 = 0.72 || = 0.03 488 493 466 468 436 | 500 -----------------------------------------------------------------| 500 | 504 530 480 472 531 = 0.71 || = 0.02 494 457 495 508 527 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 469 501 553 520 550 = 0.70 || = 0.01 256 264 260 255 262 | 252.5 d 15 1 9 9 24 6 12 10 15 | 500 | 555 530 523 517 525 = 0.69 || < 0.01 499 475 470 466 514 | 497.5 s 16 6 4 9 25 5 11 7 18 | 500 | 536 518 538 546 524 = 0.68 ||========================================================================= t 14 4 4 10 22 10 9 12 16 | 500 | 530 560 540 540 558 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 16 3 4 10 26 8 8 7 19 | 500 | 309 300 281 275 286 = 0.66 ||========================================================================= x 14 4 6 11 16 15 12 9 14 | 500 | 583 559 533 565 544 = 0.65 || smarsa_BirthdaySpacings test: no 14 test no 15 TestU01 250000 runs BigCrush Test smarsa_S smarsa_BirthdaySpacings test: test no 15 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 0 0 1 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 618 628 682 649 682 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 1 0 0 2 0 > 0.99998 || = 0.63 414 455 413 427 448 | 500 < 0.00003 0 0 1 1 0 | 0.5 | 0 0 1 0 0 > 0.99997 || = 0.62 465 391 461 435 459 | 500 < 0.00004 1 3 1 1 1 | 0.5 | 1 0 1 0 0 > 0.99996 || = 0.61 477 474 450 439 469 | 500 < 0.00005 0 0 1 0 1 | 0.5 | 1 0 1 0 0 > 0.99995 || = 0.60 651 711 649 664 715 | 500 < 0.00006 0 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 463 444 438 443 485 | 500 < 0.00007 0 1 0 2 0 | 0.5 | 1 0 0 0 1 > 0.99993 || = 0.58 479 451 458 415 410 | 500 < 0.00008 2 0 0 0 0 | 0.5 | 0 0 2 0 0 > 0.99992 || = 0.57 495 472 470 470 455 | 500 < 0.00009 0 2 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99991 || = 0.56 459 465 479 452 446 | 500 < 0.0001 0 0 1 2 0 | 0.5 | 0 0 0 0 1 > 0.9999 || = 0.55 756 746 707 700 670 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 479 455 470 481 441 | 500 < 0.0001 5 7 5 7 4 | 5 | 4 0 6 3 2 > 0.9999 || = 0.53 455 443 476 488 473 | 500 < 0.0002 6 4 8 6 6 | 5 | 3 1 1 4 3 > 0.9998 || = 0.52 485 457 482 448 471 | 500 < 0.0003 2 6 5 11 3 | 5 | 3 4 5 6 2 > 0.9997 || = 0.51 453 475 436 478 474 | 500 < 0.0004 8 7 3 5 2 | 5 | 5 7 5 5 9 > 0.9996 || = 0.50 753 708 725 690 697 | 500 < 0.0005 3 1 4 5 4 | 5 | 4 3 5 4 4 > 0.9995 || = 0.49 445 446 435 469 445 | 500 < 0.0006 3 3 9 7 3 | 5 | 6 8 6 9 9 > 0.9994 || = 0.48 674 678 697 715 711 | 500 < 0.0007 5 3 3 8 8 | 5 | 3 4 2 3 5 > 0.9993 || = 0.47 490 459 444 435 465 | 500 < 0.0008 3 3 3 4 7 | 5 | 4 1 4 6 4 > 0.9992 || = 0.46 434 468 456 473 482 | 500 < 0.0009 5 5 7 5 6 | 5 | 5 4 6 4 3 > 0.9991 || = 0.45 482 442 480 446 462 | 500 < 0.001 5 2 4 1 4 | 5 | 6 5 4 5 7 > 0.999 || = 0.44 454 473 464 480 463 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 456 464 439 465 433 | 500 < 0.001 45 41 51 59 47 | 50 | 43 37 44 49 48 > 0.999 || = 0.42 667 663 697 679 684 | 500 < 0.002 50 39 47 44 54 | 50 | 58 57 51 64 48 > 0.998 || = 0.41 434 440 434 472 453 | 500 < 0.003 52 49 42 51 39 | 50 | 38 51 64 48 53 > 0.997 || = 0.40 472 446 422 482 454 | 500 < 0.004 40 46 48 43 37 | 50 | 55 43 48 58 45 > 0.996 || = 0.39 437 422 433 438 445 | 500 < 0.005 40 56 42 40 48 | 50 | 57 66 41 58 57 > 0.995 || = 0.38 440 444 402 454 445 | 500 < 0.006 63 66 55 59 44 | 50 | 46 44 46 41 47 > 0.994 || = 0.37 684 660 668 703 696 | 500 < 0.007 42 36 50 42 43 | 50 | 37 59 68 46 71 > 0.993 || = 0.36 446 420 440 436 451 | 500 < 0.008 47 50 59 60 52 | 50 | 41 46 58 38 52 > 0.992 || = 0.35 446 436 467 424 427 | 500 < 0.009 42 46 40 50 40 | 50 | 44 47 60 63 54 > 0.991 || = 0.34 604 638 649 660 626 | 500 < 0.01 57 63 51 59 49 | 50 | 44 32 37 50 40 > 0.99 || = 0.33 433 424 423 440 431 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 450 444 401 434 372 | 500 < 0.01 478 492 485 507 453 | 497.5 | 463 482 517 515 515 > 0.99 || = 0.31 590 611 597 610 587 | 500 = 0.01 250 259 271 251 228 | 252.5 | 215 266 243 259 253 = 0.99 || = 0.30 337 364 435 379 386 | 500 = 0.02 473 489 465 456 464 | 500 | 479 492 488 508 468 = 0.98 || = 0.29 607 583 644 620 634 | 500 =================================================================| 500 | 499 493 509 499 501 = 0.97 || = 0.28 443 408 395 396 387 | 500 smarsa_BirthdaySpacings test: | 500 | 533 513 509 473 536 = 0.96 || = 0.27 587 554 590 604 623 | 500 ----------------------------------------------- | 500 | 450 493 516 474 511 = 0.95 || = 0.26 610 570 532 574 532 | 500 N = 20, n = 30000000, r = 14, d = 65536, t = 4, p = 1 | 500 | 449 515 521 485 471 = 0.94 || = 0.25 382 408 366 353 358 | 500 | 500 | 497 471 461 442 456 = 0.93 || = 0.24 485 548 540 516 522 | 500 | 500 | 493 490 505 533 510 = 0.92 || = 0.23 535 545 545 532 540 | 500 =================================================================| 500 | 512 459 482 462 516 = 0.91 || = 0.22 475 552 505 523 544 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 500 543 500 479 523 = 0.90 || = 0.21 515 512 504 509 501 | 500 -----------------------------------------------------------------| 500 | 581 566 527 510 568 = 0.89 || = 0.20 462 490 486 461 457 | 500 SD Bern.: d 3.51212 1.08127 1.15728 | 500 | 468 500 491 475 464 = 0.88 || = 0.19 483 492 470 489 473 | 500 s 3.44177 1.33633 1.40782 | 500 | 484 509 495 489 480 = 0.87 || = 0.18 487 439 451 450 460 | 500 t 3.49345 0.83587 1.40853 | 500 | 523 505 474 519 497 = 0.86 || = 0.17 527 600 575 622 581 | 500 m 3.55334 1.08957 1.21632 | 500 | 544 546 527 533 567 = 0.85 || = 0.16 428 413 412 459 439 | 500 x 3.65784 1.00946 1.15035 | 500 | 400 434 471 422 411 = 0.84 || = 0.15 553 519 536 550 525 | 500 | 500 | 462 439 499 447 447 = 0.83 || = 0.14 506 528 509 494 554 | 500 Changes: d 58 5 4 | 500 | 600 620 606 642 593 = 0.82 || = 0.13 490 475 500 488 461 | 500 s 60 3 6 | 500 | 531 486 492 469 481 = 0.81 || = 0.12 425 488 454 459 435 | 500 t 61 6 4 | 500 | 490 526 515 493 519 = 0.80 || = 0.11 578 505 522 566 514 | 500 m 54 8 6 | 500 | 541 500 500 479 523 = 0.79 || = 0.10 517 466 498 472 501 | 500 x 56 4 6 | 500 | 489 531 519 512 584 = 0.78 || = 0.09 456 446 430 482 440 | 500 -----------------------------------------------------------------| 500 | 338 354 351 369 362 = 0.77 || = 0.08 502 526 525 487 526 | 500 Aver./ d 0.49995 484 > 500: 3 5 5 3 2 2 3 4 5 2 | 500 | 485 515 554 542 520 = 0.76 || = 0.07 455 490 414 455 455 | 500 median s 0.50147 489 ----- 3 4 7 3 2 2 3 6 6 3 | 500 | 568 563 554 564 566 = 0.75 || = 0.06 476 455 477 456 435 | 500 t 0.50223 488 4 4 7 3 2 2 3 6 3 6 | 500 | 554 585 576 576 536 = 0.74 || = 0.05 532 524 516 522 532 | 500 m 0.49910 481 3 3 7 3 2 2 3 5 4 4 | 500 | 358 361 414 403 372 = 0.73 || = 0.04 485 463 495 474 497 | 500 x 0.50299 474 3 5 7 3 2 2 3 7 4 7 | 500 | 609 548 573 577 629 = 0.72 || = 0.03 518 480 509 513 506 | 500 -----------------------------------------------------------------| 500 | 443 408 399 370 359 = 0.71 || = 0.02 473 489 465 456 464 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 627 602 642 619 612 = 0.70 || = 0.01 250 259 271 251 228 | 252.5 d 6 5 19 14 28 8 2 4 15 | 500 | 389 441 416 399 409 = 0.69 || < 0.01 478 492 485 507 453 | 497.5 s 8 4 20 14 25 6 8 3 13 | 500 | 437 441 420 422 415 = 0.68 ||========================================================================= t 7 11 11 14 31 7 3 3 14 | 500 | 639 626 610 646 655 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 8 5 16 17 29 5 3 3 15 | 500 | 419 399 410 396 444 = 0.66 ||========================================================================= x 10 4 19 18 19 10 2 5 14 | 500 | 434 442 414 485 437 = 0.65 || smarsa_BirthdaySpacings test: no 15 test no 16 TestU01 250000 runs BigCrush Test smarsa_S smarsa_BirthdaySpacings test: test no 16 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 0 | 0.5 | 2 0 0 0 0 > 0.99999 || = 0.64 558 560 590 558 554 | 500 < 0.00002 0 1 1 1 0 | 0.5 | 1 0 0 1 0 > 0.99998 || = 0.63 606 586 566 553 575 | 500 < 0.00003 0 0 0 1 1 | 0.5 | 0 1 1 1 1 > 0.99997 || = 0.62 272 304 261 269 251 | 500 < 0.00004 1 1 1 1 0 | 0.5 | 0 1 1 0 0 > 0.99996 || = 0.61 601 560 619 610 617 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 0 2 0 0 1 > 0.99995 || = 0.60 597 596 610 579 579 | 500 < 0.00006 0 1 0 2 0 | 0.5 | 0 1 0 0 1 > 0.99994 || = 0.59 615 581 544 552 564 | 500 < 0.00007 0 0 1 3 2 | 0.5 | 2 0 0 0 1 > 0.99993 || = 0.58 293 308 301 303 272 | 500 < 0.00008 1 0 0 1 0 | 0.5 | 0 2 2 1 1 > 0.99992 || = 0.57 611 550 593 589 608 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 1 1 0 1 0 > 0.99991 || = 0.56 651 577 587 591 622 | 500 < 0.0001 0 0 1 0 0 | 0.5 | 0 1 0 0 1 > 0.9999 || = 0.55 299 282 320 310 303 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 615 659 576 581 611 | 500 < 0.0001 2 3 5 9 4 | 5 | 6 9 4 4 6 > 0.9999 || = 0.53 583 608 589 590 596 | 500 < 0.0002 5 8 6 5 7 | 5 | 3 1 2 2 2 > 0.9998 || = 0.52 300 292 316 296 300 | 500 < 0.0003 3 3 4 5 5 | 5 | 3 11 3 5 2 > 0.9997 || = 0.51 622 645 606 625 565 | 500 < 0.0004 0 8 3 3 2 | 5 | 6 7 3 9 4 > 0.9996 || = 0.50 652 602 597 606 590 | 500 < 0.0005 8 6 5 4 5 | 5 | 2 7 5 7 5 > 0.9995 || = 0.49 620 624 594 616 636 | 500 < 0.0006 5 6 3 3 2 | 5 | 7 6 9 7 3 > 0.9994 || = 0.48 606 589 602 605 578 | 500 < 0.0007 3 4 7 5 3 | 5 | 2 3 6 6 3 > 0.9993 || = 0.47 307 318 287 279 313 | 500 < 0.0008 4 5 6 5 6 | 5 | 5 4 2 8 1 > 0.9992 || = 0.46 611 627 582 607 652 | 500 < 0.0009 9 2 7 5 4 | 5 | 8 8 10 6 6 > 0.9991 || = 0.45 599 638 602 579 621 | 500 < 0.001 1 6 7 8 6 | 5 | 3 2 3 5 3 > 0.999 || = 0.44 292 269 294 313 287 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 604 608 565 592 626 | 500 < 0.001 40 51 53 52 44 | 50 | 45 58 47 59 35 > 0.999 || = 0.42 586 581 591 606 557 | 500 < 0.002 47 41 39 41 43 | 50 | 44 37 51 53 49 > 0.998 || = 0.41 290 296 310 270 292 | 500 < 0.003 44 50 51 46 56 | 50 | 48 54 69 53 45 > 0.997 || = 0.40 543 569 573 560 586 | 500 < 0.004 42 36 46 44 36 | 50 | 41 41 53 38 47 > 0.996 || = 0.39 593 597 602 583 589 | 500 < 0.005 58 56 53 38 50 | 50 | 48 32 61 48 49 > 0.995 || = 0.38 557 589 604 558 566 | 500 < 0.006 45 49 54 60 65 | 50 | 32 49 25 47 61 > 0.994 || = 0.37 303 261 267 268 288 | 500 < 0.007 36 46 37 34 44 | 50 | 45 56 65 61 51 > 0.993 || = 0.36 592 587 574 546 573 | 500 < 0.008 55 55 77 62 57 | 50 | 51 49 43 42 45 > 0.992 || = 0.35 583 543 596 568 499 | 500 < 0.009 48 56 63 51 53 | 50 | 48 52 55 46 48 > 0.991 || = 0.34 533 579 562 575 542 | 500 < 0.01 47 33 29 31 30 | 50 | 45 37 46 46 44 > 0.99 || = 0.33 566 534 537 534 592 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 272 292 279 289 311 | 500 < 0.01 462 473 502 459 478 | 497.5 | 447 465 515 493 474 > 0.99 || = 0.31 533 530 542 534 525 | 500 = 0.01 252 266 275 264 278 | 252.5 | 295 253 283 272 276 = 0.99 || = 0.30 579 550 576 469 569 | 500 = 0.02 504 511 502 484 510 | 500 | 434 465 509 465 450 = 0.98 || = 0.29 562 512 522 533 516 | 500 =================================================================| 500 | 479 532 515 485 486 = 0.97 || = 0.28 512 512 561 535 518 | 500 smarsa_BirthdaySpacings test: | 500 | 448 463 464 440 445 = 0.96 || = 0.27 468 488 507 511 518 | 500 ----------------------------------------------- | 500 | 547 542 519 537 556 = 0.95 || = 0.26 448 500 474 493 474 | 500 N = 20, n = 20000000, r = 0, d = 512, t = 7, p = 1 | 500 | 468 434 442 464 491 = 0.94 || = 0.25 469 490 486 480 494 | 500 | 500 | 531 486 479 472 482 = 0.93 || = 0.24 438 464 459 457 472 | 500 | 500 | 579 563 551 585 575 = 0.92 || = 0.23 464 431 448 494 429 | 500 =================================================================| 500 | 529 500 494 503 515 = 0.91 || = 0.22 621 692 633 655 664 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 361 397 390 396 382 = 0.90 || = 0.21 445 411 408 401 411 | 500 -----------------------------------------------------------------| 500 | 604 574 527 567 567 = 0.89 || = 0.20 444 425 407 438 452 | 500 SD Bern.: d 4.38289 1.03201 1.02909 | 500 | 436 463 480 459 459 = 0.88 || = 0.19 654 607 600 566 670 | 500 s 4.37687 1.16762 1.31594 | 500 | 452 475 465 512 486 = 0.87 || = 0.18 380 395 405 390 444 | 500 t 4.22378 1.83394 1.69848 | 500 | 467 546 501 552 473 = 0.86 || = 0.17 536 512 586 542 578 | 500 m 4.31718 1.51270 0.97310 | 500 | 563 516 544 547 500 = 0.85 || = 0.16 543 579 517 542 535 | 500 x 4.47059 1.44015 0.94703 | 500 | 553 519 570 556 599 = 0.84 || = 0.15 501 466 544 535 504 | 500 | 500 | 390 361 385 370 356 = 0.83 || = 0.14 319 340 307 328 312 | 500 Changes: d 52 4 2 | 500 | 580 602 614 622 597 = 0.82 || = 0.13 570 639 652 657 652 | 500 s 54 5 7 | 500 | 419 419 386 402 378 = 0.81 || = 0.12 471 428 453 410 467 | 500 t 48 7 6 | 500 | 456 431 426 433 440 = 0.80 || = 0.11 417 439 409 464 428 | 500 m 52 5 3 | 500 | 627 653 631 696 643 = 0.79 || = 0.10 524 503 530 526 534 | 500 x 52 6 2 | 500 | 439 452 406 433 412 = 0.78 || = 0.09 470 480 519 510 514 | 500 -----------------------------------------------------------------| 500 | 473 442 457 435 421 = 0.77 || = 0.08 563 543 559 583 545 | 500 Aver./ d 0.50095 518 > 500: 4 6 3 8 7 7 8 1 4 5 | 500 | 488 477 460 494 462 = 0.76 || = 0.07 518 525 521 528 536 | 500 median s 0.49942 512 ----- 6 5 3 8 7 7 8 3 5 4 | 500 | 485 486 488 446 446 = 0.75 || = 0.06 444 446 438 446 421 | 500 t 0.49838 519 8 6 4 8 7 7 8 2 5 6 | 500 | 498 478 483 471 452 = 0.74 || = 0.05 522 561 510 582 497 | 500 m 0.49972 525 5 6 4 7 7 7 8 2 6 4 | 500 | 486 495 492 493 503 = 0.73 || = 0.04 489 530 543 480 492 | 500 x 0.49769 515 5 6 4 7 7 7 7 4 3 4 | 500 | 487 510 491 496 525 = 0.72 || = 0.03 433 440 456 486 438 | 500 -----------------------------------------------------------------| 500 | 482 534 507 509 543 = 0.71 || = 0.02 504 511 502 484 510 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 533 504 509 589 477 = 0.70 || = 0.01 252 266 275 264 278 | 252.5 d 14 3 11 10 14 11 10 7 21 | 500 | 527 574 532 525 541 = 0.69 || < 0.01 462 473 502 459 478 | 497.5 s 15 5 6 9 21 10 7 11 17 | 500 | 526 542 544 538 547 = 0.68 ||========================================================================= t 19 1 4 7 23 13 7 8 19 | 500 | 557 512 529 543 572 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 17 2 5 9 17 14 10 11 16 | 500 | 272 257 309 284 259 = 0.66 ||========================================================================= x 15 5 8 8 18 10 8 10 19 | 500 | 595 579 556 574 620 = 0.65 || smarsa_BirthdaySpacings test: no 16 test no 17 TestU01 250000 runs BigCrush Test smarsa_S smarsa_BirthdaySpacings test: test no 17 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 0 3 | 0.5 | 2 0 0 3 1 > 0.99999 || = 0.64 560 577 544 571 621 | 500 < 0.00002 2 0 0 3 2 | 0.5 | 1 0 2 0 2 > 0.99998 || = 0.63 577 599 601 581 546 | 500 < 0.00003 1 1 0 1 1 | 0.5 | 0 0 1 0 1 > 0.99997 || = 0.62 299 287 275 286 262 | 500 < 0.00004 1 0 0 0 1 | 0.5 | 1 1 3 1 0 > 0.99996 || = 0.61 625 548 611 568 573 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 1 0 0 2 2 > 0.99995 || = 0.60 595 639 581 656 633 | 500 < 0.00006 0 1 1 1 0 | 0.5 | 2 0 0 0 2 > 0.99994 || = 0.59 668 595 635 555 579 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 1 0 0 2 1 > 0.99993 || = 0.58 311 297 276 302 321 | 500 < 0.00008 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 647 616 660 577 571 | 500 < 0.00009 0 0 2 1 1 | 0.5 | 0 0 1 0 2 > 0.99991 || = 0.56 605 602 603 568 597 | 500 < 0.0001 0 0 1 1 0 | 0.5 | 0 0 1 0 1 > 0.9999 || = 0.55 310 325 297 296 291 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 585 587 596 582 626 | 500 < 0.0001 6 2 5 7 8 | 5 | 8 1 8 8 12 > 0.9999 || = 0.53 606 618 617 632 595 | 500 < 0.0002 2 3 6 3 3 | 5 | 0 3 3 3 3 > 0.9998 || = 0.52 305 273 306 305 310 | 500 < 0.0003 5 9 4 5 5 | 5 | 6 5 1 11 3 > 0.9997 || = 0.51 572 633 572 633 608 | 500 < 0.0004 3 0 5 9 6 | 5 | 3 2 6 7 5 > 0.9996 || = 0.50 587 610 605 606 596 | 500 < 0.0005 9 8 6 1 4 | 5 | 3 3 8 4 4 > 0.9995 || = 0.49 617 658 641 618 587 | 500 < 0.0006 3 4 4 4 5 | 5 | 2 4 2 3 2 > 0.9994 || = 0.48 587 583 635 612 606 | 500 < 0.0007 3 7 4 5 7 | 5 | 3 4 2 2 5 > 0.9993 || = 0.47 264 304 292 278 289 | 500 < 0.0008 0 8 2 8 5 | 5 | 8 5 4 4 2 > 0.9992 || = 0.46 614 610 591 587 598 | 500 < 0.0009 5 5 1 1 2 | 5 | 10 6 7 10 5 > 0.9991 || = 0.45 607 660 571 599 623 | 500 < 0.001 10 5 9 2 6 | 5 | 6 6 4 4 4 > 0.999 || = 0.44 314 316 261 320 321 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 584 553 547 579 600 | 500 < 0.001 46 51 46 45 51 | 50 | 49 39 45 56 45 > 0.999 || = 0.42 593 543 582 597 630 | 500 < 0.002 46 63 50 41 28 | 50 | 43 45 47 46 44 > 0.998 || = 0.41 299 283 269 302 291 | 500 < 0.003 48 52 47 54 47 | 50 | 54 45 62 52 40 > 0.997 || = 0.40 575 593 580 593 589 | 500 < 0.004 39 45 49 36 47 | 50 | 46 45 35 50 50 > 0.996 || = 0.39 562 532 564 624 578 | 500 < 0.005 50 42 46 58 47 | 50 | 50 52 41 60 62 > 0.995 || = 0.38 583 561 574 526 553 | 500 < 0.006 57 59 61 52 58 | 50 | 44 47 35 50 41 > 0.994 || = 0.37 294 262 314 274 293 | 500 < 0.007 55 37 34 35 37 | 50 | 59 64 58 51 48 > 0.993 || = 0.36 580 525 563 528 558 | 500 < 0.008 66 68 72 78 59 | 50 | 50 52 37 53 33 > 0.992 || = 0.35 578 583 535 560 534 | 500 < 0.009 51 57 61 56 51 | 50 | 61 49 55 55 45 > 0.991 || = 0.34 544 618 572 567 538 | 500 < 0.01 34 34 50 42 39 | 50 | 37 37 27 42 36 > 0.99 || = 0.33 545 577 506 587 550 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 254 259 260 256 234 | 500 < 0.01 492 508 516 497 464 | 497.5 | 493 475 442 515 444 > 0.99 || = 0.31 557 487 546 528 569 | 500 = 0.01 240 243 251 249 258 | 252.5 | 254 258 268 286 246 = 0.99 || = 0.30 504 533 520 503 543 | 500 = 0.02 535 475 552 501 497 | 500 | 460 466 456 512 428 = 0.98 || = 0.29 482 494 472 493 544 | 500 =================================================================| 500 | 523 548 513 484 502 = 0.97 || = 0.28 492 534 526 492 486 | 500 smarsa_BirthdaySpacings test: | 500 | 462 449 450 458 475 = 0.96 || = 0.27 501 493 484 497 520 | 500 ----------------------------------------------- | 500 | 542 555 529 536 507 = 0.95 || = 0.26 478 518 495 505 478 | 500 N = 20, n = 20000000, r = 7, d = 512, t = 7, p = 1 | 500 | 474 421 473 442 441 = 0.94 || = 0.25 506 496 441 481 506 | 500 | 500 | 516 487 525 484 527 = 0.93 || = 0.24 455 458 489 504 460 | 500 | 500 | 532 589 592 530 546 = 0.92 || = 0.23 429 482 446 448 415 | 500 =================================================================| 500 | 452 489 476 500 487 = 0.91 || = 0.22 667 674 670 696 654 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 386 405 412 399 389 = 0.90 || = 0.21 423 422 448 431 485 | 500 -----------------------------------------------------------------| 500 | 563 562 618 562 588 = 0.89 || = 0.20 421 411 433 398 414 | 500 SD Bern.: d 4.35549 1.22043 0.98942 | 500 | 471 464 466 438 445 = 0.88 || = 0.19 606 608 651 592 602 | 500 s 4.32937 1.51204 1.07663 | 500 | 485 458 446 474 456 = 0.87 || = 0.18 417 390 422 397 397 | 500 t 4.46536 1.43179 1.73059 | 500 | 492 516 513 479 537 = 0.86 || = 0.17 622 560 578 596 588 | 500 m 4.31635 1.73002 0.71449 | 500 | 529 511 484 551 512 = 0.85 || = 0.16 554 570 554 553 537 | 500 x 4.35274 1.37763 1.34230 | 500 | 564 547 534 556 515 = 0.84 || = 0.15 521 534 525 485 535 | 500 | 500 | 399 419 365 380 384 = 0.83 || = 0.14 340 327 324 315 348 | 500 Changes: d 58 2 6 | 500 | 627 563 584 604 610 = 0.82 || = 0.13 605 625 658 622 652 | 500 s 57 5 4 | 500 | 382 385 393 408 434 = 0.81 || = 0.12 428 443 443 466 441 | 500 t 59 4 6 | 500 | 445 452 438 407 409 = 0.80 || = 0.11 423 405 427 461 420 | 500 m 53 6 7 | 500 | 697 638 648 628 668 = 0.79 || = 0.10 539 500 512 528 556 | 500 x 58 5 2 | 500 | 412 421 443 451 439 = 0.78 || = 0.09 497 532 425 516 472 | 500 -----------------------------------------------------------------| 500 | 472 454 436 447 427 = 0.77 || = 0.08 538 577 561 550 551 | 500 Aver./ d 0.50120 506 > 500: 3 6 3 8 7 7 8 2 4 5 | 500 | 476 494 472 491 452 = 0.76 || = 0.07 465 483 499 491 475 | 500 median s 0.49891 510 ----- 5 5 3 7 7 7 8 3 5 4 | 500 | 491 458 494 461 486 = 0.75 || = 0.06 441 458 459 431 442 | 500 t 0.49892 517 5 6 2 8 7 7 8 4 4 5 | 500 | 490 455 464 472 476 = 0.74 || = 0.05 515 534 561 524 559 | 500 m 0.49907 512 5 5 3 8 7 7 8 3 4 5 | 500 | 500 506 517 484 524 = 0.73 || = 0.04 473 505 506 577 525 | 500 x 0.49832 520 4 6 4 8 7 7 8 3 5 4 | 500 | 487 521 504 515 536 = 0.72 || = 0.03 428 483 446 435 441 | 500 -----------------------------------------------------------------| 500 | 517 486 570 504 499 = 0.71 || = 0.02 535 475 552 501 497 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 546 536 549 545 531 = 0.70 || = 0.01 240 243 251 249 258 | 252.5 d 14 8 4 8 23 8 9 11 16 | 500 | 517 545 556 548 558 = 0.69 || < 0.01 492 508 516 497 464 | 497.5 s 16 4 5 8 22 11 10 7 18 | 500 | 522 503 525 591 554 = 0.68 ||========================================================================= t 13 5 11 8 17 9 11 10 17 | 500 | 573 531 540 560 609 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 17 2 6 6 23 8 11 11 17 | 500 | 259 302 268 280 291 = 0.66 ||========================================================================= x 15 5 9 7 15 13 10 8 19 | 500 | 550 543 561 531 533 = 0.65 || smarsa_BirthdaySpacings test: no 17 test no 18 TestU01 250000 runs BigCrush Test smarsa_S smarsa_BirthdaySpacings test: test no 18 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 672 664 643 666 694 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 2 0 0 0 3 > 0.99998 || = 0.63 433 431 434 436 410 | 500 < 0.00003 0 0 1 1 0 | 0.5 | 1 1 1 0 0 > 0.99997 || = 0.62 494 410 456 442 433 | 500 < 0.00004 0 3 1 2 1 | 0.5 | 0 1 0 1 0 > 0.99996 || = 0.61 436 489 442 436 432 | 500 < 0.00005 1 1 0 0 0 | 0.5 | 1 3 0 2 1 > 0.99995 || = 0.60 659 699 700 684 672 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 1 0 0 1 0 > 0.99994 || = 0.59 464 401 427 506 444 | 500 < 0.00007 0 0 0 2 0 | 0.5 | 0 0 0 0 1 > 0.99993 || = 0.58 442 464 445 475 498 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 0 1 3 2 > 0.99992 || = 0.57 445 422 484 457 446 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 0 0 0 2 1 > 0.99991 || = 0.56 492 435 473 442 453 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 2 0 > 0.9999 || = 0.55 710 703 698 728 705 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 482 472 482 458 484 | 500 < 0.0001 1 7 2 6 2 | 5 | 5 5 2 11 8 > 0.9999 || = 0.53 437 469 504 450 425 | 500 < 0.0002 4 9 0 3 2 | 5 | 0 1 4 0 2 > 0.9998 || = 0.52 469 459 477 470 514 | 500 < 0.0003 8 3 7 5 3 | 5 | 8 4 5 3 3 > 0.9997 || = 0.51 478 462 462 471 457 | 500 < 0.0004 5 9 5 2 6 | 5 | 6 5 4 5 5 > 0.9996 || = 0.50 690 692 714 682 683 | 500 < 0.0005 6 4 1 4 2 | 5 | 4 5 7 8 2 > 0.9995 || = 0.49 478 428 463 493 500 | 500 < 0.0006 9 6 5 2 7 | 5 | 3 6 6 8 6 > 0.9994 || = 0.48 702 716 719 708 730 | 500 < 0.0007 2 6 6 5 7 | 5 | 2 0 9 6 6 > 0.9993 || = 0.47 449 437 466 494 429 | 500 < 0.0008 5 5 3 4 5 | 5 | 3 5 6 8 5 > 0.9992 || = 0.46 450 496 448 473 473 | 500 < 0.0009 0 5 2 6 2 | 5 | 3 5 5 10 11 > 0.9991 || = 0.45 486 458 474 468 468 | 500 < 0.001 2 3 8 1 8 | 5 | 7 5 7 10 3 > 0.999 || = 0.44 487 430 476 462 455 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 457 452 457 454 419 | 500 < 0.001 42 57 39 38 44 | 50 | 41 41 55 69 51 > 0.999 || = 0.42 690 656 737 692 664 | 500 < 0.002 51 59 42 60 59 | 50 | 58 60 47 54 46 > 0.998 || = 0.41 453 476 443 413 468 | 500 < 0.003 34 43 46 40 50 | 50 | 40 35 48 50 45 > 0.997 || = 0.40 460 426 445 416 444 | 500 < 0.004 49 35 60 43 47 | 50 | 42 52 55 55 59 > 0.996 || = 0.39 452 441 469 445 431 | 500 < 0.005 49 60 40 55 66 | 50 | 42 53 61 57 68 > 0.995 || = 0.38 512 439 446 425 451 | 500 < 0.006 49 54 38 44 56 | 50 | 50 37 35 36 43 > 0.994 || = 0.37 672 680 652 656 686 | 500 < 0.007 35 43 44 52 30 | 50 | 42 55 61 47 50 > 0.993 || = 0.36 445 430 427 468 467 | 500 < 0.008 60 66 56 60 55 | 50 | 40 43 46 52 54 > 0.992 || = 0.35 448 419 470 442 429 | 500 < 0.009 43 50 33 34 30 | 50 | 60 59 53 52 35 > 0.991 || = 0.34 600 620 656 618 634 | 500 < 0.01 63 62 51 56 62 | 50 | 47 48 53 50 45 > 0.99 || = 0.33 403 405 376 421 440 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 434 379 427 408 426 | 500 < 0.01 475 529 449 482 499 | 497.5 | 462 483 514 522 496 > 0.99 || = 0.31 588 639 615 610 619 | 500 = 0.01 250 238 214 219 239 | 252.5 | 229 240 261 280 249 = 0.99 || = 0.30 403 396 414 384 407 | 500 = 0.02 461 495 467 490 493 | 500 | 515 509 504 522 516 = 0.98 || = 0.29 562 606 612 613 566 | 500 =================================================================| 500 | 512 482 493 545 530 = 0.97 || = 0.28 415 394 378 403 438 | 500 smarsa_BirthdaySpacings test: | 500 | 516 528 516 509 544 = 0.96 || = 0.27 613 545 617 577 588 | 500 ----------------------------------------------- | 500 | 446 479 522 468 481 = 0.95 || = 0.26 576 556 565 563 518 | 500 N = 20, n = 30000000, r = 14, d = 256, t = 8, p = 1 | 500 | 469 475 522 451 469 = 0.94 || = 0.25 372 385 367 347 383 | 500 | 500 | 471 497 430 463 446 = 0.93 || = 0.24 541 565 517 555 530 | 500 | 500 | 531 482 512 575 539 = 0.92 || = 0.23 473 543 530 519 543 | 500 =================================================================| 500 | 465 496 439 444 510 = 0.91 || = 0.22 524 520 513 495 507 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 569 507 514 496 465 = 0.90 || = 0.21 490 498 487 523 492 | 500 -----------------------------------------------------------------| 500 | 536 544 534 541 567 = 0.89 || = 0.20 402 472 495 529 504 | 500 SD Bern.: d 3.41238 1.31746 1.13722 | 500 | 440 451 448 439 496 = 0.88 || = 0.19 495 513 515 461 474 | 500 s 3.58655 1.39281 1.22289 | 500 | 469 502 506 510 464 = 0.87 || = 0.18 411 485 448 462 428 | 500 t 3.69997 1.34751 1.06259 | 500 | 513 532 540 525 482 = 0.86 || = 0.17 586 605 618 573 620 | 500 m 3.52594 1.30448 1.15295 | 500 | 486 545 582 575 530 = 0.85 || = 0.16 453 402 408 423 439 | 500 x 3.39835 1.66636 1.23511 | 500 | 442 425 427 390 436 = 0.84 || = 0.15 538 577 528 541 496 | 500 | 500 | 438 413 465 456 414 = 0.83 || = 0.14 582 535 513 544 489 | 500 Changes: d 58 5 4 | 500 | 601 600 611 598 582 = 0.82 || = 0.13 531 511 477 492 466 | 500 s 59 6 8 | 500 | 444 532 466 439 511 = 0.81 || = 0.12 455 459 469 464 485 | 500 t 57 5 6 | 500 | 469 518 485 491 512 = 0.80 || = 0.11 534 538 538 527 522 | 500 m 57 7 5 | 500 | 520 483 512 513 528 = 0.79 || = 0.10 516 471 447 541 488 | 500 x 53 7 5 | 500 | 532 516 520 498 497 = 0.78 || = 0.09 456 435 460 470 417 | 500 -----------------------------------------------------------------| 500 | 352 376 367 350 379 = 0.77 || = 0.08 510 521 478 533 479 | 500 Aver./ d 0.49980 482 > 500: 3 6 5 4 2 2 3 6 4 4 | 500 | 580 549 493 553 552 = 0.76 || = 0.07 437 460 462 459 455 | 500 median s 0.49938 483 ----- 4 6 6 3 2 2 3 6 7 2 | 500 | 564 564 583 525 571 = 0.75 || = 0.06 490 475 449 485 467 | 500 t 0.50212 478 1 5 6 3 2 3 3 5 6 7 | 500 | 579 571 584 531 515 = 0.74 || = 0.05 506 561 546 505 530 | 500 m 0.50028 490 3 5 7 3 2 3 3 5 5 6 | 500 | 374 380 353 382 383 = 0.73 || = 0.04 489 468 491 447 523 | 500 x 0.50123 488 4 2 7 3 2 3 3 6 4 5 | 500 | 566 634 558 545 594 = 0.72 || = 0.03 503 523 478 528 527 | 500 -----------------------------------------------------------------| 500 | 392 407 359 416 402 = 0.71 || = 0.02 461 495 467 490 493 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 620 582 618 633 606 = 0.70 || = 0.01 250 238 214 219 239 | 252.5 d 8 3 22 15 23 8 3 7 12 | 500 | 429 405 414 418 462 = 0.69 || < 0.01 475 529 449 482 499 | 497.5 s 13 9 8 15 23 9 7 3 14 | 500 | 436 394 425 423 437 = 0.68 ||========================================================================= t 8 9 14 18 26 5 3 3 15 | 500 | 628 621 653 623 604 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 8 9 14 17 17 14 5 4 13 | 500 | 439 434 396 405 423 = 0.66 ||========================================================================= x 6 13 13 12 28 10 2 4 13 | 500 | 448 464 417 423 413 = 0.65 || smarsa_BirthdaySpacings test: no 18 test no 19 TestU01 250000 runs BigCrush Test smarsa_S smarsa_BirthdaySpacings test: test no 19 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 0 | 0.5 | 0 1 1 0 1 > 0.99999 || = 0.64 641 645 646 656 675 | 500 < 0.00002 0 0 0 1 1 | 0.5 | 2 0 0 0 1 > 0.99998 || = 0.63 426 467 419 460 436 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 0 0 1 1 0 > 0.99997 || = 0.62 431 440 442 478 473 | 500 < 0.00004 0 1 1 1 0 | 0.5 | 2 0 0 0 1 > 0.99996 || = 0.61 485 422 475 459 444 | 500 < 0.00005 0 2 0 1 0 | 0.5 | 1 1 2 0 0 > 0.99995 || = 0.60 643 672 637 665 693 | 500 < 0.00006 1 0 1 0 0 | 0.5 | 0 0 1 1 2 > 0.99994 || = 0.59 429 432 504 454 427 | 500 < 0.00007 1 1 0 0 1 | 0.5 | 0 3 0 0 0 > 0.99993 || = 0.58 455 475 437 476 453 | 500 < 0.00008 0 0 0 0 2 | 0.5 | 1 2 0 2 0 > 0.99992 || = 0.57 428 449 429 482 444 | 500 < 0.00009 0 0 1 1 0 | 0.5 | 1 0 0 1 1 > 0.99991 || = 0.56 439 472 481 436 500 | 500 < 0.0001 2 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 697 682 665 709 709 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 471 468 443 434 471 | 500 < 0.0001 5 6 3 5 4 | 5 | 7 7 5 5 6 > 0.9999 || = 0.53 496 438 448 497 434 | 500 < 0.0002 2 3 6 3 6 | 5 | 0 4 2 2 3 > 0.9998 || = 0.52 475 471 461 454 466 | 500 < 0.0003 5 8 6 4 4 | 5 | 2 2 1 6 3 > 0.9997 || = 0.51 480 507 439 499 407 | 500 < 0.0004 3 2 9 11 5 | 5 | 4 5 6 1 4 > 0.9996 || = 0.50 716 724 712 733 718 | 500 < 0.0005 5 2 2 2 4 | 5 | 2 4 5 3 2 > 0.9995 || = 0.49 500 445 460 480 439 | 500 < 0.0006 5 4 0 2 9 | 5 | 4 4 6 5 2 > 0.9994 || = 0.48 677 726 721 680 685 | 500 < 0.0007 2 3 9 4 6 | 5 | 6 9 4 3 1 > 0.9993 || = 0.47 474 501 416 451 481 | 500 < 0.0008 2 2 0 4 2 | 5 | 4 6 6 6 4 > 0.9992 || = 0.46 496 440 455 454 425 | 500 < 0.0009 6 2 8 4 4 | 5 | 5 5 3 7 4 > 0.9991 || = 0.45 474 446 494 444 496 | 500 < 0.001 7 7 4 4 7 | 5 | 7 2 5 7 5 > 0.999 || = 0.44 481 460 435 467 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 475 478 459 419 426 | 500 < 0.001 42 39 47 43 51 | 50 | 41 48 43 45 34 > 0.999 || = 0.42 650 634 684 652 657 | 500 < 0.002 52 55 47 51 47 | 50 | 44 55 46 44 53 > 0.998 || = 0.41 461 419 464 423 431 | 500 < 0.003 54 51 46 51 47 | 50 | 50 61 50 45 46 > 0.997 || = 0.40 453 445 422 428 458 | 500 < 0.004 35 47 54 40 54 | 50 | 36 47 46 46 40 > 0.996 || = 0.39 453 468 477 480 448 | 500 < 0.005 50 64 48 47 63 | 50 | 34 58 49 47 78 > 0.995 || = 0.38 447 460 432 443 404 | 500 < 0.006 53 64 53 56 59 | 50 | 46 39 48 41 42 > 0.994 || = 0.37 620 679 629 662 662 | 500 < 0.007 53 26 41 39 49 | 50 | 56 39 50 55 42 > 0.993 || = 0.36 425 440 417 414 437 | 500 < 0.008 40 59 58 67 55 | 50 | 56 54 41 37 51 > 0.992 || = 0.35 446 434 417 442 434 | 500 < 0.009 37 37 39 39 31 | 50 | 59 56 47 59 55 > 0.991 || = 0.34 614 659 661 622 612 | 500 < 0.01 65 57 62 70 64 | 50 | 43 46 52 40 37 > 0.99 || = 0.33 439 414 440 419 411 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 384 419 395 442 479 | 500 < 0.01 481 499 495 503 520 | 497.5 | 465 503 472 459 478 > 0.99 || = 0.31 644 604 642 635 657 | 500 = 0.01 235 217 239 242 256 | 252.5 | 266 203 256 258 251 = 0.99 || = 0.30 416 395 404 385 392 | 500 = 0.02 510 467 466 470 468 | 500 | 502 459 461 503 517 = 0.98 || = 0.29 576 587 564 616 588 | 500 =================================================================| 500 | 504 504 515 512 514 = 0.97 || = 0.28 428 387 378 369 389 | 500 smarsa_BirthdaySpacings test: | 500 | 509 514 505 476 505 = 0.96 || = 0.27 608 578 550 579 581 | 500 ----------------------------------------------- | 500 | 484 486 472 475 472 = 0.95 || = 0.26 562 570 566 513 577 | 500 N = 20, n = 30000000, r = 22, d = 256, t = 8, p = 1 | 500 | 445 476 459 435 492 = 0.94 || = 0.25 358 392 334 390 399 | 500 | 500 | 449 441 455 477 446 = 0.93 || = 0.24 510 555 578 523 561 | 500 | 500 | 472 495 524 493 527 = 0.92 || = 0.23 495 529 546 544 528 | 500 =================================================================| 500 | 463 434 497 471 495 = 0.91 || = 0.22 513 539 537 527 490 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 508 537 536 489 538 = 0.90 || = 0.21 505 496 502 508 519 | 500 -----------------------------------------------------------------| 500 | 555 592 511 569 607 = 0.89 || = 0.20 505 521 499 481 504 | 500 SD Bern.: d 3.30952 1.28204 1.25520 | 500 | 448 489 475 494 459 = 0.88 || = 0.19 433 464 480 462 443 | 500 s 3.51050 1.68785 1.03298 | 500 | 534 508 529 492 466 = 0.87 || = 0.18 459 479 432 424 461 | 500 t 3.45171 0.97310 0.60029 | 500 | 501 488 518 548 483 = 0.86 || = 0.17 608 631 620 631 573 | 500 m 3.44663 1.50207 1.06541 | 500 | 543 573 524 566 532 = 0.85 || = 0.16 398 408 465 435 443 | 500 x 3.53877 1.31822 1.72596 | 500 | 434 447 443 454 417 = 0.84 || = 0.15 577 536 513 536 572 | 500 | 500 | 428 440 427 448 424 = 0.83 || = 0.14 494 487 541 485 513 | 500 Changes: d 54 5 2 | 500 | 620 589 616 655 553 = 0.82 || = 0.13 466 497 450 513 480 | 500 s 60 7 6 | 500 | 486 481 438 467 473 = 0.81 || = 0.12 502 468 457 486 476 | 500 t 56 7 1 | 500 | 520 483 528 528 502 = 0.80 || = 0.11 530 510 554 514 528 | 500 m 53 7 4 | 500 | 509 485 489 491 500 = 0.79 || = 0.10 500 525 490 492 510 | 500 x 59 6 6 | 500 | 553 563 476 499 552 = 0.78 || = 0.09 491 478 463 474 465 | 500 -----------------------------------------------------------------| 500 | 396 338 406 372 360 = 0.77 || = 0.08 504 535 519 476 552 | 500 Aver./ d 0.49910 491 > 500: 5 4 7 3 2 2 3 7 6 4 | 500 | 546 555 562 575 531 = 0.76 || = 0.07 457 469 423 441 445 | 500 median s 0.49914 481 ----- 4 4 7 3 3 3 3 5 5 3 | 500 | 526 569 577 524 569 = 0.75 || = 0.06 456 477 489 512 440 | 500 t 0.49999 480 4 4 7 3 2 3 3 5 6 4 | 500 | 553 568 574 599 583 = 0.74 || = 0.05 527 501 554 532 500 | 500 m 0.50124 481 3 4 7 3 2 2 3 5 4 3 | 500 | 377 409 423 385 390 = 0.73 || = 0.04 546 465 501 498 510 | 500 x 0.49963 483 5 5 7 3 2 2 3 6 4 4 | 500 | 606 566 638 581 595 = 0.72 || = 0.03 511 521 537 462 505 | 500 -----------------------------------------------------------------| 500 | 397 364 401 407 392 = 0.71 || = 0.02 510 467 466 470 468 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 613 595 594 593 603 = 0.70 || = 0.01 235 217 239 242 256 | 252.5 d 8 10 12 14 29 5 6 2 15 | 500 | 409 426 446 399 414 = 0.69 || < 0.01 481 499 495 503 520 | 497.5 s 8 8 15 16 24 6 4 6 14 | 500 | 427 402 409 419 413 = 0.68 ||========================================================================= t 7 11 13 18 20 8 7 3 14 | 500 | 629 644 615 616 650 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 7 7 17 15 27 7 2 4 15 | 500 | 442 438 468 452 420 = 0.66 ||========================================================================= x 9 10 14 12 25 7 4 7 13 | 500 | 395 418 457 447 414 = 0.65 || smarsa_BirthdaySpacings test: no 19 test no 20 TestU01 250000 runs BigCrush Test smarsa_S smarsa_BirthdaySpacings test: test no 20 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 641 648 666 643 689 | 500 < 0.00002 2 1 1 0 0 | 0.5 | 1 1 1 1 0 > 0.99998 || = 0.63 454 444 485 458 417 | 500 < 0.00003 0 0 0 0 1 | 0.5 | 1 0 1 3 0 > 0.99997 || = 0.62 441 460 459 453 436 | 500 < 0.00004 1 0 0 1 0 | 0.5 | 1 1 0 0 0 > 0.99996 || = 0.61 420 436 457 426 462 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 2 0 1 > 0.99995 || = 0.60 665 674 706 716 658 | 500 < 0.00006 1 1 0 2 1 | 0.5 | 0 0 1 0 2 > 0.99994 || = 0.59 437 472 466 458 438 | 500 < 0.00007 2 0 1 0 0 | 0.5 | 1 1 2 0 1 > 0.99993 || = 0.58 439 488 452 441 458 | 500 < 0.00008 0 1 1 1 2 | 0.5 | 0 0 0 2 1 > 0.99992 || = 0.57 463 446 449 426 468 | 500 < 0.00009 1 1 1 0 1 | 0.5 | 1 1 0 1 1 > 0.99991 || = 0.56 470 450 460 440 457 | 500 < 0.0001 0 0 0 0 3 | 0.5 | 0 0 0 2 0 > 0.9999 || = 0.55 706 695 691 735 673 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 434 467 505 495 488 | 500 < 0.0001 7 4 4 5 8 | 5 | 5 5 7 9 6 > 0.9999 || = 0.53 486 437 462 467 457 | 500 < 0.0002 5 5 5 4 1 | 5 | 3 2 4 3 5 > 0.9998 || = 0.52 462 499 489 452 483 | 500 < 0.0003 3 1 3 3 9 | 5 | 4 6 7 4 7 > 0.9997 || = 0.51 449 446 450 463 473 | 500 < 0.0004 6 3 6 5 4 | 5 | 8 4 8 4 5 > 0.9996 || = 0.50 707 737 674 735 726 | 500 < 0.0005 6 5 2 5 7 | 5 | 5 4 12 4 9 > 0.9995 || = 0.49 498 468 444 494 485 | 500 < 0.0006 7 4 3 4 6 | 5 | 7 4 2 4 4 > 0.9994 || = 0.48 694 700 695 696 661 | 500 < 0.0007 7 5 7 2 7 | 5 | 6 8 6 1 7 > 0.9993 || = 0.47 456 439 474 452 430 | 500 < 0.0008 1 3 1 6 3 | 5 | 4 7 2 3 5 > 0.9992 || = 0.46 448 443 488 471 461 | 500 < 0.0009 5 6 4 7 6 | 5 | 8 4 4 3 5 > 0.9991 || = 0.45 490 435 426 454 463 | 500 < 0.001 4 11 6 7 4 | 5 | 9 8 4 7 7 > 0.999 || = 0.44 454 492 461 424 471 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 462 467 472 439 464 | 500 < 0.001 51 47 41 48 55 | 50 | 59 52 56 42 60 > 0.999 || = 0.42 676 692 665 701 713 | 500 < 0.002 46 52 45 43 41 | 50 | 53 41 52 61 51 > 0.998 || = 0.41 415 442 456 465 422 | 500 < 0.003 44 29 42 52 45 | 50 | 55 50 52 58 45 > 0.997 || = 0.40 439 419 436 440 466 | 500 < 0.004 42 36 50 50 51 | 50 | 41 49 55 44 51 > 0.996 || = 0.39 438 433 465 452 444 | 500 < 0.005 46 56 60 51 53 | 50 | 58 44 44 44 69 > 0.995 || = 0.38 459 448 454 419 444 | 500 < 0.006 60 48 49 52 49 | 50 | 50 37 47 42 37 > 0.994 || = 0.37 644 648 718 658 650 | 500 < 0.007 46 37 42 35 51 | 50 | 58 57 51 68 42 > 0.993 || = 0.36 447 449 474 438 425 | 500 < 0.008 62 55 56 50 60 | 50 | 54 43 48 56 50 > 0.992 || = 0.35 444 413 443 456 432 | 500 < 0.009 32 38 36 40 46 | 50 | 48 50 42 58 56 > 0.991 || = 0.34 605 617 658 643 702 | 500 < 0.01 56 61 55 59 39 | 50 | 58 36 40 52 54 > 0.99 || = 0.33 446 413 411 415 432 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 444 439 418 434 428 | 500 < 0.01 485 459 476 480 490 | 497.5 | 534 459 487 525 515 > 0.99 || = 0.31 569 679 584 626 629 | 500 = 0.01 239 248 231 257 231 | 252.5 | 224 243 233 247 229 = 0.99 || = 0.30 392 409 390 390 404 | 500 = 0.02 455 502 494 540 476 | 500 | 507 534 524 481 493 = 0.98 || = 0.29 594 612 612 590 567 | 500 =================================================================| 500 | 551 537 526 515 540 = 0.97 || = 0.28 392 403 411 428 384 | 500 smarsa_BirthdaySpacings test: | 500 | 504 505 479 520 528 = 0.96 || = 0.27 595 585 593 578 607 | 500 ----------------------------------------------- | 500 | 499 484 489 485 469 = 0.95 || = 0.26 606 527 581 540 586 | 500 N = 20, n = 30000000, r = 0, d = 16, t = 16, p = 1 | 500 | 464 511 454 521 476 = 0.94 || = 0.25 392 375 368 397 427 | 500 | 500 | 432 474 448 467 461 = 0.93 || = 0.24 505 504 579 571 562 | 500 | 500 | 488 551 511 470 543 = 0.92 || = 0.23 541 568 496 528 527 | 500 =================================================================| 500 | 444 462 443 493 520 = 0.91 || = 0.22 502 523 484 484 498 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 510 489 527 500 477 = 0.90 || = 0.21 487 488 493 518 469 | 500 -----------------------------------------------------------------| 500 | 566 524 559 548 566 = 0.89 || = 0.20 476 486 478 463 500 | 500 SD Bern.: d 3.41570 1.22780 0.90376 | 500 | 449 464 467 506 469 = 0.88 || = 0.19 493 448 452 471 489 | 500 s 3.49156 1.51667 1.08219 | 500 | 521 511 479 471 491 = 0.87 || = 0.18 474 454 448 460 428 | 500 t 3.54097 1.08865 0.75269 | 500 | 508 486 523 453 524 = 0.86 || = 0.17 581 588 525 579 569 | 500 m 3.57015 0.96794 1.27577 | 500 | 539 547 575 549 558 = 0.85 || = 0.16 438 430 420 424 461 | 500 x 3.48070 0.87220 1.24399 | 500 | 395 424 446 401 432 = 0.84 || = 0.15 577 528 549 536 527 | 500 | 500 | 469 471 411 449 447 = 0.83 || = 0.14 509 505 486 506 494 | 500 Changes: d 53 6 6 | 500 | 622 620 636 586 608 = 0.82 || = 0.13 488 465 478 508 534 | 500 s 60 7 3 | 500 | 455 491 478 525 491 = 0.81 || = 0.12 507 467 469 459 448 | 500 t 54 5 3 | 500 | 452 489 488 471 496 = 0.80 || = 0.11 559 532 549 533 522 | 500 m 55 5 3 | 500 | 496 536 481 491 509 = 0.79 || = 0.10 502 501 505 505 480 | 500 x 55 5 4 | 500 | 519 503 510 515 500 = 0.78 || = 0.09 484 456 461 458 461 | 500 -----------------------------------------------------------------| 500 | 355 344 345 354 356 = 0.77 || = 0.08 509 508 517 470 466 | 500 Aver./ d 0.49932 487 > 500: 3 6 6 3 2 2 3 5 6 4 | 500 | 558 532 528 555 553 = 0.76 || = 0.07 490 422 434 486 437 | 500 median s 0.50251 486 ----- 3 5 6 3 2 2 3 6 4 5 | 500 | 587 575 541 556 544 = 0.75 || = 0.06 529 463 473 473 500 | 500 t 0.50019 479 4 4 4 3 2 3 3 5 5 3 | 500 | 576 560 586 544 560 = 0.74 || = 0.05 527 531 536 500 529 | 500 m 0.50027 482 2 6 6 3 2 2 3 5 5 4 | 500 | 394 407 384 418 367 = 0.73 || = 0.04 445 473 527 467 459 | 500 x 0.50136 480 1 4 5 3 2 2 3 5 4 5 | 500 | 592 588 611 600 561 = 0.72 || = 0.03 473 487 517 492 498 | 500 -----------------------------------------------------------------| 500 | 390 426 377 370 376 = 0.71 || = 0.02 455 502 494 540 476 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 629 635 616 624 630 = 0.70 || = 0.01 239 248 231 257 231 | 252.5 d 7 6 22 12 25 5 4 5 15 | 500 | 412 417 403 422 395 = 0.69 || < 0.01 485 459 476 480 490 | 497.5 s 6 9 17 16 22 10 3 5 13 | 500 | 415 403 418 390 440 = 0.68 ||========================================================================= t 10 5 14 17 24 9 3 5 14 | 500 | 629 627 634 659 604 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 7 9 14 19 23 8 4 4 13 | 500 | 415 452 411 409 400 = 0.66 ||========================================================================= x 7 10 9 24 20 9 6 3 13 | 500 | 452 437 427 434 437 = 0.65 || smarsa_BirthdaySpacings test: no 20 test no 21 TestU01 250000 runs BigCrush Test smarsa_S smarsa_BirthdaySpacings test: test no 21 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 2 0 0 1 | 0.5 | 1 0 1 0 1 > 0.99999 || = 0.64 622 661 619 648 642 | 500 < 0.00002 0 0 0 1 1 | 0.5 | 0 2 0 0 0 > 0.99998 || = 0.63 438 414 446 469 425 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 0 0 0 1 3 > 0.99997 || = 0.62 448 428 416 445 419 | 500 < 0.00004 1 1 2 0 0 | 0.5 | 0 0 1 1 0 > 0.99996 || = 0.61 432 467 433 452 423 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99995 || = 0.60 693 644 733 642 743 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 0 1 0 0 1 > 0.99994 || = 0.59 460 463 459 502 423 | 500 < 0.00007 2 0 1 0 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 463 442 435 427 530 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 1 0 1 1 0 > 0.99992 || = 0.57 450 469 492 444 472 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 470 415 436 471 459 | 500 < 0.0001 0 0 1 0 1 | 0.5 | 0 0 0 1 1 > 0.9999 || = 0.55 705 684 734 725 667 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 452 448 444 461 460 | 500 < 0.0001 4 4 4 2 4 | 5 | 2 3 3 6 6 > 0.9999 || = 0.53 481 429 436 467 495 | 500 < 0.0002 7 3 2 4 8 | 5 | 3 3 4 2 3 > 0.9998 || = 0.52 482 473 468 449 462 | 500 < 0.0003 5 2 5 5 4 | 5 | 5 6 8 2 3 > 0.9997 || = 0.51 468 470 463 509 500 | 500 < 0.0004 5 4 6 3 6 | 5 | 5 5 3 1 5 > 0.9996 || = 0.50 725 705 638 688 706 | 500 < 0.0005 3 3 2 6 5 | 5 | 4 3 8 1 5 > 0.9995 || = 0.49 468 485 470 497 475 | 500 < 0.0006 5 6 5 10 7 | 5 | 12 5 9 4 2 > 0.9994 || = 0.48 756 713 693 730 695 | 500 < 0.0007 4 8 4 2 5 | 5 | 6 9 1 2 3 > 0.9993 || = 0.47 459 467 469 443 438 | 500 < 0.0008 8 6 2 7 10 | 5 | 7 3 6 6 3 > 0.9992 || = 0.46 436 456 473 476 482 | 500 < 0.0009 3 6 3 5 5 | 5 | 8 2 2 4 5 > 0.9991 || = 0.45 474 449 449 459 433 | 500 < 0.001 6 7 1 5 6 | 5 | 5 6 6 2 3 > 0.999 || = 0.44 473 445 479 463 522 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 431 438 456 438 443 | 500 < 0.001 50 49 34 49 60 | 50 | 57 45 50 30 38 > 0.999 || = 0.42 641 669 674 617 633 | 500 < 0.002 49 48 51 43 48 | 50 | 52 58 40 59 42 > 0.998 || = 0.41 440 428 393 478 441 | 500 < 0.003 43 60 50 51 58 | 50 | 57 56 43 42 43 > 0.997 || = 0.40 452 484 434 451 480 | 500 < 0.004 38 41 38 46 35 | 50 | 46 50 52 37 51 > 0.996 || = 0.39 504 444 456 482 432 | 500 < 0.005 53 52 55 57 55 | 50 | 55 60 47 54 57 > 0.995 || = 0.38 477 415 445 459 463 | 500 < 0.006 45 47 58 57 52 | 50 | 53 44 53 49 44 > 0.994 || = 0.37 701 579 714 669 683 | 500 < 0.007 42 44 55 37 37 | 50 | 48 59 59 43 53 > 0.993 || = 0.36 435 492 425 452 441 | 500 < 0.008 60 64 69 68 68 | 50 | 56 37 47 48 32 > 0.992 || = 0.35 445 431 446 437 429 | 500 < 0.009 39 47 33 49 29 | 50 | 58 55 67 67 51 > 0.991 || = 0.34 598 647 627 653 617 | 500 < 0.01 56 60 61 44 66 | 50 | 44 41 43 51 38 > 0.99 || = 0.33 461 412 415 408 397 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 425 428 444 401 417 | 500 < 0.01 475 512 504 501 508 | 497.5 | 526 505 501 480 449 > 0.99 || = 0.31 619 603 624 620 630 | 500 = 0.01 227 249 223 234 237 | 252.5 | 253 257 226 238 239 = 0.99 || = 0.30 361 390 361 382 390 | 500 = 0.02 456 503 518 467 475 | 500 | 441 481 487 456 474 = 0.98 || = 0.29 636 614 622 594 579 | 500 =================================================================| 500 | 506 536 560 541 472 = 0.97 || = 0.28 392 411 374 369 346 | 500 smarsa_BirthdaySpacings test: | 500 | 502 488 497 511 508 = 0.96 || = 0.27 570 566 596 586 547 | 500 ----------------------------------------------- | 500 | 491 504 491 477 479 = 0.95 || = 0.26 581 579 550 528 567 | 500 N = 20, n = 30000000, r = 26, d = 16, t = 16, p = 1 | 500 | 476 490 443 504 477 = 0.94 || = 0.25 395 381 368 391 367 | 500 | 500 | 464 474 493 496 464 = 0.93 || = 0.24 531 564 532 561 547 | 500 | 500 | 537 487 484 540 522 = 0.92 || = 0.23 511 569 508 501 539 | 500 =================================================================| 500 | 497 467 479 459 497 = 0.91 || = 0.22 546 522 475 508 533 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 484 496 508 505 524 = 0.90 || = 0.21 510 512 497 466 525 | 500 -----------------------------------------------------------------| 500 | 528 564 539 541 558 = 0.89 || = 0.20 472 489 492 481 469 | 500 SD Bern.: d 3.57602 1.04837 0.76457 | 500 | 474 468 476 488 467 = 0.88 || = 0.19 489 474 480 467 438 | 500 s 3.34854 1.03974 1.11140 | 500 | 465 506 491 507 508 = 0.87 || = 0.18 482 443 460 464 462 | 500 t 3.56371 1.60454 1.09507 | 500 | 538 523 554 546 530 = 0.86 || = 0.17 636 590 576 607 540 | 500 m 3.38161 1.17956 1.46633 | 500 | 499 553 541 511 553 = 0.85 || = 0.16 409 411 413 445 439 | 500 x 3.43723 1.79644 1.28203 | 500 | 422 403 431 433 422 = 0.84 || = 0.15 560 549 547 560 529 | 500 | 500 | 437 435 457 457 458 = 0.83 || = 0.14 548 500 512 515 501 | 500 Changes: d 54 5 5 | 500 | 594 598 604 567 621 = 0.82 || = 0.13 505 471 492 489 532 | 500 s 58 7 8 | 500 | 475 489 492 503 513 = 0.81 || = 0.12 460 446 465 426 463 | 500 t 54 5 6 | 500 | 492 491 481 484 541 = 0.80 || = 0.11 548 517 571 527 523 | 500 m 57 6 5 | 500 | 464 507 507 488 495 = 0.79 || = 0.10 498 516 522 519 498 | 500 x 61 8 6 | 500 | 475 502 506 490 542 = 0.78 || = 0.09 441 462 474 458 475 | 500 -----------------------------------------------------------------| 500 | 347 355 341 358 384 = 0.77 || = 0.08 472 521 535 515 514 | 500 Aver./ d 0.49749 477 > 500: 4 5 7 4 2 2 3 4 3 5 | 500 | 588 529 506 519 558 = 0.76 || = 0.07 432 468 477 413 443 | 500 median s 0.49932 489 ----- 5 4 7 3 2 2 3 6 5 4 | 500 | 556 592 539 542 564 = 0.75 || = 0.06 519 470 483 481 458 | 500 t 0.49856 484 6 5 5 3 2 2 3 6 5 2 | 500 | 522 559 568 559 505 = 0.74 || = 0.05 527 577 565 543 504 | 500 m 0.50098 482 4 5 6 3 2 4 3 4 7 4 | 500 | 394 406 360 369 397 = 0.73 || = 0.04 540 491 513 451 482 | 500 x 0.50157 482 4 5 7 3 3 3 3 6 7 2 | 500 | 615 587 600 581 613 = 0.72 || = 0.03 517 517 517 537 521 | 500 -----------------------------------------------------------------| 500 | 394 431 423 386 403 = 0.71 || = 0.02 456 503 518 467 475 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 588 611 585 599 633 = 0.70 || = 0.01 227 249 223 234 237 | 252.5 d 9 6 13 23 20 7 5 4 14 | 500 | 358 442 401 426 418 = 0.69 || < 0.01 475 512 504 501 508 | 497.5 s 9 10 10 16 28 3 6 5 14 | 500 | 408 395 437 454 416 = 0.68 ||========================================================================= t 7 7 14 17 28 5 5 4 14 | 500 | 601 611 650 674 600 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 8 5 14 18 28 8 4 3 13 | 500 | 416 466 440 442 411 = 0.66 ||========================================================================= x 8 11 8 19 22 12 6 2 13 | 500 | 443 411 442 451 457 = 0.65 || smarsa_BirthdaySpacings test: no 21 test no 22 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 22 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 503 502 489 508 497 | 500 < 0.00002 1 0 0 1 1 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 512 497 470 459 509 | 500 < 0.00003 0 0 1 1 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 468 499 505 528 477 | 500 < 0.00004 1 0 1 0 0 | 0.5 | 1 0 1 2 0 > 0.99996 || = 0.61 471 536 501 516 503 | 500 < 0.00005 1 1 0 2 1 | 0.5 | 0 0 0 1 0 > 0.99995 || = 0.60 513 441 519 516 517 | 500 < 0.00006 0 0 0 5 0 | 0.5 | 0 2 0 0 1 > 0.99994 || = 0.59 503 525 466 521 488 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 1 1 1 2 0 > 0.99993 || = 0.58 491 490 494 465 525 | 500 < 0.00008 0 0 0 1 2 | 0.5 | 1 0 1 1 1 > 0.99992 || = 0.57 496 491 479 500 491 | 500 < 0.00009 1 0 0 2 0 | 0.5 | 1 0 1 0 0 > 0.99991 || = 0.56 521 494 565 527 504 | 500 < 0.0001 1 1 0 0 0 | 0.5 | 1 0 1 0 0 > 0.9999 || = 0.55 496 545 535 495 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 477 489 514 543 478 | 500 < 0.0001 6 3 2 12 5 | 5 | 6 3 5 6 2 > 0.9999 || = 0.53 502 482 524 524 489 | 500 < 0.0002 3 3 3 5 5 | 5 | 5 0 2 2 3 > 0.9998 || = 0.52 483 491 515 455 509 | 500 < 0.0003 8 4 6 7 4 | 5 | 4 6 5 3 5 > 0.9997 || = 0.51 497 505 440 531 496 | 500 < 0.0004 4 4 6 3 6 | 5 | 5 5 5 3 7 > 0.9996 || = 0.50 509 510 519 490 491 | 500 < 0.0005 3 5 0 7 6 | 5 | 1 7 5 8 9 > 0.9995 || = 0.49 498 557 473 506 520 | 500 < 0.0006 8 5 6 6 8 | 5 | 6 4 9 8 2 > 0.9994 || = 0.48 507 507 485 517 504 | 500 < 0.0007 5 6 10 7 5 | 5 | 5 4 5 5 4 > 0.9993 || = 0.47 511 508 488 490 506 | 500 < 0.0008 2 7 6 4 4 | 5 | 8 6 2 5 4 > 0.9992 || = 0.46 542 505 500 507 509 | 500 < 0.0009 6 3 6 2 5 | 5 | 5 2 8 4 9 > 0.9991 || = 0.45 521 492 518 473 522 | 500 < 0.001 6 4 5 6 6 | 5 | 2 4 4 4 2 > 0.999 || = 0.44 518 480 479 534 490 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 486 507 490 506 513 | 500 < 0.001 51 44 50 59 54 | 50 | 47 41 50 48 47 > 0.999 || = 0.42 473 500 500 505 531 | 500 < 0.002 50 58 42 49 45 | 50 | 41 54 43 57 61 > 0.998 || = 0.41 510 520 497 516 478 | 500 < 0.003 54 45 40 61 58 | 50 | 36 53 34 45 39 > 0.997 || = 0.40 462 477 535 501 511 | 500 < 0.004 56 49 51 39 59 | 50 | 48 44 42 47 47 > 0.996 || = 0.39 503 536 534 496 468 | 500 < 0.005 49 49 48 48 49 | 50 | 52 45 52 38 51 > 0.995 || = 0.38 536 518 507 494 476 | 500 < 0.006 55 51 40 48 46 | 50 | 55 40 48 46 57 > 0.994 || = 0.37 549 524 520 478 499 | 500 < 0.007 45 44 33 63 61 | 50 | 40 59 51 44 34 > 0.993 || = 0.36 521 523 487 533 510 | 500 < 0.008 49 52 50 50 50 | 50 | 45 39 40 55 55 > 0.992 || = 0.35 539 543 499 476 528 | 500 < 0.009 48 45 58 49 52 | 50 | 52 48 42 56 62 > 0.991 || = 0.34 481 528 497 471 528 | 500 < 0.01 36 48 40 46 50 | 50 | 56 48 44 40 47 > 0.99 || = 0.33 464 485 501 510 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 475 517 505 505 461 | 500 < 0.01 493 485 452 512 524 | 497.5 | 472 471 446 476 500 > 0.99 || = 0.31 490 515 472 488 521 | 500 = 0.01 251 241 246 244 245 | 252.5 | 240 227 259 254 208 = 0.99 || = 0.30 468 476 515 507 516 | 500 = 0.02 477 511 481 478 502 | 500 | 504 486 460 527 523 = 0.98 || = 0.29 491 445 484 506 515 | 500 =================================================================| 500 | 557 516 515 549 547 = 0.97 || = 0.28 493 506 491 478 526 | 500 snpair_ClosePairs test: | 500 | 499 532 493 501 524 = 0.96 || = 0.27 486 506 466 524 488 | 500 ----------------------------------------------- | 500 | 496 517 497 479 482 = 0.95 || = 0.26 482 504 502 494 503 | 500 N = 30, n = 6000000, r = 0, t = 3, p = 0, m = 30, Torus = TRUE | 500 | 508 480 511 502 492 = 0.94 || = 0.25 524 479 540 488 485 | 500 Test based on the 2 nearest points (NP): | 500 | 548 486 499 502 491 = 0.93 || = 0.24 486 479 531 516 516 | 500 | 500 | 475 507 472 510 498 = 0.92 || = 0.23 525 494 541 513 477 | 500 =================================================================| 500 | 497 532 484 463 456 = 0.91 || = 0.22 490 510 475 519 477 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 455 491 483 491 466 = 0.90 || = 0.21 497 493 525 511 492 | 500 -----------------------------------------------------------------| 500 | 549 511 458 515 483 = 0.89 || = 0.20 502 510 485 479 508 | 500 SD Bern.: d 0.95530 0.78140 0.98435 | 500 | 495 480 501 527 553 = 0.88 || = 0.19 492 484 538 530 510 | 500 s 1.00535 0.62799 0.97721 | 500 | 485 495 521 464 517 = 0.87 || = 0.18 500 473 535 511 515 | 500 t 1.04568 1.20226 1.07570 | 500 | 498 493 530 469 470 = 0.86 || = 0.17 509 481 494 505 514 | 500 m 1.02681 1.01834 0.94279 | 500 | 488 494 521 459 474 = 0.85 || = 0.16 501 473 479 507 482 | 500 x 1.07240 0.81033 1.22043 | 500 | 540 493 503 446 527 = 0.84 || = 0.15 496 523 483 505 499 | 500 | 500 | 492 458 502 508 495 = 0.83 || = 0.14 496 557 482 523 481 | 500 Changes: d 46 5 3 | 500 | 492 491 508 529 525 = 0.82 || = 0.13 505 508 494 532 504 | 500 s 44 6 4 | 500 | 476 492 475 504 519 = 0.81 || = 0.12 544 529 505 475 451 | 500 t 40 4 4 | 500 | 507 484 479 463 456 = 0.80 || = 0.11 515 509 484 544 493 | 500 m 51 5 4 | 500 | 493 499 513 496 506 = 0.79 || = 0.10 505 500 521 482 471 | 500 x 54 7 6 | 500 | 517 466 548 496 509 = 0.78 || = 0.09 530 498 519 494 582 | 500 -----------------------------------------------------------------| 500 | 458 515 522 504 470 = 0.77 || = 0.08 525 535 492 507 491 | 500 Aver./ d 0.49954 497 > 500: 4 6 3 5 6 4 5 4 2 4 | 500 | 506 466 517 463 537 = 0.76 || = 0.07 481 490 528 503 497 | 500 median s 0.49811 499 ----- 5 5 5 8 6 3 5 4 1 5 | 500 | 511 481 500 516 456 = 0.75 || = 0.06 519 510 493 471 497 | 500 t 0.49857 500 5 4 5 6 2 6 5 4 7 3 | 500 | 495 506 465 479 514 = 0.74 || = 0.05 478 476 502 491 519 | 500 m 0.49902 503 3 8 6 4 8 6 6 3 5 7 | 500 | 494 524 489 495 484 = 0.73 || = 0.04 487 507 536 485 486 | 500 x 0.49905 502 5 4 5 5 8 5 6 4 5 4 | 500 | 492 454 466 516 473 = 0.72 || = 0.03 514 522 513 488 522 | 500 -----------------------------------------------------------------| 500 | 499 501 500 458 458 = 0.71 || = 0.02 477 511 481 478 502 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 467 520 500 542 555 = 0.70 || = 0.01 251 241 246 244 245 | 252.5 d 0 0 1 15 72 9 4 0 0 | 500 | 521 531 503 547 502 = 0.69 || < 0.01 493 485 452 512 524 | 497.5 s 0 0 3 11 70 14 3 0 0 | 500 | 483 506 529 487 479 = 0.68 ||========================================================================= t 0 0 3 12 70 14 2 0 0 | 500 | 476 485 513 486 517 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 66 16 2 0 0 | 500 | 511 480 478 504 506 = 0.66 ||========================================================================= x 0 0 2 16 68 11 3 1 0 | 500 | 514 477 486 467 487 = 0.65 || snpair_ClosePairs test: no 22 test no 23 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 23 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 0 | 0.5 | 2 0 0 0 0 > 0.99999 || = 0.64 546 508 450 516 516 | 500 < 0.00002 2 1 0 0 0 | 0.5 | 0 0 1 1 0 > 0.99998 || = 0.63 470 478 505 509 494 | 500 < 0.00003 0 0 1 2 0 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 516 506 495 475 514 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 467 498 482 502 494 | 500 < 0.00005 0 0 1 1 0 | 0.5 | 0 0 0 0 2 > 0.99995 || = 0.60 459 461 494 533 496 | 500 < 0.00006 0 2 1 0 0 | 0.5 | 0 2 1 0 1 > 0.99994 || = 0.59 539 503 473 520 469 | 500 < 0.00007 0 0 1 0 1 | 0.5 | 0 1 0 0 1 > 0.99993 || = 0.58 523 473 519 500 503 | 500 < 0.00008 1 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 427 465 472 485 536 | 500 < 0.00009 1 0 0 1 2 | 0.5 | 0 0 0 0 2 > 0.99991 || = 0.56 518 513 453 487 556 | 500 < 0.0001 0 0 2 1 0 | 0.5 | 1 0 0 0 1 > 0.9999 || = 0.55 520 508 509 515 515 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 532 535 520 497 501 | 500 < 0.0001 4 5 7 5 5 | 5 | 4 3 2 1 7 > 0.9999 || = 0.53 459 468 537 490 493 | 500 < 0.0002 4 6 1 4 3 | 5 | 2 0 3 1 0 > 0.9998 || = 0.52 513 456 512 492 522 | 500 < 0.0003 4 3 4 5 1 | 5 | 4 3 4 2 4 > 0.9997 || = 0.51 486 510 513 510 454 | 500 < 0.0004 4 4 6 6 5 | 5 | 1 5 6 6 2 > 0.9996 || = 0.50 500 495 505 509 508 | 500 < 0.0005 1 4 3 6 7 | 5 | 5 5 7 4 4 > 0.9995 || = 0.49 480 540 478 509 511 | 500 < 0.0006 5 5 4 10 7 | 5 | 9 1 3 5 2 > 0.9994 || = 0.48 519 545 535 450 501 | 500 < 0.0007 8 7 10 6 6 | 5 | 5 6 7 6 7 > 0.9993 || = 0.47 507 483 527 529 486 | 500 < 0.0008 1 7 8 5 6 | 5 | 4 4 6 6 5 > 0.9992 || = 0.46 473 477 527 499 526 | 500 < 0.0009 3 3 3 7 5 | 5 | 11 4 5 5 3 > 0.9991 || = 0.45 514 498 508 470 483 | 500 < 0.001 4 6 1 6 6 | 5 | 2 9 7 2 3 > 0.999 || = 0.44 505 494 530 524 457 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 457 504 496 506 504 | 500 < 0.001 38 50 47 60 51 | 50 | 47 40 50 38 37 > 0.999 || = 0.42 496 497 511 514 457 | 500 < 0.002 63 59 40 56 34 | 50 | 56 51 38 38 48 > 0.998 || = 0.41 516 483 515 531 449 | 500 < 0.003 53 62 59 55 51 | 50 | 41 45 47 42 48 > 0.997 || = 0.40 521 507 520 527 499 | 500 < 0.004 58 37 53 51 59 | 50 | 50 49 53 48 52 > 0.996 || = 0.39 486 478 474 521 509 | 500 < 0.005 49 46 51 49 37 | 50 | 49 56 62 42 30 > 0.995 || = 0.38 465 522 513 498 491 | 500 < 0.006 43 57 58 52 57 | 50 | 55 52 43 56 46 > 0.994 || = 0.37 485 467 505 517 506 | 500 < 0.007 50 55 44 58 48 | 50 | 44 44 52 56 53 > 0.993 || = 0.36 514 514 531 495 544 | 500 < 0.008 53 46 49 41 45 | 50 | 53 46 57 52 52 > 0.992 || = 0.35 520 475 486 533 495 | 500 < 0.009 45 45 44 51 54 | 50 | 32 49 59 45 47 > 0.991 || = 0.34 487 495 557 509 492 | 500 < 0.01 54 54 41 46 60 | 50 | 69 55 53 50 48 > 0.99 || = 0.33 526 484 493 551 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 469 468 486 489 527 | 500 < 0.01 506 511 486 519 496 | 497.5 | 496 487 514 467 461 > 0.99 || = 0.31 468 498 501 511 460 | 500 = 0.01 290 267 285 235 251 | 252.5 | 241 236 248 244 254 = 0.99 || = 0.30 494 502 471 490 540 | 500 = 0.02 513 509 497 529 494 | 500 | 486 494 484 486 537 = 0.98 || = 0.29 488 511 486 510 523 | 500 =================================================================| 500 | 516 492 484 524 508 = 0.97 || = 0.28 506 500 508 497 508 | 500 snpair_ClosePairs test: | 500 | 495 462 522 481 511 = 0.96 || = 0.27 500 500 510 512 503 | 500 ----------------------------------------------- | 500 | 523 531 537 498 480 = 0.95 || = 0.26 481 503 478 491 489 | 500 N = 30, n = 6000000, r = 0, t = 3, p = 0, m = 30, Torus = TRUE | 500 | 489 504 547 501 477 = 0.94 || = 0.25 491 507 464 501 517 | 500 A2 test based on the spacings between the | 500 | 497 506 509 516 484 = 0.93 || = 0.24 535 499 495 511 507 | 500 successive jump times of process Y_n(t): | 500 | 528 534 518 457 518 = 0.92 || = 0.23 464 533 457 482 501 | 500 =================================================================| 500 | 457 513 483 476 447 = 0.91 || = 0.22 502 486 492 497 516 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 485 503 480 488 477 = 0.90 || = 0.21 522 520 501 498 499 | 500 -----------------------------------------------------------------| 500 | 522 479 499 521 545 = 0.89 || = 0.20 557 508 521 491 489 | 500 SD Bern.: d 1.08109 0.98639 1.32881 | 500 | 514 507 496 490 492 = 0.88 || = 0.19 478 517 495 466 491 | 500 s 0.94258 1.04071 0.70034 | 500 | 470 483 485 467 502 = 0.87 || = 0.18 491 524 532 495 507 | 500 t 1.04347 0.91478 0.99848 | 500 | 495 536 514 527 491 = 0.86 || = 0.17 542 490 482 525 505 | 500 m 0.88017 0.81157 1.02128 | 500 | 476 486 519 541 513 = 0.85 || = 0.16 542 515 511 458 469 | 500 x 0.95456 1.18549 1.11679 | 500 | 485 475 476 492 498 = 0.84 || = 0.15 536 536 491 469 502 | 500 | 500 | 500 494 512 504 514 = 0.83 || = 0.14 536 507 528 500 517 | 500 Changes: d 55 5 7 | 500 | 507 499 507 484 505 = 0.82 || = 0.13 457 502 506 511 498 | 500 s 45 5 5 | 500 | 483 487 499 496 479 = 0.81 || = 0.12 503 495 558 488 500 | 500 t 47 2 3 | 500 | 524 500 492 507 499 = 0.80 || = 0.11 518 480 488 509 482 | 500 m 55 5 2 | 500 | 490 465 501 479 470 = 0.79 || = 0.10 487 503 493 515 529 | 500 x 52 6 4 | 500 | 527 477 464 492 535 = 0.78 || = 0.09 468 534 533 519 501 | 500 -----------------------------------------------------------------| 500 | 495 488 484 493 478 = 0.77 || = 0.08 518 520 490 497 497 | 500 Aver./ d 0.49798 500 > 500: 8 6 5 3 6 6 5 4 3 3 | 500 | 495 505 497 482 484 = 0.76 || = 0.07 509 526 440 536 527 | 500 median s 0.49851 500 ----- 6 7 6 3 4 5 7 4 3 5 | 500 | 499 554 486 503 498 = 0.75 || = 0.06 508 485 531 494 513 | 500 t 0.49965 499 4 5 4 5 8 6 3 2 4 6 | 500 | 501 548 499 488 528 = 0.74 || = 0.05 510 485 493 483 512 | 500 m 0.49807 498 5 4 4 6 7 4 5 3 4 3 | 500 | 495 488 490 476 505 = 0.73 || = 0.04 481 487 458 507 510 | 500 x 0.49885 501 5 5 7 5 4 6 4 4 5 5 | 500 | 504 515 510 473 502 = 0.72 || = 0.03 523 495 508 500 496 | 500 -----------------------------------------------------------------| 500 | 486 455 482 501 489 = 0.71 || = 0.02 513 509 497 529 494 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 490 511 457 493 530 = 0.70 || = 0.01 290 267 285 235 251 | 252.5 d 0 1 0 16 67 14 3 0 0 | 500 | 510 522 469 522 479 = 0.69 || < 0.01 506 511 486 519 496 | 497.5 s 0 0 1 14 73 10 3 0 0 | 500 | 465 508 524 483 470 = 0.68 ||========================================================================= t 0 0 3 11 71 12 4 0 0 | 500 | 504 510 513 489 483 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 12 75 12 1 0 0 | 500 | 515 502 491 479 520 = 0.66 ||========================================================================= x 0 0 3 10 74 12 2 0 0 | 500 | 496 481 488 522 492 = 0.65 || snpair_ClosePairs test: no 23 test no 24 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 24 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 0 0 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 530 508 490 522 502 | 500 < 0.00002 1 0 0 1 0 | 0.5 | 1 0 0 1 1 > 0.99998 || = 0.63 516 501 475 508 518 | 500 < 0.00003 1 0 0 0 2 | 0.5 | 1 1 0 0 1 > 0.99997 || = 0.62 500 480 513 533 488 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 528 497 510 492 522 | 500 < 0.00005 0 0 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 520 495 519 493 469 | 500 < 0.00006 0 3 1 2 0 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 471 517 538 515 556 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 0 1 0 0 1 > 0.99993 || = 0.58 482 532 449 471 495 | 500 < 0.00008 0 1 0 1 0 | 0.5 | 2 1 0 0 0 > 0.99992 || = 0.57 465 487 500 471 554 | 500 < 0.00009 0 1 1 0 1 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 515 483 514 481 464 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.9999 || = 0.55 523 514 459 494 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 516 502 517 493 518 | 500 < 0.0001 3 5 4 7 5 | 5 | 5 5 0 2 3 > 0.9999 || = 0.53 507 510 516 483 516 | 500 < 0.0002 5 3 8 6 4 | 5 | 2 2 2 1 1 > 0.9998 || = 0.52 512 508 466 528 495 | 500 < 0.0003 6 10 6 3 5 | 5 | 4 2 4 5 3 > 0.9997 || = 0.51 535 522 504 488 478 | 500 < 0.0004 3 3 6 7 4 | 5 | 3 6 4 5 2 > 0.9996 || = 0.50 505 487 507 473 455 | 500 < 0.0005 5 3 6 7 6 | 5 | 9 5 6 2 3 > 0.9995 || = 0.49 525 501 492 451 468 | 500 < 0.0006 3 5 3 1 6 | 5 | 4 7 5 2 1 > 0.9994 || = 0.48 489 515 505 540 533 | 500 < 0.0007 6 6 2 3 5 | 5 | 2 9 4 7 4 > 0.9993 || = 0.47 488 514 455 492 526 | 500 < 0.0008 3 4 5 5 5 | 5 | 5 10 4 7 4 > 0.9992 || = 0.46 485 530 496 545 506 | 500 < 0.0009 4 4 7 9 5 | 5 | 4 4 4 4 4 > 0.9991 || = 0.45 502 519 524 516 498 | 500 < 0.001 3 5 5 6 6 | 5 | 3 3 4 5 3 > 0.999 || = 0.44 490 459 493 533 486 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 508 533 533 502 533 | 500 < 0.001 41 48 52 54 51 | 50 | 41 53 37 40 28 > 0.999 || = 0.42 494 495 507 510 475 | 500 < 0.002 48 62 54 40 39 | 50 | 45 47 52 51 50 > 0.998 || = 0.41 522 462 542 527 540 | 500 < 0.003 41 42 50 57 61 | 50 | 42 41 53 42 47 > 0.997 || = 0.40 505 493 494 514 500 | 500 < 0.004 46 38 39 47 59 | 50 | 41 42 43 49 48 > 0.996 || = 0.39 494 520 507 473 507 | 500 < 0.005 49 56 50 34 52 | 50 | 44 39 55 40 41 > 0.995 || = 0.38 529 492 496 510 512 | 500 < 0.006 53 52 46 48 58 | 50 | 43 45 46 53 45 > 0.994 || = 0.37 508 511 492 504 490 | 500 < 0.007 47 55 64 51 45 | 50 | 58 54 46 49 37 > 0.993 || = 0.36 510 499 477 498 514 | 500 < 0.008 58 50 49 47 55 | 50 | 47 48 40 51 29 > 0.992 || = 0.35 491 477 535 505 523 | 500 < 0.009 53 43 64 43 54 | 50 | 43 48 47 45 38 > 0.991 || = 0.34 495 522 502 545 512 | 500 < 0.01 51 45 51 60 45 | 50 | 47 51 60 47 49 > 0.99 || = 0.33 479 473 501 530 515 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 502 528 516 519 509 | 500 < 0.01 487 491 519 481 519 | 497.5 | 451 468 479 467 412 > 0.99 || = 0.31 482 495 539 508 516 | 500 = 0.01 264 244 241 269 235 | 252.5 | 222 257 218 220 236 = 0.99 || = 0.30 483 521 526 486 537 | 500 = 0.02 509 479 510 508 492 | 500 | 475 485 496 478 501 = 0.98 || = 0.29 473 468 500 527 491 | 500 =================================================================| 500 | 491 483 509 432 510 = 0.97 || = 0.28 506 501 490 492 507 | 500 snpair_ClosePairs test: | 500 | 474 510 467 478 492 = 0.96 || = 0.27 523 486 518 493 483 | 500 ----------------------------------------------- | 500 | 471 464 506 481 481 = 0.95 || = 0.26 521 532 491 493 485 | 500 N = 30, n = 6000000, r = 0, t = 3, p = 0, m = 30, Torus = TRUE | 500 | 507 506 477 469 547 = 0.94 || = 0.25 518 529 492 536 527 | 500 A2 test based on the spacings between the | 500 | 471 506 502 522 524 = 0.93 || = 0.24 488 492 507 486 480 | 500 successive jump times of process Y_n(t): | 500 | 503 513 487 511 523 = 0.92 || = 0.23 500 506 490 526 492 | 500 =================================================================| 500 | 512 485 478 498 505 = 0.91 || = 0.22 519 515 532 491 485 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 472 493 503 462 492 = 0.90 || = 0.21 530 512 498 513 510 | 500 -----------------------------------------------------------------| 500 | 435 477 517 473 505 = 0.89 || = 0.20 508 490 475 489 522 | 500 SD Bern.: d 0.98119 0.74198 0.96690 | 500 | 510 517 529 509 510 = 0.88 || = 0.19 553 501 487 505 470 | 500 s 0.84678 0.99547 0.81771 | 500 | 503 449 476 501 504 = 0.87 || = 0.18 487 534 514 516 501 | 500 t 0.95307 1.05028 0.99748 | 500 | 518 496 506 499 472 = 0.86 || = 0.17 531 500 519 529 526 | 500 m 1.00490 1.08957 0.78905 | 500 | 459 499 485 521 513 = 0.85 || = 0.16 512 508 463 493 533 | 500 x 1.09312 0.98333 1.64884 | 500 | 494 483 503 533 476 = 0.84 || = 0.15 520 488 535 522 469 | 500 | 500 | 493 466 501 500 492 = 0.83 || = 0.14 530 521 509 521 522 | 500 Changes: d 42 3 2 | 500 | 497 481 482 490 472 = 0.82 || = 0.13 481 484 525 523 467 | 500 s 52 4 4 | 500 | 486 480 498 511 469 = 0.81 || = 0.12 508 495 540 506 544 | 500 t 51 4 5 | 500 | 511 510 501 488 512 = 0.80 || = 0.11 496 495 524 507 495 | 500 m 42 6 6 | 500 | 468 499 513 485 514 = 0.79 || = 0.10 491 519 474 516 486 | 500 x 51 5 0 | 500 | 499 511 496 481 487 = 0.78 || = 0.09 480 525 480 483 497 | 500 -----------------------------------------------------------------| 500 | 540 524 509 480 460 = 0.77 || = 0.08 508 507 504 470 488 | 500 Aver./ d 0.49704 503 > 500: 5 6 7 4 5 7 5 7 3 3 | 500 | 510 490 542 518 480 = 0.76 || = 0.07 468 479 458 509 489 | 500 median s 0.49804 501 ----- 4 5 6 5 6 7 7 7 1 5 | 500 | 532 476 496 501 515 = 0.75 || = 0.06 476 530 482 527 465 | 500 t 0.49852 501 5 7 3 7 5 6 4 4 6 3 | 500 | 534 535 489 534 467 = 0.74 || = 0.05 513 483 472 506 466 | 500 m 0.49554 500 6 9 4 7 8 2 4 3 5 2 | 500 | 512 505 463 494 508 = 0.73 || = 0.04 509 514 503 531 477 | 500 x 0.49971 500 2 5 4 9 5 4 5 6 4 6 | 500 | 523 502 490 481 533 = 0.72 || = 0.03 500 494 503 488 505 | 500 -----------------------------------------------------------------| 500 | 466 510 500 473 525 = 0.71 || = 0.02 509 479 510 508 492 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 483 512 531 461 512 = 0.70 || = 0.01 264 244 241 269 235 | 252.5 d 0 0 3 14 69 14 1 0 0 | 500 | 492 502 521 509 489 = 0.69 || < 0.01 487 491 519 481 519 | 497.5 s 0 0 1 11 78 11 0 0 0 | 500 | 515 506 480 484 543 = 0.68 ||========================================================================= t 0 0 3 13 70 15 0 0 0 | 500 | 452 460 491 489 495 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 2 11 69 16 2 0 0 | 500 | 490 507 500 479 479 = 0.66 ||========================================================================= x 0 1 1 18 63 15 3 0 0 | 500 | 514 509 495 479 492 = 0.65 || snpair_ClosePairs test: no 24 test no 25 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 25 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 1 0 0 | 0.5 | 1 0 1 1 1 > 0.99999 || = 0.64 0 0 0 0 0 | 500 < 0.00002 1 0 0 0 0 | 0.5 | 1 3 1 0 0 > 0.99998 || = 0.63 595 615 626 628 654 | 500 < 0.00003 0 0 0 1 1 | 0.5 | 1 1 0 1 0 > 0.99997 || = 0.62 607 629 602 601 663 | 500 < 0.00004 0 0 0 1 2 | 0.5 | 0 0 0 0 1 > 0.99996 || = 0.61 627 637 653 667 605 | 500 < 0.00005 1 1 2 0 1 | 0.5 | 0 1 0 1 1 > 0.99995 || = 0.60 637 651 628 636 657 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 1 0 1 0 1 > 0.99994 || = 0.59 0 0 0 0 0 | 500 < 0.00007 1 0 1 0 1 | 0.5 | 0 1 1 0 0 > 0.99993 || = 0.58 622 654 665 577 687 | 500 < 0.00008 0 1 0 1 0 | 0.5 | 0 2 1 0 0 > 0.99992 || = 0.57 657 656 586 628 669 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 1 0 0 4 0 > 0.99991 || = 0.56 675 635 615 637 658 | 500 < 0.0001 1 1 0 0 0 | 0.5 | 2 0 1 0 2 > 0.9999 || = 0.55 0 0 0 0 0 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 650 692 610 652 718 | 500 < 0.0001 4 4 4 3 5 | 5 | 7 8 6 7 6 > 0.9999 || = 0.53 688 584 701 646 704 | 500 < 0.0002 4 6 3 5 2 | 5 | 2 2 1 3 2 > 0.9998 || = 0.52 668 661 674 636 671 | 500 < 0.0003 3 5 2 6 4 | 5 | 0 4 5 3 2 > 0.9997 || = 0.51 0 0 0 0 0 | 500 < 0.0004 6 8 8 4 6 | 5 | 5 10 2 4 4 > 0.9996 || = 0.50 1328 1348 1265 1302 1303 | 500 < 0.0005 6 7 4 5 3 | 5 | 3 3 5 5 6 > 0.9995 || = 0.49 651 667 664 705 652 | 500 < 0.0006 1 5 7 5 0 | 5 | 3 6 6 9 5 > 0.9994 || = 0.48 673 686 675 636 661 | 500 < 0.0007 11 4 5 8 8 | 5 | 4 3 4 5 3 > 0.9993 || = 0.47 0 0 0 0 0 | 500 < 0.0008 7 2 7 6 4 | 5 | 5 9 4 5 3 > 0.9992 || = 0.46 652 686 686 668 660 | 500 < 0.0009 3 2 11 4 2 | 5 | 2 6 3 3 3 > 0.9991 || = 0.45 632 661 654 684 679 | 500 < 0.001 6 3 8 4 5 | 5 | 3 7 5 3 10 > 0.999 || = 0.44 677 632 661 647 630 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 672 643 671 660 637 | 500 < 0.001 51 46 59 50 39 | 50 | 34 58 41 47 44 > 0.999 || = 0.42 0 0 0 0 0 | 500 < 0.002 40 37 51 47 39 | 50 | 49 57 45 46 45 > 0.998 || = 0.41 654 636 641 647 575 | 500 < 0.003 45 40 51 46 54 | 50 | 53 45 63 56 58 > 0.997 || = 0.40 590 638 622 582 660 | 500 < 0.004 59 37 46 49 54 | 50 | 26 35 33 29 32 > 0.996 || = 0.39 647 596 621 662 628 | 500 < 0.005 67 55 54 68 51 | 50 | 64 65 62 73 54 > 0.995 || = 0.38 0 0 0 0 0 | 500 < 0.006 60 45 61 51 36 | 50 | 32 28 18 33 20 > 0.994 || = 0.37 630 612 631 652 582 | 500 < 0.007 21 33 25 34 30 | 50 | 58 46 58 58 66 > 0.993 || = 0.36 630 604 629 647 664 | 500 < 0.008 60 71 57 49 63 | 50 | 37 29 33 39 26 > 0.992 || = 0.35 637 630 597 541 605 | 500 < 0.009 34 33 34 35 41 | 50 | 89 71 73 66 77 > 0.991 || = 0.34 584 588 594 618 624 | 500 < 0.01 38 38 41 29 41 | 50 | 43 44 53 33 39 > 0.99 || = 0.33 0 0 0 0 0 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 604 617 598 612 572 | 500 < 0.01 475 435 479 458 448 | 497.5 | 485 478 479 480 461 > 0.99 || = 0.31 555 601 568 586 581 | 500 = 0.01 230 225 255 259 255 | 252.5 | 263 265 237 255 299 = 0.99 || = 0.30 566 613 582 581 538 | 500 = 0.02 534 511 511 529 510 | 500 | 465 502 467 515 480 = 0.98 || = 0.29 565 589 601 614 585 | 500 =================================================================| 500 | 417 475 455 449 441 = 0.97 || = 0.28 503 532 564 554 537 | 500 snpair_ClosePairs test: | 500 | 406 384 421 405 420 = 0.96 || = 0.27 531 572 552 520 524 | 500 ----------------------------------------------- | 500 | 503 484 510 474 481 = 0.95 || = 0.26 554 530 540 542 536 | 500 N = 30, n = 6000000, r = 0, t = 3, p = 0, m = 30, Torus = TRUE | 500 | 556 577 540 606 565 = 0.94 || = 0.25 551 554 501 483 528 | 500 Test on the jump times of Y | 500 | 422 465 436 426 490 = 0.93 || = 0.24 496 495 582 504 523 | 500 (superposition of Yn): | 500 | 466 479 481 508 459 = 0.92 || = 0.23 533 510 478 533 493 | 500 =================================================================| 500 | 526 542 526 535 542 = 0.91 || = 0.22 455 480 498 479 484 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 262 283 272 271 280 = 0.90 || = 0.21 487 486 417 473 475 | 500 -----------------------------------------------------------------| 500 | 601 602 607 593 638 = 0.89 || = 0.20 446 435 457 434 465 | 500 SD Bern.: d 9.02522 1.96923 2.51720 | 500 | 632 683 694 678 639 = 0.88 || = 0.19 448 469 436 447 453 | 500 s 9.09935 1.82683 2.00399 | 500 | 369 320 346 335 357 = 0.87 || = 0.18 432 421 438 455 412 | 500 t 8.94991 1.58002 2.29155 | 500 | 351 361 371 363 344 = 0.86 || = 0.17 394 412 400 394 410 | 500 m 9.03700 1.59704 2.02585 | 500 | 814 811 810 769 737 = 0.85 || = 0.16 387 371 390 381 395 | 500 x 9.06051 1.55125 2.46983 | 500 | 420 409 432 396 388 = 0.84 || = 0.15 751 774 783 793 813 | 500 | 500 | 460 414 433 434 420 = 0.83 || = 0.14 351 334 337 334 341 | 500 Changes: d 48 5 8 | 500 | 446 429 474 430 406 = 0.82 || = 0.13 716 673 719 694 711 | 500 s 50 4 5 | 500 | 462 522 454 446 458 = 0.81 || = 0.12 341 360 322 312 324 | 500 t 42 5 7 | 500 | 468 456 473 492 491 = 0.80 || = 0.11 594 604 638 600 617 | 500 m 46 2 8 | 500 | 483 467 464 464 445 = 0.79 || = 0.10 272 288 320 283 277 | 500 x 46 4 8 | 500 | 498 487 489 482 507 = 0.78 || = 0.09 562 537 552 564 507 | 500 -----------------------------------------------------------------| 500 | 528 534 521 515 511 = 0.77 || = 0.08 492 462 461 469 471 | 500 Aver./ d 0.49780 533 > 500: 4 3 6 8 8 7 8 6 3 4 | 500 | 499 494 503 541 500 = 0.76 || = 0.07 662 633 632 672 625 | 500 median s 0.50054 534 ----- 4 3 6 8 8 7 8 6 4 4 | 500 | 552 539 508 529 524 = 0.75 || = 0.06 390 375 378 397 391 | 500 t 0.49786 529 6 3 6 8 8 7 8 7 3 3 | 500 | 555 553 545 531 563 = 0.74 || = 0.05 490 452 509 468 510 | 500 m 0.49869 531 5 3 6 8 8 7 8 7 3 5 | 500 | 546 552 529 541 526 = 0.73 || = 0.04 521 542 540 528 542 | 500 x 0.49892 526 6 3 6 8 8 7 8 7 3 3 | 500 | 569 577 532 550 540 = 0.72 || = 0.03 469 413 419 439 426 | 500 -----------------------------------------------------------------| 500 | 585 580 560 628 555 = 0.71 || = 0.02 534 511 511 529 510 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 597 521 542 560 576 = 0.70 || = 0.01 230 225 255 259 255 | 252.5 d 19 4 4 8 12 5 10 5 34 | 500 | 0 0 0 0 0 = 0.69 || < 0.01 475 435 479 458 448 | 497.5 s 19 5 3 7 14 7 4 7 35 | 500 | 569 561 610 589 651 = 0.68 ||========================================================================= t 18 5 5 6 15 7 5 4 36 | 500 | 592 586 616 577 573 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 20 2 7 6 12 10 4 5 35 | 500 | 575 621 628 617 601 = 0.66 ||========================================================================= x 20 4 4 6 13 11 4 7 32 | 500 | 618 641 607 666 607 = 0.65 || snpair_ClosePairs test: no 25 test no 26 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 26 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 1 3 1 | 0.5 | 0 1 0 0 2 > 0.99999 || = 0.64 487 477 479 476 506 | 500 < 0.00002 1 0 0 0 1 | 0.5 | 0 1 2 1 1 > 0.99998 || = 0.63 489 505 527 525 498 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 1 0 0 1 1 > 0.99997 || = 0.62 516 485 484 515 482 | 500 < 0.00004 1 0 0 1 0 | 0.5 | 1 2 0 0 0 > 0.99996 || = 0.61 521 535 509 507 506 | 500 < 0.00005 1 0 0 0 0 | 0.5 | 3 0 0 0 0 > 0.99995 || = 0.60 480 497 519 505 508 | 500 < 0.00006 1 1 0 1 0 | 0.5 | 1 0 1 0 0 > 0.99994 || = 0.59 511 520 509 506 480 | 500 < 0.00007 0 2 1 2 2 | 0.5 | 1 0 0 0 0 > 0.99993 || = 0.58 498 465 483 530 517 | 500 < 0.00008 1 0 0 1 2 | 0.5 | 1 1 0 1 0 > 0.99992 || = 0.57 461 497 510 509 483 | 500 < 0.00009 1 0 1 0 1 | 0.5 | 1 0 0 0 0 > 0.99991 || = 0.56 498 506 495 485 509 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 1 1 1 0 0 > 0.9999 || = 0.55 533 492 524 526 523 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 507 452 491 550 508 | 500 < 0.0001 7 4 3 9 7 | 5 | 10 6 4 3 4 > 0.9999 || = 0.53 482 520 463 486 477 | 500 < 0.0002 9 3 3 7 4 | 5 | 4 4 1 1 4 > 0.9998 || = 0.52 492 515 518 484 497 | 500 < 0.0003 5 2 3 5 3 | 5 | 5 4 4 6 7 > 0.9997 || = 0.51 520 531 518 501 489 | 500 < 0.0004 3 1 1 5 5 | 5 | 5 3 5 5 7 > 0.9996 || = 0.50 494 500 506 510 502 | 500 < 0.0005 1 5 5 3 9 | 5 | 6 2 5 2 6 > 0.9995 || = 0.49 520 507 532 515 514 | 500 < 0.0006 3 5 3 3 3 | 5 | 5 4 2 2 5 > 0.9994 || = 0.48 480 510 514 490 500 | 500 < 0.0007 4 7 6 5 6 | 5 | 4 6 7 3 3 > 0.9993 || = 0.47 473 488 516 480 505 | 500 < 0.0008 7 7 8 5 5 | 5 | 9 3 2 7 6 > 0.9992 || = 0.46 506 487 484 476 543 | 500 < 0.0009 2 2 4 6 5 | 5 | 2 5 4 1 2 > 0.9991 || = 0.45 488 505 487 528 489 | 500 < 0.001 6 6 3 1 5 | 5 | 9 6 7 4 4 > 0.999 || = 0.44 506 516 510 483 479 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 496 529 513 491 487 | 500 < 0.001 47 42 39 49 52 | 50 | 59 43 41 34 48 > 0.999 || = 0.42 526 521 531 520 471 | 500 < 0.002 54 59 54 44 44 | 50 | 51 56 56 45 55 > 0.998 || = 0.41 490 483 501 538 468 | 500 < 0.003 52 53 47 40 52 | 50 | 39 46 50 56 49 > 0.997 || = 0.40 521 519 480 521 500 | 500 < 0.004 52 57 42 55 48 | 50 | 66 41 49 60 51 > 0.996 || = 0.39 546 502 503 526 521 | 500 < 0.005 49 39 43 48 44 | 50 | 44 49 42 43 68 > 0.995 || = 0.38 511 503 501 525 510 | 500 < 0.006 46 55 48 57 47 | 50 | 41 41 46 40 53 > 0.994 || = 0.37 497 513 496 514 503 | 500 < 0.007 38 39 58 47 50 | 50 | 44 50 55 51 57 > 0.993 || = 0.36 493 500 534 495 484 | 500 < 0.008 46 43 53 56 39 | 50 | 51 44 43 40 45 > 0.992 || = 0.35 483 494 508 477 454 | 500 < 0.009 44 51 49 48 50 | 50 | 49 44 59 52 31 > 0.991 || = 0.34 459 461 473 533 496 | 500 < 0.01 51 46 62 52 52 | 50 | 43 50 47 59 36 > 0.99 || = 0.33 507 472 457 483 474 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 502 507 507 469 485 | 500 < 0.01 479 484 495 496 478 | 497.5 | 487 464 488 480 493 > 0.99 || = 0.31 452 483 480 491 495 | 500 = 0.01 271 221 248 288 261 | 252.5 | 250 258 283 242 240 = 0.99 || = 0.30 455 511 483 500 532 | 500 = 0.02 511 510 503 512 525 | 500 | 517 507 514 520 490 = 0.98 || = 0.29 527 540 490 492 524 | 500 =================================================================| 500 | 553 494 464 483 536 = 0.97 || = 0.28 517 456 517 485 504 | 500 snpair_ClosePairs test: | 500 | 492 522 505 500 487 = 0.96 || = 0.27 519 503 518 464 469 | 500 ----------------------------------------------- | 500 | 465 500 522 530 518 = 0.95 || = 0.26 460 461 536 528 480 | 500 N = 30, n = 6000000, r = 0, t = 3, p = 0, m = 30, Torus = TRUE | 500 | 506 504 489 480 498 = 0.94 || = 0.25 486 506 516 474 502 | 500 Test on the jump times of Y | 500 | 527 535 487 503 541 = 0.93 || = 0.24 493 523 471 490 494 | 500 (superposition of Yn): | 500 | 524 510 498 502 460 = 0.92 || = 0.23 514 473 458 508 473 | 500 =================================================================| 500 | 438 482 493 466 469 = 0.91 || = 0.22 493 473 548 526 502 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 489 508 466 476 466 = 0.90 || = 0.21 499 514 502 523 509 | 500 -----------------------------------------------------------------| 500 | 465 531 477 529 562 = 0.89 || = 0.20 476 499 514 517 489 | 500 SD Bern.: d 0.97367 0.70319 1.15208 | 500 | 483 499 519 498 477 = 0.88 || = 0.19 496 491 495 492 487 | 500 s 0.95859 1.03588 0.82015 | 500 | 504 499 491 515 541 = 0.87 || = 0.18 513 483 480 478 491 | 500 t 0.95104 0.98130 0.85129 | 500 | 477 492 498 458 522 = 0.86 || = 0.17 478 499 476 491 537 | 500 m 1.01755 0.73247 1.22698 | 500 | 487 475 445 523 467 = 0.85 || = 0.16 506 507 489 486 552 | 500 x 1.11145 0.66062 1.41137 | 500 | 490 530 535 487 516 = 0.84 || = 0.15 497 468 495 501 476 | 500 | 500 | 476 559 490 515 495 = 0.83 || = 0.14 469 488 488 475 527 | 500 Changes: d 46 3 5 | 500 | 509 493 449 475 468 = 0.82 || = 0.13 524 518 517 525 541 | 500 s 56 6 2 | 500 | 520 516 493 513 508 = 0.81 || = 0.12 506 491 492 492 469 | 500 t 40 5 6 | 500 | 517 500 513 447 480 = 0.80 || = 0.11 533 541 497 517 542 | 500 m 48 7 5 | 500 | 515 542 493 487 508 = 0.79 || = 0.10 472 531 528 500 486 | 500 x 50 4 4 | 500 | 508 513 490 491 510 = 0.78 || = 0.09 533 478 502 491 518 | 500 -----------------------------------------------------------------| 500 | 478 503 489 478 541 = 0.77 || = 0.08 508 483 518 471 488 | 500 Aver./ d 0.49957 499 > 500: 8 5 4 4 5 4 6 5 3 5 | 500 | 500 489 496 513 545 = 0.76 || = 0.07 508 478 503 469 479 | 500 median s 0.50184 500 ----- 2 4 5 5 7 5 4 5 5 6 | 500 | 491 493 470 533 480 = 0.75 || = 0.06 499 487 487 510 483 | 500 t 0.49999 501 5 2 7 5 7 6 7 5 2 4 | 500 | 481 504 517 494 492 = 0.74 || = 0.05 507 492 481 522 514 | 500 m 0.49901 500 5 3 5 4 5 7 4 4 5 4 | 500 | 499 513 524 500 512 = 0.73 || = 0.04 518 535 460 486 505 | 500 x 0.50005 498 6 5 5 4 3 5 4 7 5 3 | 500 | 506 484 533 525 532 = 0.72 || = 0.03 503 497 506 530 509 | 500 -----------------------------------------------------------------| 500 | 527 489 502 511 502 = 0.71 || = 0.02 511 510 503 512 525 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 508 522 503 497 489 = 0.70 || = 0.01 271 221 248 288 261 | 252.5 d 0 0 3 11 73 11 3 0 0 | 500 | 496 466 547 489 558 = 0.69 || < 0.01 479 484 495 496 478 | 497.5 s 0 0 1 15 72 12 1 0 0 | 500 | 492 520 520 554 520 = 0.68 ||========================================================================= t 0 0 2 11 75 11 2 0 0 | 500 | 547 475 513 469 457 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 63 18 3 0 0 | 500 | 539 495 513 462 429 = 0.66 ||========================================================================= x 0 1 1 15 66 14 4 0 0 | 500 | 522 476 496 446 482 = 0.65 || snpair_ClosePairs test: no 26 test no 27 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 27 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 3 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 366 348 365 328 327 | 500 < 0.00002 1 3 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 347 359 358 335 355 | 500 < 0.00003 1 1 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 354 375 367 338 351 | 500 < 0.00004 0 1 2 1 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 366 363 373 389 354 | 500 < 0.00005 1 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 376 414 383 369 351 | 500 < 0.00006 1 1 2 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 346 410 366 421 413 | 500 < 0.00007 1 0 1 1 2 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 365 366 381 394 416 | 500 < 0.00008 0 0 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 410 374 403 401 380 | 500 < 0.00009 2 1 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 401 415 358 409 404 | 500 < 0.0001 2 1 1 1 0 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 409 384 429 407 416 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 461 430 470 431 392 | 500 < 0.0001 12 9 7 11 7 | 5 | 1 0 0 0 0 > 0.9999 || = 0.53 450 436 430 419 418 | 500 < 0.0002 7 7 8 8 8 | 5 | 0 1 0 0 0 > 0.9998 || = 0.52 460 454 422 427 431 | 500 < 0.0003 15 13 12 13 4 | 5 | 1 0 1 0 0 > 0.9997 || = 0.51 453 468 401 442 453 | 500 < 0.0004 7 8 8 12 11 | 5 | 0 1 0 0 0 > 0.9996 || = 0.50 460 456 470 475 476 | 500 < 0.0005 7 5 7 11 6 | 5 | 0 0 0 0 2 > 0.9995 || = 0.49 496 496 443 500 503 | 500 < 0.0006 13 11 12 11 10 | 5 | 0 1 0 0 0 > 0.9994 || = 0.48 478 517 464 466 441 | 500 < 0.0007 12 7 8 8 6 | 5 | 1 1 0 0 1 > 0.9993 || = 0.47 483 498 470 481 534 | 500 < 0.0008 8 4 10 5 4 | 5 | 1 0 0 0 0 > 0.9992 || = 0.46 485 482 566 474 509 | 500 < 0.0009 9 13 8 14 10 | 5 | 0 0 0 0 0 > 0.9991 || = 0.45 524 549 492 561 517 | 500 < 0.001 10 13 8 8 14 | 5 | 0 0 1 0 0 > 0.999 || = 0.44 527 535 515 551 538 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 571 523 550 503 535 | 500 < 0.001 100 90 88 101 80 | 50 | 4 4 2 0 3 > 0.999 || = 0.42 562 549 558 557 536 | 500 < 0.002 95 82 104 99 76 | 50 | 1 1 2 2 3 > 0.998 || = 0.41 569 551 533 599 582 | 500 < 0.003 100 87 98 99 97 | 50 | 4 0 2 4 2 > 0.997 || = 0.40 548 581 574 551 579 | 500 < 0.004 89 76 97 89 91 | 50 | 4 1 2 4 7 > 0.996 || = 0.39 581 546 560 606 573 | 500 < 0.005 106 73 85 101 96 | 50 | 6 5 5 3 5 > 0.995 || = 0.38 577 614 570 593 595 | 500 < 0.006 70 78 94 88 79 | 50 | 2 6 5 4 4 > 0.994 || = 0.37 594 585 597 579 590 | 500 < 0.007 88 99 78 114 93 | 50 | 6 3 4 5 2 > 0.993 || = 0.36 601 619 589 559 629 | 500 < 0.008 94 94 113 107 79 | 50 | 3 6 9 10 5 > 0.992 || = 0.35 621 651 624 579 612 | 500 < 0.009 103 101 76 106 92 | 50 | 5 9 4 4 2 > 0.991 || = 0.34 598 640 638 637 639 | 500 < 0.01 100 92 87 93 99 | 50 | 5 6 4 9 2 > 0.99 || = 0.33 629 624 658 654 642 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 631 660 641 689 606 | 500 < 0.01 945 872 920 997 882 | 497.5 | 40 41 39 45 35 > 0.99 || = 0.31 660 702 661 657 677 | 500 = 0.01 493 423 513 494 519 | 252.5 | 31 27 20 29 36 = 0.99 || = 0.30 696 669 689 688 681 | 500 = 0.02 944 988 1029 938 980 | 500 | 72 82 78 84 61 = 0.98 || = 0.29 693 661 681 695 714 | 500 =================================================================| 500 | 93 91 84 76 93 = 0.97 || = 0.28 711 710 704 731 710 | 500 snpair_ClosePairs test: | 500 | 100 91 98 94 100 = 0.96 || = 0.27 725 672 730 755 710 | 500 ----------------------------------------------- | 500 | 90 101 104 105 100 = 0.95 || = 0.26 720 760 740 701 678 | 500 N = 30, n = 6000000, r = 0, t = 3, p = 0, m = 30, Torus = TRUE | 500 | 107 120 120 123 113 = 0.94 || = 0.25 788 761 741 768 744 | 500 Test on the jump times of Y | 500 | 139 119 118 120 133 = 0.93 || = 0.24 763 804 733 768 746 | 500 (superposition of Yn): | 500 | 135 143 125 131 138 = 0.92 || = 0.23 746 752 742 841 774 | 500 =================================================================| 500 | 139 135 133 143 141 = 0.91 || = 0.22 788 694 766 834 824 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 154 156 135 165 150 = 0.90 || = 0.21 768 786 829 814 817 | 500 -----------------------------------------------------------------| 500 | 150 162 150 155 138 = 0.89 || = 0.20 785 826 792 748 845 | 500 SD Bern.: d 12.46826 6.44853 6.51232 | 500 | 148 166 192 157 161 = 0.88 || = 0.19 795 739 831 793 866 | 500 s 12.37504 5.42193 6.50570 | 500 | 158 147 166 180 155 = 0.87 || = 0.18 809 810 838 889 816 | 500 t 12.52894 6.14016 6.52936 | 500 | 149 181 174 155 165 = 0.86 || = 0.17 906 860 898 795 845 | 500 m 12.55674 7.11678 6.45038 | 500 | 198 205 177 155 190 = 0.85 || = 0.16 809 840 865 853 906 | 500 x 12.49809 5.53051 6.58340 | 500 | 195 201 192 183 168 = 0.84 || = 0.15 868 933 927 859 844 | 500 | 500 | 202 173 207 193 189 = 0.83 || = 0.14 937 869 880 876 861 | 500 Changes: d 1 0 0 | 500 | 224 211 196 215 210 = 0.82 || = 0.13 811 902 875 897 888 | 500 s 3 0 0 | 500 | 218 194 211 234 209 = 0.81 || = 0.12 881 895 883 851 863 | 500 t 3 0 0 | 500 | 223 235 219 205 219 = 0.80 || = 0.11 910 935 913 859 891 | 500 m 1 0 0 | 500 | 238 216 237 251 230 = 0.79 || = 0.10 920 946 952 943 914 | 500 x 3 0 0 | 500 | 218 263 278 249 228 = 0.78 || = 0.09 989 927 942 919 934 | 500 -----------------------------------------------------------------| 500 | 220 246 268 242 274 = 0.77 || = 0.08 976 983 945 921 962 | 500 Aver./ d 0.34017 461 > 500:10 10 10 10 6 0 0 0 0 0 | 500 | 247 247 244 235 265 = 0.76 || = 0.07 970 953 954 906 929 | 500 median s 0.34164 468 ----- 10 10 10 10 7 0 0 0 0 0 | 500 | 268 252 247 253 256 = 0.75 || = 0.06 978 932 968 1021 951 | 500 t 0.33957 464 10 10 10 10 6 0 0 0 0 0 | 500 | 262 287 280 263 271 = 0.74 || = 0.05 958 975 935 984 961 | 500 m 0.33919 466 10 10 10 10 6 0 0 0 0 0 | 500 | 262 289 273 284 262 = 0.73 || = 0.04 960 971 908 985 998 | 500 x 0.33981 453 10 10 10 10 9 0 0 0 0 0 | 500 | 282 308 270 273 298 = 0.72 || = 0.03 971 950 976 981 972 | 500 -----------------------------------------------------------------| 500 | 314 286 307 262 278 = 0.71 || = 0.02 944 988 1029 938 980 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 293 300 279 262 313 = 0.70 || = 0.01 493 423 513 494 519 | 252.5 d 46 0 2 3 4 2 2 4 38 | 500 | 291 283 293 314 315 = 0.69 || < 0.01 945 872 920 997 882 | 497.5 s 44 3 2 2 4 2 4 2 38 | 500 | 322 305 330 320 324 = 0.68 ||========================================================================= t 46 3 1 4 2 1 4 2 38 | 500 | 348 294 324 313 333 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 45 4 1 3 3 0 5 2 38 | 500 | 361 332 309 340 353 = 0.66 ||========================================================================= x 44 5 2 1 3 4 0 3 39 | 500 | 337 339 345 307 297 = 0.65 || snpair_ClosePairs test: no 27 test no 28 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 28 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 0 0 1 | 0.5 | 0 1 0 1 0 > 0.99999 || = 0.64 488 499 505 528 513 | 500 < 0.00002 0 1 0 0 1 | 0.5 | 1 1 0 0 1 > 0.99998 || = 0.63 487 501 453 514 480 | 500 < 0.00003 2 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 488 489 520 472 480 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 485 500 471 484 518 | 500 < 0.00005 0 1 1 0 1 | 0.5 | 1 0 0 0 1 > 0.99995 || = 0.60 528 519 528 516 485 | 500 < 0.00006 0 0 1 0 0 | 0.5 | 2 1 1 0 0 > 0.99994 || = 0.59 499 494 500 502 512 | 500 < 0.00007 1 0 0 1 2 | 0.5 | 0 0 1 1 1 > 0.99993 || = 0.58 450 505 473 477 535 | 500 < 0.00008 0 0 0 2 1 | 0.5 | 1 0 0 0 0 > 0.99992 || = 0.57 512 516 455 528 461 | 500 < 0.00009 1 1 2 1 1 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 469 506 507 499 523 | 500 < 0.0001 0 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 503 486 509 449 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 510 509 507 501 512 | 500 < 0.0001 4 5 7 4 8 | 5 | 5 3 3 3 3 > 0.9999 || = 0.53 477 502 500 494 484 | 500 < 0.0002 5 4 5 2 3 | 5 | 3 0 2 0 1 > 0.9998 || = 0.52 495 523 507 488 500 | 500 < 0.0003 5 10 5 2 7 | 5 | 3 2 3 2 6 > 0.9997 || = 0.51 483 495 487 532 490 | 500 < 0.0004 5 9 7 7 9 | 5 | 5 9 1 0 1 > 0.9996 || = 0.50 498 484 481 481 505 | 500 < 0.0005 4 1 5 4 7 | 5 | 2 3 4 5 6 > 0.9995 || = 0.49 486 485 479 524 493 | 500 < 0.0006 10 4 4 5 4 | 5 | 2 6 9 5 8 > 0.9994 || = 0.48 532 495 495 515 493 | 500 < 0.0007 6 3 5 7 4 | 5 | 2 5 7 4 6 > 0.9993 || = 0.47 519 538 506 508 520 | 500 < 0.0008 4 3 1 2 4 | 5 | 5 2 1 7 1 > 0.9992 || = 0.46 494 488 511 497 502 | 500 < 0.0009 3 5 5 10 10 | 5 | 1 1 2 6 4 > 0.9991 || = 0.45 522 501 491 531 503 | 500 < 0.001 4 7 2 5 1 | 5 | 5 10 10 4 3 > 0.999 || = 0.44 474 525 492 505 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 491 518 502 512 499 | 500 < 0.001 50 51 46 48 57 | 50 | 33 41 42 36 39 > 0.999 || = 0.42 503 536 473 495 518 | 500 < 0.002 35 47 54 42 32 | 50 | 55 34 35 40 48 > 0.998 || = 0.41 463 483 481 498 554 | 500 < 0.003 57 47 53 55 41 | 50 | 47 44 55 36 54 > 0.997 || = 0.40 468 497 499 505 447 | 500 < 0.004 47 44 34 48 56 | 50 | 47 38 35 45 39 > 0.996 || = 0.39 510 527 515 527 491 | 500 < 0.005 58 47 56 49 52 | 50 | 64 55 40 36 50 > 0.995 || = 0.38 521 501 491 492 503 | 500 < 0.006 33 43 60 53 52 | 50 | 51 57 46 47 48 > 0.994 || = 0.37 509 512 474 500 492 | 500 < 0.007 46 46 61 55 51 | 50 | 59 62 52 51 48 > 0.993 || = 0.36 489 510 486 459 543 | 500 < 0.008 46 46 48 48 58 | 50 | 60 55 51 59 60 > 0.992 || = 0.35 488 512 528 469 443 | 500 < 0.009 55 49 48 48 70 | 50 | 48 47 49 54 55 > 0.991 || = 0.34 521 497 514 533 495 | 500 < 0.01 36 51 39 54 46 | 50 | 50 43 44 66 47 > 0.99 || = 0.33 520 571 550 515 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 511 496 523 506 475 | 500 < 0.01 463 471 499 500 515 | 497.5 | 514 476 449 470 488 > 0.99 || = 0.31 503 473 506 498 487 | 500 = 0.01 240 241 271 261 276 | 252.5 | 261 215 252 254 245 = 0.99 || = 0.30 512 515 490 481 507 | 500 = 0.02 494 538 505 492 512 | 500 | 536 517 524 532 516 = 0.98 || = 0.29 513 550 506 502 500 | 500 =================================================================| 500 | 469 511 478 534 524 = 0.97 || = 0.28 472 501 497 490 494 | 500 snpair_ClosePairs test: | 500 | 501 505 448 540 501 = 0.96 || = 0.27 498 516 497 489 483 | 500 ----------------------------------------------- | 500 | 495 535 515 517 503 = 0.95 || = 0.26 518 537 500 480 463 | 500 N = 20, n = 4000000, r = 0, t = 5, p = 0, m = 30, Torus = TRUE | 500 | 488 494 494 465 489 = 0.94 || = 0.25 497 454 507 504 494 | 500 Test based on the 2 nearest points (NP): | 500 | 509 469 519 476 490 = 0.93 || = 0.24 496 490 493 498 475 | 500 | 500 | 507 498 472 543 477 = 0.92 || = 0.23 530 526 526 524 485 | 500 =================================================================| 500 | 518 490 502 504 516 = 0.91 || = 0.22 531 482 521 545 521 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 495 483 484 474 493 = 0.90 || = 0.21 499 482 510 458 513 | 500 -----------------------------------------------------------------| 500 | 481 487 486 531 517 = 0.89 || = 0.20 515 505 490 481 494 | 500 SD Bern.: d 1.06486 1.33408 1.19557 | 500 | 483 513 519 496 520 = 0.88 || = 0.19 489 506 495 484 509 | 500 s 0.99415 0.54247 1.27969 | 500 | 483 488 539 498 532 = 0.87 || = 0.18 485 508 512 522 526 | 500 t 0.96162 1.16933 1.18126 | 500 | 512 495 483 479 485 = 0.86 || = 0.17 489 507 518 499 475 | 500 m 0.94380 0.55883 1.46769 | 500 | 493 498 525 494 478 = 0.85 || = 0.16 452 493 515 505 513 | 500 x 1.03218 1.39998 0.89932 | 500 | 507 550 538 510 475 = 0.84 || = 0.15 517 492 517 457 505 | 500 | 500 | 449 514 511 507 479 = 0.83 || = 0.14 489 519 514 507 563 | 500 Changes: d 49 6 4 | 500 | 516 464 485 520 512 = 0.82 || = 0.13 472 465 519 513 535 | 500 s 44 2 2 | 500 | 503 446 485 494 499 = 0.81 || = 0.12 498 485 493 481 466 | 500 t 47 4 4 | 500 | 489 475 484 476 536 = 0.80 || = 0.11 509 506 499 456 472 | 500 m 49 5 1 | 500 | 539 498 540 496 454 = 0.79 || = 0.10 539 484 481 486 506 | 500 x 51 3 4 | 500 | 530 476 531 509 457 = 0.78 || = 0.09 584 529 486 502 472 | 500 -----------------------------------------------------------------| 500 | 469 517 448 503 543 = 0.77 || = 0.08 523 479 508 505 524 | 500 Aver./ d 0.49974 499 > 500: 5 3 5 8 4 4 3 7 4 7 | 500 | 519 499 482 482 511 = 0.76 || = 0.07 506 473 497 494 525 | 500 median s 0.49915 498 ----- 3 5 6 7 5 7 4 3 3 4 | 500 | 566 491 519 507 493 = 0.75 || = 0.06 481 466 477 463 533 | 500 t 0.49882 500 6 6 5 6 3 5 4 5 5 4 | 500 | 522 512 560 511 493 = 0.74 || = 0.05 515 492 480 501 461 | 500 m 0.50133 502 7 4 4 4 7 5 5 6 4 7 | 500 | 526 511 509 517 487 = 0.73 || = 0.04 460 493 503 505 525 | 500 x 0.49865 500 8 7 2 4 6 4 5 4 4 5 | 500 | 501 494 497 505 518 = 0.72 || = 0.03 525 512 510 540 519 | 500 -----------------------------------------------------------------| 500 | 444 483 485 467 490 = 0.71 || = 0.02 494 538 505 492 512 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 477 475 524 503 473 = 0.70 || = 0.01 240 241 271 261 276 | 252.5 d 0 0 4 13 70 12 1 1 0 | 500 | 508 465 527 497 504 = 0.69 || < 0.01 463 471 499 500 515 | 497.5 s 0 0 3 12 71 12 2 1 0 | 500 | 523 515 471 476 509 = 0.68 ||========================================================================= t 0 0 5 8 73 13 2 0 0 | 500 | 463 476 487 488 504 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 15 69 15 1 0 0 | 500 | 492 523 476 524 470 = 0.66 ||========================================================================= x 0 0 3 14 68 14 2 0 0 | 500 | 505 532 497 522 493 = 0.65 || snpair_ClosePairs test: no 28 test no 29 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 29 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 521 498 504 500 450 | 500 < 0.00002 0 2 1 2 0 | 0.5 | 1 0 1 0 0 > 0.99998 || = 0.63 526 488 511 543 484 | 500 < 0.00003 0 0 1 0 0 | 0.5 | 0 1 0 0 0 > 0.99997 || = 0.62 485 469 516 509 508 | 500 < 0.00004 0 1 1 2 1 | 0.5 | 0 1 2 1 1 > 0.99996 || = 0.61 519 558 472 487 530 | 500 < 0.00005 0 1 0 1 0 | 0.5 | 1 0 1 0 0 > 0.99995 || = 0.60 509 510 492 527 511 | 500 < 0.00006 1 0 0 1 0 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 479 498 491 510 522 | 500 < 0.00007 1 1 0 1 0 | 0.5 | 1 0 1 0 1 > 0.99993 || = 0.58 439 496 532 519 476 | 500 < 0.00008 0 1 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 472 511 466 481 527 | 500 < 0.00009 0 2 1 0 0 | 0.5 | 0 0 0 2 1 > 0.99991 || = 0.56 491 561 494 486 506 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 1 3 0 0 0 > 0.9999 || = 0.55 501 458 543 475 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 462 521 463 473 516 | 500 < 0.0001 3 9 5 8 1 | 5 | 4 5 5 4 4 > 0.9999 || = 0.53 489 519 501 489 499 | 500 < 0.0002 4 1 4 5 4 | 5 | 1 1 4 0 2 > 0.9998 || = 0.52 521 542 513 513 514 | 500 < 0.0003 5 5 7 5 5 | 5 | 2 6 6 3 0 > 0.9997 || = 0.51 470 528 505 479 520 | 500 < 0.0004 4 2 9 3 8 | 5 | 4 5 4 3 3 > 0.9996 || = 0.50 472 487 521 465 520 | 500 < 0.0005 5 7 7 6 4 | 5 | 3 3 5 5 1 > 0.9995 || = 0.49 513 524 463 500 510 | 500 < 0.0006 8 1 4 8 6 | 5 | 9 4 7 2 4 > 0.9994 || = 0.48 523 498 501 552 511 | 500 < 0.0007 5 3 6 7 5 | 5 | 3 7 1 7 4 > 0.9993 || = 0.47 517 542 505 488 525 | 500 < 0.0008 7 4 4 5 10 | 5 | 2 4 8 9 6 > 0.9992 || = 0.46 508 485 497 515 491 | 500 < 0.0009 3 5 4 5 3 | 5 | 6 6 9 5 2 > 0.9991 || = 0.45 521 506 518 493 450 | 500 < 0.001 5 1 5 8 4 | 5 | 0 8 2 4 4 > 0.999 || = 0.44 517 522 520 522 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 519 491 530 487 528 | 500 < 0.001 49 38 55 60 50 | 50 | 34 49 51 42 30 > 0.999 || = 0.42 502 460 504 543 509 | 500 < 0.002 46 48 48 36 38 | 50 | 54 56 40 50 49 > 0.998 || = 0.41 535 509 490 471 486 | 500 < 0.003 46 49 51 55 63 | 50 | 36 37 52 55 52 > 0.997 || = 0.40 487 483 513 478 468 | 500 < 0.004 51 35 53 47 56 | 50 | 46 43 44 45 38 > 0.996 || = 0.39 501 465 510 489 468 | 500 < 0.005 25 58 39 45 54 | 50 | 41 57 41 49 47 > 0.995 || = 0.38 471 501 508 520 507 | 500 < 0.006 42 46 50 42 66 | 50 | 54 52 47 49 45 > 0.994 || = 0.37 479 473 499 507 475 | 500 < 0.007 51 54 50 38 51 | 50 | 48 54 58 56 53 > 0.993 || = 0.36 558 520 531 518 467 | 500 < 0.008 46 59 47 52 54 | 50 | 56 51 55 51 53 > 0.992 || = 0.35 556 494 497 500 516 | 500 < 0.009 45 43 52 64 44 | 50 | 55 51 48 58 49 > 0.991 || = 0.34 484 508 523 482 571 | 500 < 0.01 59 48 51 50 46 | 50 | 57 57 47 58 54 > 0.99 || = 0.33 489 491 533 507 469 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 514 488 494 483 484 | 500 < 0.01 460 478 496 489 522 | 497.5 | 481 507 483 513 470 > 0.99 || = 0.31 514 524 504 472 492 | 500 = 0.01 269 236 242 287 234 | 252.5 | 264 250 266 233 269 = 0.99 || = 0.30 509 513 523 503 502 | 500 = 0.02 483 485 496 497 482 | 500 | 541 492 530 530 526 = 0.98 || = 0.29 534 488 481 498 510 | 500 =================================================================| 500 | 519 534 511 496 530 = 0.97 || = 0.28 500 518 469 504 469 | 500 snpair_ClosePairs test: | 500 | 518 475 510 478 500 = 0.96 || = 0.27 545 489 520 503 509 | 500 ----------------------------------------------- | 500 | 474 458 525 521 508 = 0.95 || = 0.26 481 507 484 535 507 | 500 N = 20, n = 4000000, r = 0, t = 5, p = 0, m = 30, Torus = TRUE | 500 | 517 498 501 488 493 = 0.94 || = 0.25 504 510 532 506 484 | 500 A2 test based on the spacings between the | 500 | 468 519 491 551 478 = 0.93 || = 0.24 475 504 476 468 527 | 500 successive jump times of process Y_n(t): | 500 | 501 490 512 475 478 = 0.92 || = 0.23 539 491 476 508 496 | 500 =================================================================| 500 | 527 501 492 502 479 = 0.91 || = 0.22 526 508 499 500 517 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 507 505 491 481 511 = 0.90 || = 0.21 483 499 496 494 511 | 500 -----------------------------------------------------------------| 500 | 498 544 527 479 509 = 0.89 || = 0.20 507 498 508 468 508 | 500 SD Bern.: d 1.06507 1.30141 1.17956 | 500 | 499 486 517 483 485 = 0.88 || = 0.19 517 503 512 499 520 | 500 s 1.01903 1.09963 0.86644 | 500 | 492 495 502 540 492 = 0.87 || = 0.18 468 462 502 514 525 | 500 t 0.92423 0.59020 0.81648 | 500 | 487 494 467 479 486 = 0.86 || = 0.17 493 492 464 452 477 | 500 m 0.98041 1.23592 0.75003 | 500 | 485 482 501 472 499 = 0.85 || = 0.16 505 514 501 495 513 | 500 x 1.03659 1.17531 1.11230 | 500 | 498 528 480 502 523 = 0.84 || = 0.15 531 532 475 515 500 | 500 | 500 | 474 493 506 509 511 = 0.83 || = 0.14 445 517 479 488 465 | 500 Changes: d 48 5 5 | 500 | 493 553 547 521 494 = 0.82 || = 0.13 476 513 521 470 502 | 500 s 57 4 3 | 500 | 470 488 504 495 523 = 0.81 || = 0.12 540 481 506 530 521 | 500 t 52 4 5 | 500 | 487 500 510 486 491 = 0.80 || = 0.11 539 461 530 461 487 | 500 m 57 5 3 | 500 | 508 460 477 519 506 = 0.79 || = 0.10 509 505 529 496 479 | 500 x 49 2 5 | 500 | 528 492 502 501 467 = 0.78 || = 0.09 502 498 464 489 476 | 500 -----------------------------------------------------------------| 500 | 474 528 498 550 506 = 0.77 || = 0.08 472 500 480 498 505 | 500 Aver./ d 0.49962 501 > 500: 5 6 6 6 9 3 7 5 1 7 | 500 | 517 498 451 515 514 = 0.76 || = 0.07 501 478 504 538 526 | 500 median s 0.50136 498 ----- 1 6 5 5 5 7 5 3 4 4 | 500 | 495 499 465 470 467 = 0.75 || = 0.06 483 472 523 478 519 | 500 t 0.50014 502 4 7 3 7 7 5 5 3 7 7 | 500 | 480 508 513 501 518 = 0.74 || = 0.05 463 454 506 517 529 | 500 m 0.50021 499 5 3 5 5 4 4 3 7 4 5 | 500 | 501 454 491 500 525 = 0.73 || = 0.04 506 533 475 510 519 | 500 x 0.49884 506 7 5 7 4 5 7 5 5 5 4 | 500 | 517 491 484 506 465 = 0.72 || = 0.03 501 494 505 541 526 | 500 -----------------------------------------------------------------| 500 | 475 514 489 508 475 = 0.71 || = 0.02 483 485 496 497 482 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 506 486 455 489 460 = 0.70 || = 0.01 269 236 242 287 234 | 252.5 d 0 0 3 17 65 13 3 0 0 | 500 | 498 512 466 497 544 = 0.69 || < 0.01 460 478 496 489 522 | 497.5 s 0 0 2 13 72 11 3 0 0 | 500 | 453 518 505 488 445 = 0.68 ||========================================================================= t 0 0 2 16 68 14 1 0 0 | 500 | 504 509 476 490 512 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 13 74 9 4 0 0 | 500 | 506 461 520 494 516 = 0.66 ||========================================================================= x 0 0 3 18 62 17 0 1 0 | 500 | 508 517 497 504 462 = 0.65 || snpair_ClosePairs test: no 29 test no 30 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 30 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 2 | 0.5 | 0 0 1 0 1 > 0.99999 || = 0.64 524 477 521 481 525 | 500 < 0.00002 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 474 490 491 471 534 | 500 < 0.00003 0 4 1 0 0 | 0.5 | 0 0 0 4 2 > 0.99997 || = 0.62 494 502 507 507 495 | 500 < 0.00004 1 0 0 0 0 | 0.5 | 0 1 0 1 0 > 0.99996 || = 0.61 534 489 496 515 468 | 500 < 0.00005 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 492 497 503 495 509 | 500 < 0.00006 1 1 0 0 0 | 0.5 | 1 1 1 0 0 > 0.99994 || = 0.59 522 470 480 524 526 | 500 < 0.00007 0 1 0 0 0 | 0.5 | 2 0 0 1 1 > 0.99993 || = 0.58 493 520 494 495 521 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 1 2 1 1 2 > 0.99992 || = 0.57 498 512 497 513 525 | 500 < 0.00009 1 0 0 2 1 | 0.5 | 0 2 1 0 1 > 0.99991 || = 0.56 496 515 482 461 507 | 500 < 0.0001 1 0 0 0 1 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 520 476 502 489 478 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 471 464 449 478 540 | 500 < 0.0001 5 8 1 3 5 | 5 | 4 6 5 7 7 > 0.9999 || = 0.53 459 504 518 491 528 | 500 < 0.0002 7 2 8 5 5 | 5 | 3 1 3 4 3 > 0.9998 || = 0.52 478 509 500 513 472 | 500 < 0.0003 2 1 2 1 5 | 5 | 7 7 4 9 7 > 0.9997 || = 0.51 531 496 494 508 517 | 500 < 0.0004 5 7 6 4 5 | 5 | 7 6 2 6 2 > 0.9996 || = 0.50 509 508 506 515 496 | 500 < 0.0005 5 10 7 7 4 | 5 | 3 3 8 6 9 > 0.9995 || = 0.49 472 474 487 499 478 | 500 < 0.0006 8 6 6 3 7 | 5 | 6 7 5 5 8 > 0.9994 || = 0.48 450 504 491 530 488 | 500 < 0.0007 0 1 3 7 3 | 5 | 4 3 2 6 5 > 0.9993 || = 0.47 511 476 508 481 472 | 500 < 0.0008 7 6 7 4 5 | 5 | 1 7 9 1 4 > 0.9992 || = 0.46 486 532 516 528 506 | 500 < 0.0009 2 1 3 9 3 | 5 | 1 7 3 1 3 > 0.9991 || = 0.45 504 477 534 488 516 | 500 < 0.001 7 6 3 7 7 | 5 | 6 7 5 6 6 > 0.999 || = 0.44 469 490 450 514 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 504 525 483 502 477 | 500 < 0.001 48 48 46 50 49 | 50 | 42 54 46 51 54 > 0.999 || = 0.42 534 475 473 465 494 | 500 < 0.002 47 45 46 49 60 | 50 | 58 39 35 46 62 > 0.998 || = 0.41 526 532 493 540 537 | 500 < 0.003 56 29 55 56 42 | 50 | 41 60 43 45 43 > 0.997 || = 0.40 564 482 515 522 482 | 500 < 0.004 52 57 50 57 51 | 50 | 55 53 49 49 46 > 0.996 || = 0.39 495 430 520 478 506 | 500 < 0.005 46 45 58 55 55 | 50 | 41 49 56 53 41 > 0.995 || = 0.38 484 483 520 516 457 | 500 < 0.006 50 46 59 56 53 | 50 | 45 56 48 50 47 > 0.994 || = 0.37 486 521 535 464 551 | 500 < 0.007 46 58 53 53 57 | 50 | 52 64 37 64 59 > 0.993 || = 0.36 488 539 522 474 465 | 500 < 0.008 40 50 50 48 39 | 50 | 50 56 37 45 57 > 0.992 || = 0.35 471 506 504 496 477 | 500 < 0.009 49 47 58 59 37 | 50 | 51 45 53 47 53 > 0.991 || = 0.34 498 502 478 519 521 | 500 < 0.01 53 57 46 43 56 | 50 | 54 54 62 44 55 > 0.99 || = 0.33 492 532 487 490 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 517 502 509 463 474 | 500 < 0.01 487 482 521 526 499 | 497.5 | 489 530 466 494 517 > 0.99 || = 0.31 517 516 466 517 499 | 500 = 0.01 237 251 263 217 259 | 252.5 | 260 272 238 254 256 = 0.99 || = 0.30 507 483 480 534 513 | 500 = 0.02 518 492 491 470 505 | 500 | 524 477 552 459 468 = 0.98 || = 0.29 508 480 502 512 498 | 500 =================================================================| 500 | 476 507 474 554 515 = 0.97 || = 0.28 495 493 488 486 497 | 500 snpair_ClosePairs test: | 500 | 489 534 504 529 495 = 0.96 || = 0.27 501 533 494 525 532 | 500 ----------------------------------------------- | 500 | 511 540 513 508 456 = 0.95 || = 0.26 531 463 510 515 504 | 500 N = 20, n = 4000000, r = 0, t = 5, p = 0, m = 30, Torus = TRUE | 500 | 485 524 507 500 488 = 0.94 || = 0.25 475 482 506 474 508 | 500 A2 test based on the spacings between the | 500 | 504 469 499 500 528 = 0.93 || = 0.24 524 488 517 504 486 | 500 successive jump times of process Y_n(t): | 500 | 541 517 523 492 475 = 0.92 || = 0.23 500 514 520 506 516 | 500 =================================================================| 500 | 526 517 493 455 496 = 0.91 || = 0.22 512 473 482 503 518 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 516 462 488 494 494 = 0.90 || = 0.21 521 508 502 478 455 | 500 -----------------------------------------------------------------| 500 | 480 508 518 524 476 = 0.89 || = 0.20 486 512 471 493 487 | 500 SD Bern.: d 0.96391 0.62480 0.85011 | 500 | 498 501 508 514 508 = 0.88 || = 0.19 478 531 490 487 497 | 500 s 1.00267 1.16848 1.05503 | 500 | 531 460 474 492 463 = 0.87 || = 0.18 505 480 484 469 502 | 500 t 0.98638 0.76326 1.28281 | 500 | 539 488 495 489 472 = 0.86 || = 0.17 498 522 511 496 530 | 500 m 1.03251 0.76195 0.79788 | 500 | 513 472 497 525 515 = 0.85 || = 0.16 529 533 488 469 533 | 500 x 1.00547 1.07291 0.97925 | 500 | 505 509 566 500 495 = 0.84 || = 0.15 492 471 548 473 488 | 500 | 500 | 505 491 530 526 489 = 0.83 || = 0.14 518 511 495 491 512 | 500 Changes: d 54 3 7 | 500 | 492 507 519 472 474 = 0.82 || = 0.13 499 520 444 511 495 | 500 s 51 5 6 | 500 | 504 491 518 542 468 = 0.81 || = 0.12 531 493 507 526 507 | 500 t 51 6 3 | 500 | 513 485 486 459 494 = 0.80 || = 0.11 458 544 518 530 513 | 500 m 49 4 5 | 500 | 492 515 537 494 493 = 0.79 || = 0.10 514 527 501 531 549 | 500 x 48 5 2 | 500 | 513 491 505 515 483 = 0.78 || = 0.09 484 509 490 513 542 | 500 -----------------------------------------------------------------| 500 | 495 514 468 511 486 = 0.77 || = 0.08 472 482 534 495 531 | 500 Aver./ d 0.50065 498 > 500: 2 5 6 3 6 3 4 3 7 6 | 500 | 499 509 504 493 504 = 0.76 || = 0.07 541 488 496 511 498 | 500 median s 0.50015 502 ----- 3 7 4 7 4 5 5 5 4 8 | 500 | 496 500 461 523 478 = 0.75 || = 0.06 472 464 458 514 518 | 500 t 0.50134 501 3 5 6 6 4 3 5 7 6 5 | 500 | 508 487 518 531 474 = 0.74 || = 0.05 484 475 477 485 503 | 500 m 0.50130 500 4 4 6 4 6 4 6 4 5 4 | 500 | 497 491 517 497 501 = 0.73 || = 0.04 498 534 500 483 498 | 500 x 0.49664 498 8 7 5 4 3 8 3 4 2 4 | 500 | 466 511 517 479 512 = 0.72 || = 0.03 499 515 490 465 511 | 500 -----------------------------------------------------------------| 500 | 483 519 502 466 557 = 0.71 || = 0.02 518 492 491 470 505 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 497 511 487 505 491 = 0.70 || = 0.01 237 251 263 217 259 | 252.5 d 0 0 1 15 69 15 1 0 0 | 500 | 472 483 461 526 456 = 0.69 || < 0.01 487 482 521 526 499 | 497.5 s 0 1 0 19 64 17 0 0 0 | 500 | 511 473 523 522 499 = 0.68 ||========================================================================= t 0 0 3 11 75 9 3 0 0 | 500 | 513 535 525 551 498 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 17 62 18 2 0 0 | 500 | 464 518 492 473 518 = 0.66 ||========================================================================= x 0 0 1 18 66 13 3 0 0 | 500 | 456 502 506 498 483 = 0.65 || snpair_ClosePairs test: no 30 test no 31 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 31 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 0 2 0 0 2 > 0.99999 || = 0.64 0 0 0 0 0 | 500 < 0.00002 1 1 1 1 2 | 0.5 | 0 2 0 1 1 > 0.99998 || = 0.63 749 732 745 789 764 | 500 < 0.00003 0 0 0 0 1 | 0.5 | 0 1 0 4 0 > 0.99997 || = 0.62 798 774 782 760 790 | 500 < 0.00004 1 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 0 0 0 0 0 | 500 < 0.00005 0 0 1 0 0 | 0.5 | 0 2 0 1 0 > 0.99995 || = 0.60 780 813 752 852 802 | 500 < 0.00006 0 1 0 0 0 | 0.5 | 0 1 0 1 0 > 0.99994 || = 0.59 780 810 801 726 854 | 500 < 0.00007 1 0 0 1 0 | 0.5 | 0 1 1 0 1 > 0.99993 || = 0.58 0 0 0 0 0 | 500 < 0.00008 1 1 0 0 2 | 0.5 | 0 1 2 0 1 > 0.99992 || = 0.57 812 804 824 820 783 | 500 < 0.00009 1 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 0 0 0 0 0 | 500 < 0.0001 1 0 0 0 0 | 0.5 | 1 0 1 1 0 > 0.9999 || = 0.55 837 768 813 804 853 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 822 855 829 823 828 | 500 < 0.0001 6 5 4 2 6 | 5 | 1 10 4 8 5 > 0.9999 || = 0.53 0 0 0 0 0 | 500 < 0.0002 2 2 2 2 6 | 5 | 2 0 4 4 4 > 0.9998 || = 0.52 877 781 809 778 762 | 500 < 0.0003 7 2 0 4 8 | 5 | 5 8 2 4 6 > 0.9997 || = 0.51 1619 1558 1598 1639 1583 | 500 < 0.0004 7 4 8 5 5 | 5 | 5 5 6 3 1 > 0.9996 || = 0.50 0 0 0 0 0 | 500 < 0.0005 12 5 1 5 6 | 5 | 5 5 5 1 7 > 0.9995 || = 0.49 808 858 787 827 820 | 500 < 0.0006 4 2 1 5 2 | 5 | 9 6 3 10 7 > 0.9994 || = 0.48 0 0 0 0 0 | 500 < 0.0007 4 8 4 5 5 | 5 | 6 6 2 6 3 > 0.9993 || = 0.47 766 791 855 816 789 | 500 < 0.0008 6 4 2 2 5 | 5 | 5 5 5 7 2 > 0.9992 || = 0.46 779 796 790 751 756 | 500 < 0.0009 4 3 7 3 6 | 5 | 8 2 2 3 2 > 0.9991 || = 0.45 0 0 0 0 0 | 500 < 0.001 6 7 6 4 7 | 5 | 0 0 0 0 0 > 0.999 || = 0.44 773 748 858 832 812 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 0 0 0 0 0 | 500 < 0.001 58 42 35 37 56 | 50 | 46 47 33 46 37 > 0.999 || = 0.42 767 784 771 791 776 | 500 < 0.002 49 41 58 45 52 | 50 | 55 51 60 74 48 > 0.998 || = 0.41 771 781 774 765 721 | 500 < 0.003 39 36 36 37 29 | 50 | 46 45 43 51 52 > 0.997 || = 0.40 0 0 0 0 0 | 500 < 0.004 56 59 49 62 62 | 50 | 44 40 34 47 43 > 0.996 || = 0.39 772 737 787 775 800 | 500 < 0.005 51 48 61 58 50 | 50 | 47 49 54 60 45 > 0.995 || = 0.38 762 762 773 768 778 | 500 < 0.006 67 66 52 62 61 | 50 | 18 37 35 31 38 > 0.994 || = 0.37 0 0 0 0 0 | 500 < 0.007 27 37 44 33 24 | 50 | 74 74 60 81 79 > 0.993 || = 0.36 749 805 798 757 753 | 500 < 0.008 43 30 39 30 32 | 50 | 53 43 39 39 49 > 0.992 || = 0.35 730 718 753 719 723 | 500 < 0.009 40 37 45 35 42 | 50 | 44 40 47 49 59 > 0.991 || = 0.34 0 0 0 0 0 | 500 < 0.01 38 55 47 57 54 | 50 | 50 48 75 52 72 > 0.99 || = 0.33 707 695 739 713 723 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 682 708 717 698 695 | 500 < 0.01 468 451 466 456 462 | 497.5 | 477 474 480 530 522 > 0.99 || = 0.31 0 0 0 0 0 | 500 = 0.01 267 230 218 243 225 | 252.5 | 190 192 191 174 189 = 0.99 || = 0.30 736 733 716 736 670 | 500 = 0.02 549 540 541 574 587 | 500 | 457 444 454 444 432 = 0.98 || = 0.29 718 660 660 741 676 | 500 =================================================================| 500 | 553 527 529 519 553 = 0.97 || = 0.28 702 694 654 641 658 | 500 snpair_ClosePairs test: | 500 | 555 543 537 540 552 = 0.96 || = 0.27 0 0 0 0 0 | 500 ----------------------------------------------- | 500 | 415 430 429 411 449 = 0.95 || = 0.26 641 656 694 614 641 | 500 N = 20, n = 4000000, r = 0, t = 5, p = 0, m =30, Torus = TRUE | 500 | 482 463 507 482 475 = 0.94 || = 0.25 664 641 669 654 616 | 500 Test on the jump times of Y | 500 | 519 552 545 544 531 = 0.93 || = 0.24 613 643 642 642 630 | 500 (superposition of Yn): | 500 | 594 647 578 615 613 = 0.92 || = 0.23 0 0 0 0 0 | 500 =================================================================| 500 | 329 343 343 350 340 = 0.91 || = 0.22 614 569 582 583 606 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 340 337 356 343 369 = 0.90 || = 0.21 607 579 564 564 522 | 500 -----------------------------------------------------------------| 500 | 792 733 772 761 758 = 0.89 || = 0.20 554 552 543 549 586 | 500 SD Bern.: d 13.06391 1.63421 1.87015 | 500 | 417 406 401 407 385 = 0.88 || = 0.19 507 537 501 556 494 | 500 s 12.96503 1.70084 1.43876 | 500 | 427 434 398 414 474 = 0.87 || = 0.18 464 580 531 550 503 | 500 t 13.10293 1.26711 1.89302 | 500 | 432 473 445 440 434 = 0.86 || = 0.17 476 509 521 492 507 | 500 m 13.16684 1.83285 2.07467 | 500 | 500 484 498 477 492 = 0.85 || = 0.16 499 474 503 515 513 | 500 x 13.00673 1.91197 1.89936 | 500 | 525 495 511 466 492 = 0.84 || = 0.15 450 454 459 485 419 | 500 | 500 | 480 474 507 466 474 = 0.83 || = 0.14 423 438 406 412 422 | 500 Changes: d 58 3 4 | 500 | 538 554 550 482 550 = 0.82 || = 0.13 417 451 428 435 408 | 500 s 56 5 4 | 500 | 561 521 533 537 528 = 0.81 || = 0.12 385 433 371 398 429 | 500 t 56 4 7 | 500 | 577 565 560 571 586 = 0.80 || = 0.11 750 745 696 783 730 | 500 m 57 3 7 | 500 | 577 565 598 615 579 = 0.79 || = 0.10 370 375 327 309 366 | 500 x 59 6 5 | 500 | 0 0 0 0 0 = 0.78 || = 0.09 649 600 616 650 617 | 500 -----------------------------------------------------------------| 500 | 612 611 589 634 624 = 0.77 || = 0.08 326 296 279 276 260 | 500 Aver./ d 0.49930 553 > 500: 5 2 8 7 6 7 6 8 4 4 | 500 | 653 644 633 627 656 = 0.76 || = 0.07 570 552 533 516 532 | 500 median s 0.49951 552 ----- 4 4 8 7 6 7 6 8 3 4 | 500 | 597 641 712 630 641 = 0.75 || = 0.06 469 435 453 518 490 | 500 t 0.50094 537 4 5 8 7 6 7 6 8 5 5 | 500 | 622 664 663 658 750 = 0.74 || = 0.05 577 627 594 569 595 | 500 m 0.49909 544 5 4 8 7 6 7 6 8 2 5 | 500 | 0 0 0 0 0 = 0.73 || = 0.04 478 498 475 463 499 | 500 x 0.50197 532 4 4 8 7 6 7 6 8 3 5 | 500 | 710 661 707 689 694 = 0.72 || = 0.03 404 369 422 380 423 | 500 -----------------------------------------------------------------| 500 | 696 733 657 760 683 = 0.71 || = 0.02 549 540 541 574 587 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 0 0 0 0 0 = 0.70 || = 0.01 267 230 218 243 225 | 252.5 d 25 7 1 5 9 2 5 4 43 | 500 | 727 712 648 699 702 = 0.69 || < 0.01 468 451 466 456 462 | 497.5 s 25 3 7 6 5 4 6 3 42 | 500 | 675 774 735 718 702 = 0.68 ||========================================================================= t 27 4 4 3 8 7 4 2 42 | 500 | 0 0 0 0 0 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 28 2 3 5 9 4 4 4 42 | 500 | 713 770 726 728 737 = 0.66 ||========================================================================= x 26 5 2 5 9 4 3 4 43 | 500 | 771 735 789 762 783 = 0.65 || snpair_ClosePairs test: no 31 test no 32 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 32 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 1 1 | 0.5 | 0 1 1 1 1 > 0.99999 || = 0.64 506 509 471 502 484 | 500 < 0.00002 0 2 1 0 0 | 0.5 | 0 0 1 1 0 > 0.99998 || = 0.63 523 505 491 485 532 | 500 < 0.00003 0 1 0 2 0 | 0.5 | 1 0 1 0 0 > 0.99997 || = 0.62 524 499 458 484 455 | 500 < 0.00004 1 0 0 1 2 | 0.5 | 2 1 0 0 0 > 0.99996 || = 0.61 485 470 465 539 490 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 1 0 0 1 > 0.99995 || = 0.60 501 531 501 459 503 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 1 1 0 1 > 0.99994 || = 0.59 460 481 528 518 483 | 500 < 0.00007 0 1 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 495 500 525 558 487 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 485 508 497 508 497 | 500 < 0.00009 0 1 0 0 0 | 0.5 | 1 0 1 0 1 > 0.99991 || = 0.56 494 493 497 489 523 | 500 < 0.0001 1 2 0 0 0 | 0.5 | 0 0 0 1 1 > 0.9999 || = 0.55 492 502 522 522 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 466 523 499 477 493 | 500 < 0.0001 3 8 1 4 3 | 5 | 4 4 5 4 6 > 0.9999 || = 0.53 511 541 548 483 490 | 500 < 0.0002 3 6 3 5 4 | 5 | 2 3 2 2 3 > 0.9998 || = 0.52 500 511 490 502 495 | 500 < 0.0003 6 5 1 0 3 | 5 | 6 5 6 9 11 > 0.9997 || = 0.51 478 525 530 510 492 | 500 < 0.0004 7 2 7 7 5 | 5 | 6 7 4 2 6 > 0.9996 || = 0.50 491 526 475 526 499 | 500 < 0.0005 1 7 4 2 2 | 5 | 6 4 6 4 3 > 0.9995 || = 0.49 513 493 480 524 512 | 500 < 0.0006 7 5 5 4 6 | 5 | 9 4 6 6 8 > 0.9994 || = 0.48 518 478 517 499 510 | 500 < 0.0007 9 4 6 8 4 | 5 | 3 5 5 2 4 > 0.9993 || = 0.47 539 489 512 537 481 | 500 < 0.0008 7 2 5 6 5 | 5 | 2 4 7 3 6 > 0.9992 || = 0.46 512 504 512 535 513 | 500 < 0.0009 1 3 5 5 3 | 5 | 3 2 6 4 9 > 0.9991 || = 0.45 490 492 512 463 476 | 500 < 0.001 2 5 7 2 3 | 5 | 3 3 3 2 5 > 0.999 || = 0.44 514 470 512 503 521 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 490 495 493 530 497 | 500 < 0.001 46 47 44 43 38 | 50 | 44 41 50 38 61 > 0.999 || = 0.42 511 471 483 495 494 | 500 < 0.002 47 42 47 39 48 | 50 | 37 45 48 48 40 > 0.998 || = 0.41 511 513 473 494 469 | 500 < 0.003 48 54 47 44 49 | 50 | 50 49 57 42 53 > 0.997 || = 0.40 542 502 534 473 482 | 500 < 0.004 52 55 44 45 38 | 50 | 43 55 53 53 48 > 0.996 || = 0.39 531 486 480 478 492 | 500 < 0.005 48 55 49 55 52 | 50 | 62 42 42 48 40 > 0.995 || = 0.38 491 546 521 516 516 | 500 < 0.006 48 41 52 47 63 | 50 | 50 42 43 46 40 > 0.994 || = 0.37 493 510 568 499 526 | 500 < 0.007 59 55 40 46 40 | 50 | 54 50 52 68 58 > 0.993 || = 0.36 509 465 506 478 491 | 500 < 0.008 39 53 46 51 45 | 50 | 54 45 51 56 56 > 0.992 || = 0.35 529 475 513 475 470 | 500 < 0.009 52 51 56 45 49 | 50 | 54 52 54 57 38 > 0.991 || = 0.34 481 516 471 531 477 | 500 < 0.01 61 52 52 41 56 | 50 | 58 50 52 54 49 > 0.99 || = 0.33 454 504 498 523 478 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 494 553 556 520 503 | 500 < 0.01 500 505 477 456 478 | 497.5 | 506 471 502 510 483 > 0.99 || = 0.31 495 473 471 479 494 | 500 = 0.01 238 245 261 249 263 | 252.5 | 228 242 236 261 270 = 0.99 || = 0.30 506 515 482 509 523 | 500 = 0.02 536 489 502 477 482 | 500 | 521 493 483 494 525 = 0.98 || = 0.29 474 523 531 518 479 | 500 =================================================================| 500 | 498 529 493 528 514 = 0.97 || = 0.28 503 519 539 486 494 | 500 snpair_ClosePairs test: | 500 | 502 538 491 480 533 = 0.96 || = 0.27 484 475 482 483 529 | 500 ----------------------------------------------- | 500 | 486 535 525 507 470 = 0.95 || = 0.26 495 485 471 534 469 | 500 N = 20, n = 4000000, r = 0, t = 5, p = 0, m = 30, Torus = TRUE | 500 | 519 513 504 521 518 = 0.94 || = 0.25 487 489 482 528 469 | 500 Test on the jump times of Y | 500 | 479 487 507 490 536 = 0.93 || = 0.24 528 539 514 528 476 | 500 (superposition of Yn): | 500 | 497 517 509 485 477 = 0.92 || = 0.23 479 506 506 533 490 | 500 =================================================================| 500 | 459 493 448 502 520 = 0.91 || = 0.22 521 479 476 522 522 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 484 517 502 473 539 = 0.90 || = 0.21 502 526 499 511 548 | 500 -----------------------------------------------------------------| 500 | 511 494 528 475 480 = 0.89 || = 0.20 505 521 474 494 487 | 500 SD Bern.: d 0.89573 0.85832 1.01044 | 500 | 511 502 501 493 512 = 0.88 || = 0.19 523 481 486 469 494 | 500 s 0.97204 0.72007 0.76063 | 500 | 519 529 479 517 502 = 0.87 || = 0.18 537 498 495 514 516 | 500 t 0.99913 0.70886 0.63276 | 500 | 522 499 518 482 503 = 0.86 || = 0.17 514 471 483 509 489 | 500 m 0.96206 0.88133 1.15469 | 500 | 471 493 487 486 480 = 0.85 || = 0.16 512 480 472 481 488 | 500 x 0.92438 1.12127 1.16590 | 500 | 485 508 512 485 509 = 0.84 || = 0.15 504 476 490 481 485 | 500 | 500 | 513 540 477 493 540 = 0.83 || = 0.14 499 499 528 517 469 | 500 Changes: d 46 5 3 | 500 | 531 503 494 510 523 = 0.82 || = 0.13 460 487 522 488 548 | 500 s 41 3 4 | 500 | 506 511 503 526 490 = 0.81 || = 0.12 472 493 478 506 506 | 500 t 49 3 3 | 500 | 514 494 494 496 497 = 0.80 || = 0.11 494 480 493 487 504 | 500 m 47 4 3 | 500 | 517 484 531 492 500 = 0.79 || = 0.10 480 511 503 524 527 | 500 x 50 3 5 | 500 | 480 498 480 497 523 = 0.78 || = 0.09 513 543 507 510 505 | 500 -----------------------------------------------------------------| 500 | 508 514 501 444 511 = 0.77 || = 0.08 472 486 500 489 463 | 500 Aver./ d 0.50112 500 > 500: 3 5 5 4 8 2 6 6 7 4 | 500 | 481 487 530 470 493 = 0.76 || = 0.07 474 472 502 514 500 | 500 median s 0.50217 498 ----- 2 1 6 6 3 7 4 2 7 5 | 500 | 523 489 464 536 490 = 0.75 || = 0.06 490 488 534 502 520 | 500 t 0.50005 500 6 3 4 5 6 6 4 5 6 5 | 500 | 519 547 484 508 496 = 0.74 || = 0.05 487 468 502 488 495 | 500 m 0.49966 499 3 5 7 5 5 6 6 2 3 6 | 500 | 498 490 516 499 491 = 0.73 || = 0.04 497 474 470 492 486 | 500 x 0.50207 497 4 5 3 4 4 2 4 4 7 7 | 500 | 488 492 511 473 505 = 0.72 || = 0.03 458 495 489 472 506 | 500 -----------------------------------------------------------------| 500 | 531 463 491 486 522 = 0.71 || = 0.02 536 489 502 477 482 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 489 461 526 476 476 = 0.70 || = 0.01 238 245 261 249 263 | 252.5 d 0 0 1 11 75 14 0 0 0 | 500 | 525 459 521 527 544 = 0.69 || < 0.01 500 505 477 456 478 | 497.5 s 0 0 0 16 66 16 3 0 0 | 500 | 497 524 532 476 506 = 0.68 ||========================================================================= t 0 0 1 16 67 14 2 1 0 | 500 | 488 524 477 504 497 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 15 67 17 1 0 0 | 500 | 518 484 506 505 468 = 0.66 ||========================================================================= x 0 0 1 13 69 16 2 0 0 | 500 | 504 499 478 508 527 = 0.65 || snpair_ClosePairs test: no 32 test no 33 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 33 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 1 1 1 | 0.5 | 0 1 1 0 1 > 0.99999 || = 0.64 482 525 491 510 462 | 500 < 0.00002 1 1 0 0 1 | 0.5 | 2 1 0 0 1 > 0.99998 || = 0.63 519 528 504 498 516 | 500 < 0.00003 0 1 0 0 0 | 0.5 | 0 1 1 0 0 > 0.99997 || = 0.62 555 529 449 532 511 | 500 < 0.00004 2 0 1 1 0 | 0.5 | 1 1 1 0 1 > 0.99996 || = 0.61 509 498 501 500 518 | 500 < 0.00005 0 0 1 1 0 | 0.5 | 1 0 1 1 0 > 0.99995 || = 0.60 504 504 476 515 507 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 500 520 490 495 504 | 500 < 0.00007 0 2 0 0 0 | 0.5 | 0 0 2 1 0 > 0.99993 || = 0.58 493 502 504 526 478 | 500 < 0.00008 1 0 0 0 1 | 0.5 | 1 0 0 1 0 > 0.99992 || = 0.57 519 519 470 468 499 | 500 < 0.00009 0 2 1 2 2 | 0.5 | 0 0 0 0 1 > 0.99991 || = 0.56 485 526 467 500 475 | 500 < 0.0001 1 1 1 0 0 | 0.5 | 1 0 0 0 3 > 0.9999 || = 0.55 519 458 516 460 509 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 507 532 518 525 489 | 500 < 0.0001 5 8 5 5 5 | 5 | 6 4 6 3 7 > 0.9999 || = 0.53 511 507 515 505 495 | 500 < 0.0002 3 6 2 3 3 | 5 | 1 5 3 2 2 > 0.9998 || = 0.52 467 491 490 518 485 | 500 < 0.0003 4 5 6 2 2 | 5 | 3 4 5 2 7 > 0.9997 || = 0.51 508 512 504 537 493 | 500 < 0.0004 4 6 8 2 4 | 5 | 4 4 1 4 7 > 0.9996 || = 0.50 540 488 507 489 507 | 500 < 0.0005 5 5 4 9 5 | 5 | 2 4 3 3 8 > 0.9995 || = 0.49 470 483 494 519 518 | 500 < 0.0006 5 5 3 4 5 | 5 | 6 5 5 8 4 > 0.9994 || = 0.48 489 493 493 494 490 | 500 < 0.0007 1 6 6 7 2 | 5 | 6 4 4 4 3 > 0.9993 || = 0.47 504 533 539 488 520 | 500 < 0.0008 5 7 8 6 8 | 5 | 4 11 2 3 5 > 0.9992 || = 0.46 512 531 450 482 473 | 500 < 0.0009 7 3 6 3 6 | 5 | 4 5 6 3 2 > 0.9991 || = 0.45 474 513 520 497 497 | 500 < 0.001 4 8 10 7 5 | 5 | 3 3 3 6 7 > 0.999 || = 0.44 481 454 541 516 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 528 557 461 489 526 | 500 < 0.001 43 59 58 48 45 | 50 | 39 49 38 38 52 > 0.999 || = 0.42 525 527 493 488 504 | 500 < 0.002 44 51 52 50 42 | 50 | 59 49 58 58 39 > 0.998 || = 0.41 480 521 506 509 497 | 500 < 0.003 61 61 48 57 45 | 50 | 48 46 37 42 52 > 0.997 || = 0.40 519 523 548 518 500 | 500 < 0.004 46 55 48 49 45 | 50 | 55 73 56 43 46 > 0.996 || = 0.39 521 529 544 513 512 | 500 < 0.005 59 46 44 53 48 | 50 | 50 58 57 52 49 > 0.995 || = 0.38 522 493 508 527 503 | 500 < 0.006 45 42 44 50 61 | 50 | 53 38 50 36 55 > 0.994 || = 0.37 468 533 494 509 533 | 500 < 0.007 41 44 50 59 50 | 50 | 60 57 40 37 51 > 0.993 || = 0.36 500 507 513 486 477 | 500 < 0.008 63 57 45 45 55 | 50 | 46 51 51 37 55 > 0.992 || = 0.35 448 473 504 489 510 | 500 < 0.009 59 64 41 44 55 | 50 | 33 39 48 50 41 > 0.991 || = 0.34 486 468 473 523 537 | 500 < 0.01 48 66 44 49 50 | 50 | 58 50 53 55 37 > 0.99 || = 0.33 509 488 513 485 498 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 494 507 519 478 489 | 500 < 0.01 509 545 474 504 496 | 497.5 | 501 510 488 448 477 > 0.99 || = 0.31 527 503 571 512 524 | 500 = 0.01 267 248 270 251 280 | 252.5 | 247 227 244 229 236 = 0.99 || = 0.30 509 513 455 548 474 | 500 = 0.02 486 531 469 514 485 | 500 | 518 478 489 481 514 = 0.98 || = 0.29 474 512 519 467 556 | 500 =================================================================| 500 | 528 498 525 542 466 = 0.97 || = 0.28 454 477 543 516 542 | 500 snpair_ClosePairs test: | 500 | 514 542 483 444 483 = 0.96 || = 0.27 499 499 523 493 472 | 500 ----------------------------------------------- | 500 | 491 492 468 497 535 = 0.95 || = 0.26 506 498 518 435 524 | 500 N = 20, n = 4000000, r = 0, t = 5, p = 0, m = 30, Torus = TRUE | 500 | 492 479 481 475 451 = 0.94 || = 0.25 499 484 489 529 500 | 500 Test on the jump times of Y | 500 | 510 498 484 461 543 = 0.93 || = 0.24 480 505 473 545 479 | 500 (superposition of Yn): | 500 | 511 502 483 530 500 = 0.92 || = 0.23 455 475 486 508 486 | 500 =================================================================| 500 | 476 483 445 488 440 = 0.91 || = 0.22 513 526 474 473 467 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 529 496 516 493 472 = 0.90 || = 0.21 510 459 494 493 506 | 500 -----------------------------------------------------------------| 500 | 478 496 538 476 521 = 0.89 || = 0.20 486 464 509 518 494 | 500 SD Bern.: d 0.94635 1.15209 1.19138 | 500 | 514 502 505 487 502 = 0.88 || = 0.19 491 500 481 499 490 | 500 s 1.09406 1.30064 1.36155 | 500 | 527 477 517 497 495 = 0.87 || = 0.18 507 515 512 497 501 | 500 t 1.13850 0.76195 1.07383 | 500 | 489 489 480 491 479 = 0.86 || = 0.17 523 505 527 534 515 | 500 m 1.10329 0.64218 1.33031 | 500 | 514 522 522 492 517 = 0.85 || = 0.16 473 496 492 508 455 | 500 x 1.00028 0.79285 0.94598 | 500 | 496 468 484 478 513 = 0.84 || = 0.15 503 490 495 461 513 | 500 | 500 | 508 459 478 473 488 = 0.83 || = 0.14 518 513 504 536 494 | 500 Changes: d 54 6 7 | 500 | 496 472 512 502 466 = 0.82 || = 0.13 512 527 505 536 512 | 500 s 52 2 4 | 500 | 501 479 509 482 519 = 0.81 || = 0.12 485 506 485 513 485 | 500 t 50 1 7 | 500 | 517 499 535 506 466 = 0.80 || = 0.11 511 528 507 520 540 | 500 m 45 6 5 | 500 | 500 491 475 548 496 = 0.79 || = 0.10 533 495 517 526 494 | 500 x 58 4 5 | 500 | 540 515 494 514 496 = 0.78 || = 0.09 496 505 526 462 513 | 500 -----------------------------------------------------------------| 500 | 488 501 510 466 500 = 0.77 || = 0.08 521 485 505 488 516 | 500 Aver./ d 0.50037 502 > 500: 5 7 3 5 5 6 5 3 6 6 | 500 | 524 490 468 528 535 = 0.76 || = 0.07 521 542 482 480 488 | 500 median s 0.49804 499 ----- 5 6 3 6 7 8 5 4 2 3 | 500 | 474 523 473 507 518 = 0.75 || = 0.06 492 453 474 448 473 | 500 t 0.49942 504 5 6 5 7 5 5 7 3 7 1 | 500 | 478 452 521 512 499 = 0.74 || = 0.05 480 511 513 481 516 | 500 m 0.49762 498 4 7 5 6 4 6 6 6 1 2 | 500 | 476 488 485 479 523 = 0.73 || = 0.04 540 471 507 537 468 | 500 x 0.49886 500 5 5 4 6 4 3 6 5 5 3 | 500 | 479 417 472 497 544 = 0.72 || = 0.03 471 483 436 516 523 | 500 -----------------------------------------------------------------| 500 | 471 505 494 483 513 = 0.71 || = 0.02 486 531 469 514 485 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 488 492 549 514 499 = 0.70 || = 0.01 267 248 270 251 280 | 252.5 d 0 0 3 13 72 12 1 0 0 | 500 | 507 484 529 504 508 = 0.69 || < 0.01 509 545 474 504 496 | 497.5 s 0 1 3 13 63 18 3 0 0 | 500 | 502 548 492 533 494 = 0.68 ||========================================================================= t 0 0 5 15 64 13 3 1 0 | 500 | 484 485 554 469 478 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 13 64 17 3 0 0 | 500 | 464 515 515 498 504 = 0.66 ||========================================================================= x 0 0 3 14 69 14 1 0 0 | 500 | 469 490 533 540 512 = 0.65 || snpair_ClosePairs test: no 33 test no 34 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 34 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 489 467 475 501 518 | 500 < 0.00002 0 0 0 2 0 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 524 486 508 507 463 | 500 < 0.00003 1 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 527 489 543 537 512 | 500 < 0.00004 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 497 482 502 515 501 | 500 < 0.00005 0 3 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 479 468 514 520 453 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 510 527 556 496 471 | 500 < 0.00007 1 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99993 || = 0.58 444 531 478 473 515 | 500 < 0.00008 1 0 0 1 0 | 0.5 | 1 0 0 0 1 > 0.99992 || = 0.57 509 470 493 516 492 | 500 < 0.00009 0 1 0 1 1 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 487 470 553 512 485 | 500 < 0.0001 0 0 1 1 1 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 519 479 501 519 524 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 498 505 531 482 491 | 500 < 0.0001 4 6 1 8 5 | 5 | 2 0 1 1 1 > 0.9999 || = 0.53 489 538 518 513 512 | 500 < 0.0002 3 3 4 8 1 | 5 | 0 2 2 1 1 > 0.9998 || = 0.52 463 522 488 498 466 | 500 < 0.0003 6 4 6 5 6 | 5 | 3 2 3 2 1 > 0.9997 || = 0.51 494 518 480 467 483 | 500 < 0.0004 0 4 3 9 7 | 5 | 2 4 3 3 1 > 0.9996 || = 0.50 485 511 450 487 526 | 500 < 0.0005 3 6 7 4 4 | 5 | 4 3 3 5 8 > 0.9995 || = 0.49 487 474 519 552 521 | 500 < 0.0006 4 5 6 4 4 | 5 | 1 3 3 5 3 > 0.9994 || = 0.48 498 458 542 498 555 | 500 < 0.0007 5 9 4 7 6 | 5 | 1 4 5 5 4 > 0.9993 || = 0.47 510 480 504 484 484 | 500 < 0.0008 4 5 6 7 7 | 5 | 2 3 2 7 3 > 0.9992 || = 0.46 501 501 535 502 488 | 500 < 0.0009 2 8 3 6 5 | 5 | 2 6 2 2 5 > 0.9991 || = 0.45 487 485 465 474 493 | 500 < 0.001 7 4 4 9 7 | 5 | 2 4 1 4 3 > 0.999 || = 0.44 462 499 484 508 524 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 457 524 529 527 511 | 500 < 0.001 38 54 44 67 52 | 50 | 19 31 25 35 30 > 0.999 || = 0.42 503 528 490 492 513 | 500 < 0.002 54 48 46 38 40 | 50 | 35 36 40 36 48 > 0.998 || = 0.41 520 515 491 500 524 | 500 < 0.003 51 50 48 38 45 | 50 | 52 41 62 37 53 > 0.997 || = 0.40 505 536 519 495 505 | 500 < 0.004 44 44 34 41 52 | 50 | 51 46 53 39 41 > 0.996 || = 0.39 541 521 501 474 489 | 500 < 0.005 53 51 53 32 56 | 50 | 46 46 57 59 46 > 0.995 || = 0.38 476 488 499 463 476 | 500 < 0.006 56 47 55 57 50 | 50 | 44 54 63 50 50 > 0.994 || = 0.37 535 507 468 505 534 | 500 < 0.007 51 50 48 57 55 | 50 | 50 43 50 59 55 > 0.993 || = 0.36 473 511 481 537 533 | 500 < 0.008 44 42 40 52 59 | 50 | 42 51 46 46 46 > 0.992 || = 0.35 494 503 465 509 499 | 500 < 0.009 55 65 42 48 44 | 50 | 52 57 49 56 51 > 0.991 || = 0.34 498 485 498 433 533 | 500 < 0.01 43 46 58 58 54 | 50 | 73 56 41 65 47 > 0.99 || = 0.33 524 525 517 465 534 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 509 478 540 538 475 | 500 < 0.01 489 497 468 488 507 | 497.5 | 464 461 486 482 467 > 0.99 || = 0.31 514 445 506 483 538 | 500 = 0.01 226 265 270 241 254 | 252.5 | 233 269 256 274 247 = 0.99 || = 0.30 536 468 490 502 492 | 500 = 0.02 519 462 482 454 442 | 500 | 528 561 531 489 529 = 0.98 || = 0.29 529 500 500 472 513 | 500 =================================================================| 500 | 503 515 505 508 512 = 0.97 || = 0.28 521 518 493 460 502 | 500 snpair_ClosePairs test: | 500 | 497 474 510 504 507 = 0.96 || = 0.27 509 485 472 461 491 | 500 ----------------------------------------------- | 500 | 471 514 505 514 521 = 0.95 || = 0.26 465 491 530 479 496 | 500 N = 10, n = 3000000, r = 0, t = 9, p = 0, m = 30, Torus = TRUE | 500 | 498 499 508 481 479 = 0.94 || = 0.25 512 508 487 515 531 | 500 Test based on the 2 nearest points (NP): | 500 | 535 529 480 531 490 = 0.93 || = 0.24 471 509 495 456 497 | 500 | 500 | 484 478 531 492 502 = 0.92 || = 0.23 501 491 517 462 464 | 500 =================================================================| 500 | 513 489 433 504 524 = 0.91 || = 0.22 501 517 536 522 520 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 468 493 467 515 481 = 0.90 || = 0.21 546 516 520 493 480 | 500 -----------------------------------------------------------------| 500 | 506 462 501 515 490 = 0.89 || = 0.20 524 528 507 524 467 | 500 SD Bern.: d 1.02481 0.84065 1.91928 | 500 | 515 525 504 483 538 = 0.88 || = 0.19 489 482 500 546 473 | 500 s 1.10334 0.86181 1.28203 | 500 | 479 542 477 492 489 = 0.87 || = 0.18 490 507 501 534 492 | 500 t 1.05449 1.07570 1.54608 | 500 | 524 475 491 492 530 = 0.86 || = 0.17 473 498 478 514 460 | 500 m 1.08740 1.51865 1.51732 | 500 | 512 498 511 487 460 = 0.85 || = 0.16 511 487 499 483 467 | 500 x 1.01500 0.80909 1.05976 | 500 | 461 527 505 453 506 = 0.84 || = 0.15 502 535 531 538 489 | 500 | 500 | 523 452 465 536 490 = 0.83 || = 0.14 561 524 501 546 527 | 500 Changes: d 50 6 3 | 500 | 490 509 491 526 503 = 0.82 || = 0.13 493 535 511 502 508 | 500 s 46 5 3 | 500 | 465 504 515 506 512 = 0.81 || = 0.12 514 495 513 498 513 | 500 t 44 3 2 | 500 | 527 523 515 485 523 = 0.80 || = 0.11 521 497 540 528 501 | 500 m 46 4 5 | 500 | 548 475 491 495 462 = 0.79 || = 0.10 501 491 479 463 518 | 500 x 47 6 6 | 500 | 495 491 456 495 491 = 0.78 || = 0.09 528 548 466 492 492 | 500 -----------------------------------------------------------------| 500 | 490 471 484 489 498 = 0.77 || = 0.08 491 549 499 512 508 | 500 Aver./ d 0.49825 501 > 500: 4 6 8 6 5 3 5 5 5 4 | 500 | 506 459 497 517 486 = 0.76 || = 0.07 496 506 467 520 522 | 500 median s 0.49796 499 ----- 7 4 6 5 5 6 1 3 5 5 | 500 | 509 490 511 449 500 = 0.75 || = 0.06 516 503 522 521 531 | 500 t 0.49943 501 4 6 5 4 6 6 5 4 5 7 | 500 | 468 511 497 490 510 = 0.74 || = 0.05 481 525 509 502 519 | 500 m 0.50059 502 5 7 3 5 4 5 8 4 5 6 | 500 | 481 487 508 516 531 = 0.73 || = 0.04 515 464 507 514 502 | 500 x 0.49960 501 7 5 4 5 7 3 5 4 5 6 | 500 | 519 492 490 524 521 = 0.72 || = 0.03 497 538 469 484 498 | 500 -----------------------------------------------------------------| 500 | 492 528 527 516 472 = 0.71 || = 0.02 519 462 482 454 442 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 463 467 464 482 479 = 0.70 || = 0.01 226 265 270 241 254 | 252.5 d 0 0 1 18 65 14 3 0 0 | 500 | 520 498 498 523 505 = 0.69 || < 0.01 489 497 468 488 507 | 497.5 s 0 0 2 18 58 20 3 0 0 | 500 | 506 493 512 468 502 = 0.68 ||========================================================================= t 0 1 1 15 67 15 2 0 0 | 500 | 507 490 482 527 490 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 3 13 66 15 3 0 0 | 500 | 465 462 466 518 458 = 0.66 ||========================================================================= x 0 0 2 15 65 18 1 0 0 | 500 | 499 522 528 514 478 = 0.65 || snpair_ClosePairs test: no 34 test no 35 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 35 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 2 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 514 559 516 491 501 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 497 525 488 477 501 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99997 || = 0.62 516 489 523 524 443 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 482 475 497 472 492 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 497 522 521 536 521 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 512 516 489 525 495 | 500 < 0.00007 0 1 1 1 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 469 500 474 520 502 | 500 < 0.00008 0 1 1 1 1 | 0.5 | 0 0 1 0 0 > 0.99992 || = 0.57 522 512 500 521 524 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99991 || = 0.56 526 488 525 471 493 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 481 567 468 494 516 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 531 498 497 503 516 | 500 < 0.0001 0 2 2 7 4 | 5 | 0 0 3 0 0 > 0.9999 || = 0.53 511 516 520 480 509 | 500 < 0.0002 4 2 6 4 2 | 5 | 1 4 2 1 4 > 0.9998 || = 0.52 512 515 477 467 501 | 500 < 0.0003 6 6 0 8 5 | 5 | 4 1 2 1 2 > 0.9997 || = 0.51 489 487 524 520 519 | 500 < 0.0004 5 5 4 8 5 | 5 | 4 4 1 1 1 > 0.9996 || = 0.50 524 483 535 480 475 | 500 < 0.0005 5 5 4 6 3 | 5 | 6 6 3 4 4 > 0.9995 || = 0.49 501 483 483 490 511 | 500 < 0.0006 6 4 9 6 4 | 5 | 2 4 3 4 4 > 0.9994 || = 0.48 506 503 524 488 514 | 500 < 0.0007 7 7 4 3 8 | 5 | 5 5 2 2 6 > 0.9993 || = 0.47 488 507 488 546 458 | 500 < 0.0008 3 3 3 2 5 | 5 | 4 7 6 6 2 > 0.9992 || = 0.46 513 483 484 496 465 | 500 < 0.0009 7 5 6 4 8 | 5 | 6 6 8 2 3 > 0.9991 || = 0.45 483 474 492 477 481 | 500 < 0.001 5 3 3 5 7 | 5 | 3 3 6 2 4 > 0.999 || = 0.44 526 483 508 535 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 480 507 544 511 543 | 500 < 0.001 48 42 41 53 51 | 50 | 35 40 36 23 30 > 0.999 || = 0.42 454 480 500 517 510 | 500 < 0.002 45 60 37 51 58 | 50 | 48 54 28 30 43 > 0.998 || = 0.41 482 527 496 503 511 | 500 < 0.003 51 61 47 43 39 | 50 | 38 46 46 50 50 > 0.997 || = 0.40 516 509 488 526 504 | 500 < 0.004 61 41 47 45 45 | 50 | 43 44 48 43 45 > 0.996 || = 0.39 502 468 526 539 531 | 500 < 0.005 55 55 41 49 47 | 50 | 49 48 53 46 49 > 0.995 || = 0.38 516 491 486 470 496 | 500 < 0.006 41 54 53 36 57 | 50 | 48 43 40 53 45 > 0.994 || = 0.37 466 535 493 501 510 | 500 < 0.007 43 55 40 53 35 | 50 | 49 63 53 51 49 > 0.993 || = 0.36 478 513 523 535 503 | 500 < 0.008 41 48 57 42 38 | 50 | 46 49 37 50 50 > 0.992 || = 0.35 501 513 495 500 517 | 500 < 0.009 64 48 73 48 61 | 50 | 49 51 36 57 36 > 0.991 || = 0.34 502 493 514 495 496 | 500 < 0.01 42 42 51 66 44 | 50 | 62 54 54 50 59 > 0.99 || = 0.33 501 446 497 470 503 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 474 503 534 468 537 | 500 < 0.01 491 506 487 486 475 | 497.5 | 467 492 431 453 456 > 0.99 || = 0.31 522 506 517 507 520 | 500 = 0.01 245 238 240 242 251 | 252.5 | 252 255 254 268 263 = 0.99 || = 0.30 493 477 498 472 491 | 500 = 0.02 497 509 464 516 493 | 500 | 495 545 537 507 490 = 0.98 || = 0.29 486 484 530 498 524 | 500 =================================================================| 500 | 551 515 499 535 528 = 0.97 || = 0.28 487 523 498 534 461 | 500 snpair_ClosePairs test: | 500 | 504 527 491 509 496 = 0.96 || = 0.27 488 488 512 514 475 | 500 ----------------------------------------------- | 500 | 485 474 512 489 504 = 0.95 || = 0.26 517 536 503 492 495 | 500 N = 10, n = 3000000, r = 0, t = 9, p = 0, m = 30, Torus = TRUE | 500 | 521 549 495 438 515 = 0.94 || = 0.25 510 502 496 525 478 | 500 A2 test based on the spacings between the | 500 | 530 533 481 506 530 = 0.93 || = 0.24 509 478 472 528 477 | 500 successive jump times of process Y_n(t): | 500 | 496 465 491 516 487 = 0.92 || = 0.23 500 497 517 532 473 | 500 =================================================================| 500 | 506 512 486 529 476 = 0.91 || = 0.22 463 529 492 468 488 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 484 476 496 497 493 = 0.90 || = 0.21 507 498 527 527 514 | 500 -----------------------------------------------------------------| 500 | 509 478 543 513 520 = 0.89 || = 0.20 527 489 530 466 492 | 500 SD Bern.: d 0.90987 1.13810 1.08589 | 500 | 481 464 504 508 468 = 0.88 || = 0.19 485 476 499 491 472 | 500 s 1.04182 1.00448 0.90376 | 500 | 515 484 514 505 511 = 0.87 || = 0.18 499 516 462 500 455 | 500 t 0.96076 1.44085 1.54931 | 500 | 489 466 493 493 506 = 0.86 || = 0.17 485 474 521 494 484 | 500 m 1.06148 1.10870 1.58382 | 500 | 514 467 471 462 462 = 0.85 || = 0.16 475 491 508 509 520 | 500 x 0.97281 1.26157 1.24801 | 500 | 517 504 534 479 533 = 0.84 || = 0.15 523 505 491 538 535 | 500 | 500 | 478 536 465 501 511 = 0.83 || = 0.14 483 534 474 502 469 | 500 Changes: d 50 4 1 | 500 | 499 465 505 502 508 = 0.82 || = 0.13 486 508 521 483 460 | 500 s 55 4 5 | 500 | 467 489 483 506 482 = 0.81 || = 0.12 523 485 498 500 524 | 500 t 58 3 5 | 500 | 473 498 472 497 510 = 0.80 || = 0.11 515 509 471 490 524 | 500 m 44 4 4 | 500 | 481 528 513 457 524 = 0.79 || = 0.10 462 501 496 457 503 | 500 x 48 5 1 | 500 | 507 532 525 499 481 = 0.78 || = 0.09 504 472 486 578 475 | 500 -----------------------------------------------------------------| 500 | 540 487 461 514 491 = 0.77 || = 0.08 518 505 504 503 500 | 500 Aver./ d 0.49954 501 > 500: 7 3 5 6 5 6 5 4 4 5 | 500 | 489 494 509 490 537 = 0.76 || = 0.07 504 513 517 502 513 | 500 median s 0.50019 501 ----- 6 6 4 5 5 6 6 5 2 7 | 500 | 475 506 500 476 525 = 0.75 || = 0.06 555 482 471 486 552 | 500 t 0.49991 498 4 3 6 5 3 4 5 4 5 3 | 500 | 511 454 493 478 503 = 0.74 || = 0.05 507 532 504 503 493 | 500 m 0.49854 501 6 3 6 4 6 6 6 2 6 7 | 500 | 501 512 496 489 470 = 0.73 || = 0.04 522 475 503 517 498 | 500 x 0.50066 503 3 5 2 7 7 8 6 6 6 5 | 500 | 485 521 538 467 488 = 0.72 || = 0.03 534 512 487 493 507 | 500 -----------------------------------------------------------------| 500 | 500 464 462 502 510 = 0.71 || = 0.02 497 509 464 516 493 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 492 468 481 509 493 = 0.70 || = 0.01 245 238 240 242 251 | 252.5 d 0 0 1 11 76 11 2 0 0 | 500 | 538 503 480 508 512 = 0.69 || < 0.01 491 506 487 486 475 | 497.5 s 0 0 2 17 65 13 3 1 0 | 500 | 510 515 505 505 503 = 0.68 ||========================================================================= t 0 0 1 14 68 17 1 0 0 | 500 | 502 503 494 517 482 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 16 64 16 1 1 0 | 500 | 456 498 512 452 519 = 0.66 ||========================================================================= x 0 0 2 17 67 14 1 0 0 | 500 | 486 501 549 523 514 = 0.65 || snpair_ClosePairs test: no 35 test no 36 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 36 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 0 2 | 0.5 | 0 1 1 0 3 > 0.99999 || = 0.64 461 505 516 488 495 | 500 < 0.00002 1 0 0 0 0 | 0.5 | 0 1 1 0 0 > 0.99998 || = 0.63 533 511 506 505 527 | 500 < 0.00003 2 2 0 0 1 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 493 499 523 501 494 | 500 < 0.00004 2 0 0 0 0 | 0.5 | 1 1 0 1 1 > 0.99996 || = 0.61 497 462 511 502 496 | 500 < 0.00005 0 0 0 2 0 | 0.5 | 1 1 0 0 0 > 0.99995 || = 0.60 521 472 512 522 474 | 500 < 0.00006 2 0 2 0 0 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 474 536 502 481 479 | 500 < 0.00007 0 0 1 0 1 | 0.5 | 0 1 0 0 1 > 0.99993 || = 0.58 515 528 515 481 517 | 500 < 0.00008 3 2 0 4 1 | 0.5 | 0 1 0 1 0 > 0.99992 || = 0.57 481 520 446 495 516 | 500 < 0.00009 0 0 1 0 1 | 0.5 | 1 0 0 1 2 > 0.99991 || = 0.56 518 508 514 518 520 | 500 < 0.0001 2 1 0 1 0 | 0.5 | 1 0 2 1 1 > 0.9999 || = 0.55 504 514 520 495 474 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 501 506 499 490 529 | 500 < 0.0001 13 5 4 7 6 | 5 | 4 6 5 5 8 > 0.9999 || = 0.53 526 489 510 526 509 | 500 < 0.0002 7 5 5 6 1 | 5 | 3 4 2 2 5 > 0.9998 || = 0.52 485 497 492 468 473 | 500 < 0.0003 1 6 3 1 3 | 5 | 3 5 4 3 5 > 0.9997 || = 0.51 522 503 501 481 480 | 500 < 0.0004 2 5 5 5 10 | 5 | 4 3 4 7 5 > 0.9996 || = 0.50 493 490 525 457 502 | 500 < 0.0005 5 8 6 7 4 | 5 | 6 5 5 5 7 > 0.9995 || = 0.49 530 470 490 496 530 | 500 < 0.0006 3 9 2 3 5 | 5 | 6 5 1 8 5 > 0.9994 || = 0.48 503 512 483 504 473 | 500 < 0.0007 4 9 8 8 3 | 5 | 5 7 5 4 6 > 0.9993 || = 0.47 524 498 455 520 478 | 500 < 0.0008 4 6 6 6 5 | 5 | 6 5 3 4 2 > 0.9992 || = 0.46 538 508 492 522 498 | 500 < 0.0009 8 6 5 4 2 | 5 | 7 2 3 4 5 > 0.9991 || = 0.45 552 461 463 549 474 | 500 < 0.001 3 5 5 2 4 | 5 | 5 2 4 9 3 > 0.999 || = 0.44 483 511 541 557 461 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 520 497 521 499 497 | 500 < 0.001 50 64 49 49 43 | 50 | 49 44 36 51 51 > 0.999 || = 0.42 485 516 493 485 526 | 500 < 0.002 49 51 47 48 46 | 50 | 43 60 65 42 56 > 0.998 || = 0.41 547 527 430 499 497 | 500 < 0.003 44 45 48 67 37 | 50 | 48 39 43 45 44 > 0.997 || = 0.40 460 504 532 502 486 | 500 < 0.004 58 48 61 57 30 | 50 | 46 58 29 47 47 > 0.996 || = 0.39 507 527 504 525 510 | 500 < 0.005 55 45 42 48 44 | 50 | 53 51 52 53 48 > 0.995 || = 0.38 493 481 496 513 486 | 500 < 0.006 48 47 49 44 50 | 50 | 39 56 51 62 56 > 0.994 || = 0.37 502 514 494 500 489 | 500 < 0.007 60 59 44 55 51 | 50 | 35 53 50 51 59 > 0.993 || = 0.36 528 521 501 519 536 | 500 < 0.008 56 38 50 46 44 | 50 | 47 48 46 64 47 > 0.992 || = 0.35 513 487 430 495 525 | 500 < 0.009 47 45 41 57 44 | 50 | 47 52 60 47 36 > 0.991 || = 0.34 490 480 511 506 537 | 500 < 0.01 52 60 50 51 50 | 50 | 58 62 44 46 55 > 0.99 || = 0.33 497 504 459 520 533 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 478 487 478 492 546 | 500 < 0.01 519 502 481 522 439 | 497.5 | 465 523 476 508 499 > 0.99 || = 0.31 470 527 544 483 472 | 500 = 0.01 255 249 241 262 259 | 252.5 | 265 268 244 251 238 = 0.99 || = 0.30 488 496 512 504 473 | 500 = 0.02 507 480 492 479 520 | 500 | 477 517 482 466 525 = 0.98 || = 0.29 528 460 515 493 507 | 500 =================================================================| 500 | 507 529 520 520 533 = 0.97 || = 0.28 432 508 490 510 499 | 500 snpair_ClosePairs test: | 500 | 526 481 527 493 452 = 0.96 || = 0.27 525 486 494 491 503 | 500 ----------------------------------------------- | 500 | 512 499 487 502 512 = 0.95 || = 0.26 527 519 526 461 526 | 500 N = 10, n = 3000000, r = 0, t = 9, p = 0, m = 30, Torus = TRUE | 500 | 501 461 528 526 518 = 0.94 || = 0.25 449 468 457 518 472 | 500 A2 test based on the spacings between the | 500 | 477 489 484 476 518 = 0.93 || = 0.24 478 515 493 520 454 | 500 successive jump times of process Y_n(t): | 500 | 477 531 502 524 542 = 0.92 || = 0.23 507 533 519 467 498 | 500 =================================================================| 500 | 456 469 465 488 495 = 0.91 || = 0.22 473 481 481 497 486 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 503 508 537 453 495 = 0.90 || = 0.21 448 462 515 489 505 | 500 -----------------------------------------------------------------| 500 | 539 509 489 539 495 = 0.89 || = 0.20 498 524 528 449 515 | 500 SD Bern.: d 1.06453 0.74736 1.00747 | 500 | 503 475 501 488 508 = 0.88 || = 0.19 492 476 510 503 506 | 500 s 1.00269 1.10508 1.01932 | 500 | 509 536 460 507 490 = 0.87 || = 0.18 520 510 479 475 508 | 500 t 1.05261 0.79663 1.46223 | 500 | 525 482 474 508 456 = 0.86 || = 0.17 521 501 483 542 531 | 500 m 0.96990 0.97413 0.97413 | 500 | 494 472 510 517 472 = 0.85 || = 0.16 476 492 506 520 527 | 500 x 1.05368 1.21962 0.93104 | 500 | 532 508 522 554 496 = 0.84 || = 0.15 467 480 500 492 511 | 500 | 500 | 508 475 489 504 484 = 0.83 || = 0.14 483 452 487 507 497 | 500 Changes: d 49 5 3 | 500 | 529 497 463 546 495 = 0.82 || = 0.13 489 492 495 482 516 | 500 s 56 4 5 | 500 | 513 520 517 479 499 = 0.81 || = 0.12 443 536 464 495 520 | 500 t 56 2 6 | 500 | 504 478 497 481 498 = 0.80 || = 0.11 475 491 507 502 542 | 500 m 48 5 3 | 500 | 531 510 525 518 491 = 0.79 || = 0.10 515 534 539 502 498 | 500 x 39 2 4 | 500 | 485 506 505 503 487 = 0.78 || = 0.09 477 498 511 510 511 | 500 -----------------------------------------------------------------| 500 | 520 506 529 503 470 = 0.77 || = 0.08 490 515 532 506 508 | 500 Aver./ d 0.50262 503 > 500: 5 3 4 4 7 7 4 7 9 5 | 500 | 504 511 491 488 466 = 0.76 || = 0.07 501 490 491 524 520 | 500 median s 0.50125 503 ----- 3 4 5 5 6 7 6 6 5 5 | 500 | 520 473 520 502 489 = 0.75 || = 0.06 464 469 516 470 505 | 500 t 0.49990 501 4 4 5 5 3 7 7 6 5 4 | 500 | 488 517 495 501 501 = 0.74 || = 0.05 500 472 557 496 519 | 500 m 0.50040 501 6 6 3 6 6 3 4 6 7 5 | 500 | 491 565 522 504 498 = 0.73 || = 0.04 510 479 495 510 551 | 500 x 0.49751 498 8 8 5 6 2 5 2 2 1 7 | 500 | 514 491 513 462 463 = 0.72 || = 0.03 498 538 500 468 477 | 500 -----------------------------------------------------------------| 500 | 526 470 493 497 525 = 0.71 || = 0.02 507 480 492 479 520 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 488 492 508 492 496 = 0.70 || = 0.01 255 249 241 262 259 | 252.5 d 0 1 3 16 63 16 2 0 0 | 500 | 496 509 500 486 460 = 0.69 || < 0.01 519 502 481 522 439 | 497.5 s 0 0 1 18 65 16 1 0 0 | 500 | 477 532 523 461 480 = 0.68 ||========================================================================= t 0 2 2 8 73 15 1 0 0 | 500 | 512 525 488 484 495 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 11 75 9 4 0 0 | 500 | 518 517 509 480 470 = 0.66 ||========================================================================= x 0 0 3 17 62 16 3 0 0 | 500 | 509 469 480 527 547 = 0.65 || snpair_ClosePairs test: no 36 test no 37 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 37 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 1 1 0 0 1 > 0.99999 || = 0.64 1117 1102 1057 1081 1037 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 0 0 0 0 0 | 500 < 0.00003 1 0 1 0 1 | 0.5 | 0 3 0 0 1 > 0.99997 || = 0.62 1086 1092 1144 1107 1056 | 500 < 0.00004 0 0 1 0 0 | 0.5 | 2 0 0 0 0 > 0.99996 || = 0.61 0 0 0 0 0 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 0 1 0 1 0 > 0.99995 || = 0.60 1153 1094 1152 1116 1144 | 500 < 0.00006 0 1 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99994 || = 0.59 0 0 0 0 0 | 500 < 0.00007 0 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 1155 1175 1076 1133 1137 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 1 0 1 0 1 > 0.99992 || = 0.57 0 0 0 0 0 | 500 < 0.00009 0 1 3 0 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 0 0 0 0 0 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 3 1 0 1 1 > 0.9999 || = 0.55 1120 1099 1145 1161 1142 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 0 0 0 0 0 | 500 < 0.0001 1 3 6 2 4 | 5 | 7 7 1 2 4 > 0.9999 || = 0.53 1156 1165 1108 1171 1075 | 500 < 0.0002 9 10 2 2 4 | 5 | 1 1 2 1 1 > 0.9998 || = 0.52 0 0 0 0 0 | 500 < 0.0003 2 6 3 11 9 | 5 | 5 8 5 5 9 > 0.9997 || = 0.51 2335 2320 2281 2296 2347 | 500 < 0.0004 5 5 9 3 6 | 5 | 2 3 2 5 3 > 0.9996 || = 0.50 0 0 0 0 0 | 500 < 0.0005 3 4 5 4 7 | 5 | 1 2 5 6 3 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 6 5 7 2 3 | 5 | 3 2 4 7 2 > 0.9994 || = 0.48 1156 1133 1127 1139 1199 | 500 < 0.0007 7 4 9 7 6 | 5 | 6 6 4 8 6 > 0.9993 || = 0.47 0 0 0 0 0 | 500 < 0.0008 7 5 4 9 6 | 5 | 12 8 7 14 11 > 0.9992 || = 0.46 1108 1099 1081 1122 1202 | 500 < 0.0009 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9991 || = 0.45 0 0 0 0 0 | 500 < 0.001 11 12 10 7 7 | 5 | 11 11 6 10 8 > 0.999 || = 0.44 1164 1090 1095 1087 1101 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 0 0 0 0 0 | 500 < 0.001 51 54 55 47 52 | 50 | 48 48 36 58 47 > 0.999 || = 0.42 1168 1113 1082 1101 1059 | 500 < 0.002 52 36 40 47 54 | 50 | 26 32 44 46 23 > 0.998 || = 0.41 0 0 0 0 0 | 500 < 0.003 48 32 40 36 39 | 50 | 26 48 38 42 42 > 0.997 || = 0.40 0 0 0 0 0 | 500 < 0.004 44 50 51 61 49 | 50 | 57 68 60 44 66 > 0.996 || = 0.39 1087 1080 1109 1062 1075 | 500 < 0.005 26 36 23 31 26 | 50 | 39 36 38 37 37 > 0.995 || = 0.38 0 0 0 0 0 | 500 < 0.006 76 74 77 78 78 | 50 | 50 37 37 55 30 > 0.994 || = 0.37 1092 1088 1017 1072 1043 | 500 < 0.007 45 46 45 47 52 | 50 | 55 38 54 55 50 > 0.993 || = 0.36 0 0 0 0 0 | 500 < 0.008 0 0 0 0 0 | 50 | 52 44 42 46 59 > 0.992 || = 0.35 1063 1104 1020 1046 1036 | 500 < 0.009 60 47 59 69 59 | 50 | 67 59 67 58 56 > 0.991 || = 0.34 0 0 0 0 0 | 500 < 0.01 61 83 68 68 62 | 50 | 0 0 0 0 0 > 0.99 || = 0.33 1039 960 982 986 1047 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 0 0 0 0 0 | 500 < 0.01 463 458 458 484 471 | 497.5 | 420 410 416 441 410 > 0.99 || = 0.31 941 1007 1001 1018 998 | 500 = 0.01 253 235 243 280 272 | 252.5 | 267 253 278 279 270 = 0.99 || = 0.30 0 0 0 0 0 | 500 = 0.02 523 508 507 523 558 | 500 | 552 561 561 526 566 = 0.98 || = 0.29 959 984 969 1003 942 | 500 =================================================================| 500 | 384 407 366 358 401 = 0.97 || = 0.28 0 0 0 0 0 | 500 snpair_ClosePairs test: | 500 | 463 495 482 468 518 = 0.96 || = 0.27 968 954 996 941 946 | 500 ----------------------------------------------- | 500 | 582 588 618 593 585 = 0.95 || = 0.26 0 0 0 0 0 | 500 N = 10, n = 3000000, r = 0, t = 9, p = 0, m = 30, Torus = TRUE | 500 | 338 318 328 333 327 = 0.94 || = 0.25 914 897 880 941 846 | 500 Test on the jump times of Y | 500 | 385 399 365 383 378 = 0.93 || = 0.24 0 0 0 0 0 | 500 (superposition of Yn): | 500 | 413 417 385 413 403 = 0.92 || = 0.23 886 893 830 897 887 | 500 =================================================================| 500 | 445 460 437 457 425 = 0.91 || = 0.22 810 832 842 770 810 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 541 507 539 462 501 = 0.90 || = 0.21 0 0 0 0 0 | 500 -----------------------------------------------------------------| 500 | 502 492 558 525 553 = 0.89 || = 0.20 820 787 785 758 776 | 500 SD Bern.: d 20.25721 2.84501 2.88032 | 500 | 528 557 593 570 580 = 0.88 || = 0.19 0 0 0 0 0 | 500 s 20.20334 3.13908 2.75164 | 500 | 610 598 607 632 608 = 0.87 || = 0.18 696 753 754 729 731 | 500 t 20.05418 3.03928 2.70615 | 500 | 663 620 687 632 633 = 0.86 || = 0.17 694 711 720 651 680 | 500 m 20.16851 3.05898 2.44211 | 500 | 0 0 0 0 0 = 0.85 || = 0.16 625 619 686 672 692 | 500 x 20.13111 2.91040 2.91486 | 500 | 703 653 633 677 721 = 0.84 || = 0.15 0 0 0 0 0 | 500 | 500 | 761 721 749 718 698 = 0.83 || = 0.14 643 626 622 649 628 | 500 Changes: d 73 4 4 | 500 | 0 0 0 0 0 = 0.82 || = 0.13 563 566 629 555 562 | 500 s 75 4 4 | 500 | 716 730 777 702 761 = 0.81 || = 0.12 553 553 560 552 521 | 500 t 72 6 6 | 500 | 801 821 855 832 785 = 0.80 || = 0.11 517 495 489 524 509 | 500 m 72 5 5 | 500 | 0 0 0 0 0 = 0.79 || = 0.10 473 474 489 423 501 | 500 x 72 4 4 | 500 | 787 853 833 805 810 = 0.78 || = 0.09 446 434 445 433 449 | 500 -----------------------------------------------------------------| 500 | 0 0 0 0 0 = 0.77 || = 0.08 410 400 373 421 413 | 500 Aver./ d 0.49886 502 > 500: 4 7 6 5 4 5 4 6 8 3 | 500 | 844 910 888 904 898 = 0.76 || = 0.07 384 366 365 362 402 | 500 median s 0.49918 495 ----- 3 6 6 5 4 5 4 6 7 3 | 500 | 0 0 0 0 0 = 0.75 || = 0.06 606 635 634 677 637 | 500 t 0.50038 489 3 6 6 5 4 5 4 6 8 3 | 500 | 915 906 988 913 881 = 0.74 || = 0.05 506 541 526 559 523 | 500 m 0.49829 523 4 7 6 5 4 5 4 6 7 3 | 500 | 971 972 931 967 914 = 0.73 || = 0.04 432 455 441 440 432 | 500 x 0.49836 518 4 8 6 5 4 5 4 6 8 4 | 500 | 0 0 0 0 0 = 0.72 || = 0.03 353 371 372 359 394 | 500 -----------------------------------------------------------------| 500 | 961 962 995 1012 1037 = 0.71 || = 0.02 523 508 507 523 558 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 0 0 0 0 0 = 0.70 || = 0.01 253 235 243 280 272 | 252.5 d 41 3 2 3 5 3 3 1 40 | 500 | 983 1061 986 995 1009 = 0.69 || < 0.01 463 458 458 484 471 | 497.5 s 41 2 2 4 6 1 4 1 40 | 500 | 0 0 0 0 0 = 0.68 ||========================================================================= t 42 1 3 1 5 3 3 0 43 | 500 | 0 0 0 0 0 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 40 4 2 3 1 6 3 1 41 | 500 | 1028 1061 1053 1102 1048 = 0.66 ||========================================================================= x 41 4 1 1 5 3 4 2 40 | 500 | 0 0 0 0 0 = 0.65 || snpair_ClosePairs test: no 37 test no 38 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 38 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 2 2 0 0 > 0.99999 || = 0.64 513 499 484 524 510 | 500 < 0.00002 1 0 1 0 0 | 0.5 | 0 1 0 1 3 > 0.99998 || = 0.63 495 498 522 509 548 | 500 < 0.00003 0 1 1 0 0 | 0.5 | 0 0 1 0 1 > 0.99997 || = 0.62 502 530 487 490 462 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 1 1 1 1 1 > 0.99996 || = 0.61 507 498 458 496 456 | 500 < 0.00005 2 0 2 2 0 | 0.5 | 2 0 0 0 2 > 0.99995 || = 0.60 521 529 502 463 508 | 500 < 0.00006 0 1 1 1 0 | 0.5 | 0 1 0 2 0 > 0.99994 || = 0.59 467 524 513 459 463 | 500 < 0.00007 1 1 0 0 1 | 0.5 | 1 0 0 1 1 > 0.99993 || = 0.58 488 506 529 486 471 | 500 < 0.00008 2 1 0 2 1 | 0.5 | 1 0 0 0 2 > 0.99992 || = 0.57 485 482 502 495 529 | 500 < 0.00009 1 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 506 502 485 498 504 | 500 < 0.0001 0 1 0 1 0 | 0.5 | 1 2 1 0 0 > 0.9999 || = 0.55 502 482 535 486 515 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 472 517 498 466 527 | 500 < 0.0001 7 5 5 6 3 | 5 | 6 7 5 5 10 > 0.9999 || = 0.53 501 539 497 473 521 | 500 < 0.0002 2 3 3 7 2 | 5 | 3 5 3 3 3 > 0.9998 || = 0.52 513 512 489 529 492 | 500 < 0.0003 2 7 7 7 5 | 5 | 6 6 5 2 4 > 0.9997 || = 0.51 510 504 499 519 524 | 500 < 0.0004 10 5 5 1 6 | 5 | 10 1 1 0 3 > 0.9996 || = 0.50 468 525 480 484 494 | 500 < 0.0005 3 6 6 8 6 | 5 | 7 9 3 10 7 > 0.9995 || = 0.49 492 482 512 501 486 | 500 < 0.0006 9 6 7 7 6 | 5 | 7 4 1 6 4 > 0.9994 || = 0.48 488 503 485 528 508 | 500 < 0.0007 4 4 1 3 4 | 5 | 7 5 3 3 0 > 0.9993 || = 0.47 478 495 519 489 502 | 500 < 0.0008 11 5 5 5 4 | 5 | 4 4 6 6 2 > 0.9992 || = 0.46 505 511 466 473 472 | 500 < 0.0009 11 7 3 5 5 | 5 | 1 8 4 9 4 > 0.9991 || = 0.45 520 492 470 473 484 | 500 < 0.001 5 5 4 5 4 | 5 | 6 3 6 3 5 > 0.999 || = 0.44 509 532 497 485 473 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 493 451 542 496 503 | 500 < 0.001 64 53 46 54 45 | 50 | 57 52 37 47 42 > 0.999 || = 0.42 474 502 511 484 507 | 500 < 0.002 49 42 54 50 49 | 50 | 52 54 42 55 38 > 0.998 || = 0.41 496 515 497 514 522 | 500 < 0.003 44 56 63 57 45 | 50 | 49 49 46 43 54 > 0.997 || = 0.40 491 470 509 525 480 | 500 < 0.004 42 58 54 45 51 | 50 | 57 40 49 56 48 > 0.996 || = 0.39 538 504 484 486 506 | 500 < 0.005 48 42 54 52 44 | 50 | 49 52 55 53 48 > 0.995 || = 0.38 490 505 482 480 509 | 500 < 0.006 42 55 44 53 46 | 50 | 53 43 48 52 49 > 0.994 || = 0.37 550 521 495 513 517 | 500 < 0.007 56 62 52 47 52 | 50 | 45 48 64 51 50 > 0.993 || = 0.36 521 517 467 496 467 | 500 < 0.008 69 53 45 52 37 | 50 | 45 62 51 49 37 > 0.992 || = 0.35 515 476 497 485 513 | 500 < 0.009 44 41 48 44 43 | 50 | 49 44 50 52 48 > 0.991 || = 0.34 525 500 482 516 502 | 500 < 0.01 48 46 49 62 48 | 50 | 67 40 49 59 70 > 0.99 || = 0.33 504 507 480 500 544 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 520 506 492 491 497 | 500 < 0.01 506 508 509 516 460 | 497.5 | 523 484 491 517 484 > 0.99 || = 0.31 528 457 481 483 467 | 500 = 0.01 232 263 272 256 231 | 252.5 | 238 223 270 257 255 = 0.99 || = 0.30 551 496 492 499 546 | 500 = 0.02 493 470 496 507 486 | 500 | 485 492 510 513 465 = 0.98 || = 0.29 484 506 500 519 477 | 500 =================================================================| 500 | 584 518 526 503 513 = 0.97 || = 0.28 483 518 506 518 520 | 500 snpair_ClosePairs test: | 500 | 477 493 533 526 461 = 0.96 || = 0.27 548 504 569 515 512 | 500 ----------------------------------------------- | 500 | 468 494 461 480 502 = 0.95 || = 0.26 493 484 556 511 486 | 500 N = 10, n = 3000000, r = 0, t = 9, p = 0, m = 30, Torus = TRUE | 500 | 469 498 482 469 506 = 0.94 || = 0.25 512 519 476 495 512 | 500 Test on the jump times of Y | 500 | 547 485 526 535 488 = 0.93 || = 0.24 478 510 513 535 497 | 500 (superposition of Yn): | 500 | 482 525 500 535 531 = 0.92 || = 0.23 477 523 511 496 504 | 500 =================================================================| 500 | 486 478 512 490 493 = 0.91 || = 0.22 521 517 492 526 490 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 484 475 501 540 486 = 0.90 || = 0.21 514 527 513 491 539 | 500 -----------------------------------------------------------------| 500 | 501 498 501 496 505 = 0.89 || = 0.20 513 491 538 512 494 | 500 SD Bern.: d 1.00566 1.26711 0.95230 | 500 | 494 521 500 511 534 = 0.88 || = 0.19 564 492 530 522 516 | 500 s 0.91266 1.01243 0.95754 | 500 | 498 500 499 484 470 = 0.87 || = 0.18 510 496 525 538 475 | 500 t 1.09637 0.77884 0.97720 | 500 | 519 493 431 525 509 = 0.86 || = 0.17 499 509 525 505 519 | 500 m 0.93091 0.76979 0.66213 | 500 | 521 499 471 497 491 = 0.85 || = 0.16 458 490 519 520 510 | 500 x 1.02639 0.81280 1.27027 | 500 | 511 498 540 504 497 = 0.84 || = 0.15 534 482 457 467 520 | 500 | 500 | 504 475 502 560 502 = 0.83 || = 0.14 503 472 467 512 496 | 500 Changes: d 46 3 6 | 500 | 496 515 448 517 496 = 0.82 || = 0.13 478 556 497 508 490 | 500 s 49 5 5 | 500 | 506 495 506 463 482 = 0.81 || = 0.12 511 496 535 490 546 | 500 t 45 4 4 | 500 | 482 457 523 503 556 = 0.80 || = 0.11 479 498 505 482 494 | 500 m 44 8 5 | 500 | 477 525 474 507 479 = 0.79 || = 0.10 481 464 480 454 479 | 500 x 58 4 3 | 500 | 494 557 511 501 469 = 0.78 || = 0.09 498 464 492 493 467 | 500 -----------------------------------------------------------------| 500 | 517 525 478 505 463 = 0.77 || = 0.08 483 525 512 492 541 | 500 Aver./ d 0.49913 498 > 500: 3 5 5 9 3 6 4 2 6 3 | 500 | 482 511 460 503 521 = 0.76 || = 0.07 499 467 497 500 498 | 500 median s 0.50013 498 ----- 4 2 8 6 5 8 3 5 2 2 | 500 | 493 487 500 484 503 = 0.75 || = 0.06 509 512 522 468 528 | 500 t 0.49849 500 6 6 7 0 5 5 4 4 5 6 | 500 | 487 489 476 513 485 = 0.74 || = 0.05 483 497 468 506 498 | 500 m 0.50157 500 4 6 7 2 4 2 5 7 6 7 | 500 | 502 493 498 484 484 = 0.73 || = 0.04 516 496 502 447 494 | 500 x 0.49921 499 2 5 5 7 5 7 6 4 4 5 | 500 | 493 506 535 516 521 = 0.72 || = 0.03 481 477 521 491 495 | 500 -----------------------------------------------------------------| 500 | 482 481 520 471 498 = 0.71 || = 0.02 493 470 496 507 486 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 483 522 506 528 536 = 0.70 || = 0.01 232 263 272 256 231 | 252.5 d 0 0 0 13 77 5 5 1 0 | 500 | 498 498 462 494 464 = 0.69 || < 0.01 506 508 509 516 460 | 497.5 s 0 0 1 13 73 12 2 0 0 | 500 | 474 482 545 476 499 = 0.68 ||========================================================================= t 0 1 1 15 65 16 2 1 0 | 500 | 468 483 512 492 532 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 12 73 13 1 0 0 | 500 | 515 510 463 504 514 = 0.66 ||========================================================================= x 0 0 0 19 67 11 4 0 0 | 500 | 482 493 482 511 503 = 0.65 || snpair_ClosePairs test: no 38 test no 39 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 39 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 1 0 | 0.5 | 1 0 1 0 0 > 0.99999 || = 0.64 489 552 515 467 475 | 500 < 0.00002 0 1 1 0 0 | 0.5 | 0 1 0 0 1 > 0.99998 || = 0.63 526 506 504 516 510 | 500 < 0.00003 0 1 0 0 1 | 0.5 | 1 1 0 1 0 > 0.99997 || = 0.62 483 519 500 514 477 | 500 < 0.00004 2 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 471 544 501 510 501 | 500 < 0.00005 1 2 1 0 0 | 0.5 | 2 0 2 0 0 > 0.99995 || = 0.60 492 509 503 500 474 | 500 < 0.00006 0 0 1 1 0 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 497 546 522 541 519 | 500 < 0.00007 0 0 1 1 0 | 0.5 | 0 0 0 0 2 > 0.99993 || = 0.58 489 531 487 508 473 | 500 < 0.00008 1 0 0 0 0 | 0.5 | 1 1 0 0 1 > 0.99992 || = 0.57 524 530 479 485 488 | 500 < 0.00009 0 1 1 0 1 | 0.5 | 1 0 0 0 2 > 0.99991 || = 0.56 453 479 476 492 507 | 500 < 0.0001 0 0 1 0 0 | 0.5 | 0 0 1 0 1 > 0.9999 || = 0.55 478 487 487 482 520 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 482 490 499 482 512 | 500 < 0.0001 5 7 7 3 2 | 5 | 7 3 4 1 7 > 0.9999 || = 0.53 538 529 531 543 501 | 500 < 0.0002 4 7 4 5 1 | 5 | 2 2 1 3 1 > 0.9998 || = 0.52 442 479 499 510 503 | 500 < 0.0003 3 2 5 6 6 | 5 | 4 6 2 6 4 > 0.9997 || = 0.51 479 481 510 504 492 | 500 < 0.0004 4 7 4 5 3 | 5 | 4 6 5 11 3 > 0.9996 || = 0.50 516 529 503 539 523 | 500 < 0.0005 8 7 2 10 2 | 5 | 4 5 7 4 6 > 0.9995 || = 0.49 534 475 509 446 519 | 500 < 0.0006 5 9 10 4 6 | 5 | 5 6 3 7 4 > 0.9994 || = 0.48 506 486 500 464 526 | 500 < 0.0007 6 1 2 6 2 | 5 | 5 5 5 7 3 > 0.9993 || = 0.47 523 468 464 489 502 | 500 < 0.0008 3 8 6 2 2 | 5 | 7 5 7 3 5 > 0.9992 || = 0.46 481 465 469 502 494 | 500 < 0.0009 6 4 3 4 2 | 5 | 4 5 4 2 2 > 0.9991 || = 0.45 522 527 495 485 470 | 500 < 0.001 6 7 4 4 12 | 5 | 5 4 10 6 12 > 0.999 || = 0.44 510 496 485 512 474 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 502 493 479 493 537 | 500 < 0.001 50 59 47 49 38 | 50 | 47 47 48 50 47 > 0.999 || = 0.42 506 495 521 523 475 | 500 < 0.002 40 43 42 39 45 | 50 | 50 51 40 52 55 > 0.998 || = 0.41 530 504 494 476 505 | 500 < 0.003 62 56 52 50 49 | 50 | 45 45 48 45 73 > 0.997 || = 0.40 503 493 512 495 496 | 500 < 0.004 44 39 59 51 52 | 50 | 54 44 46 52 39 > 0.996 || = 0.39 489 532 491 481 500 | 500 < 0.005 45 48 60 49 45 | 50 | 44 42 56 46 44 > 0.995 || = 0.38 511 512 477 481 506 | 500 < 0.006 48 48 54 54 52 | 50 | 45 39 55 56 39 > 0.994 || = 0.37 478 499 480 454 491 | 500 < 0.007 36 52 45 41 49 | 50 | 49 56 57 53 54 > 0.993 || = 0.36 522 481 524 476 469 | 500 < 0.008 59 61 55 46 45 | 50 | 53 45 47 39 47 > 0.992 || = 0.35 493 453 511 511 491 | 500 < 0.009 52 66 57 41 42 | 50 | 44 48 47 48 59 > 0.991 || = 0.34 489 531 500 498 495 | 500 < 0.01 56 50 49 43 50 | 50 | 43 42 57 58 44 > 0.99 || = 0.33 476 490 499 555 509 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 510 495 481 485 516 | 500 < 0.01 492 522 520 463 467 | 497.5 | 474 459 501 499 501 > 0.99 || = 0.31 539 471 530 508 505 | 500 = 0.01 285 227 253 224 268 | 252.5 | 255 261 258 279 242 = 0.99 || = 0.30 526 509 491 477 495 | 500 = 0.02 468 498 504 496 506 | 500 | 518 534 517 497 502 = 0.98 || = 0.29 488 492 499 514 476 | 500 =================================================================| 500 | 521 503 518 508 513 = 0.97 || = 0.28 504 525 466 508 495 | 500 snpair_ClosePairs test: | 500 | 513 486 505 517 517 = 0.96 || = 0.27 496 476 532 462 498 | 500 ----------------------------------------------- | 500 | 484 508 469 484 539 = 0.95 || = 0.26 491 523 515 495 517 | 500 N = 10, n = 3000000, r = 0, t = 9, p = 0, m = 30, Torus = TRUE | 500 | 529 504 545 446 489 = 0.94 || = 0.25 503 524 482 508 522 | 500 Test on the jump times of Y | 500 | 495 530 520 558 469 = 0.93 || = 0.24 487 481 515 527 518 | 500 (superposition of Yn): | 500 | 509 526 492 513 479 = 0.92 || = 0.23 495 503 524 517 484 | 500 =================================================================| 500 | 513 525 504 537 503 = 0.91 || = 0.22 493 493 509 498 475 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 507 456 508 497 531 = 0.90 || = 0.21 514 493 442 489 471 | 500 -----------------------------------------------------------------| 500 | 533 481 513 525 498 = 0.89 || = 0.20 529 516 481 504 493 | 500 SD Bern.: d 0.94563 1.11948 0.64218 | 500 | 497 527 529 512 493 = 0.88 || = 0.19 526 508 528 504 515 | 500 s 1.09720 1.16333 0.87792 | 500 | 492 485 487 495 476 = 0.87 || = 0.18 520 529 522 487 506 | 500 t 0.87095 0.86529 0.77626 | 500 | 495 519 492 480 505 = 0.86 || = 0.17 512 512 477 473 491 | 500 m 1.06077 0.85715 0.75269 | 500 | 511 448 521 478 468 = 0.85 || = 0.16 495 436 486 504 528 | 500 x 0.84105 0.76588 1.40283 | 500 | 478 498 511 520 527 = 0.84 || = 0.15 515 536 520 529 479 | 500 | 500 | 492 532 475 523 534 = 0.83 || = 0.14 522 487 510 459 518 | 500 Changes: d 50 3 4 | 500 | 444 456 467 528 481 = 0.82 || = 0.13 497 499 456 545 469 | 500 s 51 5 4 | 500 | 465 513 505 487 468 = 0.81 || = 0.12 528 511 522 544 516 | 500 t 46 4 3 | 500 | 479 448 520 499 507 = 0.80 || = 0.11 468 499 503 498 459 | 500 m 53 4 7 | 500 | 479 459 458 506 525 = 0.79 || = 0.10 503 497 499 515 507 | 500 x 47 4 6 | 500 | 521 494 481 495 485 = 0.78 || = 0.09 521 519 493 462 516 | 500 -----------------------------------------------------------------| 500 | 497 478 470 518 513 = 0.77 || = 0.08 491 496 512 500 520 | 500 Aver./ d 0.49919 497 > 500: 4 7 4 5 9 2 5 3 3 7 | 500 | 529 493 489 490 520 = 0.76 || = 0.07 516 485 521 462 518 | 500 median s 0.50005 499 ----- 4 5 5 4 2 5 8 2 4 8 | 500 | 495 483 501 504 499 = 0.75 || = 0.06 507 506 495 519 515 | 500 t 0.50024 501 7 6 5 3 3 4 6 4 6 8 | 500 | 477 480 518 531 523 = 0.74 || = 0.05 490 487 522 502 519 | 500 m 0.50224 500 3 6 6 3 3 5 6 5 5 7 | 500 | 477 494 510 486 501 = 0.73 || = 0.04 471 462 503 475 509 | 500 x 0.49984 502 9 6 3 4 5 6 3 7 4 6 | 500 | 510 505 496 482 521 = 0.72 || = 0.03 469 524 476 505 503 | 500 -----------------------------------------------------------------| 500 | 490 538 498 533 490 = 0.71 || = 0.02 468 498 504 496 506 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 502 515 483 521 492 = 0.70 || = 0.01 285 227 253 224 268 | 252.5 d 0 0 3 11 71 15 1 0 0 | 500 | 476 480 487 501 512 = 0.69 || < 0.01 492 522 520 463 467 | 497.5 s 0 0 4 11 61 23 2 0 0 | 500 | 510 502 534 489 499 = 0.68 ||========================================================================= t 0 0 1 13 77 9 1 0 0 | 500 | 529 531 504 498 484 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 67 14 3 0 0 | 500 | 512 508 491 471 476 = 0.66 ||========================================================================= x 0 0 0 19 72 10 0 0 0 | 500 | 487 489 508 501 490 = 0.65 || snpair_ClosePairs test: no 39 test no 40 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 40 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 469 473 490 493 466 | 500 < 0.00002 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 494 534 486 475 534 | 500 < 0.00003 1 2 0 0 2 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 558 504 479 508 508 | 500 < 0.00004 0 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 493 451 462 510 480 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 470 504 475 472 476 | 500 < 0.00006 1 0 1 0 2 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 520 479 512 513 525 | 500 < 0.00007 0 0 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 512 471 512 504 454 | 500 < 0.00008 1 2 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 480 473 518 505 505 | 500 < 0.00009 0 0 0 2 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 497 530 513 508 503 | 500 < 0.0001 1 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 459 495 485 488 462 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 480 487 475 479 500 | 500 < 0.0001 5 6 1 6 6 | 5 | 0 0 0 0 0 > 0.9999 || = 0.53 546 460 515 480 547 | 500 < 0.0002 6 6 3 3 4 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 503 500 477 493 506 | 500 < 0.0003 4 8 4 5 8 | 5 | 0 0 0 0 0 > 0.9997 || = 0.51 490 507 527 482 522 | 500 < 0.0004 7 6 7 2 4 | 5 | 0 0 0 0 0 > 0.9996 || = 0.50 500 499 498 501 489 | 500 < 0.0005 8 4 3 8 5 | 5 | 0 0 0 0 0 > 0.9995 || = 0.49 511 505 499 484 462 | 500 < 0.0006 6 7 6 5 3 | 5 | 0 1 0 1 0 > 0.9994 || = 0.48 494 504 515 530 479 | 500 < 0.0007 4 2 4 7 6 | 5 | 2 0 0 1 2 > 0.9993 || = 0.47 519 508 498 522 506 | 500 < 0.0008 9 7 4 10 7 | 5 | 1 0 0 0 0 > 0.9992 || = 0.46 509 495 497 537 470 | 500 < 0.0009 5 5 4 2 6 | 5 | 2 2 0 2 0 > 0.9991 || = 0.45 455 479 476 516 475 | 500 < 0.001 6 7 6 6 4 | 5 | 1 3 3 3 4 > 0.999 || = 0.44 516 478 458 534 477 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 500 547 469 480 490 | 500 < 0.001 60 58 42 54 53 | 50 | 6 6 3 7 6 > 0.999 || = 0.42 511 539 472 491 507 | 500 < 0.002 46 56 46 53 52 | 50 | 36 35 26 27 26 > 0.998 || = 0.41 522 506 552 533 552 | 500 < 0.003 68 55 69 50 65 | 50 | 29 38 33 31 28 > 0.997 || = 0.40 434 470 483 479 486 | 500 < 0.004 51 43 47 50 56 | 50 | 57 48 31 40 31 > 0.996 || = 0.39 472 529 521 496 474 | 500 < 0.005 47 48 48 38 45 | 50 | 50 40 45 48 37 > 0.995 || = 0.38 506 465 477 465 523 | 500 < 0.006 47 52 44 41 44 | 50 | 41 36 50 47 36 > 0.994 || = 0.37 530 511 511 493 453 | 500 < 0.007 40 46 47 50 53 | 50 | 42 43 41 48 43 > 0.993 || = 0.36 504 465 556 502 523 | 500 < 0.008 55 44 35 55 44 | 50 | 40 45 51 37 43 > 0.992 || = 0.35 495 474 515 517 501 | 500 < 0.009 45 52 48 55 47 | 50 | 42 39 54 50 45 > 0.991 || = 0.34 517 513 502 496 487 | 500 < 0.01 45 61 50 54 50 | 50 | 45 49 53 57 47 > 0.99 || = 0.33 482 510 498 488 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 502 492 476 504 500 | 500 < 0.01 504 515 476 500 509 | 497.5 | 388 379 387 392 342 > 0.99 || = 0.31 521 508 528 509 510 | 500 = 0.01 266 273 268 241 282 | 252.5 | 258 261 264 245 282 = 0.99 || = 0.30 484 507 501 534 544 | 500 = 0.02 430 515 504 545 516 | 500 | 541 543 581 542 544 = 0.98 || = 0.29 505 491 491 507 508 | 500 =================================================================| 500 | 551 505 511 511 521 = 0.97 || = 0.28 473 486 504 478 456 | 500 snpair_ClosePairs test: | 500 | 519 475 496 527 531 = 0.96 || = 0.27 544 515 512 555 469 | 500 ----------------------------------------------- | 500 | 482 522 450 510 523 = 0.95 || = 0.26 550 468 477 489 495 | 500 N = 5, n = 2000000, r = 0, t = 16, p = 0, m = 30, Torus = TRUE | 500 | 488 502 498 517 465 = 0.94 || = 0.25 507 510 472 513 510 | 500 Test based on the 2 nearest points (NP): | 500 | 528 526 522 534 566 = 0.93 || = 0.24 488 481 529 488 475 | 500 | 500 | 543 556 503 492 531 = 0.92 || = 0.23 478 527 489 477 503 | 500 =================================================================| 500 | 506 525 497 526 546 = 0.91 || = 0.22 535 513 509 490 468 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 511 519 523 487 535 = 0.90 || = 0.21 521 494 516 475 475 | 500 -----------------------------------------------------------------| 500 | 509 492 510 494 527 = 0.89 || = 0.20 496 500 485 516 504 | 500 SD Bern.: d 1.25599 1.12661 2.43267 | 500 | 522 480 485 491 538 = 0.88 || = 0.19 496 493 482 519 488 | 500 s 1.17958 0.84776 2.36803 | 500 | 497 501 499 520 456 = 0.87 || = 0.18 527 513 456 456 482 | 500 t 1.17634 1.20724 2.67228 | 500 | 514 474 492 470 512 = 0.86 || = 0.17 489 467 462 481 477 | 500 m 1.06906 0.79538 2.48075 | 500 | 495 506 459 504 463 = 0.85 || = 0.16 525 484 538 495 479 | 500 x 1.37230 0.88247 2.77771 | 500 | 510 577 488 479 508 = 0.84 || = 0.15 508 503 492 493 520 | 500 | 500 | 508 501 512 491 519 = 0.83 || = 0.14 483 476 513 534 515 | 500 Changes: d 59 5 2 | 500 | 465 515 520 523 557 = 0.82 || = 0.13 504 501 516 511 501 | 500 s 55 4 0 | 500 | 503 476 504 485 455 = 0.81 || = 0.12 522 449 514 465 537 | 500 t 46 2 1 | 500 | 476 534 492 489 513 = 0.80 || = 0.11 464 509 517 492 488 | 500 m 45 2 1 | 500 | 470 521 474 455 522 = 0.79 || = 0.10 536 533 531 498 478 | 500 x 45 3 0 | 500 | 533 514 518 508 508 = 0.78 || = 0.09 513 494 534 488 506 | 500 -----------------------------------------------------------------| 500 | 486 488 516 518 514 = 0.77 || = 0.08 500 503 520 481 502 | 500 Aver./ d 0.50035 503 > 500: 5 6 6 6 6 4 3 4 7 7 | 500 | 496 487 524 485 481 = 0.76 || = 0.07 503 477 493 488 513 | 500 median s 0.50160 503 ----- 5 5 4 6 6 3 7 6 6 8 | 500 | 503 517 499 519 496 = 0.75 || = 0.06 493 519 481 488 512 | 500 t 0.49914 502 6 6 5 7 2 6 4 6 5 5 | 500 | 476 543 539 509 510 = 0.74 || = 0.05 531 469 504 514 495 | 500 m 0.50067 498 4 3 4 5 6 4 7 6 3 7 | 500 | 465 505 513 493 528 = 0.73 || = 0.04 434 477 511 446 520 | 500 x 0.50074 504 9 4 4 5 3 6 4 6 7 8 | 500 | 511 469 473 523 493 = 0.72 || = 0.03 468 497 492 525 540 | 500 -----------------------------------------------------------------| 500 | 517 488 531 533 480 = 0.71 || = 0.02 430 515 504 545 516 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 455 506 514 512 504 = 0.70 || = 0.01 266 273 268 241 282 | 252.5 d 1 1 4 12 67 11 5 0 0 | 500 | 480 513 505 510 489 = 0.69 || < 0.01 504 515 476 500 509 | 497.5 s 1 0 2 18 64 13 2 1 0 | 500 | 505 522 484 518 487 = 0.68 ||========================================================================= t 1 0 2 17 66 12 2 1 0 | 500 | 493 513 524 470 473 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 1 0 2 9 72 15 2 0 0 | 500 | 557 486 537 535 514 = 0.66 ||========================================================================= x 1 0 3 19 56 17 5 0 0 | 500 | 491 535 440 514 461 = 0.65 || snpair_ClosePairs test: no 40 test no 41 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 41 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 1 2 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 508 520 528 509 513 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 478 498 483 510 514 | 500 < 0.00003 1 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 548 476 516 508 509 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 459 538 488 495 494 | 500 < 0.00005 1 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 495 469 498 517 495 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 468 473 493 498 491 | 500 < 0.00007 0 2 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 482 471 504 476 486 | 500 < 0.00008 0 0 0 2 2 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 478 518 480 466 515 | 500 < 0.00009 1 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 506 493 497 492 474 | 500 < 0.0001 0 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 468 526 508 484 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 531 519 499 498 555 | 500 < 0.0001 3 6 3 5 5 | 5 | 0 0 0 0 0 > 0.9999 || = 0.53 517 509 499 571 514 | 500 < 0.0002 6 4 4 6 1 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 456 483 507 473 482 | 500 < 0.0003 3 1 5 3 3 | 5 | 0 0 0 0 0 > 0.9997 || = 0.51 478 484 511 507 460 | 500 < 0.0004 9 5 7 7 5 | 5 | 0 0 0 0 0 > 0.9996 || = 0.50 552 464 487 479 447 | 500 < 0.0005 2 1 4 4 5 | 5 | 0 0 0 0 0 > 0.9995 || = 0.49 518 478 465 472 518 | 500 < 0.0006 5 6 2 3 6 | 5 | 0 0 0 1 0 > 0.9994 || = 0.48 445 537 510 503 500 | 500 < 0.0007 7 3 1 7 3 | 5 | 0 2 0 0 0 > 0.9993 || = 0.47 512 498 521 502 447 | 500 < 0.0008 6 7 5 3 9 | 5 | 0 0 2 0 0 > 0.9992 || = 0.46 511 504 539 504 510 | 500 < 0.0009 4 2 2 4 0 | 5 | 0 1 5 1 0 > 0.9991 || = 0.45 515 495 502 482 504 | 500 < 0.001 2 3 6 3 3 | 5 | 1 1 2 6 3 > 0.999 || = 0.44 465 473 524 470 542 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 523 500 472 513 448 | 500 < 0.001 47 38 39 45 40 | 50 | 1 4 9 8 3 > 0.999 || = 0.42 479 493 498 498 514 | 500 < 0.002 40 47 47 49 34 | 50 | 32 36 29 29 28 > 0.998 || = 0.41 497 497 486 500 508 | 500 < 0.003 54 37 65 62 56 | 50 | 38 37 42 41 33 > 0.997 || = 0.40 490 512 479 492 502 | 500 < 0.004 59 47 60 40 51 | 50 | 41 45 37 41 33 > 0.996 || = 0.39 539 509 511 500 458 | 500 < 0.005 42 55 44 41 50 | 50 | 42 43 41 56 43 > 0.995 || = 0.38 467 506 505 524 503 | 500 < 0.006 63 62 37 46 50 | 50 | 49 43 37 54 52 > 0.994 || = 0.37 473 466 534 511 485 | 500 < 0.007 56 53 62 39 58 | 50 | 46 48 52 42 58 > 0.993 || = 0.36 499 513 478 510 502 | 500 < 0.008 51 50 50 37 55 | 50 | 46 45 39 45 39 > 0.992 || = 0.35 510 496 495 497 490 | 500 < 0.009 40 52 49 48 52 | 50 | 39 37 48 50 46 > 0.991 || = 0.34 494 496 500 546 487 | 500 < 0.01 50 50 48 47 55 | 50 | 60 54 46 61 53 > 0.99 || = 0.33 500 510 536 525 502 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 499 496 484 525 480 | 500 < 0.01 502 491 501 454 501 | 497.5 | 394 392 380 427 388 > 0.99 || = 0.31 477 495 494 506 524 | 500 = 0.01 243 261 272 225 288 | 252.5 | 207 252 250 240 248 = 0.99 || = 0.30 485 505 494 485 522 | 500 = 0.02 523 506 467 514 486 | 500 | 501 538 560 550 499 = 0.98 || = 0.29 481 485 510 498 535 | 500 =================================================================| 500 | 504 513 515 506 536 = 0.97 || = 0.28 502 494 488 497 469 | 500 snpair_ClosePairs test: | 500 | 496 510 516 511 519 = 0.96 || = 0.27 500 475 504 533 491 | 500 ----------------------------------------------- | 500 | 509 505 485 480 539 = 0.95 || = 0.26 497 541 483 480 510 | 500 N = 5, n = 2000000, r = 0, t = 16, p = 0, m = 30, Torus = TRUE | 500 | 497 491 510 473 499 = 0.94 || = 0.25 462 501 521 478 495 | 500 A2 test based on the spacings between the | 500 | 529 477 514 499 521 = 0.93 || = 0.24 489 499 478 473 494 | 500 successive jump times of process Y_n(t): | 500 | 495 501 534 470 501 = 0.92 || = 0.23 475 453 478 482 513 | 500 =================================================================| 500 | 514 481 496 500 477 = 0.91 || = 0.22 530 483 491 512 472 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 504 511 484 485 473 = 0.90 || = 0.21 507 468 503 531 475 | 500 -----------------------------------------------------------------| 500 | 507 529 490 515 559 = 0.89 || = 0.20 520 521 503 523 531 | 500 SD Bern.: d 1.15392 1.07384 2.55783 | 500 | 534 511 516 519 470 = 0.88 || = 0.19 527 531 460 499 453 | 500 s 1.13689 1.01341 2.37520 | 500 | 515 553 510 478 477 = 0.87 || = 0.18 518 501 474 536 503 | 500 t 1.09662 1.27263 2.34637 | 500 | 539 500 525 476 506 = 0.86 || = 0.17 526 511 505 505 516 | 500 m 1.01519 1.15815 2.29417 | 500 | 542 511 494 497 485 = 0.85 || = 0.16 483 461 521 531 505 | 500 x 1.18151 1.01143 2.65989 | 500 | 501 482 530 514 507 = 0.84 || = 0.15 529 488 510 510 481 | 500 | 500 | 508 478 486 510 516 = 0.83 || = 0.14 492 524 496 505 497 | 500 Changes: d 49 4 1 | 500 | 470 482 520 486 444 = 0.82 || = 0.13 509 481 504 480 498 | 500 s 50 4 1 | 500 | 497 496 456 528 512 = 0.81 || = 0.12 478 542 511 491 523 | 500 t 51 4 2 | 500 | 474 534 484 484 515 = 0.80 || = 0.11 508 489 502 459 501 | 500 m 44 2 3 | 500 | 473 548 555 502 527 = 0.79 || = 0.10 498 535 483 503 498 | 500 x 51 3 3 | 500 | 504 491 520 521 523 = 0.78 || = 0.09 481 521 486 503 508 | 500 -----------------------------------------------------------------| 500 | 473 527 443 513 543 = 0.77 || = 0.08 517 560 515 538 507 | 500 Aver./ d 0.49958 500 > 500: 5 6 4 2 5 3 7 4 8 5 | 500 | 487 476 483 512 508 = 0.76 || = 0.07 489 538 477 468 478 | 500 median s 0.49963 498 ----- 5 6 3 5 3 4 4 7 5 5 | 500 | 493 515 511 513 469 = 0.75 || = 0.06 527 497 487 535 487 | 500 t 0.50127 500 5 6 5 4 5 4 6 4 5 6 | 500 | 551 508 483 484 532 = 0.74 || = 0.05 507 459 476 507 544 | 500 m 0.49895 500 6 6 4 7 4 3 6 6 5 3 | 500 | 523 536 497 488 512 = 0.73 || = 0.04 492 492 511 490 493 | 500 x 0.49990 502 6 5 4 5 7 4 6 8 5 5 | 500 | 496 526 498 514 507 = 0.72 || = 0.03 499 484 503 507 519 | 500 -----------------------------------------------------------------| 500 | 542 448 553 471 495 = 0.71 || = 0.02 523 506 467 514 486 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 507 485 533 500 474 = 0.70 || = 0.01 243 261 272 225 288 | 252.5 d 1 0 2 14 63 18 3 0 0 | 500 | 479 522 464 519 486 = 0.69 || < 0.01 502 491 501 454 501 | 497.5 s 1 0 2 14 66 15 3 0 0 | 500 | 508 498 512 480 489 = 0.68 ||========================================================================= t 1 0 1 9 76 10 4 0 0 | 500 | 526 478 485 517 526 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 0 15 70 12 2 1 0 | 500 | 536 509 518 467 517 = 0.66 ||========================================================================= x 1 0 5 12 66 14 3 0 0 | 500 | 532 474 545 536 531 = 0.65 || snpair_ClosePairs test: no 41 test no 42 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 42 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 1 2 | 0.5 | 0 1 0 0 1 > 0.99999 || = 0.64 533 470 506 495 518 | 500 < 0.00002 0 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 496 490 515 524 462 | 500 < 0.00003 0 1 0 1 0 | 0.5 | 1 0 2 2 0 > 0.99997 || = 0.62 503 478 483 492 469 | 500 < 0.00004 0 0 0 1 1 | 0.5 | 0 0 1 1 1 > 0.99996 || = 0.61 470 510 450 475 523 | 500 < 0.00005 0 1 0 0 0 | 0.5 | 0 1 0 0 1 > 0.99995 || = 0.60 521 531 507 487 524 | 500 < 0.00006 0 1 0 2 0 | 0.5 | 0 1 1 1 0 > 0.99994 || = 0.59 481 480 558 504 508 | 500 < 0.00007 1 0 1 1 1 | 0.5 | 0 1 0 0 1 > 0.99993 || = 0.58 473 491 507 524 512 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 1 2 0 0 3 > 0.99992 || = 0.57 537 519 464 514 507 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 1 0 2 2 0 > 0.99991 || = 0.56 524 530 502 520 531 | 500 < 0.0001 1 0 1 1 2 | 0.5 | 2 0 0 0 1 > 0.9999 || = 0.55 473 505 499 508 537 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 479 495 483 493 555 | 500 < 0.0001 3 3 3 8 7 | 5 | 5 6 6 6 8 > 0.9999 || = 0.53 471 486 484 529 461 | 500 < 0.0002 6 3 5 5 7 | 5 | 1 3 1 2 1 > 0.9998 || = 0.52 497 505 492 522 504 | 500 < 0.0003 8 3 4 3 9 | 5 | 9 7 8 2 8 > 0.9997 || = 0.51 466 485 504 513 532 | 500 < 0.0004 9 3 6 5 6 | 5 | 8 2 4 6 2 > 0.9996 || = 0.50 499 537 473 492 468 | 500 < 0.0005 3 6 5 4 3 | 5 | 4 4 6 6 8 > 0.9995 || = 0.49 462 517 487 487 489 | 500 < 0.0006 1 5 3 4 1 | 5 | 5 7 5 6 0 > 0.9994 || = 0.48 499 500 500 491 459 | 500 < 0.0007 6 4 5 3 4 | 5 | 5 5 0 7 3 > 0.9993 || = 0.47 490 529 514 495 476 | 500 < 0.0008 7 4 2 5 4 | 5 | 3 2 6 0 6 > 0.9992 || = 0.46 511 483 490 558 503 | 500 < 0.0009 2 3 6 5 2 | 5 | 4 8 9 8 4 > 0.9991 || = 0.45 507 511 504 532 491 | 500 < 0.001 5 2 4 7 5 | 5 | 5 9 5 7 6 > 0.999 || = 0.44 501 513 504 506 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 497 517 523 505 483 | 500 < 0.001 50 36 43 49 48 | 50 | 49 53 50 50 46 > 0.999 || = 0.42 503 512 487 529 483 | 500 < 0.002 49 42 61 43 52 | 50 | 53 56 48 41 49 > 0.998 || = 0.41 476 496 493 511 518 | 500 < 0.003 48 62 52 53 62 | 50 | 51 49 53 54 47 > 0.997 || = 0.40 530 478 511 504 503 | 500 < 0.004 64 51 53 52 54 | 50 | 52 44 58 53 46 > 0.996 || = 0.39 544 502 503 503 508 | 500 < 0.005 51 55 41 46 57 | 50 | 49 52 47 36 49 > 0.995 || = 0.38 476 506 505 491 488 | 500 < 0.006 47 44 46 45 63 | 50 | 52 47 50 64 57 > 0.994 || = 0.37 465 513 521 501 493 | 500 < 0.007 51 55 58 61 49 | 50 | 45 50 57 41 57 > 0.993 || = 0.36 466 517 506 509 523 | 500 < 0.008 46 40 39 32 54 | 50 | 55 60 65 55 49 > 0.992 || = 0.35 520 524 506 504 542 | 500 < 0.009 48 48 58 51 54 | 50 | 56 52 48 54 50 > 0.991 || = 0.34 541 552 506 528 441 | 500 < 0.01 52 50 61 64 46 | 50 | 52 53 48 60 43 > 0.99 || = 0.33 549 514 546 513 470 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 500 491 492 474 473 | 500 < 0.01 506 483 512 496 539 | 497.5 | 514 516 524 508 493 > 0.99 || = 0.31 476 487 487 512 486 | 500 = 0.01 227 283 257 227 247 | 252.5 | 237 282 236 231 246 = 0.99 || = 0.30 557 479 527 462 509 | 500 = 0.02 509 491 509 487 510 | 500 | 515 507 516 471 511 = 0.98 || = 0.29 510 488 465 513 483 | 500 =================================================================| 500 | 500 520 484 508 523 = 0.97 || = 0.28 515 486 502 497 488 | 500 snpair_ClosePairs test: | 500 | 478 505 538 502 550 = 0.96 || = 0.27 511 512 500 532 522 | 500 ----------------------------------------------- | 500 | 482 549 489 479 516 = 0.95 || = 0.26 481 489 509 520 500 | 500 N = 5, n = 2000000, r = 0, t = 16, p = 0, m = 30, Torus = TRUE | 500 | 486 488 474 496 491 = 0.94 || = 0.25 491 511 530 479 548 | 500 A2 test based on the spacings between the | 500 | 463 492 469 511 501 = 0.93 || = 0.24 536 454 477 493 488 | 500 successive jump times of process Y_n(t): | 500 | 477 506 530 457 513 = 0.92 || = 0.23 482 521 484 475 518 | 500 =================================================================| 500 | 478 461 509 507 485 = 0.91 || = 0.22 481 469 500 492 490 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 483 493 508 502 486 = 0.90 || = 0.21 504 496 479 519 472 | 500 -----------------------------------------------------------------| 500 | 463 493 545 494 495 = 0.89 || = 0.20 480 504 502 536 442 | 500 SD Bern.: d 1.07632 0.68735 0.46926 | 500 | 550 503 515 531 518 = 0.88 || = 0.19 498 490 473 497 495 | 500 s 0.99359 1.09141 0.64529 | 500 | 494 472 524 456 506 = 0.87 || = 0.18 492 471 514 489 485 | 500 t 0.97063 1.14074 0.85832 | 500 | 509 473 486 492 490 = 0.86 || = 0.17 502 519 508 496 490 | 500 m 0.90532 1.22208 1.20059 | 500 | 543 501 531 490 498 = 0.85 || = 0.16 469 489 483 523 470 | 500 x 1.05813 0.93319 0.61836 | 500 | 527 477 470 518 541 = 0.84 || = 0.15 507 500 509 517 451 | 500 | 500 | 506 506 489 514 499 = 0.83 || = 0.14 505 449 518 521 486 | 500 Changes: d 48 5 5 | 500 | 557 490 497 516 537 = 0.82 || = 0.13 495 484 502 499 497 | 500 s 53 4 4 | 500 | 469 499 537 487 488 = 0.81 || = 0.12 477 539 496 443 475 | 500 t 48 5 4 | 500 | 478 522 502 497 524 = 0.80 || = 0.11 532 476 470 465 482 | 500 m 43 5 5 | 500 | 518 478 482 503 531 = 0.79 || = 0.10 518 518 496 508 493 | 500 x 43 4 2 | 500 | 506 536 521 477 481 = 0.78 || = 0.09 486 488 515 474 480 | 500 -----------------------------------------------------------------| 500 | 475 481 514 505 482 = 0.77 || = 0.08 489 473 494 493 512 | 500 Aver./ d 0.50057 498 > 500: 3 5 5 5 5 3 6 5 6 2 | 500 | 539 499 534 508 503 = 0.76 || = 0.07 527 488 462 495 488 | 500 median s 0.50024 500 ----- 4 3 4 7 6 5 3 6 3 7 | 500 | 497 504 490 520 503 = 0.75 || = 0.06 498 530 484 509 503 | 500 t 0.50099 502 6 5 4 8 5 5 5 5 6 5 | 500 | 527 521 466 487 472 = 0.74 || = 0.05 481 516 501 509 510 | 500 m 0.49964 502 3 4 5 7 7 8 3 5 5 5 | 500 | 523 482 456 468 495 = 0.73 || = 0.04 484 495 503 511 523 | 500 x 0.50242 497 7 0 3 4 3 9 6 5 4 6 | 500 | 493 521 519 474 516 = 0.72 || = 0.03 463 534 496 474 529 | 500 -----------------------------------------------------------------| 500 | 496 514 480 504 487 = 0.71 || = 0.02 509 491 509 487 510 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 491 509 510 487 475 = 0.70 || = 0.01 227 283 257 227 247 | 252.5 d 0 0 0 20 62 15 4 0 0 | 500 | 518 469 505 476 519 = 0.69 || < 0.01 506 483 512 496 539 | 497.5 s 0 0 3 11 73 12 2 0 0 | 500 | 521 537 546 503 526 = 0.68 ||========================================================================= t 0 0 2 14 71 10 4 0 0 | 500 | 514 462 468 541 532 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 16 72 11 1 0 0 | 500 | 490 454 500 486 522 = 0.66 ||========================================================================= x 0 0 3 13 65 17 3 0 0 | 500 | 534 479 447 498 484 = 0.65 || snpair_ClosePairs test: no 42 test no 43 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 43 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 2 1 | 0.5 | 1 0 0 0 0 > 0.99999 || = 0.64 1569 1603 1479 1498 1582 | 500 < 0.00002 1 0 1 0 1 | 0.5 | 0 0 0 1 0 > 0.99998 || = 0.63 0 0 0 0 0 | 500 < 0.00003 0 2 0 1 1 | 0.5 | 0 1 1 0 0 > 0.99997 || = 0.62 0 0 0 0 0 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 0 2 0 2 0 > 0.99996 || = 0.61 1458 1574 1596 1582 1475 | 500 < 0.00005 0 1 1 0 0 | 0.5 | 0 0 1 1 0 > 0.99995 || = 0.60 0 0 0 0 0 | 500 < 0.00006 0 1 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 0 0 0 0 0 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 1 0 2 > 0.99993 || = 0.58 1628 1546 1617 1520 1581 | 500 < 0.00008 0 1 3 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 0 0 0 0 0 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 0 0 0 0 0 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 3 4 0 3 3 > 0.9999 || = 0.55 0 0 0 0 0 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 1636 1615 1585 1608 1662 | 500 < 0.0001 1 5 8 4 4 | 5 | 4 7 3 7 5 > 0.9999 || = 0.53 0 0 0 0 0 | 500 < 0.0002 1 7 4 2 6 | 5 | 2 2 1 0 0 > 0.9998 || = 0.52 0 0 0 0 0 | 500 < 0.0003 4 2 2 2 2 | 5 | 3 2 3 0 3 > 0.9997 || = 0.51 3201 3336 3240 3234 3275 | 500 < 0.0004 8 3 3 2 6 | 5 | 5 5 4 6 5 > 0.9996 || = 0.50 0 0 0 0 0 | 500 < 0.0005 8 7 9 9 6 | 5 | 4 6 7 9 5 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 4 5 4 7 6 | 5 | 6 4 6 7 7 > 0.9994 || = 0.48 1610 1636 1594 1686 1655 | 500 < 0.0007 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9993 || = 0.47 0 0 0 0 0 | 500 < 0.0008 6 5 13 5 7 | 5 | 7 14 9 13 6 > 0.9992 || = 0.46 0 0 0 0 0 | 500 < 0.0009 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9991 || = 0.45 1588 1570 1609 1578 1560 | 500 < 0.001 11 11 20 8 13 | 5 | 0 0 0 0 0 > 0.999 || = 0.44 0 0 0 0 0 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 0 0 0 0 0 | 500 < 0.001 43 45 63 39 50 | 50 | 31 40 33 42 31 > 0.999 || = 0.42 0 0 0 0 0 | 500 < 0.002 28 35 34 29 39 | 50 | 53 46 51 54 69 > 0.998 || = 0.41 1648 1532 1512 1535 1555 | 500 < 0.003 53 43 60 40 50 | 50 | 28 19 27 31 18 > 0.997 || = 0.40 0 0 0 0 0 | 500 < 0.004 38 32 34 31 27 | 50 | 78 67 86 82 100 > 0.996 || = 0.39 0 0 0 0 0 | 500 < 0.005 29 42 30 39 46 | 50 | 0 0 0 0 0 > 0.995 || = 0.38 1529 1486 1523 1540 1578 | 500 < 0.006 36 49 48 50 48 | 50 | 55 61 55 59 56 > 0.994 || = 0.37 0 0 0 0 0 | 500 < 0.007 70 52 60 53 63 | 50 | 78 74 70 74 79 > 0.993 || = 0.36 0 0 0 0 0 | 500 < 0.008 75 69 61 63 62 | 50 | 0 0 0 0 0 > 0.992 || = 0.35 1448 1538 1469 1464 1520 | 500 < 0.009 0 0 0 0 0 | 50 | 90 107 99 91 78 > 0.991 || = 0.34 0 0 0 0 0 | 500 < 0.01 76 88 82 76 92 | 50 | 0 0 0 0 0 > 0.99 || = 0.33 0 0 0 0 0 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 1413 1379 1356 1449 1380 | 500 < 0.01 448 455 472 420 477 | 497.5 | 413 414 421 433 431 > 0.99 || = 0.31 0 0 0 0 0 | 500 = 0.01 236 225 258 224 219 | 252.5 | 249 251 252 264 256 = 0.99 || = 0.30 0 0 0 0 0 | 500 = 0.02 508 567 578 546 508 | 500 | 349 355 331 342 339 = 0.98 || = 0.29 1404 1307 1402 1367 1351 | 500 =================================================================| 500 | 497 506 493 484 492 = 0.97 || = 0.28 0 0 0 0 0 | 500 snpair_ClosePairs test: | 500 | 739 743 679 677 726 = 0.96 || = 0.27 1242 1257 1279 1274 1265 | 500 ----------------------------------------------- | 500 | 441 464 416 416 401 = 0.95 || = 0.26 0 0 0 0 0 | 500 N = 5, n = 2000000, r = 0, t = 16, p = 0, m = 30, Torus = TRUE | 500 | 482 502 520 504 511 = 0.94 || = 0.25 0 0 0 0 0 | 500 Test on the jump times of Y | 500 | 568 556 533 557 569 = 0.93 || = 0.24 1307 1215 1216 1156 1216 | 500 (superposition of Yn): | 500 | 0 0 0 0 0 = 0.92 || = 0.23 0 0 0 0 0 | 500 =================================================================| 500 | 650 573 629 686 619 = 0.91 || = 0.22 1153 1172 1133 1165 1141 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 697 710 739 719 700 = 0.90 || = 0.21 0 0 0 0 0 | 500 -----------------------------------------------------------------| 500 | 0 0 0 0 0 = 0.89 || = 0.20 0 0 0 0 0 | 500 SD Bern.: d 28.10017 3.32551 4.80801 | 500 | 731 796 817 817 779 = 0.88 || = 0.19 1066 1070 1058 1046 1092 | 500 s 28.13649 3.16291 5.06454 | 500 | 815 898 908 865 820 = 0.87 || = 0.18 0 0 0 0 0 | 500 t 27.94083 3.14163 4.99067 | 500 | 0 0 0 0 0 = 0.86 || = 0.17 956 953 980 998 976 | 500 m 27.98078 3.00083 4.75694 | 500 | 954 916 922 952 952 = 0.85 || = 0.16 0 0 0 0 0 | 500 x 28.07201 3.24106 5.18080 | 500 | 0 0 0 0 0 = 0.84 || = 0.15 902 908 891 897 869 | 500 | 500 | 1086 969 1045 1149 1072 = 0.83 || = 0.14 819 839 853 796 779 | 500 Changes: d 68 5 8 | 500 | 0 0 0 0 0 = 0.82 || = 0.13 0 0 0 0 0 | 500 s 68 3 6 | 500 | 0 0 0 0 0 = 0.81 || = 0.12 734 727 728 779 756 | 500 t 68 6 8 | 500 | 1121 1104 1091 1094 1121 = 0.80 || = 0.11 0 0 0 0 0 | 500 m 70 3 8 | 500 | 0 0 0 0 0 = 0.79 || = 0.10 713 689 681 694 730 | 500 x 70 3 8 | 500 | 1169 1199 1231 1243 1206 = 0.78 || = 0.09 594 619 652 603 599 | 500 -----------------------------------------------------------------| 500 | 0 0 0 0 0 = 0.77 || = 0.08 530 544 569 528 579 | 500 Aver./ d 0.50137 217 > 500: 4 6 4 3 3 3 4 4 5 3 | 500 | 0 0 0 0 0 = 0.76 || = 0.07 473 455 485 498 518 | 500 median s 0.50007 232 ----- 4 6 4 3 3 3 4 4 5 5 | 500 | 1313 1219 1329 1243 1278 = 0.75 || = 0.06 404 457 448 450 397 | 500 t 0.49921 235 5 6 4 3 3 3 4 4 5 4 | 500 | 0 0 0 0 0 = 0.74 || = 0.05 373 390 393 379 383 | 500 m 0.50139 233 4 6 4 3 3 3 4 4 5 5 | 500 | 1395 1373 1271 1335 1354 = 0.73 || = 0.04 566 617 559 595 594 | 500 x 0.49956 269 5 6 4 3 3 3 4 4 5 5 | 500 | 0 0 0 0 0 = 0.72 || = 0.03 217 232 235 233 269 | 500 -----------------------------------------------------------------| 500 | 0 0 0 0 0 = 0.71 || = 0.02 508 567 578 546 508 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 1449 1434 1419 1408 1395 = 0.70 || = 0.01 236 225 258 224 219 | 252.5 d 54 1 2 2 4 1 1 1 35 | 500 | 0 0 0 0 0 = 0.69 || < 0.01 448 455 472 420 477 | 497.5 s 53 1 1 4 3 1 1 2 35 | 500 | 0 0 0 0 0 = 0.68 ||========================================================================= t 53 2 1 1 5 1 1 2 35 | 500 | 1509 1505 1504 1470 1438 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 53 2 2 1 4 1 2 0 36 | 500 | 0 0 0 0 0 = 0.66 ||========================================================================= x 55 0 2 0 6 0 0 2 36 | 500 | 0 0 0 0 0 = 0.65 || snpair_ClosePairs test: no 43 test no 44 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 44 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 1 0 0 | 0.5 | 1 1 2 0 0 > 0.99999 || = 0.64 498 498 478 498 491 | 500 < 0.00002 0 1 1 0 0 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 460 493 488 475 493 | 500 < 0.00003 0 0 1 0 0 | 0.5 | 0 0 4 0 0 > 0.99997 || = 0.62 466 482 492 482 546 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 0 0 0 2 1 > 0.99996 || = 0.61 478 521 463 519 537 | 500 < 0.00005 0 1 0 1 1 | 0.5 | 0 0 1 1 0 > 0.99995 || = 0.60 517 488 503 520 504 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 0 1 0 1 1 > 0.99994 || = 0.59 511 459 493 512 493 | 500 < 0.00007 1 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99993 || = 0.58 492 472 562 507 536 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 1 1 0 1 0 > 0.99992 || = 0.57 516 504 487 502 496 | 500 < 0.00009 0 1 0 0 2 | 0.5 | 0 1 0 0 1 > 0.99991 || = 0.56 495 453 487 499 504 | 500 < 0.0001 1 0 0 0 1 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 494 522 502 499 494 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 493 481 517 489 521 | 500 < 0.0001 2 6 3 1 5 | 5 | 3 4 8 5 4 > 0.9999 || = 0.53 525 477 520 499 524 | 500 < 0.0002 5 6 5 3 3 | 5 | 2 5 0 0 2 > 0.9998 || = 0.52 520 524 509 529 472 | 500 < 0.0003 3 7 4 7 5 | 5 | 5 6 5 7 3 > 0.9997 || = 0.51 474 486 492 500 498 | 500 < 0.0004 6 9 6 2 6 | 5 | 12 4 3 3 6 > 0.9996 || = 0.50 482 496 493 501 505 | 500 < 0.0005 11 7 6 7 5 | 5 | 7 2 2 5 5 > 0.9995 || = 0.49 512 475 532 529 465 | 500 < 0.0006 8 2 4 7 4 | 5 | 11 8 3 6 5 > 0.9994 || = 0.48 495 523 496 490 476 | 500 < 0.0007 4 3 3 5 5 | 5 | 2 2 5 6 7 > 0.9993 || = 0.47 507 482 498 498 518 | 500 < 0.0008 10 6 2 4 5 | 5 | 5 6 5 4 4 > 0.9992 || = 0.46 533 489 512 493 495 | 500 < 0.0009 4 6 3 5 3 | 5 | 6 1 3 4 6 > 0.9991 || = 0.45 494 493 553 573 487 | 500 < 0.001 7 5 7 8 7 | 5 | 4 6 2 4 12 > 0.999 || = 0.44 509 453 506 501 477 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 477 491 512 500 487 | 500 < 0.001 60 57 43 49 48 | 50 | 57 44 36 44 54 > 0.999 || = 0.42 515 477 502 492 487 | 500 < 0.002 64 55 47 47 52 | 50 | 48 55 47 50 39 > 0.998 || = 0.41 529 501 513 503 517 | 500 < 0.003 48 49 48 56 66 | 50 | 40 50 43 41 41 > 0.997 || = 0.40 517 523 531 480 508 | 500 < 0.004 64 48 46 51 57 | 50 | 49 47 44 48 50 > 0.996 || = 0.39 488 508 498 488 521 | 500 < 0.005 59 41 54 51 49 | 50 | 53 48 49 46 42 > 0.995 || = 0.38 481 465 526 503 486 | 500 < 0.006 41 46 29 51 45 | 50 | 53 50 52 67 52 > 0.994 || = 0.37 478 522 442 504 486 | 500 < 0.007 47 57 47 50 58 | 50 | 53 48 46 54 55 > 0.993 || = 0.36 532 492 507 481 503 | 500 < 0.008 57 34 50 48 57 | 50 | 45 56 66 50 42 > 0.992 || = 0.35 502 525 520 464 552 | 500 < 0.009 59 49 70 35 43 | 50 | 47 62 50 61 56 > 0.991 || = 0.34 481 512 513 499 539 | 500 < 0.01 63 48 48 47 55 | 50 | 40 41 41 53 54 > 0.99 || = 0.33 507 493 537 482 486 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 505 507 524 522 500 | 500 < 0.01 562 484 482 485 530 | 497.5 | 485 501 474 514 485 > 0.99 || = 0.31 488 487 526 531 498 | 500 = 0.01 246 265 250 243 216 | 252.5 | 226 217 232 244 245 = 0.99 || = 0.30 530 491 521 506 470 | 500 = 0.02 486 520 471 499 473 | 500 | 504 499 523 537 539 = 0.98 || = 0.29 506 491 515 445 480 | 500 =================================================================| 500 | 508 479 503 509 514 = 0.97 || = 0.28 497 498 482 499 524 | 500 snpair_ClosePairs test: | 500 | 492 553 487 530 415 = 0.96 || = 0.27 507 538 501 513 475 | 500 ----------------------------------------------- | 500 | 528 542 503 492 497 = 0.95 || = 0.26 464 533 507 479 485 | 500 N = 5, n = 2000000, r = 0, t = 16, p = 0, m = 30, Torus = TRUE | 500 | 450 515 475 506 437 = 0.94 || = 0.25 539 494 496 513 510 | 500 Test on the jump times of Y | 500 | 517 545 504 461 542 = 0.93 || = 0.24 526 502 533 494 494 | 500 (superposition of Yn): | 500 | 487 546 459 500 492 = 0.92 || = 0.23 482 488 502 515 508 | 500 =================================================================| 500 | 478 524 490 505 491 = 0.91 || = 0.22 523 493 470 518 532 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 521 502 492 458 517 = 0.90 || = 0.21 507 469 535 551 516 | 500 -----------------------------------------------------------------| 500 | 481 500 494 483 487 = 0.89 || = 0.20 496 488 495 484 501 | 500 SD Bern.: d 1.03758 1.39065 0.79411 | 500 | 487 510 454 525 495 = 0.88 || = 0.19 501 497 501 479 509 | 500 s 1.00620 0.98638 0.82380 | 500 | 502 502 474 461 488 = 0.87 || = 0.18 545 526 479 506 490 | 500 t 0.96302 1.37763 1.13898 | 500 | 519 481 498 492 530 = 0.86 || = 0.17 493 514 490 470 500 | 500 m 0.90810 0.75799 1.07010 | 500 | 493 501 493 495 493 = 0.85 || = 0.16 501 497 528 537 521 | 500 x 1.09303 1.02617 0.92457 | 500 | 497 490 484 492 479 = 0.84 || = 0.15 457 527 475 527 512 | 500 | 500 | 517 511 522 512 498 = 0.83 || = 0.14 449 495 544 511 500 | 500 Changes: d 63 4 3 | 500 | 503 527 475 537 458 = 0.82 || = 0.13 511 476 494 507 533 | 500 s 51 3 4 | 500 | 456 488 496 512 460 = 0.81 || = 0.12 491 501 489 505 525 | 500 t 48 4 4 | 500 | 481 503 494 482 508 = 0.80 || = 0.11 484 515 504 480 493 | 500 m 45 2 3 | 500 | 538 501 493 487 470 = 0.79 || = 0.10 497 508 494 535 526 | 500 x 51 5 4 | 500 | 462 464 518 498 490 = 0.78 || = 0.09 490 521 533 488 510 | 500 -----------------------------------------------------------------| 500 | 508 511 495 495 493 = 0.77 || = 0.08 484 491 482 485 491 | 500 Aver./ d 0.49884 497 > 500: 4 4 6 5 7 5 3 5 5 4 | 500 | 514 513 503 491 553 = 0.76 || = 0.07 519 504 508 489 485 | 500 median s 0.50012 498 ----- 6 6 3 5 3 3 3 5 6 7 | 500 | 499 500 477 496 463 = 0.75 || = 0.06 472 555 496 505 506 | 500 t 0.49837 498 2 4 6 8 8 6 4 6 1 4 | 500 | 544 491 512 479 466 = 0.74 || = 0.05 531 458 460 522 503 | 500 m 0.49903 499 3 7 5 5 4 5 2 1 4 6 | 500 | 502 466 509 487 511 = 0.73 || = 0.04 474 534 486 494 472 | 500 x 0.49842 498 5 6 6 4 3 5 6 5 2 3 | 500 | 497 464 512 502 533 = 0.72 || = 0.03 543 491 485 527 503 | 500 -----------------------------------------------------------------| 500 | 473 509 508 491 503 = 0.71 || = 0.02 486 520 471 499 473 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 496 493 511 489 532 = 0.70 || = 0.01 246 265 250 243 216 | 252.5 d 0 0 2 13 69 15 2 0 0 | 500 | 539 515 475 474 491 = 0.69 || < 0.01 562 484 482 485 530 | 497.5 s 0 0 3 12 69 13 4 0 0 | 500 | 474 542 462 518 513 = 0.68 ||========================================================================= t 0 0 2 14 70 13 2 0 0 | 500 | 503 485 517 500 478 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 7 80 11 1 1 0 | 500 | 491 481 515 487 507 = 0.66 ||========================================================================= x 0 1 2 13 66 16 3 0 0 | 500 | 544 491 525 484 532 = 0.65 || snpair_ClosePairs test: no 44 test no 45 TestU01 250000 runs BigCrush Test smarsa_S snpair_ClosePairs test: test no 45 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 3 | 0.5 | 0 1 0 1 0 > 0.99999 || = 0.64 530 517 477 502 511 | 500 < 0.00002 2 1 0 0 3 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 488 495 533 522 465 | 500 < 0.00003 1 0 0 0 2 | 0.5 | 0 0 1 0 0 > 0.99997 || = 0.62 530 472 474 493 542 | 500 < 0.00004 1 0 2 1 0 | 0.5 | 3 0 0 0 0 > 0.99996 || = 0.61 496 526 530 536 509 | 500 < 0.00005 0 2 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99995 || = 0.60 479 507 490 507 510 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99994 || = 0.59 509 488 477 490 519 | 500 < 0.00007 0 1 1 0 0 | 0.5 | 0 2 0 0 0 > 0.99993 || = 0.58 486 466 474 490 492 | 500 < 0.00008 2 0 0 2 0 | 0.5 | 0 1 1 1 0 > 0.99992 || = 0.57 493 536 545 491 484 | 500 < 0.00009 0 0 0 1 1 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 494 533 529 493 534 | 500 < 0.0001 0 0 0 1 0 | 0.5 | 0 0 1 2 1 > 0.9999 || = 0.55 526 472 507 505 530 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 508 503 481 516 502 | 500 < 0.0001 6 5 3 6 9 | 5 | 5 5 4 4 1 > 0.9999 || = 0.53 509 493 509 548 520 | 500 < 0.0002 5 3 2 5 3 | 5 | 1 1 3 2 3 > 0.9998 || = 0.52 505 523 501 531 508 | 500 < 0.0003 6 4 5 2 3 | 5 | 6 5 8 6 6 > 0.9997 || = 0.51 542 512 507 499 518 | 500 < 0.0004 3 7 5 5 10 | 5 | 3 4 6 8 3 > 0.9996 || = 0.50 521 497 500 521 485 | 500 < 0.0005 4 3 5 3 6 | 5 | 7 3 5 5 2 > 0.9995 || = 0.49 516 530 493 472 487 | 500 < 0.0006 3 6 5 1 12 | 5 | 4 8 5 6 2 > 0.9994 || = 0.48 517 482 451 506 502 | 500 < 0.0007 5 6 9 3 5 | 5 | 4 4 6 5 5 > 0.9993 || = 0.47 515 493 535 523 479 | 500 < 0.0008 6 4 6 11 5 | 5 | 2 2 2 2 4 > 0.9992 || = 0.46 516 486 570 505 488 | 500 < 0.0009 9 5 3 7 6 | 5 | 3 6 3 7 3 > 0.9991 || = 0.45 485 487 541 470 503 | 500 < 0.001 2 5 4 6 3 | 5 | 2 3 1 5 5 > 0.999 || = 0.44 496 478 498 472 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 479 498 552 518 507 | 500 < 0.001 49 48 47 49 62 | 50 | 37 41 43 50 34 > 0.999 || = 0.42 485 497 510 477 508 | 500 < 0.002 58 50 46 47 49 | 50 | 61 51 50 48 40 > 0.998 || = 0.41 501 513 509 501 480 | 500 < 0.003 36 54 41 48 38 | 50 | 58 49 58 53 52 > 0.997 || = 0.40 500 494 515 492 483 | 500 < 0.004 55 57 50 51 44 | 50 | 57 53 46 34 53 > 0.996 || = 0.39 549 504 509 501 501 | 500 < 0.005 38 53 44 48 48 | 50 | 50 56 57 55 54 > 0.995 || = 0.38 485 493 535 527 512 | 500 < 0.006 44 49 52 51 55 | 50 | 55 47 41 59 46 > 0.994 || = 0.37 483 504 506 504 470 | 500 < 0.007 53 46 48 47 45 | 50 | 46 52 47 59 48 > 0.993 || = 0.36 502 471 490 495 477 | 500 < 0.008 52 52 42 54 63 | 50 | 53 56 54 38 49 > 0.992 || = 0.35 476 478 474 500 490 | 500 < 0.009 71 43 55 44 50 | 50 | 52 47 49 43 51 > 0.991 || = 0.34 515 481 516 486 471 | 500 < 0.01 53 47 54 50 51 | 50 | 45 61 51 50 47 > 0.99 || = 0.33 490 523 474 508 480 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 486 523 497 487 505 | 500 < 0.01 509 499 479 489 505 | 497.5 | 514 513 496 489 474 > 0.99 || = 0.31 493 497 485 481 486 | 500 = 0.01 247 247 265 261 265 | 252.5 | 237 227 230 277 238 = 0.99 || = 0.30 480 537 482 490 526 | 500 = 0.02 520 520 513 469 545 | 500 | 449 482 474 532 515 = 0.98 || = 0.29 506 487 506 474 500 | 500 =================================================================| 500 | 530 528 525 489 517 = 0.97 || = 0.28 506 485 497 482 512 | 500 snpair_ClosePairs test: | 500 | 473 549 534 504 530 = 0.96 || = 0.27 471 485 483 481 520 | 500 ----------------------------------------------- | 500 | 528 521 502 518 525 = 0.95 || = 0.26 491 469 504 506 497 | 500 N = 5, n = 2000000, r = 0, t = 16, p = 0, m = 30, Torus = TRUE | 500 | 493 506 502 468 517 = 0.94 || = 0.25 530 481 515 505 502 | 500 Test on the jump times of Y | 500 | 513 507 512 530 490 = 0.93 || = 0.24 516 478 468 510 480 | 500 (superposition of Yn): | 500 | 471 509 496 524 518 = 0.92 || = 0.23 530 474 494 501 505 | 500 =================================================================| 500 | 506 498 505 489 485 = 0.91 || = 0.22 468 511 456 493 470 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 501 498 449 465 492 = 0.90 || = 0.21 484 446 474 513 474 | 500 -----------------------------------------------------------------| 500 | 514 527 485 518 522 = 0.89 || = 0.20 474 505 499 491 496 | 500 SD Bern.: d 0.89059 1.36376 0.98231 | 500 | 537 478 492 507 506 = 0.88 || = 0.19 449 514 485 503 511 | 500 s 0.95513 0.56062 0.78396 | 500 | 478 495 499 513 511 = 0.87 || = 0.18 519 507 515 522 512 | 500 t 1.06090 0.71449 0.75667 | 500 | 514 481 473 551 514 = 0.86 || = 0.17 471 496 492 501 489 | 500 m 0.85917 0.40267 1.13985 | 500 | 475 488 501 493 456 = 0.85 || = 0.16 515 486 490 479 459 | 500 x 0.91268 1.04837 0.91258 | 500 | 509 519 502 493 463 = 0.84 || = 0.15 501 504 547 472 502 | 500 | 500 | 489 444 503 461 498 = 0.83 || = 0.14 476 496 482 522 485 | 500 Changes: d 52 5 6 | 500 | 523 488 450 526 487 = 0.82 || = 0.13 514 529 504 495 526 | 500 s 52 4 7 | 500 | 507 504 474 487 503 = 0.81 || = 0.12 483 482 495 457 503 | 500 t 48 3 7 | 500 | 508 475 457 502 492 = 0.80 || = 0.11 484 511 505 516 527 | 500 m 54 6 4 | 500 | 502 504 534 524 508 = 0.79 || = 0.10 508 517 499 472 474 | 500 x 45 6 4 | 500 | 507 534 489 518 478 = 0.78 || = 0.09 528 537 515 495 496 | 500 -----------------------------------------------------------------| 500 | 515 500 536 501 519 = 0.77 || = 0.08 481 512 503 511 486 | 500 Aver./ d 0.50134 501 > 500: 5 5 5 3 5 6 4 6 7 5 | 500 | 493 490 524 494 496 = 0.76 || = 0.07 482 522 506 507 488 | 500 median s 0.50092 498 ----- 6 6 2 5 2 6 4 5 3 7 | 500 | 505 553 488 508 504 = 0.75 || = 0.06 481 480 474 486 474 | 500 t 0.49952 500 7 4 3 4 7 6 5 4 3 6 | 500 | 494 549 497 497 504 = 0.74 || = 0.05 505 501 507 483 481 | 500 m 0.50228 501 4 5 5 4 5 5 7 6 5 6 | 500 | 482 511 520 502 498 = 0.73 || = 0.04 501 491 508 483 472 | 500 x 0.50077 502 4 6 4 4 5 8 7 4 5 6 | 500 | 493 495 484 471 499 = 0.72 || = 0.03 475 485 490 519 566 | 500 -----------------------------------------------------------------| 500 | 539 478 500 477 474 = 0.71 || = 0.02 520 520 513 469 545 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 481 485 444 512 520 = 0.70 || = 0.01 247 247 265 261 265 | 252.5 d 0 0 2 10 75 13 1 0 0 | 500 | 500 532 510 506 528 = 0.69 || < 0.01 509 499 479 489 505 | 497.5 s 0 0 2 8 74 14 3 0 0 | 500 | 498 501 540 499 526 = 0.68 ||========================================================================= t 0 0 4 15 65 13 3 1 0 | 500 | 486 489 499 503 472 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 15 74 10 2 0 0 | 500 | 523 498 529 477 486 = 0.66 ||========================================================================= x 0 0 0 15 74 10 2 0 0 | 500 | 503 478 499 518 519 = 0.65 || snpair_ClosePairs test: no 45 test no 46 TestU01 250000 runs BigCrush Test smarsa_S test no 46 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 2 | 0.5 | 2 0 1 0 1 > 0.99999 || = 0.64 452 502 491 466 484 | 500 < 0.00002 0 0 2 0 0 | 0.5 | 2 0 0 0 0 > 0.99998 || = 0.63 474 538 469 466 510 | 500 < 0.00003 2 1 0 0 0 | 0.5 | 2 1 0 0 0 > 0.99997 || = 0.62 508 486 513 488 536 | 500 < 0.00004 2 1 0 0 1 | 0.5 | 0 2 0 1 0 > 0.99996 || = 0.61 477 480 450 509 514 | 500 < 0.00005 1 1 0 1 0 | 0.5 | 0 1 1 0 1 > 0.99995 || = 0.60 496 474 547 509 525 | 500 < 0.00006 1 2 1 1 0 | 0.5 | 0 1 0 1 0 > 0.99994 || = 0.59 523 518 507 530 455 | 500 < 0.00007 1 0 0 1 0 | 0.5 | 0 1 0 0 2 > 0.99993 || = 0.58 500 512 510 487 543 | 500 < 0.00008 0 0 0 0 1 | 0.5 | 0 0 1 0 3 > 0.99992 || = 0.57 500 495 509 498 477 | 500 < 0.00009 0 1 0 1 1 | 0.5 | 1 1 1 1 2 > 0.99991 || = 0.56 522 481 495 501 483 | 500 < 0.0001 2 0 0 0 0 | 0.5 | 1 1 1 0 1 > 0.9999 || = 0.55 467 529 494 531 482 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 505 525 500 499 500 | 500 < 0.0001 10 7 3 4 5 | 5 | 8 8 5 3 10 > 0.9999 || = 0.53 494 518 434 499 516 | 500 < 0.0002 8 5 3 9 7 | 5 | 2 3 2 3 1 > 0.9998 || = 0.52 482 486 525 463 500 | 500 < 0.0003 7 8 5 3 9 | 5 | 8 6 8 5 6 > 0.9997 || = 0.51 538 521 487 470 511 | 500 < 0.0004 2 4 6 5 5 | 5 | 8 10 5 4 5 > 0.9996 || = 0.50 480 502 508 489 523 | 500 < 0.0005 7 7 2 2 4 | 5 | 5 4 3 4 7 > 0.9995 || = 0.49 475 474 519 498 462 | 500 < 0.0006 3 9 7 5 6 | 5 | 5 7 4 6 5 > 0.9994 || = 0.48 477 536 475 486 487 | 500 < 0.0007 6 4 1 5 7 | 5 | 4 8 9 6 6 > 0.9993 || = 0.47 504 457 486 497 449 | 500 < 0.0008 4 4 0 1 6 | 5 | 5 3 3 3 4 > 0.9992 || = 0.46 493 486 534 503 477 | 500 < 0.0009 2 4 5 6 4 | 5 | 4 3 2 4 4 > 0.9991 || = 0.45 502 492 495 520 488 | 500 < 0.001 7 5 3 4 8 | 5 | 2 5 6 9 9 > 0.999 || = 0.44 514 490 490 509 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 505 499 477 534 485 | 500 < 0.001 56 57 35 44 61 | 50 | 51 57 47 47 57 > 0.999 || = 0.42 492 508 538 524 506 | 500 < 0.002 48 49 52 57 41 | 50 | 34 42 46 48 46 > 0.998 || = 0.41 506 501 497 501 493 | 500 < 0.003 40 46 51 46 55 | 50 | 50 62 51 54 54 > 0.997 || = 0.40 531 507 506 498 493 | 500 < 0.004 46 45 57 46 44 | 50 | 44 42 44 41 67 > 0.996 || = 0.39 512 467 502 492 514 | 500 < 0.005 48 53 49 46 47 | 50 | 53 47 39 49 58 > 0.995 || = 0.38 457 461 536 495 518 | 500 < 0.006 53 51 57 42 52 | 50 | 59 62 44 55 51 > 0.994 || = 0.37 496 461 477 489 491 | 500 < 0.007 42 60 59 43 51 | 50 | 50 51 58 43 46 > 0.993 || = 0.36 485 544 520 497 468 | 500 < 0.008 45 54 52 48 53 | 50 | 37 47 42 53 55 > 0.992 || = 0.35 493 486 488 508 489 | 500 < 0.009 72 57 34 67 52 | 50 | 65 45 46 50 51 > 0.991 || = 0.34 504 505 496 497 491 | 500 < 0.01 45 48 47 47 50 | 50 | 57 49 53 54 52 > 0.99 || = 0.33 499 521 510 516 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 516 493 568 468 443 | 500 < 0.01 495 520 493 486 506 | 497.5 | 500 504 470 494 537 > 0.99 || = 0.31 508 467 501 462 526 | 500 = 0.01 240 256 246 266 243 | 252.5 | 235 241 245 242 237 = 0.99 || = 0.30 535 513 492 466 461 | 500 = 0.02 497 513 493 495 494 | 500 | 468 506 534 499 549 = 0.98 || = 0.29 480 516 484 485 497 | 500 =================================================================| 500 | 481 504 509 468 493 = 0.97 || = 0.28 529 480 508 492 488 | 500 | 500 | 524 483 485 531 520 = 0.96 || = 0.27 508 519 488 563 479 | 500 sknuth_SimpPoker test: | 500 | 462 502 457 471 514 = 0.95 || = 0.26 504 491 505 448 533 | 500 ----------------------------------------------- | 500 | 493 507 514 492 458 = 0.94 || = 0.25 520 510 544 542 486 | 500 N = 1, n = 400000000, r = 0, d = 8, k = 8 | 500 | 465 487 496 467 516 = 0.93 || = 0.24 524 469 507 522 488 | 500 | 500 | 529 499 464 505 465 = 0.92 || = 0.23 522 532 516 500 478 | 500 =================================================================| 500 | 506 477 501 475 512 = 0.91 || = 0.22 488 532 479 511 500 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 500 483 490 504 494 = 0.90 || = 0.21 505 507 529 526 529 | 500 -----------------------------------------------------------------| 500 | 508 547 510 527 500 = 0.89 || = 0.20 514 507 498 539 541 | 500 SD Bern.: d 0.94246 1.23916 1.28593 | 500 | 507 488 551 502 494 = 0.88 || = 0.19 508 479 525 517 495 | 500 s 0.94586 0.73520 1.01044 | 500 | 492 513 527 480 517 = 0.87 || = 0.18 504 496 536 462 482 | 500 t 1.07032 1.16590 0.86297 | 500 | 491 491 482 528 493 = 0.86 || = 0.17 484 508 491 496 488 | 500 m 1.03657 1.04742 0.64838 | 500 | 541 521 502 481 510 = 0.85 || = 0.16 523 531 506 504 495 | 500 x 1.05198 0.76195 0.98129 | 500 | 467 494 503 496 518 = 0.84 || = 0.15 505 493 498 518 513 | 500 | 500 | 503 507 501 514 492 = 0.83 || = 0.14 489 487 458 533 521 | 500 Changes: d 51 5 4 | 500 | 468 483 472 540 507 = 0.82 || = 0.13 527 477 523 486 537 | 500 s 52 3 5 | 500 | 494 499 489 488 468 = 0.81 || = 0.12 482 548 474 488 528 | 500 t 54 4 5 | 500 | 507 482 493 450 518 = 0.80 || = 0.11 502 518 500 510 552 | 500 m 44 4 7 | 500 | 520 518 485 457 486 = 0.79 || = 0.10 479 471 507 529 513 | 500 x 54 5 4 | 500 | 484 512 526 504 498 = 0.78 || = 0.09 469 477 500 523 451 | 500 -----------------------------------------------------------------| 500 | 516 484 465 544 500 = 0.77 || = 0.08 475 525 517 474 523 | 500 Aver./ d 0.49875 502 > 500: 3 6 8 5 6 4 6 6 4 4 | 500 | 492 490 515 518 510 = 0.76 || = 0.07 491 511 468 506 472 | 500 median s 0.49941 501 ----- 6 4 7 4 4 6 4 6 4 5 | 500 | 467 517 492 513 499 = 0.75 || = 0.06 496 497 526 506 502 | 500 t 0.49877 500 4 5 6 6 4 5 2 6 6 4 | 500 | 510 511 508 490 510 = 0.74 || = 0.05 507 483 531 504 475 | 500 m 0.49893 499 5 6 6 2 6 4 5 5 6 2 | 500 | 524 503 536 500 494 = 0.73 || = 0.04 529 477 509 476 538 | 500 x 0.50033 498 5 6 3 4 1 4 7 3 4 6 | 500 | 471 489 514 509 480 = 0.72 || = 0.03 533 520 451 482 509 | 500 -----------------------------------------------------------------| 500 | 547 539 533 487 492 = 0.71 || = 0.02 497 513 493 495 494 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 518 502 476 525 509 = 0.70 || = 0.01 240 256 246 266 243 | 252.5 d 0 0 1 17 65 17 1 0 0 | 500 | 535 455 464 499 490 = 0.69 || < 0.01 495 520 493 486 506 | 497.5 s 0 0 1 14 72 12 2 0 0 | 500 | 505 539 489 511 518 = 0.68 ||========================================================================= t 0 0 3 15 64 16 2 1 0 | 500 | 525 484 462 467 544 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 16 65 16 2 0 0 | 500 | 530 479 478 556 535 = 0.66 ||========================================================================= x 0 0 4 11 69 15 2 0 0 | 500 | 464 475 506 512 461 = 0.65 || no 46 test no 47 TestU01 250000 runs BigCrush Test smarsa_S sknuth_SimpPoker test: test no 47 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 0 | 0.5 | 0 1 0 1 1 > 0.99999 || = 0.64 520 492 474 479 496 | 500 < 0.00002 0 2 1 1 1 | 0.5 | 1 0 1 2 0 > 0.99998 || = 0.63 522 512 518 529 484 | 500 < 0.00003 0 1 0 3 1 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 432 518 521 496 522 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 1 0 1 0 1 > 0.99996 || = 0.61 457 501 507 484 502 | 500 < 0.00005 0 0 1 1 0 | 0.5 | 1 1 0 0 0 > 0.99995 || = 0.60 541 527 523 509 480 | 500 < 0.00006 0 0 1 1 1 | 0.5 | 1 0 1 2 0 > 0.99994 || = 0.59 509 471 486 475 493 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 0 3 0 1 0 > 0.99993 || = 0.58 469 482 488 504 504 | 500 < 0.00008 0 1 0 1 0 | 0.5 | 2 1 2 2 2 > 0.99992 || = 0.57 487 523 496 494 498 | 500 < 0.00009 0 1 1 0 1 | 0.5 | 0 1 1 0 0 > 0.99991 || = 0.56 445 505 451 510 502 | 500 < 0.0001 0 1 0 1 0 | 0.5 | 1 1 0 2 1 > 0.9999 || = 0.55 480 501 490 474 490 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 510 484 490 500 465 | 500 < 0.0001 1 7 5 9 5 | 5 | 7 8 6 11 5 > 0.9999 || = 0.53 503 519 510 552 488 | 500 < 0.0002 4 2 5 6 5 | 5 | 1 1 3 5 1 > 0.9998 || = 0.52 503 517 493 568 509 | 500 < 0.0003 7 1 1 3 4 | 5 | 1 6 7 2 2 > 0.9997 || = 0.51 468 522 508 480 490 | 500 < 0.0004 7 3 3 9 1 | 5 | 4 5 5 7 8 > 0.9996 || = 0.50 469 561 522 535 508 | 500 < 0.0005 7 5 4 3 3 | 5 | 2 3 6 4 4 > 0.9995 || = 0.49 482 498 518 473 448 | 500 < 0.0006 5 5 6 11 2 | 5 | 6 7 6 6 5 > 0.9994 || = 0.48 520 526 528 502 518 | 500 < 0.0007 6 4 4 1 4 | 5 | 7 6 3 3 3 > 0.9993 || = 0.47 484 490 516 525 465 | 500 < 0.0008 0 4 6 7 5 | 5 | 3 4 5 2 4 > 0.9992 || = 0.46 458 507 520 457 508 | 500 < 0.0009 3 7 5 11 4 | 5 | 5 4 6 5 5 > 0.9991 || = 0.45 515 521 522 495 502 | 500 < 0.001 3 2 5 2 4 | 5 | 4 5 3 9 10 > 0.999 || = 0.44 465 518 504 508 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 507 500 476 522 456 | 500 < 0.001 43 40 44 62 37 | 50 | 40 49 50 54 47 > 0.999 || = 0.42 523 488 526 504 515 | 500 < 0.002 52 53 61 58 51 | 50 | 59 39 52 53 44 > 0.998 || = 0.41 541 492 513 473 498 | 500 < 0.003 47 42 62 60 41 | 50 | 48 52 49 54 49 > 0.997 || = 0.40 529 488 488 512 505 | 500 < 0.004 48 39 51 49 57 | 50 | 50 52 49 56 46 > 0.996 || = 0.39 510 525 468 472 498 | 500 < 0.005 41 47 41 66 46 | 50 | 56 60 47 61 53 > 0.995 || = 0.38 522 529 492 514 516 | 500 < 0.006 57 47 47 50 34 | 50 | 64 57 41 39 58 > 0.994 || = 0.37 496 441 535 468 484 | 500 < 0.007 47 59 48 41 55 | 50 | 48 48 45 52 44 > 0.993 || = 0.36 506 484 470 498 485 | 500 < 0.008 51 48 75 43 50 | 50 | 58 42 51 49 53 > 0.992 || = 0.35 476 501 576 490 511 | 500 < 0.009 48 45 48 42 48 | 50 | 38 48 47 56 48 > 0.991 || = 0.34 531 490 477 485 498 | 500 < 0.01 73 48 50 45 46 | 50 | 56 41 59 56 41 > 0.99 || = 0.33 476 488 504 468 515 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 534 508 535 484 525 | 500 < 0.01 507 468 527 516 465 | 497.5 | 517 488 490 530 483 > 0.99 || = 0.31 462 499 503 486 487 | 500 = 0.01 249 254 259 266 280 | 252.5 | 250 242 264 249 237 = 0.99 || = 0.30 496 499 497 502 536 | 500 = 0.02 499 490 506 556 520 | 500 | 530 506 496 510 447 = 0.98 || = 0.29 480 514 507 470 485 | 500 =================================================================| 500 | 477 503 433 493 472 = 0.97 || = 0.28 507 469 482 562 523 | 500 sknuth_SimpPoker test: | 500 | 530 472 478 487 529 = 0.96 || = 0.27 506 485 491 501 528 | 500 ----------------------------------------------- | 500 | 492 516 508 495 496 = 0.95 || = 0.26 500 515 465 484 495 | 500 N = 1, n = 400000000, r = 27, d = 8, k = 8 | 500 | 484 501 489 490 501 = 0.94 || = 0.25 494 482 521 523 509 | 500 | 500 | 521 471 457 513 504 = 0.93 || = 0.24 487 520 503 496 507 | 500 | 500 | 497 521 517 525 469 = 0.92 || = 0.23 502 469 522 509 485 | 500 =================================================================| 500 | 484 485 464 524 500 = 0.91 || = 0.22 527 500 510 499 510 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 471 496 493 549 498 = 0.90 || = 0.21 517 493 499 483 490 | 500 -----------------------------------------------------------------| 500 | 477 458 462 452 573 = 0.89 || = 0.20 464 498 547 498 492 | 500 SD Bern.: d 1.17108 1.21633 1.15382 | 500 | 514 486 498 497 537 = 0.88 || = 0.19 539 479 494 491 533 | 500 s 0.93591 0.92349 0.92997 | 500 | 469 475 480 512 546 = 0.87 || = 0.18 532 525 514 474 456 | 500 t 1.09823 1.43249 0.65146 | 500 | 551 497 531 491 503 = 0.86 || = 0.17 446 481 496 512 477 | 500 m 1.05104 1.25282 0.89038 | 500 | 514 476 520 472 454 = 0.85 || = 0.16 510 544 492 490 468 | 500 x 1.13316 1.11140 0.72836 | 500 | 517 530 488 510 497 = 0.84 || = 0.15 510 503 491 487 459 | 500 | 500 | 495 499 509 470 546 = 0.83 || = 0.14 534 506 496 469 502 | 500 Changes: d 56 7 7 | 500 | 462 472 507 488 448 = 0.82 || = 0.13 457 540 484 465 526 | 500 s 52 4 2 | 500 | 520 496 441 493 514 = 0.81 || = 0.12 542 474 508 496 455 | 500 t 49 4 5 | 500 | 480 506 528 517 535 = 0.80 || = 0.11 478 509 513 508 536 | 500 m 54 3 4 | 500 | 560 478 483 537 490 = 0.79 || = 0.10 476 523 492 479 519 | 500 x 60 6 4 | 500 | 484 531 524 496 526 = 0.78 || = 0.09 534 497 507 521 504 | 500 -----------------------------------------------------------------| 500 | 522 499 513 502 498 = 0.77 || = 0.08 487 505 515 522 498 | 500 Aver./ d 0.50018 503 > 500: 5 6 5 5 6 5 6 6 5 4 | 500 | 537 501 556 488 499 = 0.76 || = 0.07 482 490 491 487 514 | 500 median s 0.49983 499 ----- 3 7 3 4 4 7 6 6 1 5 | 500 | 452 500 497 514 508 = 0.75 || = 0.06 514 470 449 493 503 | 500 t 0.49837 503 6 3 6 5 8 3 6 6 4 3 | 500 | 507 487 473 460 536 = 0.74 || = 0.05 508 501 511 499 500 | 500 m 0.50142 498 5 2 4 2 6 5 5 7 3 5 | 500 | 506 512 543 528 494 = 0.73 || = 0.04 484 490 487 468 539 | 500 x 0.49950 500 7 5 5 5 6 3 4 5 6 3 | 500 | 535 520 479 519 481 = 0.72 || = 0.03 507 496 469 478 504 | 500 -----------------------------------------------------------------| 500 | 496 530 525 507 513 = 0.71 || = 0.02 499 490 506 556 520 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 517 464 503 519 495 = 0.70 || = 0.01 249 254 259 266 280 | 252.5 d 0 1 3 18 60 17 2 0 0 | 500 | 470 525 452 529 447 = 0.69 || < 0.01 507 468 527 516 465 | 497.5 s 0 0 1 13 71 15 1 0 0 | 500 | 495 540 536 532 479 = 0.68 ||========================================================================= t 0 1 4 12 69 12 2 1 0 | 500 | 505 537 506 500 471 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 17 67 11 4 1 0 | 500 | 502 484 475 462 558 = 0.66 ||========================================================================= x 0 0 6 11 66 14 3 1 0 | 500 | 533 479 489 511 515 = 0.65 || sknuth_SimpPoker test: no 47 test no 48 TestU01 250000 runs BigCrush Test smarsa_S sknuth_SimpPoker test: test no 48 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 2 0 1 | 0.5 | 2 0 1 0 0 > 0.99999 || = 0.64 480 477 504 508 481 | 500 < 0.00002 1 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 513 529 486 551 501 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 1 0 0 0 1 > 0.99997 || = 0.62 456 477 490 515 502 | 500 < 0.00004 1 1 0 0 1 | 0.5 | 0 2 1 0 0 > 0.99996 || = 0.61 507 455 491 493 524 | 500 < 0.00005 0 2 0 0 2 | 0.5 | 1 0 1 1 0 > 0.99995 || = 0.60 472 507 486 466 508 | 500 < 0.00006 0 0 1 1 0 | 0.5 | 0 1 0 1 1 > 0.99994 || = 0.59 516 479 467 530 511 | 500 < 0.00007 0 0 0 2 1 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 508 542 538 495 533 | 500 < 0.00008 0 0 2 0 0 | 0.5 | 0 0 1 0 1 > 0.99992 || = 0.57 507 504 487 534 514 | 500 < 0.00009 0 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 484 528 498 512 454 | 500 < 0.0001 0 1 0 1 0 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 521 505 491 500 526 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 540 504 522 497 473 | 500 < 0.0001 2 5 7 5 6 | 5 | 5 3 4 3 3 > 0.9999 || = 0.53 500 493 480 525 484 | 500 < 0.0002 6 7 6 4 7 | 5 | 1 1 4 4 2 > 0.9998 || = 0.52 497 500 501 508 515 | 500 < 0.0003 6 7 9 6 8 | 5 | 6 4 7 3 4 > 0.9997 || = 0.51 505 479 495 546 494 | 500 < 0.0004 6 10 6 5 5 | 5 | 6 2 8 6 6 > 0.9996 || = 0.50 469 482 507 535 503 | 500 < 0.0005 4 5 9 4 3 | 5 | 5 7 6 9 4 > 0.9995 || = 0.49 510 485 522 484 487 | 500 < 0.0006 5 4 4 3 5 | 5 | 1 5 5 2 4 > 0.9994 || = 0.48 488 504 529 506 466 | 500 < 0.0007 7 2 9 5 4 | 5 | 9 6 2 3 1 > 0.9993 || = 0.47 502 514 474 483 518 | 500 < 0.0008 7 9 4 5 2 | 5 | 3 3 2 7 8 > 0.9992 || = 0.46 481 529 488 523 508 | 500 < 0.0009 3 4 10 5 6 | 5 | 0 7 7 3 1 > 0.9991 || = 0.45 476 486 487 500 465 | 500 < 0.001 7 6 6 5 6 | 5 | 4 3 7 6 6 > 0.999 || = 0.44 498 514 494 495 520 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 480 524 536 477 484 | 500 < 0.001 53 59 70 47 52 | 50 | 40 41 52 46 39 > 0.999 || = 0.42 494 481 534 476 496 | 500 < 0.002 41 41 60 51 36 | 50 | 51 50 46 48 50 > 0.998 || = 0.41 519 516 518 521 494 | 500 < 0.003 50 42 46 36 51 | 50 | 39 47 49 52 53 > 0.997 || = 0.40 520 476 530 511 537 | 500 < 0.004 47 60 48 50 58 | 50 | 58 55 49 39 42 > 0.996 || = 0.39 463 507 501 518 452 | 500 < 0.005 55 62 48 48 45 | 50 | 58 56 53 57 47 > 0.995 || = 0.38 492 514 476 506 487 | 500 < 0.006 57 44 53 43 48 | 50 | 37 58 43 44 48 > 0.994 || = 0.37 488 506 537 505 483 | 500 < 0.007 42 35 47 53 55 | 50 | 41 66 47 53 56 > 0.993 || = 0.36 536 498 488 499 515 | 500 < 0.008 52 40 53 77 42 | 50 | 59 58 51 55 62 > 0.992 || = 0.35 498 496 479 520 544 | 500 < 0.009 46 59 50 50 54 | 50 | 44 51 40 46 55 > 0.991 || = 0.34 519 526 470 521 499 | 500 < 0.01 53 47 36 55 49 | 50 | 52 44 41 46 49 > 0.99 || = 0.33 482 486 492 512 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 529 505 508 498 488 | 500 < 0.01 496 489 511 510 490 | 497.5 | 479 526 471 486 501 > 0.99 || = 0.31 520 486 522 426 490 | 500 = 0.01 243 264 246 241 258 | 252.5 | 251 250 277 218 252 = 0.99 || = 0.30 513 514 476 498 482 | 500 = 0.02 492 483 513 512 525 | 500 | 525 457 492 482 480 = 0.98 || = 0.29 513 505 514 495 484 | 500 =================================================================| 500 | 531 472 481 540 469 = 0.97 || = 0.28 518 487 497 515 512 | 500 sknuth_SimpPoker test: | 500 | 502 509 479 508 497 = 0.96 || = 0.27 469 470 465 491 471 | 500 ----------------------------------------------- | 500 | 488 497 501 547 508 = 0.95 || = 0.26 539 462 548 474 492 | 500 N = 1, n = 100000000, r = 0, d = 32, k = 32 | 500 | 529 509 500 491 511 = 0.94 || = 0.25 489 488 489 481 499 | 500 | 500 | 515 517 485 482 486 = 0.93 || = 0.24 434 484 530 482 475 | 500 | 500 | 481 474 504 449 518 = 0.92 || = 0.23 499 488 515 550 509 | 500 =================================================================| 500 | 462 503 549 486 524 = 0.91 || = 0.22 486 501 496 516 493 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 495 512 499 508 506 = 0.90 || = 0.21 526 527 474 511 491 | 500 -----------------------------------------------------------------| 500 | 541 536 503 473 518 = 0.89 || = 0.20 527 506 501 512 501 | 500 SD Bern.: d 0.98293 0.72973 1.20142 | 500 | 484 516 503 469 504 = 0.88 || = 0.19 472 495 500 546 484 | 500 s 0.90131 1.35787 1.07010 | 500 | 521 496 507 515 503 = 0.87 || = 0.18 461 519 570 522 524 | 500 t 0.92951 1.22290 0.73656 | 500 | 522 480 506 499 510 = 0.86 || = 0.17 454 490 491 514 500 | 500 m 1.07662 1.43039 0.76979 | 500 | 510 505 483 509 452 = 0.85 || = 0.16 481 487 476 454 501 | 500 x 0.94142 0.89486 0.90929 | 500 | 516 496 501 535 516 = 0.84 || = 0.15 466 503 507 505 500 | 500 | 500 | 480 489 495 492 490 = 0.83 || = 0.14 507 504 514 486 531 | 500 Changes: d 46 6 7 | 500 | 486 502 495 463 500 = 0.82 || = 0.13 517 497 487 464 520 | 500 s 55 5 2 | 500 | 504 497 505 497 462 = 0.81 || = 0.12 505 479 506 515 486 | 500 t 53 5 5 | 500 | 514 538 523 478 495 = 0.80 || = 0.11 517 515 489 508 538 | 500 m 45 5 6 | 500 | 536 496 506 493 551 = 0.79 || = 0.10 472 503 504 480 507 | 500 x 47 7 4 | 500 | 510 515 509 517 518 = 0.78 || = 0.09 503 531 491 516 477 | 500 -----------------------------------------------------------------| 500 | 480 441 499 519 523 = 0.77 || = 0.08 517 525 499 488 509 | 500 Aver./ d 0.50087 502 > 500: 6 4 5 5 4 6 4 6 6 5 | 500 | 494 516 529 499 533 = 0.76 || = 0.07 514 505 499 482 512 | 500 median s 0.49984 503 ----- 7 5 4 6 6 6 5 4 5 5 | 500 | 487 485 466 485 510 = 0.75 || = 0.06 504 529 507 518 473 | 500 t 0.49951 499 3 5 5 4 6 3 5 5 6 4 | 500 | 461 472 451 510 508 = 0.74 || = 0.05 533 505 478 497 494 | 500 m 0.49997 500 4 6 5 6 4 6 6 4 4 3 | 500 | 532 495 472 462 468 = 0.73 || = 0.04 493 456 487 461 491 | 500 x 0.50018 500 5 6 3 2 4 6 5 6 6 5 | 500 | 505 518 479 527 476 = 0.72 || = 0.03 523 510 482 447 520 | 500 -----------------------------------------------------------------| 500 | 505 491 509 496 494 = 0.71 || = 0.02 492 483 513 512 525 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 491 480 506 479 495 = 0.70 || = 0.01 243 264 246 241 258 | 252.5 d 0 0 2 12 72 15 0 0 0 | 500 | 499 536 505 475 479 = 0.69 || < 0.01 496 489 511 510 490 | 497.5 s 0 0 2 10 74 15 0 0 0 | 500 | 507 479 510 493 556 = 0.68 ||========================================================================= t 0 0 1 12 74 11 2 1 0 | 500 | 531 532 494 502 483 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 4 11 71 9 5 0 0 | 500 | 491 507 474 527 526 = 0.66 ||========================================================================= x 0 0 3 11 72 13 2 0 0 | 500 | 482 521 542 502 490 = 0.65 || sknuth_SimpPoker test: no 48 test no 49 TestU01 250000 runs BigCrush Test smarsa_S sknuth_SimpPoker test: test no 49 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 0 2 0 | 0.5 | 0 1 0 1 1 > 0.99999 || = 0.64 510 490 466 514 503 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 445 495 515 496 514 | 500 < 0.00003 1 0 0 0 0 | 0.5 | 0 1 1 1 1 > 0.99997 || = 0.62 495 480 514 479 490 | 500 < 0.00004 0 2 1 0 0 | 0.5 | 1 1 2 0 0 > 0.99996 || = 0.61 510 540 449 493 501 | 500 < 0.00005 2 0 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99995 || = 0.60 510 494 489 482 555 | 500 < 0.00006 0 0 0 1 0 | 0.5 | 0 0 1 1 0 > 0.99994 || = 0.59 529 544 465 499 488 | 500 < 0.00007 0 0 3 0 1 | 0.5 | 0 0 1 0 1 > 0.99993 || = 0.58 543 529 530 522 557 | 500 < 0.00008 0 0 1 0 0 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 513 492 473 484 521 | 500 < 0.00009 2 1 0 0 0 | 0.5 | 2 0 0 1 1 > 0.99991 || = 0.56 483 446 502 481 502 | 500 < 0.0001 0 1 1 0 1 | 0.5 | 1 0 0 1 0 > 0.9999 || = 0.55 521 512 508 512 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 498 513 504 504 495 | 500 < 0.0001 5 6 6 4 2 | 5 | 5 3 5 5 6 > 0.9999 || = 0.53 491 492 506 519 500 | 500 < 0.0002 5 5 5 5 5 | 5 | 2 4 2 3 3 > 0.9998 || = 0.52 514 486 509 486 544 | 500 < 0.0003 6 7 4 3 6 | 5 | 5 3 7 5 1 > 0.9997 || = 0.51 531 518 476 473 464 | 500 < 0.0004 8 10 3 5 3 | 5 | 6 2 2 1 3 > 0.9996 || = 0.50 496 460 499 546 479 | 500 < 0.0005 6 3 5 3 4 | 5 | 7 3 6 7 6 > 0.9995 || = 0.49 502 523 551 487 512 | 500 < 0.0006 3 4 5 5 6 | 5 | 5 4 1 6 5 > 0.9994 || = 0.48 499 516 487 501 472 | 500 < 0.0007 4 6 6 5 8 | 5 | 8 1 5 2 6 > 0.9993 || = 0.47 508 457 478 495 491 | 500 < 0.0008 7 7 1 8 6 | 5 | 7 1 4 3 5 > 0.9992 || = 0.46 517 513 483 511 479 | 500 < 0.0009 3 3 6 6 6 | 5 | 5 6 6 3 7 > 0.9991 || = 0.45 520 520 483 485 512 | 500 < 0.001 3 4 2 2 11 | 5 | 6 5 3 4 6 > 0.999 || = 0.44 473 504 467 498 479 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 469 511 506 499 517 | 500 < 0.001 50 55 43 46 57 | 50 | 56 32 41 39 48 > 0.999 || = 0.42 472 553 506 489 481 | 500 < 0.002 61 53 44 53 48 | 50 | 45 42 49 56 46 > 0.998 || = 0.41 497 490 516 513 508 | 500 < 0.003 45 46 47 42 42 | 50 | 48 43 54 48 42 > 0.997 || = 0.40 499 479 522 495 520 | 500 < 0.004 51 39 39 61 47 | 50 | 47 65 44 41 53 > 0.996 || = 0.39 499 514 505 510 518 | 500 < 0.005 47 46 68 44 51 | 50 | 50 46 35 41 52 > 0.995 || = 0.38 494 517 491 527 471 | 500 < 0.006 59 48 47 59 51 | 50 | 59 56 53 42 40 > 0.994 || = 0.37 521 507 495 488 494 | 500 < 0.007 54 43 54 50 52 | 50 | 52 48 62 55 45 > 0.993 || = 0.36 498 464 516 483 481 | 500 < 0.008 59 53 55 56 54 | 50 | 53 41 45 54 58 > 0.992 || = 0.35 488 465 507 482 484 | 500 < 0.009 53 56 54 61 50 | 50 | 47 53 48 51 56 > 0.991 || = 0.34 510 497 497 499 501 | 500 < 0.01 50 57 54 65 61 | 50 | 42 36 47 47 53 > 0.99 || = 0.33 507 481 507 503 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 499 482 538 490 500 | 500 < 0.01 529 496 505 537 513 | 497.5 | 499 462 478 474 493 > 0.99 || = 0.31 537 506 500 491 490 | 500 = 0.01 237 236 271 244 266 | 252.5 | 263 288 257 276 247 = 0.99 || = 0.30 481 516 518 530 489 | 500 = 0.02 503 511 467 483 502 | 500 | 473 491 521 510 545 = 0.98 || = 0.29 517 483 465 518 510 | 500 =================================================================| 500 | 487 518 507 479 532 = 0.97 || = 0.28 512 486 485 540 498 | 500 sknuth_SimpPoker test: | 500 | 530 471 484 496 498 = 0.96 || = 0.27 515 506 477 506 522 | 500 ----------------------------------------------- | 500 | 487 495 488 496 488 = 0.95 || = 0.26 487 507 527 520 519 | 500 N = 1, n = 100000000, r = 25, d = 32, k = 32 | 500 | 489 498 475 470 496 = 0.94 || = 0.25 513 490 505 497 505 | 500 | 500 | 523 515 507 531 532 = 0.93 || = 0.24 499 511 498 473 486 | 500 | 500 | 486 472 475 500 522 = 0.92 || = 0.23 514 506 523 505 477 | 500 =================================================================| 500 | 517 535 549 484 502 = 0.91 || = 0.22 489 482 473 478 482 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 461 504 515 517 458 = 0.90 || = 0.21 493 507 508 525 486 | 500 -----------------------------------------------------------------| 500 | 524 476 484 506 494 = 0.89 || = 0.20 511 469 514 542 512 | 500 SD Bern.: d 0.95184 0.82866 0.69460 | 500 | 472 518 473 505 494 = 0.88 || = 0.19 475 535 534 482 497 | 500 s 1.06959 0.81771 1.41773 | 500 | 500 537 516 484 469 = 0.87 || = 0.18 477 499 500 513 481 | 500 t 0.97007 1.11500 1.04932 | 500 | 468 510 481 506 504 = 0.86 || = 0.17 476 483 546 478 495 | 500 m 0.90723 1.19138 0.93640 | 500 | 440 507 487 490 479 = 0.85 || = 0.16 512 517 485 494 523 | 500 x 0.91125 0.73384 0.81403 | 500 | 516 495 527 532 462 = 0.84 || = 0.15 452 490 502 517 515 | 500 | 500 | 464 491 473 499 526 = 0.83 || = 0.14 516 513 499 457 505 | 500 Changes: d 54 6 3 | 500 | 524 510 490 488 503 = 0.82 || = 0.13 488 442 517 508 519 | 500 s 54 2 6 | 500 | 529 515 509 546 520 = 0.81 || = 0.12 499 507 490 476 546 | 500 t 55 3 4 | 500 | 459 511 476 522 505 = 0.80 || = 0.11 485 477 489 501 502 | 500 m 55 7 4 | 500 | 508 533 475 480 523 = 0.79 || = 0.10 531 462 517 480 497 | 500 x 43 4 3 | 500 | 517 534 538 526 482 = 0.78 || = 0.09 488 505 509 479 481 | 500 -----------------------------------------------------------------| 500 | 511 511 493 508 507 = 0.77 || = 0.08 491 499 497 457 507 | 500 Aver./ d 0.50060 499 > 500: 3 3 6 4 4 7 5 7 4 5 | 500 | 509 487 462 496 453 = 0.76 || = 0.07 480 457 506 493 505 | 500 median s 0.50159 504 ----- 5 4 5 5 7 5 4 6 7 4 | 500 | 546 464 522 507 482 = 0.75 || = 0.06 476 565 489 503 517 | 500 t 0.49838 501 6 5 5 6 5 6 6 3 4 5 | 500 | 513 499 501 488 492 = 0.74 || = 0.05 493 509 508 513 492 | 500 m 0.50146 499 3 4 7 4 3 4 5 6 6 3 | 500 | 488 484 471 509 474 = 0.73 || = 0.04 484 472 519 454 517 | 500 x 0.49898 500 8 6 5 2 5 5 7 3 4 5 | 500 | 498 504 490 471 467 = 0.72 || = 0.03 506 515 496 489 509 | 500 -----------------------------------------------------------------| 500 | 515 507 499 529 480 = 0.71 || = 0.02 503 511 467 483 502 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 490 541 523 489 506 = 0.70 || = 0.01 237 236 271 244 266 | 252.5 d 0 0 3 13 71 13 1 0 0 | 500 | 523 468 521 477 507 = 0.69 || < 0.01 529 496 505 537 513 | 497.5 s 0 0 2 16 70 10 3 0 0 | 500 | 496 486 475 541 497 = 0.68 ||========================================================================= t 0 0 1 19 67 10 4 0 0 | 500 | 499 520 475 519 504 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 9 77 12 2 0 0 | 500 | 508 479 549 503 469 = 0.66 ||========================================================================= x 0 0 1 10 80 6 4 0 0 | 500 | 541 521 535 518 509 = 0.65 || sknuth_SimpPoker test: no 49 test no 50 TestU01 250000 runs BigCrush Test smarsa_S sknuth_CouponCollector test: test no 50 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 1 1 0 | 0.5 | 0 2 1 1 0 > 0.99999 || = 0.64 503 516 469 497 473 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 494 462 494 561 474 | 500 < 0.00003 0 0 1 3 0 | 0.5 | 0 1 2 0 1 > 0.99997 || = 0.62 515 529 525 500 543 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 0 1 0 0 0 > 0.99996 || = 0.61 504 503 503 537 512 | 500 < 0.00005 0 0 1 2 0 | 0.5 | 1 0 0 1 3 > 0.99995 || = 0.60 485 503 533 510 549 | 500 < 0.00006 0 1 0 0 0 | 0.5 | 0 0 0 2 1 > 0.99994 || = 0.59 467 508 495 490 506 | 500 < 0.00007 1 0 2 2 0 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 516 497 483 497 440 | 500 < 0.00008 0 1 1 1 0 | 0.5 | 1 0 0 0 1 > 0.99992 || = 0.57 531 512 510 478 518 | 500 < 0.00009 0 0 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 512 506 511 532 502 | 500 < 0.0001 0 1 0 1 1 | 0.5 | 0 1 1 0 0 > 0.9999 || = 0.55 500 479 447 482 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 501 530 502 476 480 | 500 < 0.0001 1 4 8 12 2 | 5 | 2 6 4 4 6 > 0.9999 || = 0.53 484 506 528 492 519 | 500 < 0.0002 4 3 3 6 2 | 5 | 1 3 6 1 3 > 0.9998 || = 0.52 470 524 487 513 499 | 500 < 0.0003 7 3 3 4 9 | 5 | 6 5 3 2 10 > 0.9997 || = 0.51 501 495 470 479 527 | 500 < 0.0004 5 4 1 7 2 | 5 | 7 5 5 5 4 > 0.9996 || = 0.50 535 492 492 486 542 | 500 < 0.0005 6 3 3 8 4 | 5 | 5 2 4 6 9 > 0.9995 || = 0.49 494 527 524 477 485 | 500 < 0.0006 5 4 7 5 4 | 5 | 7 7 1 4 6 > 0.9994 || = 0.48 549 510 479 463 489 | 500 < 0.0007 4 10 8 1 5 | 5 | 8 7 3 1 2 > 0.9993 || = 0.47 470 479 484 487 503 | 500 < 0.0008 5 6 4 6 6 | 5 | 7 5 1 8 4 > 0.9992 || = 0.46 491 480 477 545 438 | 500 < 0.0009 2 6 8 9 2 | 5 | 5 4 5 7 8 > 0.9991 || = 0.45 492 503 528 549 546 | 500 < 0.001 2 6 7 5 5 | 5 | 3 1 1 6 7 > 0.999 || = 0.44 498 483 516 513 467 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 498 486 508 496 496 | 500 < 0.001 41 49 52 63 41 | 50 | 51 45 33 44 59 > 0.999 || = 0.42 502 529 510 489 477 | 500 < 0.002 53 64 58 60 53 | 50 | 52 48 50 38 44 > 0.998 || = 0.41 525 514 479 487 485 | 500 < 0.003 49 60 51 35 55 | 50 | 59 52 54 44 49 > 0.997 || = 0.40 510 457 479 457 492 | 500 < 0.004 54 51 48 45 47 | 50 | 47 61 61 54 46 > 0.996 || = 0.39 478 538 496 517 501 | 500 < 0.005 49 43 47 46 44 | 50 | 60 39 54 54 46 > 0.995 || = 0.38 495 495 507 503 510 | 500 < 0.006 44 49 49 45 54 | 50 | 50 46 46 57 45 > 0.994 || = 0.37 513 483 518 458 455 | 500 < 0.007 59 41 44 52 49 | 50 | 56 41 43 39 49 > 0.993 || = 0.36 513 480 475 540 525 | 500 < 0.008 56 44 57 50 59 | 50 | 42 60 51 55 48 > 0.992 || = 0.35 504 481 556 487 509 | 500 < 0.009 42 44 54 46 48 | 50 | 52 57 51 48 39 > 0.991 || = 0.34 497 504 485 499 486 | 500 < 0.01 44 55 36 39 45 | 50 | 40 55 47 54 47 > 0.99 || = 0.33 479 514 493 481 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 523 493 510 510 499 | 500 < 0.01 491 500 496 481 495 | 497.5 | 509 504 490 487 472 > 0.99 || = 0.31 482 530 521 519 480 | 500 = 0.01 269 223 265 253 263 | 252.5 | 253 259 252 269 247 = 0.99 || = 0.30 512 518 548 490 487 | 500 = 0.02 499 482 498 503 479 | 500 | 495 490 508 498 456 = 0.98 || = 0.29 505 527 528 515 527 | 500 =================================================================| 500 | 506 497 510 495 470 = 0.97 || = 0.28 500 485 493 467 500 | 500 sknuth_CouponCollector test: | 500 | 511 481 510 527 532 = 0.96 || = 0.27 487 478 496 488 467 | 500 ----------------------------------------------- | 500 | 458 549 508 515 520 = 0.95 || = 0.26 483 490 499 506 489 | 500 N = 1, n = 200000000, r = 0, d = 8 | 500 | 519 488 503 499 501 = 0.94 || = 0.25 480 476 475 505 509 | 500 | 500 | 560 532 534 503 524 = 0.93 || = 0.24 458 518 471 476 523 | 500 | 500 | 507 532 500 488 484 = 0.92 || = 0.23 499 481 497 523 555 | 500 =================================================================| 500 | 486 528 478 516 545 = 0.91 || = 0.22 513 476 509 515 537 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 508 493 508 518 485 = 0.90 || = 0.21 516 484 475 484 487 | 500 -----------------------------------------------------------------| 500 | 499 500 454 496 508 = 0.89 || = 0.20 500 471 510 488 504 | 500 SD Bern.: d 0.89567 0.85012 0.89374 | 500 | 521 500 528 506 527 = 0.88 || = 0.19 501 515 493 511 507 | 500 s 0.95696 1.02617 1.04550 | 500 | 475 512 491 515 491 = 0.87 || = 0.18 513 491 509 523 494 | 500 t 0.93333 0.87220 1.01834 | 500 | 529 501 514 486 487 = 0.86 || = 0.17 509 509 463 501 484 | 500 m 0.97292 1.18464 0.96276 | 500 | 481 506 500 528 482 = 0.85 || = 0.16 485 496 499 519 500 | 500 x 1.09691 0.75799 0.78778 | 500 | 478 489 487 497 474 = 0.84 || = 0.15 474 472 479 480 495 | 500 | 500 | 510 496 494 496 509 = 0.83 || = 0.14 493 543 551 485 491 | 500 Changes: d 54 6 7 | 500 | 499 470 509 536 525 = 0.82 || = 0.13 496 492 491 485 515 | 500 s 50 3 3 | 500 | 530 469 503 500 526 = 0.81 || = 0.12 452 494 501 474 462 | 500 t 44 3 4 | 500 | 488 454 527 518 541 = 0.80 || = 0.11 508 477 468 511 529 | 500 m 55 3 5 | 500 | 528 470 555 551 479 = 0.79 || = 0.10 503 506 500 490 503 | 500 x 46 6 1 | 500 | 499 519 507 497 509 = 0.78 || = 0.09 506 480 476 494 512 | 500 -----------------------------------------------------------------| 500 | 528 516 493 532 471 = 0.77 || = 0.08 488 543 478 468 488 | 500 Aver./ d 0.50189 500 > 500: 4 5 3 5 4 5 6 6 5 7 | 500 | 515 544 488 475 461 = 0.76 || = 0.07 460 509 499 484 526 | 500 median s 0.50206 500 ----- 4 4 2 5 5 7 7 6 3 6 | 500 | 519 520 518 496 493 = 0.75 || = 0.06 498 485 522 542 462 | 500 t 0.50127 499 3 3 3 6 5 5 6 4 5 6 | 500 | 503 483 486 517 544 = 0.74 || = 0.05 513 502 503 486 480 | 500 m 0.50258 497 3 5 5 5 3 3 5 6 5 5 | 500 | 506 503 478 507 514 = 0.73 || = 0.04 481 489 497 459 517 | 500 x 0.50042 499 4 4 6 4 2 6 4 5 5 5 | 500 | 477 488 490 519 516 = 0.72 || = 0.03 509 474 471 495 491 | 500 -----------------------------------------------------------------| 500 | 483 502 496 454 487 = 0.71 || = 0.02 499 482 498 503 479 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 451 512 488 484 505 = 0.70 || = 0.01 269 223 265 253 263 | 252.5 d 0 0 2 9 78 9 3 0 0 | 500 | 478 485 517 476 546 = 0.69 || < 0.01 491 500 496 481 495 | 497.5 s 0 0 1 12 71 16 1 0 0 | 500 | 503 537 518 511 498 = 0.68 ||========================================================================= t 0 0 2 12 73 10 4 0 0 | 500 | 497 535 523 501 491 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 13 72 11 4 0 0 | 500 | 511 482 510 476 499 = 0.66 ||========================================================================= x 0 0 3 13 64 16 5 0 0 | 500 | 548 520 471 503 478 = 0.65 || sknuth_CouponCollector test: no 50 test no 51 TestU01 250000 runs BigCrush Test smarsa_S sknuth_CouponCollector test: test no 51 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 1 0 0 1 > 0.99999 || = 0.64 480 475 530 513 499 | 500 < 0.00002 0 1 2 0 0 | 0.5 | 1 1 0 3 0 > 0.99998 || = 0.63 482 460 517 514 515 | 500 < 0.00003 0 0 0 0 1 | 0.5 | 1 0 1 0 1 > 0.99997 || = 0.62 497 482 468 462 498 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 1 0 0 1 > 0.99996 || = 0.61 450 504 476 496 524 | 500 < 0.00005 1 1 2 0 0 | 0.5 | 0 2 0 1 2 > 0.99995 || = 0.60 518 484 541 474 505 | 500 < 0.00006 0 1 1 0 0 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 463 509 527 525 532 | 500 < 0.00007 1 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 511 513 477 480 541 | 500 < 0.00008 0 1 1 0 0 | 0.5 | 1 0 0 2 0 > 0.99992 || = 0.57 485 472 487 471 493 | 500 < 0.00009 1 0 1 0 1 | 0.5 | 1 0 1 1 0 > 0.99991 || = 0.56 478 510 481 512 477 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 3 0 > 0.9999 || = 0.55 496 477 497 557 519 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 506 513 496 479 448 | 500 < 0.0001 3 4 7 0 2 | 5 | 5 5 2 11 5 > 0.9999 || = 0.53 506 537 519 480 493 | 500 < 0.0002 4 8 3 3 6 | 5 | 2 3 2 4 2 > 0.9998 || = 0.52 491 528 504 473 497 | 500 < 0.0003 7 7 5 7 8 | 5 | 5 7 3 3 5 > 0.9997 || = 0.51 495 489 541 493 471 | 500 < 0.0004 5 5 7 5 3 | 5 | 7 8 5 6 6 > 0.9996 || = 0.50 462 530 453 508 504 | 500 < 0.0005 6 6 8 4 6 | 5 | 3 8 6 4 5 > 0.9995 || = 0.49 483 497 545 522 536 | 500 < 0.0006 7 5 4 6 3 | 5 | 3 1 3 5 3 > 0.9994 || = 0.48 498 510 502 478 508 | 500 < 0.0007 9 4 4 3 4 | 5 | 2 5 7 6 3 > 0.9993 || = 0.47 500 550 526 471 501 | 500 < 0.0008 5 5 5 5 5 | 5 | 6 7 4 7 5 > 0.9992 || = 0.46 482 474 497 517 509 | 500 < 0.0009 4 4 1 8 3 | 5 | 4 5 2 4 8 > 0.9991 || = 0.45 483 555 505 499 493 | 500 < 0.001 6 6 5 4 7 | 5 | 4 2 7 1 6 > 0.999 || = 0.44 553 507 538 493 541 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 468 496 470 491 537 | 500 < 0.001 56 54 49 45 47 | 50 | 41 51 41 51 48 > 0.999 || = 0.42 487 540 509 468 475 | 500 < 0.002 41 45 54 50 37 | 50 | 41 46 54 43 45 > 0.998 || = 0.41 531 465 493 496 519 | 500 < 0.003 40 47 52 45 32 | 50 | 43 45 53 61 68 > 0.997 || = 0.40 496 490 482 508 493 | 500 < 0.004 57 50 57 48 60 | 50 | 38 52 50 53 64 > 0.996 || = 0.39 500 508 502 469 499 | 500 < 0.005 47 52 34 39 55 | 50 | 51 36 51 55 57 > 0.995 || = 0.38 500 492 462 521 524 | 500 < 0.006 42 44 59 42 57 | 50 | 51 49 45 47 52 > 0.994 || = 0.37 478 496 545 521 476 | 500 < 0.007 42 65 45 53 41 | 50 | 51 58 54 51 51 > 0.993 || = 0.36 495 492 483 520 531 | 500 < 0.008 44 45 55 63 57 | 50 | 42 57 33 46 44 > 0.992 || = 0.35 476 517 491 504 496 | 500 < 0.009 56 60 50 66 51 | 50 | 50 34 57 53 46 > 0.991 || = 0.34 531 533 490 488 496 | 500 < 0.01 56 48 35 53 46 | 50 | 47 46 53 52 64 > 0.99 || = 0.33 502 508 517 511 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 518 491 446 522 518 | 500 < 0.01 481 510 490 504 483 | 497.5 | 455 474 491 512 539 > 0.99 || = 0.31 500 495 505 504 467 | 500 = 0.01 240 257 270 268 236 | 252.5 | 256 229 255 254 225 = 0.99 || = 0.30 498 503 493 463 470 | 500 = 0.02 507 526 479 495 537 | 500 | 489 511 483 521 475 = 0.98 || = 0.29 525 500 505 483 513 | 500 =================================================================| 500 | 452 505 477 494 484 = 0.97 || = 0.28 509 507 525 514 491 | 500 sknuth_CouponCollector test: | 500 | 471 491 503 494 481 = 0.96 || = 0.27 487 491 493 512 461 | 500 ----------------------------------------------- | 500 | 547 499 490 496 517 = 0.95 || = 0.26 511 476 481 506 515 | 500 N = 1, n = 200000000, r = 10, d = 8 | 500 | 507 493 481 508 520 = 0.94 || = 0.25 478 493 538 500 455 | 500 | 500 | 489 482 482 518 494 = 0.93 || = 0.24 495 463 498 507 502 | 500 | 500 | 522 471 506 467 524 = 0.92 || = 0.23 486 501 493 479 479 | 500 =================================================================| 500 | 489 530 499 457 500 = 0.91 || = 0.22 457 481 520 496 520 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 525 512 504 485 474 = 0.90 || = 0.21 517 510 538 545 500 | 500 -----------------------------------------------------------------| 500 | 505 520 514 488 506 = 0.89 || = 0.20 527 525 465 519 499 | 500 SD Bern.: d 1.07864 1.01143 0.92889 | 500 | 512 492 511 555 540 = 0.88 || = 0.19 523 512 493 481 510 | 500 s 0.94172 0.94280 1.12126 | 500 | 510 526 513 552 474 = 0.87 || = 0.18 496 457 554 488 535 | 500 t 1.02279 1.16848 0.99547 | 500 | 539 490 459 482 525 = 0.86 || = 0.17 494 500 505 483 468 | 500 m 1.05203 1.16848 0.69890 | 500 | 530 474 495 513 452 = 0.85 || = 0.16 515 488 508 532 465 | 500 x 1.03840 1.28360 1.30525 | 500 | 527 512 491 483 531 = 0.84 || = 0.15 467 505 487 519 517 | 500 | 500 | 535 509 485 470 516 = 0.83 || = 0.14 482 496 477 489 471 | 500 Changes: d 40 4 2 | 500 | 510 478 518 475 492 = 0.82 || = 0.13 490 492 528 509 522 | 500 s 55 7 5 | 500 | 567 531 489 497 481 = 0.81 || = 0.12 498 504 505 554 513 | 500 t 54 6 7 | 500 | 541 493 507 476 482 = 0.80 || = 0.11 529 501 473 482 472 | 500 m 48 1 6 | 500 | 506 523 463 505 527 = 0.79 || = 0.10 502 511 522 502 529 | 500 x 57 4 3 | 500 | 490 499 468 544 515 = 0.78 || = 0.09 534 491 484 515 490 | 500 -----------------------------------------------------------------| 500 | 467 493 521 521 527 = 0.77 || = 0.08 490 526 524 469 509 | 500 Aver./ d 0.50075 498 > 500: 5 4 5 3 2 4 4 5 10 4 | 500 | 457 499 518 514 519 = 0.76 || = 0.07 475 498 507 503 491 | 500 median s 0.50026 499 ----- 4 5 4 5 5 6 4 4 6 3 | 500 | 521 511 501 544 488 = 0.75 || = 0.06 545 455 523 499 500 | 500 t 0.49832 500 6 6 5 4 6 5 5 5 5 3 | 500 | 506 521 482 527 488 = 0.74 || = 0.05 514 496 512 468 499 | 500 m 0.49981 499 5 5 6 7 3 3 4 7 3 5 | 500 | 490 454 482 473 467 = 0.73 || = 0.04 475 480 509 479 488 | 500 x 0.50100 499 2 6 4 3 7 4 4 5 5 4 | 500 | 482 491 500 504 536 = 0.72 || = 0.03 508 473 481 518 474 | 500 -----------------------------------------------------------------| 500 | 511 513 515 461 479 = 0.71 || = 0.02 507 526 479 495 537 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 532 490 536 548 482 = 0.70 || = 0.01 240 257 270 268 236 | 252.5 d 0 0 2 14 66 15 3 1 0 | 500 | 520 481 475 474 510 = 0.69 || < 0.01 481 510 490 504 483 | 497.5 s 0 0 2 14 70 12 3 0 0 | 500 | 535 516 510 525 482 = 0.68 ||========================================================================= t 0 0 3 13 67 15 3 0 0 | 500 | 470 554 536 485 529 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 19 70 6 6 0 0 | 500 | 520 495 485 486 485 = 0.66 ||========================================================================= x 0 0 3 18 60 20 0 0 0 | 500 | 459 511 453 471 493 = 0.65 || sknuth_CouponCollector test: no 51 test no 52 TestU01 250000 runs BigCrush Test smarsa_S sknuth_CouponCollector test: test no 52 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 2 0 2 | 0.5 | 1 2 1 1 5 > 0.99999 || = 0.64 500 484 480 528 523 | 500 < 0.00002 0 0 0 2 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 526 454 487 472 489 | 500 < 0.00003 0 1 1 0 0 | 0.5 | 1 0 1 0 0 > 0.99997 || = 0.62 469 510 514 484 462 | 500 < 0.00004 1 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 497 512 470 522 509 | 500 < 0.00005 1 1 1 1 0 | 0.5 | 0 0 1 1 1 > 0.99995 || = 0.60 513 474 501 494 471 | 500 < 0.00006 0 0 1 0 0 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 515 508 499 488 532 | 500 < 0.00007 0 2 0 0 0 | 0.5 | 0 0 0 0 2 > 0.99993 || = 0.58 501 486 515 512 488 | 500 < 0.00008 1 1 0 0 0 | 0.5 | 0 1 2 0 1 > 0.99992 || = 0.57 469 495 541 505 532 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 1 1 1 1 0 > 0.99991 || = 0.56 488 524 438 502 497 | 500 < 0.0001 1 1 3 1 0 | 0.5 | 1 1 0 1 0 > 0.9999 || = 0.55 520 524 446 496 505 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 518 522 469 533 520 | 500 < 0.0001 5 7 9 4 2 | 5 | 4 5 6 5 9 > 0.9999 || = 0.53 532 461 495 486 506 | 500 < 0.0002 6 4 2 2 9 | 5 | 3 3 2 0 3 > 0.9998 || = 0.52 506 487 525 511 485 | 500 < 0.0003 3 7 10 7 4 | 5 | 4 5 5 5 5 > 0.9997 || = 0.51 515 501 547 507 501 | 500 < 0.0004 5 2 2 7 4 | 5 | 3 8 3 3 4 > 0.9996 || = 0.50 494 502 500 478 490 | 500 < 0.0005 3 5 5 9 6 | 5 | 5 5 3 2 4 > 0.9995 || = 0.49 514 478 509 482 526 | 500 < 0.0006 8 8 6 1 4 | 5 | 8 4 4 5 10 > 0.9994 || = 0.48 501 507 502 498 510 | 500 < 0.0007 3 5 3 2 7 | 5 | 5 2 3 5 0 > 0.9993 || = 0.47 511 480 520 491 483 | 500 < 0.0008 4 3 2 6 8 | 5 | 6 4 4 2 7 > 0.9992 || = 0.46 505 508 495 493 548 | 500 < 0.0009 7 9 1 7 8 | 5 | 8 1 5 6 5 > 0.9991 || = 0.45 535 527 520 493 487 | 500 < 0.001 3 7 4 5 4 | 5 | 2 5 8 4 9 > 0.999 || = 0.44 506 490 505 479 515 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 520 528 569 535 496 | 500 < 0.001 47 57 44 50 56 | 50 | 48 42 43 37 56 > 0.999 || = 0.42 504 467 513 482 516 | 500 < 0.002 57 49 60 31 50 | 50 | 48 56 70 52 41 > 0.998 || = 0.41 511 491 504 499 561 | 500 < 0.003 61 63 62 57 43 | 50 | 51 61 62 47 51 > 0.997 || = 0.40 459 531 509 488 491 | 500 < 0.004 54 50 48 56 56 | 50 | 48 55 49 42 41 > 0.996 || = 0.39 531 522 516 476 478 | 500 < 0.005 45 47 52 48 54 | 50 | 43 44 45 42 55 > 0.995 || = 0.38 504 529 463 462 504 | 500 < 0.006 54 43 56 55 40 | 50 | 41 33 47 49 44 > 0.994 || = 0.37 535 502 506 473 484 | 500 < 0.007 48 47 48 53 50 | 50 | 53 56 53 31 47 > 0.993 || = 0.36 462 489 487 498 541 | 500 < 0.008 60 51 56 52 48 | 50 | 55 54 45 41 52 > 0.992 || = 0.35 519 511 481 473 458 | 500 < 0.009 44 56 49 56 37 | 50 | 48 55 53 43 47 > 0.991 || = 0.34 499 516 488 506 486 | 500 < 0.01 70 54 60 43 44 | 50 | 54 48 43 49 57 > 0.99 || = 0.33 522 500 493 465 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 513 504 513 486 467 | 500 < 0.01 540 517 535 501 478 | 497.5 | 489 504 510 433 491 > 0.99 || = 0.31 501 534 475 544 463 | 500 = 0.01 238 248 240 250 298 | 252.5 | 213 236 247 253 256 = 0.99 || = 0.30 485 503 504 466 555 | 500 = 0.02 497 500 495 505 527 | 500 | 551 517 537 508 526 = 0.98 || = 0.29 494 489 495 450 480 | 500 =================================================================| 500 | 506 483 519 520 522 = 0.97 || = 0.28 478 495 476 495 470 | 500 sknuth_CouponCollector test: | 500 | 502 458 504 505 503 = 0.96 || = 0.27 481 469 528 480 484 | 500 ----------------------------------------------- | 500 | 490 497 464 522 510 = 0.95 || = 0.26 495 507 505 521 513 | 500 N = 1, n = 200000000, r = 20, d = 8 | 500 | 474 469 487 536 503 = 0.94 || = 0.25 513 505 498 473 495 | 500 | 500 | 497 487 523 518 490 = 0.93 || = 0.24 530 526 484 493 489 | 500 | 500 | 498 486 451 498 522 = 0.92 || = 0.23 498 552 501 489 496 | 500 =================================================================| 500 | 537 527 484 507 505 = 0.91 || = 0.22 496 517 499 530 514 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 500 476 505 512 514 = 0.90 || = 0.21 512 475 489 498 495 | 500 -----------------------------------------------------------------| 500 | 498 518 503 484 473 = 0.89 || = 0.20 543 544 506 510 504 | 500 SD Bern.: d 0.97415 1.24641 0.62799 | 500 | 493 512 470 484 480 = 0.88 || = 0.19 488 506 479 494 510 | 500 s 0.96992 0.82381 1.14249 | 500 | 475 476 500 498 472 = 0.87 || = 0.18 469 519 525 523 474 | 500 t 1.02766 0.96484 1.20059 | 500 | 519 536 527 508 485 = 0.86 || = 0.17 508 475 472 522 486 | 500 m 0.95683 1.07104 1.26790 | 500 | 474 530 500 508 480 = 0.85 || = 0.16 466 477 501 509 521 | 500 x 0.97444 0.94492 0.81402 | 500 | 467 516 515 494 500 = 0.84 || = 0.15 499 503 479 499 507 | 500 | 500 | 524 473 496 516 490 = 0.83 || = 0.14 477 496 541 488 483 | 500 Changes: d 47 7 5 | 500 | 466 490 512 533 505 = 0.82 || = 0.13 548 501 502 519 506 | 500 s 52 4 4 | 500 | 504 525 527 494 495 = 0.81 || = 0.12 492 502 528 483 494 | 500 t 52 7 6 | 500 | 489 542 508 535 488 = 0.80 || = 0.11 493 471 493 532 520 | 500 m 50 4 2 | 500 | 504 494 503 514 502 = 0.79 || = 0.10 520 491 490 520 475 | 500 x 52 3 8 | 500 | 513 474 496 521 517 = 0.78 || = 0.09 458 482 480 530 474 | 500 -----------------------------------------------------------------| 500 | 450 496 481 527 511 = 0.77 || = 0.08 493 450 493 498 519 | 500 Aver./ d 0.49879 500 > 500: 4 3 4 7 9 8 4 4 3 4 | 500 | 483 523 456 485 504 = 0.76 || = 0.07 496 524 521 494 505 | 500 median s 0.49950 501 ----- 4 5 6 8 5 5 5 3 6 3 | 500 | 490 481 452 518 494 = 0.75 || = 0.06 501 456 531 510 457 | 500 t 0.49945 501 4 5 4 4 9 5 6 4 6 5 | 500 | 501 514 483 534 539 = 0.74 || = 0.05 525 517 509 482 493 | 500 m 0.50144 498 4 6 3 2 1 6 5 6 5 8 | 500 | 510 494 508 450 504 = 0.73 || = 0.04 505 489 483 480 519 | 500 x 0.49985 497 6 5 3 3 6 6 4 6 2 8 | 500 | 496 499 471 497 480 = 0.72 || = 0.03 482 512 488 482 535 | 500 -----------------------------------------------------------------| 500 | 479 495 505 477 474 = 0.71 || = 0.02 497 500 495 505 527 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 505 480 514 526 485 = 0.70 || = 0.01 238 248 240 250 298 | 252.5 d 0 0 2 15 71 11 2 0 0 | 500 | 468 478 508 525 496 = 0.69 || < 0.01 540 517 535 501 478 | 497.5 s 0 0 2 16 65 17 1 0 0 | 500 | 488 490 482 488 490 = 0.68 ||========================================================================= t 0 0 4 10 71 14 1 1 0 | 500 | 519 514 526 535 483 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 10 72 16 0 0 0 | 500 | 474 528 520 496 516 = 0.66 ||========================================================================= x 0 0 0 13 75 9 4 0 0 | 500 | 519 506 541 474 504 = 0.65 || sknuth_CouponCollector test: no 52 test no 53 TestU01 250000 runs BigCrush Test smarsa_S sknuth_CouponCollector test: test no 53 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 1 1 1 0 > 0.99999 || = 0.64 513 525 487 492 476 | 500 < 0.00002 0 2 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 510 505 516 531 496 | 500 < 0.00003 2 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 497 483 474 516 515 | 500 < 0.00004 2 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 484 468 475 492 490 | 500 < 0.00005 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 498 487 491 513 516 | 500 < 0.00006 0 1 1 0 1 | 0.5 | 0 3 0 1 1 > 0.99994 || = 0.59 527 502 517 483 496 | 500 < 0.00007 1 1 2 0 2 | 0.5 | 1 1 0 0 0 > 0.99993 || = 0.58 481 480 526 515 539 | 500 < 0.00008 0 0 1 0 0 | 0.5 | 0 0 0 1 2 > 0.99992 || = 0.57 479 481 482 491 522 | 500 < 0.00009 0 1 0 0 0 | 0.5 | 2 0 0 0 1 > 0.99991 || = 0.56 523 482 495 529 476 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 1 0 1 > 0.9999 || = 0.55 496 475 506 475 519 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 543 496 531 482 489 | 500 < 0.0001 5 7 5 1 4 | 5 | 3 5 3 3 5 > 0.9999 || = 0.53 499 488 486 502 509 | 500 < 0.0002 7 7 3 1 4 | 5 | 1 1 2 1 4 > 0.9998 || = 0.52 476 547 485 495 453 | 500 < 0.0003 7 6 4 6 4 | 5 | 2 5 4 7 7 > 0.9997 || = 0.51 491 461 486 493 463 | 500 < 0.0004 6 6 6 4 6 | 5 | 6 3 6 4 9 > 0.9996 || = 0.50 506 523 519 540 481 | 500 < 0.0005 4 10 4 3 7 | 5 | 7 4 6 0 4 > 0.9995 || = 0.49 535 496 509 556 506 | 500 < 0.0006 4 4 4 4 1 | 5 | 6 4 3 3 4 > 0.9994 || = 0.48 508 505 504 477 511 | 500 < 0.0007 5 6 4 2 5 | 5 | 4 10 6 2 2 > 0.9993 || = 0.47 448 505 471 523 488 | 500 < 0.0008 4 10 8 7 5 | 5 | 6 6 5 3 5 > 0.9992 || = 0.46 470 459 509 534 516 | 500 < 0.0009 8 2 5 4 8 | 5 | 6 5 2 4 3 > 0.9991 || = 0.45 470 489 440 540 529 | 500 < 0.001 12 6 6 4 2 | 5 | 3 1 7 5 5 > 0.999 || = 0.44 537 505 509 522 481 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 481 513 496 525 524 | 500 < 0.001 62 64 49 36 46 | 50 | 44 44 44 32 48 > 0.999 || = 0.42 496 515 513 467 482 | 500 < 0.002 31 38 56 41 40 | 50 | 44 57 53 57 41 > 0.998 || = 0.41 491 486 490 515 458 | 500 < 0.003 40 46 35 57 53 | 50 | 43 36 52 43 59 > 0.997 || = 0.40 495 529 508 469 511 | 500 < 0.004 39 47 55 38 42 | 50 | 55 49 57 52 56 > 0.996 || = 0.39 495 471 506 457 483 | 500 < 0.005 54 48 43 52 60 | 50 | 41 54 41 42 55 > 0.995 || = 0.38 474 526 525 464 538 | 500 < 0.006 48 48 54 55 61 | 50 | 64 59 57 53 52 > 0.994 || = 0.37 474 538 485 467 508 | 500 < 0.007 46 59 52 54 48 | 50 | 60 53 36 56 66 > 0.993 || = 0.36 536 502 536 495 510 | 500 < 0.008 39 60 49 69 41 | 50 | 53 53 56 49 64 > 0.992 || = 0.35 482 492 493 528 545 | 500 < 0.009 44 47 49 38 36 | 50 | 40 56 49 60 54 > 0.991 || = 0.34 501 502 472 513 509 | 500 < 0.01 42 60 50 40 48 | 50 | 54 45 47 36 50 > 0.99 || = 0.33 501 532 495 500 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 543 499 486 503 497 | 500 < 0.01 445 517 492 480 475 | 497.5 | 498 506 492 480 545 > 0.99 || = 0.31 501 493 502 484 468 | 500 = 0.01 243 278 262 241 247 | 252.5 | 254 272 251 255 240 = 0.99 || = 0.30 498 522 490 496 572 | 500 = 0.02 472 493 494 501 477 | 500 | 519 506 478 510 470 = 0.98 || = 0.29 473 506 506 530 516 | 500 =================================================================| 500 | 497 512 457 490 486 = 0.97 || = 0.28 496 451 490 531 496 | 500 sknuth_CouponCollector test: | 500 | 501 511 492 475 499 = 0.96 || = 0.27 527 463 473 513 529 | 500 ----------------------------------------------- | 500 | 523 506 532 467 497 = 0.95 || = 0.26 526 529 524 518 499 | 500 N = 1, n = 200000000, r = 27, d = 8 | 500 | 502 511 530 497 487 = 0.94 || = 0.25 531 486 486 480 499 | 500 | 500 | 503 505 470 506 497 = 0.93 || = 0.24 510 497 508 487 498 | 500 | 500 | 498 492 481 521 505 = 0.92 || = 0.23 482 492 484 506 464 | 500 =================================================================| 500 | 519 492 507 502 513 = 0.91 || = 0.22 489 505 524 504 510 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 495 512 534 484 494 = 0.90 || = 0.21 495 460 534 516 511 | 500 -----------------------------------------------------------------| 500 | 500 493 472 500 495 = 0.89 || = 0.20 469 502 516 515 503 | 500 SD Bern.: d 0.90844 1.40283 1.13898 | 500 | 514 511 495 500 481 = 0.88 || = 0.19 485 526 490 537 493 | 500 s 0.91967 1.15209 0.95754 | 500 | 495 497 486 491 535 = 0.87 || = 0.18 493 508 535 522 501 | 500 t 0.95116 0.84658 0.97001 | 500 | 486 497 527 494 506 = 0.86 || = 0.17 506 507 501 496 528 | 500 m 0.93879 1.49740 1.29059 | 500 | 473 491 502 527 507 = 0.85 || = 0.16 512 495 500 496 488 | 500 x 0.99332 1.17956 1.18295 | 500 | 531 512 496 514 491 = 0.84 || = 0.15 529 512 504 523 516 | 500 | 500 | 504 467 541 477 482 = 0.83 || = 0.14 484 491 484 491 499 | 500 Changes: d 48 3 5 | 500 | 489 479 523 492 515 = 0.82 || = 0.13 519 561 512 466 459 | 500 s 54 4 4 | 500 | 522 480 520 512 520 = 0.81 || = 0.12 453 479 533 498 472 | 500 t 60 6 6 | 500 | 521 523 508 482 527 = 0.80 || = 0.11 501 545 493 513 493 | 500 m 46 4 8 | 500 | 470 496 512 494 500 = 0.79 || = 0.10 525 489 480 451 503 | 500 x 49 4 2 | 500 | 513 499 469 486 504 = 0.78 || = 0.09 500 505 521 497 486 | 500 -----------------------------------------------------------------| 500 | 498 500 543 492 531 = 0.77 || = 0.08 496 481 478 510 500 | 500 Aver./ d 0.50134 499 > 500: 4 6 4 5 3 3 4 6 4 8 | 500 | 499 490 490 512 540 = 0.76 || = 0.07 522 543 510 541 487 | 500 median s 0.49863 499 ----- 6 6 4 6 6 2 5 1 3 8 | 500 | 509 487 479 492 493 = 0.75 || = 0.06 511 497 494 480 497 | 500 t 0.49942 500 5 5 6 4 6 4 5 5 6 3 | 500 | 471 494 517 473 477 = 0.74 || = 0.05 510 509 510 476 533 | 500 m 0.49894 498 5 4 8 3 7 4 5 1 3 5 | 500 | 538 486 446 481 531 = 0.73 || = 0.04 482 472 532 509 487 | 500 x 0.50139 498 1 4 5 6 6 5 3 6 5 3 | 500 | 517 493 505 499 516 = 0.72 || = 0.03 515 526 463 504 449 | 500 -----------------------------------------------------------------| 500 | 513 481 483 472 459 = 0.71 || = 0.02 472 493 494 501 477 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 489 521 521 483 490 = 0.70 || = 0.01 243 278 262 241 247 | 252.5 d 0 0 3 11 72 15 0 0 0 | 500 | 503 505 486 481 512 = 0.69 || < 0.01 445 517 492 480 475 | 497.5 s 0 0 1 10 74 13 3 0 0 | 500 | 494 477 467 532 485 = 0.68 ||========================================================================= t 0 0 2 11 70 18 0 0 0 | 500 | 488 510 503 512 490 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 14 70 15 1 0 0 | 500 | 481 486 514 488 485 = 0.66 ||========================================================================= x 0 0 2 13 71 12 2 1 0 | 500 | 513 493 523 511 511 = 0.65 || sknuth_CouponCollector test: no 53 test no 54 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Gap test: test no 54 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99999 || = 0.64 519 474 454 522 519 | 500 < 0.00002 0 0 1 1 1 | 0.5 | 1 1 0 0 0 > 0.99998 || = 0.63 501 494 504 523 482 | 500 < 0.00003 0 0 1 1 0 | 0.5 | 0 0 0 3 1 > 0.99997 || = 0.62 525 483 469 488 527 | 500 < 0.00004 1 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 535 501 499 496 509 | 500 < 0.00005 1 0 1 0 1 | 0.5 | 1 0 1 1 0 > 0.99995 || = 0.60 430 505 499 493 530 | 500 < 0.00006 2 1 0 1 1 | 0.5 | 1 1 0 0 0 > 0.99994 || = 0.59 484 512 427 462 482 | 500 < 0.00007 0 2 0 2 0 | 0.5 | 2 1 0 0 3 > 0.99993 || = 0.58 487 542 480 444 519 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 2 0 0 0 0 > 0.99992 || = 0.57 537 509 509 477 514 | 500 < 0.00009 1 1 0 1 0 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 487 483 473 529 482 | 500 < 0.0001 1 0 0 1 0 | 0.5 | 0 3 0 0 1 > 0.9999 || = 0.55 471 534 502 474 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 535 493 525 499 525 | 500 < 0.0001 7 6 3 7 3 | 5 | 8 6 1 5 5 > 0.9999 || = 0.53 493 501 528 509 510 | 500 < 0.0002 6 3 3 3 3 | 5 | 4 1 4 2 3 > 0.9998 || = 0.52 498 485 513 501 503 | 500 < 0.0003 1 8 3 3 5 | 5 | 5 4 9 8 1 > 0.9997 || = 0.51 483 484 533 471 486 | 500 < 0.0004 4 4 5 5 4 | 5 | 6 6 3 6 7 > 0.9996 || = 0.50 461 489 501 501 467 | 500 < 0.0005 2 4 3 1 10 | 5 | 5 6 4 12 1 > 0.9995 || = 0.49 499 536 565 497 481 | 500 < 0.0006 2 4 4 8 7 | 5 | 3 6 3 5 7 > 0.9994 || = 0.48 474 505 526 532 506 | 500 < 0.0007 2 3 5 6 6 | 5 | 6 8 10 5 3 > 0.9993 || = 0.47 471 482 523 537 491 | 500 < 0.0008 4 4 5 4 5 | 5 | 2 4 5 12 10 > 0.9992 || = 0.46 488 519 505 511 520 | 500 < 0.0009 6 10 5 5 5 | 5 | 2 7 4 3 6 > 0.9991 || = 0.45 487 535 575 507 481 | 500 < 0.001 7 6 11 6 0 | 5 | 7 9 6 5 3 > 0.999 || = 0.44 515 531 500 496 451 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 463 526 512 511 466 | 500 < 0.001 41 52 47 48 48 | 50 | 48 57 49 63 46 > 0.999 || = 0.42 506 533 492 468 491 | 500 < 0.002 52 53 43 55 44 | 50 | 48 40 39 53 44 > 0.998 || = 0.41 485 488 494 499 515 | 500 < 0.003 56 44 62 59 51 | 50 | 51 51 54 52 51 > 0.997 || = 0.40 493 511 511 490 540 | 500 < 0.004 41 47 40 51 55 | 50 | 50 47 56 67 55 > 0.996 || = 0.39 467 481 519 523 504 | 500 < 0.005 49 47 47 55 60 | 50 | 49 51 57 44 45 > 0.995 || = 0.38 498 460 509 512 467 | 500 < 0.006 42 51 65 59 49 | 50 | 53 47 58 46 67 > 0.994 || = 0.37 521 490 495 470 465 | 500 < 0.007 39 48 55 57 52 | 50 | 36 58 55 48 48 > 0.993 || = 0.36 482 500 491 501 478 | 500 < 0.008 47 59 49 38 44 | 50 | 51 55 46 51 51 > 0.992 || = 0.35 479 470 484 520 492 | 500 < 0.009 43 41 41 50 51 | 50 | 39 49 49 42 48 > 0.991 || = 0.34 499 536 479 490 563 | 500 < 0.01 56 45 52 44 49 | 50 | 52 36 45 62 58 > 0.99 || = 0.33 484 474 467 493 535 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 487 527 506 533 519 | 500 < 0.01 466 487 501 516 503 | 497.5 | 477 491 508 528 513 > 0.99 || = 0.31 494 469 501 508 497 | 500 = 0.01 254 276 266 244 261 | 252.5 | 252 253 247 252 271 = 0.99 || = 0.30 502 505 501 491 455 | 500 = 0.02 484 489 525 518 480 | 500 | 503 502 513 527 520 = 0.98 || = 0.29 531 500 502 498 465 | 500 =================================================================| 500 | 487 490 516 512 541 = 0.97 || = 0.28 514 518 510 452 511 | 500 sknuth_Gap test: | 500 | 500 531 495 518 530 = 0.96 || = 0.27 498 477 467 509 486 | 500 ----------------------------------------------- | 500 | 527 519 505 500 495 = 0.95 || = 0.26 521 519 522 499 468 | 500 N = 1, n = 500000000, r = 0, Alpha = 0, Beta = 0.0625 | 500 | 506 517 495 464 471 = 0.94 || = 0.25 513 496 429 506 521 | 500 | 500 | 489 482 501 521 548 = 0.93 || = 0.24 480 516 501 481 481 | 500 | 500 | 524 484 494 524 506 = 0.92 || = 0.23 510 483 517 519 489 | 500 =================================================================| 500 | 531 511 507 540 484 = 0.91 || = 0.22 491 513 523 515 485 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 517 506 485 477 489 = 0.90 || = 0.21 516 491 525 503 511 | 500 -----------------------------------------------------------------| 500 | 496 535 517 464 454 = 0.89 || = 0.20 505 469 543 534 472 | 500 SD Bern.: d 0.98638 0.98231 0.82623 | 500 | 490 474 489 466 515 = 0.88 || = 0.19 494 524 527 511 453 | 500 s 0.91096 0.72007 0.95440 | 500 | 505 494 470 498 518 = 0.87 || = 0.18 543 489 469 438 514 | 500 t 1.07091 1.13810 0.84183 | 500 | 528 507 492 529 509 = 0.86 || = 0.17 488 494 514 499 514 | 500 m 1.02867 0.94492 1.21385 | 500 | 500 496 467 483 532 = 0.85 || = 0.16 517 507 506 556 518 | 500 x 1.04475 0.64683 0.96483 | 500 | 512 487 492 514 513 = 0.84 || = 0.15 518 497 484 487 509 | 500 | 500 | 541 469 476 481 507 = 0.83 || = 0.14 523 462 480 515 504 | 500 Changes: d 50 3 7 | 500 | 574 530 521 514 473 = 0.82 || = 0.13 520 489 464 508 499 | 500 s 57 5 7 | 500 | 499 484 503 536 522 = 0.81 || = 0.12 512 496 504 492 515 | 500 t 44 5 2 | 500 | 482 499 453 532 513 = 0.80 || = 0.11 500 498 521 512 498 | 500 m 54 2 4 | 500 | 513 505 461 484 523 = 0.79 || = 0.10 460 465 532 507 519 | 500 x 50 6 7 | 500 | 524 499 473 476 455 = 0.78 || = 0.09 498 496 519 491 483 | 500 -----------------------------------------------------------------| 500 | 504 480 499 491 519 = 0.77 || = 0.08 481 502 509 529 533 | 500 Aver./ d 0.50094 499 > 500: 4 6 7 2 2 2 5 7 6 5 | 500 | 487 502 485 534 470 = 0.76 || = 0.07 513 501 502 514 497 | 500 median s 0.50063 499 ----- 5 2 4 3 8 6 3 5 4 6 | 500 | 517 516 483 499 459 = 0.75 || = 0.06 493 496 532 475 516 | 500 t 0.49754 502 8 6 8 5 7 6 4 2 3 6 | 500 | 464 484 511 474 492 = 0.74 || = 0.05 501 533 471 488 520 | 500 m 0.50022 500 4 6 6 6 5 3 3 4 4 7 | 500 | 504 531 514 510 511 = 0.73 || = 0.04 499 530 532 448 479 | 500 x 0.50145 504 5 7 3 4 4 6 5 5 7 7 | 500 | 509 513 482 491 497 = 0.72 || = 0.03 539 473 476 499 487 | 500 -----------------------------------------------------------------| 500 | 503 484 495 507 513 = 0.71 || = 0.02 484 489 525 518 480 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 484 519 517 500 477 = 0.70 || = 0.01 254 276 266 244 261 | 252.5 d 0 1 0 12 73 14 0 1 0 | 500 | 474 499 498 454 507 = 0.69 || < 0.01 466 487 501 516 503 | 497.5 s 0 0 0 14 69 18 0 0 0 | 500 | 519 475 510 496 492 = 0.68 ||========================================================================= t 0 2 2 13 69 13 1 1 0 | 500 | 469 491 495 503 481 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 5 14 65 16 1 0 0 | 500 | 500 530 505 484 524 = 0.66 ||========================================================================= x 0 0 5 12 70 12 2 0 0 | 500 | 467 458 482 476 494 = 0.65 || sknuth_Gap test: no 54 test no 55 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Gap test: test no 55 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 1 4 0 1 0 > 0.99999 || = 0.64 471 493 495 507 503 | 500 < 0.00002 2 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 488 516 536 531 516 | 500 < 0.00003 0 1 0 1 1 | 0.5 | 2 0 0 2 0 > 0.99997 || = 0.62 513 506 484 523 484 | 500 < 0.00004 1 0 0 0 0 | 0.5 | 0 2 0 0 0 > 0.99996 || = 0.61 469 482 476 509 495 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 1 1 1 1 > 0.99995 || = 0.60 478 520 475 506 496 | 500 < 0.00006 0 0 0 2 1 | 0.5 | 0 0 0 0 1 > 0.99994 || = 0.59 495 516 456 482 534 | 500 < 0.00007 2 2 0 0 2 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 501 472 451 500 502 | 500 < 0.00008 0 1 0 0 2 | 0.5 | 0 0 0 1 0 > 0.99992 || = 0.57 470 465 507 500 514 | 500 < 0.00009 0 0 0 0 2 | 0.5 | 0 0 0 0 3 > 0.99991 || = 0.56 520 447 491 517 474 | 500 < 0.0001 1 0 1 1 0 | 0.5 | 1 0 0 0 3 > 0.9999 || = 0.55 510 472 466 502 482 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 472 514 534 507 524 | 500 < 0.0001 6 4 1 4 8 | 5 | 5 7 1 5 8 > 0.9999 || = 0.53 483 500 467 509 499 | 500 < 0.0002 4 5 3 3 2 | 5 | 2 3 3 2 4 > 0.9998 || = 0.52 513 499 478 495 499 | 500 < 0.0003 5 3 9 8 9 | 5 | 6 6 2 4 6 > 0.9997 || = 0.51 501 512 453 502 521 | 500 < 0.0004 8 9 3 5 8 | 5 | 9 7 4 10 5 > 0.9996 || = 0.50 526 502 493 466 475 | 500 < 0.0005 4 3 7 4 6 | 5 | 8 6 2 9 5 > 0.9995 || = 0.49 503 506 500 487 499 | 500 < 0.0006 3 4 5 4 7 | 5 | 5 11 3 2 5 > 0.9994 || = 0.48 522 502 495 499 509 | 500 < 0.0007 2 2 1 6 7 | 5 | 6 8 6 3 10 > 0.9993 || = 0.47 496 521 497 493 519 | 500 < 0.0008 2 6 2 8 5 | 5 | 4 3 7 10 2 > 0.9992 || = 0.46 515 522 465 490 519 | 500 < 0.0009 4 1 4 9 6 | 5 | 5 5 3 2 5 > 0.9991 || = 0.45 517 474 495 536 521 | 500 < 0.001 5 4 5 4 4 | 5 | 1 5 6 2 11 > 0.999 || = 0.44 446 515 476 480 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 499 490 469 494 491 | 500 < 0.001 43 41 40 55 62 | 50 | 51 61 37 49 61 > 0.999 || = 0.42 496 476 534 523 502 | 500 < 0.002 53 43 36 36 44 | 50 | 58 46 58 59 63 > 0.998 || = 0.41 504 506 553 453 498 | 500 < 0.003 47 54 56 38 48 | 50 | 55 44 46 47 52 > 0.997 || = 0.40 518 483 491 459 525 | 500 < 0.004 45 47 48 53 52 | 50 | 52 50 42 55 42 > 0.996 || = 0.39 474 527 529 501 558 | 500 < 0.005 58 54 58 41 40 | 50 | 60 47 50 44 57 > 0.995 || = 0.38 502 482 490 497 479 | 500 < 0.006 53 47 45 56 57 | 50 | 58 53 53 54 57 > 0.994 || = 0.37 454 510 478 518 491 | 500 < 0.007 51 49 57 51 39 | 50 | 54 54 59 47 60 > 0.993 || = 0.36 488 550 468 517 521 | 500 < 0.008 53 55 51 61 52 | 50 | 50 38 41 47 54 > 0.992 || = 0.35 456 507 510 481 503 | 500 < 0.009 40 55 40 52 49 | 50 | 54 64 45 57 59 > 0.991 || = 0.34 515 549 498 485 494 | 500 < 0.01 52 55 43 51 47 | 50 | 49 45 55 49 45 > 0.99 || = 0.33 554 481 457 530 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 471 498 474 507 493 | 500 < 0.01 495 500 474 494 490 | 497.5 | 541 502 486 508 550 > 0.99 || = 0.31 481 499 504 495 530 | 500 = 0.01 271 258 288 287 270 | 252.5 | 262 274 234 243 246 = 0.99 || = 0.30 515 486 508 522 499 | 500 = 0.02 496 514 552 471 464 | 500 | 469 478 484 532 511 = 0.98 || = 0.29 512 537 502 488 506 | 500 =================================================================| 500 | 512 517 533 526 470 = 0.97 || = 0.28 513 513 515 510 490 | 500 sknuth_Gap test: | 500 | 546 501 507 510 498 = 0.96 || = 0.27 477 494 524 491 521 | 500 ----------------------------------------------- | 500 | 535 498 510 519 473 = 0.95 || = 0.26 471 498 529 490 443 | 500 N = 1, n = 300000000, r = 25, Alpha = 0, Beta = 0.03125 | 500 | 485 500 485 507 514 = 0.94 || = 0.25 471 496 490 482 487 | 500 | 500 | 482 482 466 489 506 = 0.93 || = 0.24 521 512 509 498 496 | 500 | 500 | 505 503 500 460 488 = 0.92 || = 0.23 484 498 521 492 468 | 500 =================================================================| 500 | 518 494 532 520 514 = 0.91 || = 0.22 485 503 543 487 492 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 523 465 495 539 493 = 0.90 || = 0.21 507 491 529 515 483 | 500 -----------------------------------------------------------------| 500 | 484 474 518 497 509 = 0.89 || = 0.20 502 525 529 481 534 | 500 SD Bern.: d 1.04605 0.74736 0.76326 | 500 | 487 505 506 510 500 = 0.88 || = 0.19 513 511 487 514 507 | 500 s 0.89621 0.71589 1.07010 | 500 | 543 500 497 522 515 = 0.87 || = 0.18 468 478 503 516 534 | 500 t 1.13565 1.11769 1.03394 | 500 | 506 488 458 514 486 = 0.86 || = 0.17 520 544 514 489 473 | 500 m 0.92370 1.11230 0.68735 | 500 | 474 535 492 509 474 = 0.85 || = 0.16 529 511 513 524 487 | 500 x 0.89642 0.97207 1.16504 | 500 | 477 499 482 519 496 = 0.84 || = 0.15 520 501 471 524 489 | 500 | 500 | 502 498 483 465 496 = 0.83 || = 0.14 480 492 469 471 486 | 500 Changes: d 47 5 3 | 500 | 514 504 502 450 522 = 0.82 || = 0.13 476 490 544 514 529 | 500 s 52 5 5 | 500 | 533 481 507 515 519 = 0.81 || = 0.12 523 514 523 525 494 | 500 t 44 6 5 | 500 | 503 488 489 530 476 = 0.80 || = 0.11 529 461 490 481 528 | 500 m 45 4 8 | 500 | 518 528 515 522 475 = 0.79 || = 0.10 565 502 513 481 512 | 500 x 55 7 3 | 500 | 490 500 479 501 465 = 0.78 || = 0.09 523 495 503 481 499 | 500 -----------------------------------------------------------------| 500 | 469 511 548 487 493 = 0.77 || = 0.08 495 506 516 513 510 | 500 Aver./ d 0.50045 501 > 500: 4 7 5 4 6 5 2 5 6 7 | 500 | 498 510 496 463 481 = 0.76 || = 0.07 516 537 507 489 475 | 500 median s 0.49849 500 ----- 7 6 5 5 6 4 4 3 3 5 | 500 | 504 458 541 470 515 = 0.75 || = 0.06 499 508 489 497 499 | 500 t 0.49763 498 7 6 9 4 2 2 5 5 4 4 | 500 | 495 491 483 472 500 = 0.74 || = 0.05 446 501 509 475 507 | 500 m 0.50113 501 4 6 2 6 2 6 9 3 7 7 | 500 | 495 496 505 468 486 = 0.73 || = 0.04 482 479 540 502 466 | 500 x 0.50006 499 4 5 3 4 7 5 4 3 4 5 | 500 | 508 463 544 487 532 = 0.72 || = 0.03 524 486 477 515 516 | 500 -----------------------------------------------------------------| 500 | 511 477 476 499 503 = 0.71 || = 0.02 496 514 552 471 464 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 480 491 459 522 498 = 0.70 || = 0.01 271 258 288 287 270 | 252.5 d 0 0 3 17 65 13 3 0 0 | 500 | 494 500 478 513 472 = 0.69 || < 0.01 495 500 474 494 490 | 497.5 s 0 0 1 11 77 10 2 0 0 | 500 | 532 528 511 523 512 = 0.68 ||========================================================================= t 0 0 2 20 58 17 4 0 0 | 500 | 480 479 517 501 479 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 12 73 13 1 0 0 | 500 | 499 542 543 465 492 = 0.66 ||========================================================================= x 0 0 1 14 74 10 2 0 0 | 500 | 477 485 513 503 518 = 0.65 || sknuth_Gap test: no 55 test no 56 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Gap test: test no 56 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 0 | 0.5 | 0 0 1 1 0 > 0.99999 || = 0.64 555 461 504 527 502 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 1 1 0 0 1 > 0.99998 || = 0.63 454 525 515 463 487 | 500 < 0.00003 1 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 493 491 508 477 546 | 500 < 0.00004 0 0 1 0 0 | 0.5 | 1 1 0 0 0 > 0.99996 || = 0.61 492 483 497 498 475 | 500 < 0.00005 2 1 1 1 1 | 0.5 | 0 0 1 1 2 > 0.99995 || = 0.60 525 519 486 541 503 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 0 1 2 0 0 > 0.99994 || = 0.59 478 500 504 499 494 | 500 < 0.00007 0 2 2 0 1 | 0.5 | 3 0 1 3 1 > 0.99993 || = 0.58 499 484 477 472 487 | 500 < 0.00008 0 0 0 0 1 | 0.5 | 0 2 0 0 1 > 0.99992 || = 0.57 516 513 499 514 498 | 500 < 0.00009 2 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99991 || = 0.56 532 486 558 483 528 | 500 < 0.0001 1 1 0 0 0 | 0.5 | 0 2 1 1 0 > 0.9999 || = 0.55 441 541 449 528 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 448 530 488 526 471 | 500 < 0.0001 6 5 4 3 5 | 5 | 5 7 7 6 5 > 0.9999 || = 0.53 525 495 513 503 482 | 500 < 0.0002 5 4 2 5 5 | 5 | 0 2 3 6 2 > 0.9998 || = 0.52 495 484 537 513 538 | 500 < 0.0003 1 8 7 4 3 | 5 | 5 9 4 2 5 > 0.9997 || = 0.51 520 503 469 503 488 | 500 < 0.0004 4 4 3 6 3 | 5 | 7 8 8 10 5 > 0.9996 || = 0.50 507 510 484 489 472 | 500 < 0.0005 4 5 5 12 3 | 5 | 8 6 9 5 11 > 0.9995 || = 0.49 515 532 495 521 488 | 500 < 0.0006 1 7 2 2 7 | 5 | 5 1 6 3 3 > 0.9994 || = 0.48 532 549 489 483 483 | 500 < 0.0007 7 4 5 5 5 | 5 | 4 5 4 4 8 > 0.9993 || = 0.47 527 526 484 491 524 | 500 < 0.0008 6 6 2 2 5 | 5 | 7 6 3 9 7 > 0.9992 || = 0.46 452 519 511 497 491 | 500 < 0.0009 5 5 5 7 7 | 5 | 4 4 8 5 5 > 0.9991 || = 0.45 523 501 551 475 480 | 500 < 0.001 4 3 3 3 6 | 5 | 6 7 1 5 4 > 0.999 || = 0.44 504 471 471 458 503 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 484 500 501 497 526 | 500 < 0.001 43 51 38 49 49 | 50 | 51 55 53 55 55 > 0.999 || = 0.42 513 491 501 495 499 | 500 < 0.002 43 43 42 47 33 | 50 | 60 59 42 49 57 > 0.998 || = 0.41 518 466 517 516 476 | 500 < 0.003 44 46 51 57 61 | 50 | 44 45 62 46 49 > 0.997 || = 0.40 498 504 497 497 501 | 500 < 0.004 56 39 45 58 42 | 50 | 43 46 50 56 60 > 0.996 || = 0.39 515 460 518 474 482 | 500 < 0.005 38 49 55 40 49 | 50 | 52 43 45 45 51 > 0.995 || = 0.38 519 496 488 501 533 | 500 < 0.006 57 56 56 51 44 | 50 | 47 59 55 60 57 > 0.994 || = 0.37 464 472 513 461 490 | 500 < 0.007 56 60 45 48 47 | 50 | 57 44 48 56 61 > 0.993 || = 0.36 501 498 495 463 487 | 500 < 0.008 51 57 47 62 51 | 50 | 38 49 55 54 57 > 0.992 || = 0.35 485 473 525 503 517 | 500 < 0.009 48 44 53 51 44 | 50 | 49 58 54 53 40 > 0.991 || = 0.34 478 495 501 501 511 | 500 < 0.01 49 52 58 54 57 | 50 | 46 51 39 43 49 > 0.99 || = 0.33 480 478 529 492 529 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 492 530 485 510 525 | 500 < 0.01 485 497 490 517 477 | 497.5 | 487 509 503 517 536 > 0.99 || = 0.31 549 510 506 505 522 | 500 = 0.01 226 258 255 269 256 | 252.5 | 211 239 254 272 252 = 0.99 || = 0.30 513 497 545 526 529 | 500 = 0.02 527 515 507 499 494 | 500 | 486 509 520 511 490 = 0.98 || = 0.29 504 506 440 479 497 | 500 =================================================================| 500 | 510 506 479 506 490 = 0.97 || = 0.28 473 482 515 477 501 | 500 sknuth_Gap test: | 500 | 500 514 543 495 502 = 0.96 || = 0.27 522 527 510 519 501 | 500 ----------------------------------------------- | 500 | 542 491 529 496 506 = 0.95 || = 0.26 522 511 513 516 525 | 500 N = 1, n = 100000000, r = 0, Alpha = 0, Beta = 0.0078125 | 500 | 487 514 518 515 527 = 0.94 || = 0.25 492 497 449 495 504 | 500 | 500 | 510 481 505 509 456 = 0.93 || = 0.24 518 489 487 475 490 | 500 | 500 | 486 525 500 489 497 = 0.92 || = 0.23 500 499 493 495 508 | 500 =================================================================| 500 | 494 499 478 523 499 = 0.91 || = 0.22 490 510 495 505 456 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 503 512 517 492 508 = 0.90 || = 0.21 518 470 500 504 543 | 500 -----------------------------------------------------------------| 500 | 514 502 523 481 472 = 0.89 || = 0.20 469 505 479 512 515 | 500 SD Bern.: d 1.01132 0.90044 0.90487 | 500 | 528 506 516 498 499 = 0.88 || = 0.19 458 486 483 497 529 | 500 s 0.97788 0.90929 0.87105 | 500 | 502 480 510 480 533 = 0.87 || = 0.18 509 512 507 507 503 | 500 t 0.92765 0.89710 0.93104 | 500 | 478 503 480 482 495 = 0.86 || = 0.17 467 491 489 528 482 | 500 m 0.90935 0.88247 0.79158 | 500 | 514 485 505 524 501 = 0.85 || = 0.16 482 517 476 541 510 | 500 x 0.90998 1.10236 0.99648 | 500 | 517 522 520 522 470 = 0.84 || = 0.15 516 484 491 484 525 | 500 | 500 | 501 507 519 507 503 = 0.83 || = 0.14 511 479 513 487 460 | 500 Changes: d 54 4 5 | 500 | 513 472 474 506 508 = 0.82 || = 0.13 519 493 503 482 498 | 500 s 59 4 4 | 500 | 524 510 515 504 501 = 0.81 || = 0.12 485 580 488 485 492 | 500 t 47 5 7 | 500 | 516 488 497 501 484 = 0.80 || = 0.11 512 511 493 474 485 | 500 m 46 5 5 | 500 | 504 519 523 448 520 = 0.79 || = 0.10 499 519 504 521 497 | 500 x 53 5 3 | 500 | 466 530 498 501 518 = 0.78 || = 0.09 486 482 503 476 514 | 500 -----------------------------------------------------------------| 500 | 517 497 490 525 494 = 0.77 || = 0.08 503 481 470 522 485 | 500 Aver./ d 0.50092 503 > 500: 4 5 5 5 7 5 4 8 9 3 | 500 | 510 522 513 480 464 = 0.76 || = 0.07 471 502 479 501 525 | 500 median s 0.49978 501 ----- 5 5 5 2 6 5 3 6 7 6 | 500 | 507 502 517 473 509 = 0.75 || = 0.06 487 487 521 470 499 | 500 t 0.50232 501 6 4 3 7 5 4 5 4 8 7 | 500 | 503 442 519 496 505 = 0.74 || = 0.05 503 491 505 512 510 | 500 m 0.50032 501 6 4 5 6 2 7 5 5 5 7 | 500 | 512 514 473 514 478 = 0.73 || = 0.04 511 532 455 541 554 | 500 x 0.49878 499 5 4 7 7 4 3 3 4 6 4 | 500 | 482 490 494 484 476 = 0.72 || = 0.03 497 501 509 492 475 | 500 -----------------------------------------------------------------| 500 | 521 533 469 517 476 = 0.71 || = 0.02 527 515 507 499 494 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 509 471 507 541 491 = 0.70 || = 0.01 226 258 255 269 256 | 252.5 d 0 0 5 9 75 10 2 0 0 | 500 | 462 512 501 487 518 = 0.69 || < 0.01 485 497 490 517 477 | 497.5 s 0 0 2 11 75 11 1 1 0 | 500 | 504 475 484 524 487 = 0.68 ||========================================================================= t 0 0 4 8 79 7 3 0 0 | 500 | 489 505 496 464 491 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 15 69 16 0 0 0 | 500 | 483 442 482 507 482 = 0.66 ||========================================================================= x 0 0 0 13 70 16 2 0 0 | 500 | 504 465 497 525 496 = 0.65 || sknuth_Gap test: no 56 test no 57 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Gap test: test no 57 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 0 | 0.5 | 1 0 0 0 0 > 0.99999 || = 0.64 495 497 512 549 502 | 500 < 0.00002 0 1 0 0 2 | 0.5 | 0 2 1 0 0 > 0.99998 || = 0.63 491 512 469 506 476 | 500 < 0.00003 1 1 0 0 0 | 0.5 | 1 3 1 1 0 > 0.99997 || = 0.62 483 473 457 499 545 | 500 < 0.00004 1 1 0 1 0 | 0.5 | 0 0 2 0 0 > 0.99996 || = 0.61 478 484 492 524 497 | 500 < 0.00005 0 1 1 0 1 | 0.5 | 1 1 1 0 1 > 0.99995 || = 0.60 482 529 520 473 535 | 500 < 0.00006 0 1 0 0 0 | 0.5 | 0 2 0 1 0 > 0.99994 || = 0.59 495 499 492 499 513 | 500 < 0.00007 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 507 489 521 510 499 | 500 < 0.00008 0 0 0 0 1 | 0.5 | 2 0 1 0 0 > 0.99992 || = 0.57 533 487 528 497 529 | 500 < 0.00009 1 1 0 0 0 | 0.5 | 1 0 1 1 1 > 0.99991 || = 0.56 484 480 507 452 506 | 500 < 0.0001 0 1 1 2 0 | 0.5 | 0 0 0 0 1 > 0.9999 || = 0.55 506 510 491 471 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 465 521 502 503 501 | 500 < 0.0001 3 8 3 3 5 | 5 | 6 8 7 3 3 > 0.9999 || = 0.53 479 536 471 482 497 | 500 < 0.0002 6 7 3 0 2 | 5 | 3 2 3 3 2 > 0.9998 || = 0.52 487 512 489 478 489 | 500 < 0.0003 5 3 8 6 7 | 5 | 7 6 3 1 2 > 0.9997 || = 0.51 495 490 461 511 522 | 500 < 0.0004 7 5 6 8 4 | 5 | 5 5 6 9 2 > 0.9996 || = 0.50 477 528 508 504 458 | 500 < 0.0005 5 5 5 5 5 | 5 | 5 3 3 3 2 > 0.9995 || = 0.49 528 461 506 497 483 | 500 < 0.0006 6 5 6 5 9 | 5 | 5 3 2 3 3 > 0.9994 || = 0.48 475 486 525 502 450 | 500 < 0.0007 9 9 6 5 4 | 5 | 5 1 7 7 10 > 0.9993 || = 0.47 485 489 504 526 484 | 500 < 0.0008 5 4 5 6 7 | 5 | 6 5 4 8 7 > 0.9992 || = 0.46 512 505 493 493 483 | 500 < 0.0009 6 1 5 7 5 | 5 | 3 4 7 8 2 > 0.9991 || = 0.45 500 480 501 507 508 | 500 < 0.001 8 7 4 1 9 | 5 | 5 5 5 8 5 > 0.999 || = 0.44 495 506 492 519 469 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 506 562 563 515 480 | 500 < 0.001 60 54 51 46 57 | 50 | 50 42 47 53 38 > 0.999 || = 0.42 486 453 517 528 571 | 500 < 0.002 39 45 49 46 44 | 50 | 57 58 40 51 53 > 0.998 || = 0.41 509 498 523 500 486 | 500 < 0.003 45 53 50 62 52 | 50 | 61 47 53 66 43 > 0.997 || = 0.40 527 514 481 469 509 | 500 < 0.004 67 55 58 46 59 | 50 | 53 60 56 63 61 > 0.996 || = 0.39 530 478 517 484 497 | 500 < 0.005 53 60 49 64 49 | 50 | 43 39 48 51 39 > 0.995 || = 0.38 540 469 516 476 524 | 500 < 0.006 46 42 52 41 56 | 50 | 50 64 47 51 48 > 0.994 || = 0.37 491 524 549 532 476 | 500 < 0.007 61 59 54 60 46 | 50 | 64 49 53 53 50 > 0.993 || = 0.36 491 488 467 471 516 | 500 < 0.008 54 41 44 60 46 | 50 | 47 47 44 46 46 > 0.992 || = 0.35 500 475 520 490 479 | 500 < 0.009 58 53 48 49 53 | 50 | 41 47 52 55 39 > 0.991 || = 0.34 476 496 474 523 486 | 500 < 0.01 48 70 38 48 52 | 50 | 44 70 47 37 45 > 0.99 || = 0.33 480 504 488 494 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 478 468 476 474 528 | 500 < 0.01 531 532 493 522 514 | 497.5 | 510 523 487 526 462 > 0.99 || = 0.31 503 486 506 499 504 | 500 = 0.01 251 276 253 286 252 | 252.5 | 265 225 252 253 247 = 0.99 || = 0.30 506 472 485 514 501 | 500 = 0.02 524 465 515 503 517 | 500 | 519 473 509 530 501 = 0.98 || = 0.29 512 507 503 490 480 | 500 =================================================================| 500 | 521 507 508 506 482 = 0.97 || = 0.28 527 499 532 484 462 | 500 sknuth_Gap test: | 500 | 484 487 522 475 505 = 0.96 || = 0.27 488 495 481 561 468 | 500 ----------------------------------------------- | 500 | 474 499 469 516 526 = 0.95 || = 0.26 492 462 473 483 476 | 500 N = 1, n = 10000000, r = 20, Alpha = 0, Beta = 0.000976562 | 500 | 511 506 468 505 501 = 0.94 || = 0.25 463 515 499 489 486 | 500 | 500 | 516 499 501 502 540 = 0.93 || = 0.24 474 515 492 498 497 | 500 | 500 | 485 528 489 490 485 = 0.92 || = 0.23 492 466 493 477 524 | 500 =================================================================| 500 | 474 504 490 506 519 = 0.91 || = 0.22 525 496 485 482 529 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 515 517 488 505 464 = 0.90 || = 0.21 527 508 545 514 480 | 500 -----------------------------------------------------------------| 500 | 515 477 491 500 502 = 0.89 || = 0.20 505 485 486 466 523 | 500 SD Bern.: d 0.87806 1.23754 1.04932 | 500 | 492 480 488 508 475 = 0.88 || = 0.19 486 484 518 517 531 | 500 s 0.93844 1.27342 1.39568 | 500 | 522 519 466 511 516 = 0.87 || = 0.18 473 510 496 540 484 | 500 t 0.97255 0.73656 0.67114 | 500 | 502 512 491 478 474 = 0.86 || = 0.17 513 490 460 451 498 | 500 m 1.00030 1.16161 1.14598 | 500 | 521 510 508 519 515 = 0.85 || = 0.16 503 484 489 533 469 | 500 x 1.03022 0.71027 1.10508 | 500 | 480 513 509 502 483 = 0.84 || = 0.15 506 509 498 483 491 | 500 | 500 | 500 495 492 460 532 = 0.83 || = 0.14 549 509 508 454 490 | 500 Changes: d 40 5 4 | 500 | 494 499 484 504 549 = 0.82 || = 0.13 513 530 492 511 510 | 500 s 48 6 7 | 500 | 468 502 454 481 525 = 0.81 || = 0.12 485 505 504 505 517 | 500 t 47 5 6 | 500 | 491 509 507 540 456 = 0.80 || = 0.11 502 539 519 464 539 | 500 m 54 6 3 | 500 | 523 483 524 517 488 = 0.79 || = 0.10 482 487 517 472 477 | 500 x 55 6 4 | 500 | 498 490 517 508 502 = 0.78 || = 0.09 487 510 541 511 501 | 500 -----------------------------------------------------------------| 500 | 498 531 517 496 502 = 0.77 || = 0.08 525 496 506 516 487 | 500 Aver./ d 0.49908 498 > 500: 6 6 5 4 5 3 1 6 5 6 | 500 | 534 522 473 472 507 = 0.76 || = 0.07 495 480 515 491 519 | 500 median s 0.50037 499 ----- 6 6 4 2 4 5 7 3 6 5 | 500 | 501 484 474 503 485 = 0.75 || = 0.06 522 487 491 492 495 | 500 t 0.49756 499 8 5 3 5 7 5 4 5 2 4 | 500 | 506 485 562 493 551 = 0.74 || = 0.05 525 516 515 485 473 | 500 m 0.50147 500 5 5 2 3 6 3 7 5 6 8 | 500 | 512 484 489 483 474 = 0.73 || = 0.04 471 518 510 494 502 | 500 x 0.49991 499 6 4 3 5 3 7 6 4 6 6 | 500 | 509 481 499 508 493 = 0.72 || = 0.03 522 503 546 482 536 | 500 -----------------------------------------------------------------| 500 | 495 487 484 477 483 = 0.71 || = 0.02 524 465 515 503 517 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 483 501 502 506 486 = 0.70 || = 0.01 251 276 253 286 252 | 252.5 d 0 0 1 12 72 15 1 0 0 | 500 | 496 514 516 521 510 = 0.69 || < 0.01 531 532 493 522 514 | 497.5 s 0 0 1 12 73 14 1 0 0 | 500 | 476 532 491 486 519 = 0.68 ||========================================================================= t 0 0 1 15 74 6 5 0 0 | 500 | 488 544 521 498 511 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 68 12 4 0 0 | 500 | 450 506 474 546 491 = 0.66 ||========================================================================= x 0 0 1 16 66 14 3 1 0 | 500 | 527 533 486 542 503 = 0.65 || sknuth_Gap test: no 57 test no 58 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Gap test: test no 58 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 1 1 1 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 497 505 556 503 491 | 500 < 0.00002 0 0 1 2 1 | 0.5 | 1 0 1 0 0 > 0.99998 || = 0.63 500 461 475 480 510 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 0 0 1 1 1 > 0.99997 || = 0.62 548 504 485 498 490 | 500 < 0.00004 1 0 0 0 1 | 0.5 | 0 0 0 1 0 > 0.99996 || = 0.61 490 524 488 466 488 | 500 < 0.00005 1 0 0 0 1 | 0.5 | 1 0 0 1 1 > 0.99995 || = 0.60 545 524 497 499 463 | 500 < 0.00006 0 2 0 0 0 | 0.5 | 0 1 0 3 0 > 0.99994 || = 0.59 507 495 507 497 500 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 533 497 480 493 515 | 500 < 0.00008 1 1 1 3 0 | 0.5 | 0 0 0 1 0 > 0.99992 || = 0.57 500 475 517 509 481 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 2 1 1 0 1 > 0.99991 || = 0.56 497 517 532 495 502 | 500 < 0.0001 2 0 0 1 0 | 0.5 | 0 0 1 1 0 > 0.9999 || = 0.55 483 508 504 535 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 520 520 495 525 495 | 500 < 0.0001 5 5 4 9 4 | 5 | 4 2 4 9 3 > 0.9999 || = 0.53 498 502 485 495 470 | 500 < 0.0002 6 8 1 2 7 | 5 | 5 3 5 6 2 > 0.9998 || = 0.52 468 506 466 490 464 | 500 < 0.0003 5 2 6 5 6 | 5 | 5 5 2 5 5 > 0.9997 || = 0.51 521 464 474 510 517 | 500 < 0.0004 3 3 5 7 8 | 5 | 5 12 6 3 4 > 0.9996 || = 0.50 498 509 506 484 500 | 500 < 0.0005 4 8 2 4 7 | 5 | 5 4 7 5 5 > 0.9995 || = 0.49 534 499 460 519 510 | 500 < 0.0006 3 4 2 5 6 | 5 | 1 2 4 6 3 > 0.9994 || = 0.48 454 507 506 505 487 | 500 < 0.0007 6 5 3 6 1 | 5 | 7 4 6 6 3 > 0.9993 || = 0.47 482 497 499 526 474 | 500 < 0.0008 6 5 5 3 3 | 5 | 6 5 1 4 5 > 0.9992 || = 0.46 477 508 469 478 498 | 500 < 0.0009 5 7 4 7 6 | 5 | 4 4 5 4 3 > 0.9991 || = 0.45 516 516 468 508 432 | 500 < 0.001 8 4 4 6 3 | 5 | 7 3 6 4 5 > 0.999 || = 0.44 508 549 519 486 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 529 487 458 503 483 | 500 < 0.001 51 51 36 54 51 | 50 | 49 44 46 52 38 > 0.999 || = 0.42 489 520 516 517 472 | 500 < 0.002 44 61 46 49 51 | 50 | 47 47 51 38 56 > 0.998 || = 0.41 523 467 504 508 467 | 500 < 0.003 53 48 48 55 57 | 50 | 51 39 46 51 41 > 0.997 || = 0.40 493 515 482 503 487 | 500 < 0.004 47 39 49 45 48 | 50 | 52 55 44 36 53 > 0.996 || = 0.39 512 494 506 515 538 | 500 < 0.005 44 49 41 54 51 | 50 | 44 56 61 47 62 > 0.995 || = 0.38 456 517 463 508 554 | 500 < 0.006 49 43 61 50 44 | 50 | 58 42 62 55 57 > 0.994 || = 0.37 479 462 522 484 513 | 500 < 0.007 51 46 49 38 49 | 50 | 44 57 32 45 51 > 0.993 || = 0.36 484 496 547 484 483 | 500 < 0.008 37 37 61 48 51 | 50 | 41 41 53 53 41 > 0.992 || = 0.35 460 497 525 517 486 | 500 < 0.009 49 55 49 45 54 | 50 | 39 56 52 60 53 > 0.991 || = 0.34 502 508 514 512 509 | 500 < 0.01 64 44 60 53 43 | 50 | 63 43 47 36 54 > 0.99 || = 0.33 504 463 498 493 525 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 495 496 502 512 490 | 500 < 0.01 489 473 500 491 499 | 497.5 | 488 480 494 473 506 > 0.99 || = 0.31 522 503 533 500 502 | 500 = 0.01 266 267 238 301 277 | 252.5 | 268 261 266 238 234 = 0.99 || = 0.30 490 507 499 525 499 | 500 = 0.02 492 509 490 481 517 | 500 | 500 457 477 480 527 = 0.98 || = 0.29 514 511 499 534 513 | 500 =================================================================| 500 | 507 511 446 460 516 = 0.97 || = 0.28 482 503 516 517 486 | 500 sknuth_Gap test: | 500 | 546 473 489 492 457 = 0.96 || = 0.27 483 504 556 462 511 | 500 ----------------------------------------------- | 500 | 501 489 499 500 485 = 0.95 || = 0.26 542 507 502 531 470 | 500 N = 1, n = 10000000, r = 20, Alpha = 0, Beta = 0.000976562 | 500 | 506 508 526 476 502 = 0.94 || = 0.25 479 511 515 512 491 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 488 499 480 506 492 = 0.93 || = 0.24 506 526 466 486 538 | 500 | 500 | 496 512 486 502 503 = 0.92 || = 0.23 479 515 475 494 517 | 500 =================================================================| 500 | 513 502 534 486 503 = 0.91 || = 0.22 497 472 510 508 473 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 476 519 521 463 542 = 0.90 || = 0.21 492 498 516 504 508 | 500 -----------------------------------------------------------------| 500 | 492 532 500 544 570 = 0.89 || = 0.20 470 489 526 505 513 | 500 SD Bern.: d 0.91704 0.95859 1.02226 | 500 | 510 492 537 504 521 = 0.88 || = 0.19 498 487 532 491 539 | 500 s 0.87710 1.04262 1.00647 | 500 | 522 511 538 534 517 = 0.87 || = 0.18 513 475 498 479 506 | 500 t 1.00556 1.13369 1.16676 | 500 | 514 503 491 514 522 = 0.86 || = 0.17 500 501 498 498 506 | 500 m 0.92049 0.72836 1.19138 | 500 | 532 505 473 466 501 = 0.85 || = 0.16 476 483 506 488 495 | 500 x 1.01876 0.56418 1.06823 | 500 | 508 518 491 491 479 = 0.84 || = 0.15 528 496 487 514 519 | 500 | 500 | 484 475 490 505 469 = 0.83 || = 0.14 508 474 498 506 484 | 500 Changes: d 54 6 5 | 500 | 472 525 513 512 491 = 0.82 || = 0.13 522 527 509 521 512 | 500 s 48 3 6 | 500 | 464 515 522 495 528 = 0.81 || = 0.12 510 457 529 510 495 | 500 t 51 5 6 | 500 | 482 508 484 451 457 = 0.80 || = 0.11 521 512 495 536 528 | 500 m 48 6 7 | 500 | 469 510 501 506 484 = 0.79 || = 0.10 474 507 489 482 487 | 500 x 54 5 5 | 500 | 521 522 493 495 488 = 0.78 || = 0.09 512 505 484 488 506 | 500 -----------------------------------------------------------------| 500 | 469 484 495 550 504 = 0.77 || = 0.08 485 520 489 498 466 | 500 Aver./ d 0.50037 500 > 500: 5 6 3 4 5 5 6 3 5 6 | 500 | 516 521 450 480 469 = 0.76 || = 0.07 530 484 498 507 523 | 500 median s 0.50051 504 ----- 5 4 7 4 6 6 5 6 8 5 | 500 | 494 538 546 500 527 = 0.75 || = 0.06 494 527 517 540 480 | 500 t 0.49848 499 4 4 7 7 4 4 4 2 5 3 | 500 | 479 491 499 504 506 = 0.74 || = 0.05 502 490 498 497 523 | 500 m 0.49730 500 4 5 7 6 8 4 3 3 6 2 | 500 | 491 499 499 459 504 = 0.73 || = 0.04 503 498 516 509 503 | 500 x 0.49945 501 7 6 6 6 1 4 4 5 7 6 | 500 | 477 451 466 488 472 = 0.72 || = 0.03 492 493 535 482 496 | 500 -----------------------------------------------------------------| 500 | 504 511 483 500 531 = 0.71 || = 0.02 492 509 490 481 517 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 522 511 501 525 522 = 0.70 || = 0.01 266 267 238 301 277 | 252.5 d 0 0 1 14 75 8 3 0 0 | 500 | 518 481 499 463 478 = 0.69 || < 0.01 489 473 500 491 499 | 497.5 s 0 0 1 16 74 9 1 0 0 | 500 | 514 471 469 492 497 = 0.68 ||========================================================================= t 0 0 2 14 70 11 4 0 0 | 500 | 475 489 501 494 517 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 9 78 11 1 1 0 | 500 | 507 463 491 507 506 = 0.66 ||========================================================================= x 0 1 0 15 70 13 1 1 0 | 500 | 502 523 506 491 493 = 0.65 || sknuth_Gap test: no 58 test no 59 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Gap test: test no 59 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 2 | 0.5 | 3 0 1 1 0 > 0.99999 || = 0.64 525 499 492 515 510 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 508 501 492 486 518 | 500 < 0.00003 1 0 0 2 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 501 500 468 509 498 | 500 < 0.00004 0 0 2 0 0 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 558 488 504 542 475 | 500 < 0.00005 0 1 0 0 1 | 0.5 | 1 0 0 1 1 > 0.99995 || = 0.60 474 457 511 500 469 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 0 1 0 0 1 > 0.99994 || = 0.59 443 489 464 533 491 | 500 < 0.00007 2 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 507 535 467 505 475 | 500 < 0.00008 1 0 1 1 0 | 0.5 | 0 2 2 0 0 > 0.99992 || = 0.57 474 508 508 530 464 | 500 < 0.00009 1 1 0 0 2 | 0.5 | 0 2 0 0 1 > 0.99991 || = 0.56 541 468 522 481 509 | 500 < 0.0001 0 1 0 3 1 | 0.5 | 0 0 1 4 0 > 0.9999 || = 0.55 519 454 485 503 502 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 463 498 505 468 474 | 500 < 0.0001 5 6 3 7 7 | 5 | 5 5 4 6 3 > 0.9999 || = 0.53 497 516 499 507 495 | 500 < 0.0002 6 3 8 6 4 | 5 | 3 1 1 1 2 > 0.9998 || = 0.52 495 482 493 527 476 | 500 < 0.0003 4 3 8 4 7 | 5 | 10 1 3 4 3 > 0.9997 || = 0.51 488 517 512 527 489 | 500 < 0.0004 7 6 3 3 5 | 5 | 4 3 5 5 2 > 0.9996 || = 0.50 506 501 512 476 472 | 500 < 0.0005 4 4 5 5 4 | 5 | 5 5 4 4 4 > 0.9995 || = 0.49 468 501 489 508 508 | 500 < 0.0006 3 4 5 5 5 | 5 | 5 4 4 5 2 > 0.9994 || = 0.48 474 530 515 499 535 | 500 < 0.0007 3 4 3 5 4 | 5 | 5 3 4 6 4 > 0.9993 || = 0.47 515 506 487 483 552 | 500 < 0.0008 2 5 4 2 3 | 5 | 6 3 2 6 3 > 0.9992 || = 0.46 468 500 489 497 515 | 500 < 0.0009 7 5 3 7 11 | 5 | 2 3 9 7 5 > 0.9991 || = 0.45 521 483 500 513 470 | 500 < 0.001 4 4 4 2 3 | 5 | 5 3 6 8 3 > 0.999 || = 0.44 457 564 523 480 497 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 528 478 502 524 533 | 500 < 0.001 45 44 46 46 53 | 50 | 50 31 42 52 31 > 0.999 || = 0.42 508 489 466 464 489 | 500 < 0.002 64 44 52 55 53 | 50 | 43 45 42 49 44 > 0.998 || = 0.41 509 499 480 499 500 | 500 < 0.003 47 55 44 64 49 | 50 | 52 49 42 64 59 > 0.997 || = 0.40 482 480 489 488 484 | 500 < 0.004 49 50 51 52 52 | 50 | 46 55 53 48 53 > 0.996 || = 0.39 502 471 472 464 543 | 500 < 0.005 47 41 45 37 50 | 50 | 56 59 41 44 52 > 0.995 || = 0.38 490 527 493 520 483 | 500 < 0.006 48 58 45 50 60 | 50 | 54 53 48 63 48 > 0.994 || = 0.37 523 512 527 491 511 | 500 < 0.007 46 47 48 51 51 | 50 | 47 51 46 41 45 > 0.993 || = 0.36 490 510 536 498 499 | 500 < 0.008 55 49 51 58 47 | 50 | 42 44 47 42 58 > 0.992 || = 0.35 479 497 451 518 492 | 500 < 0.009 49 56 48 58 47 | 50 | 57 44 40 42 61 > 0.991 || = 0.34 499 510 488 544 523 | 500 < 0.01 48 43 78 49 57 | 50 | 48 55 43 55 41 > 0.99 || = 0.33 492 511 536 507 531 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 525 462 504 518 500 | 500 < 0.01 498 487 508 520 519 | 497.5 | 495 486 444 500 492 > 0.99 || = 0.31 494 491 526 513 481 | 500 = 0.01 245 276 244 256 242 | 252.5 | 237 251 245 255 247 = 0.99 || = 0.30 479 450 499 460 522 | 500 = 0.02 529 505 500 509 481 | 500 | 508 460 513 519 478 = 0.98 || = 0.29 525 492 485 553 486 | 500 =================================================================| 500 | 518 501 550 478 529 = 0.97 || = 0.28 503 522 519 530 467 | 500 sknuth_Gap test: | 500 | 506 544 491 527 540 = 0.96 || = 0.27 500 493 529 503 485 | 500 ----------------------------------------------- | 500 | 475 480 519 521 504 = 0.95 || = 0.26 519 490 454 495 529 | 500 N = 1, n = 10000000, r = 20, Alpha = 0, Beta = 0.000976562 | 500 | 491 475 491 522 563 = 0.94 || = 0.25 488 498 484 492 534 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 506 491 494 512 527 = 0.93 || = 0.24 540 527 497 481 501 | 500 | 500 | 506 481 509 486 465 = 0.92 || = 0.23 528 521 550 489 534 | 500 =================================================================| 500 | 497 455 494 489 542 = 0.91 || = 0.22 491 473 504 496 461 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 530 501 508 523 509 = 0.90 || = 0.21 475 465 489 471 525 | 500 -----------------------------------------------------------------| 500 | 468 519 488 486 493 = 0.89 || = 0.20 474 543 490 519 498 | 500 SD Bern.: d 1.04573 0.76195 0.70319 | 500 | 495 478 491 518 498 = 0.88 || = 0.19 515 536 496 482 514 | 500 s 0.98326 0.82137 1.09598 | 500 | 497 502 510 478 475 = 0.87 || = 0.18 498 501 508 490 472 | 500 t 0.96429 1.34230 0.95963 | 500 | 511 512 504 509 503 = 0.86 || = 0.17 499 536 499 459 503 | 500 m 0.95975 1.03974 1.13545 | 500 | 507 510 553 494 504 = 0.85 || = 0.16 560 501 518 463 458 | 500 x 1.03657 0.61836 1.25441 | 500 | 548 493 487 485 532 = 0.84 || = 0.15 514 466 523 483 498 | 500 | 500 | 487 515 538 488 529 = 0.83 || = 0.14 515 496 488 467 498 | 500 Changes: d 53 4 6 | 500 | 487 496 479 478 506 = 0.82 || = 0.13 496 504 475 490 488 | 500 s 44 6 3 | 500 | 516 509 495 532 504 = 0.81 || = 0.12 509 509 485 544 528 | 500 t 45 7 2 | 500 | 463 494 535 515 482 = 0.80 || = 0.11 501 521 503 469 486 | 500 m 48 4 6 | 500 | 517 532 520 476 508 = 0.79 || = 0.10 531 470 504 501 487 | 500 x 43 6 4 | 500 | 519 502 511 501 550 = 0.78 || = 0.09 522 506 508 483 507 | 500 -----------------------------------------------------------------| 500 | 521 507 498 516 501 = 0.77 || = 0.08 469 506 499 489 490 | 500 Aver./ d 0.50010 500 > 500: 4 7 5 3 5 3 7 5 5 5 | 500 | 480 501 516 493 538 = 0.76 || = 0.07 503 516 483 465 506 | 500 median s 0.49871 501 ----- 6 7 4 5 4 4 6 6 7 2 | 500 | 477 502 465 486 503 = 0.75 || = 0.06 458 494 497 511 469 | 500 t 0.50198 500 2 5 4 5 3 5 7 8 5 4 | 500 | 475 486 504 504 480 = 0.74 || = 0.05 476 496 446 485 488 | 500 m 0.50269 501 4 2 4 6 3 7 8 6 4 7 | 500 | 515 497 502 517 488 = 0.73 || = 0.04 473 494 460 486 514 | 500 x 0.50135 498 5 3 5 5 5 2 3 5 7 6 | 500 | 496 509 506 505 477 = 0.72 || = 0.03 478 528 484 453 509 | 500 -----------------------------------------------------------------| 500 | 510 482 544 494 460 = 0.71 || = 0.02 529 505 500 509 481 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 568 542 504 512 502 = 0.70 || = 0.01 245 276 244 256 242 | 252.5 d 0 0 1 20 65 11 3 1 0 | 500 | 504 463 509 526 495 = 0.69 || < 0.01 498 487 508 520 519 | 497.5 s 0 0 3 11 73 13 1 0 0 | 500 | 504 503 508 511 465 = 0.68 ||========================================================================= t 0 0 4 8 76 10 3 0 0 | 500 | 484 515 513 511 473 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 13 71 15 1 0 0 | 500 | 473 536 516 529 487 = 0.66 ||========================================================================= x 0 0 0 19 62 17 3 0 0 | 500 | 475 514 511 473 489 = 0.65 || sknuth_Gap test: no 59 test no 60 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Gap test: test no 60 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 465 490 483 475 536 | 500 < 0.00002 0 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 539 499 530 481 520 | 500 < 0.00003 1 2 1 0 3 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 507 494 502 505 515 | 500 < 0.00004 1 2 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 511 491 482 515 527 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 487 495 521 531 507 | 500 < 0.00006 0 0 0 2 2 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 546 505 526 503 518 | 500 < 0.00007 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 513 517 509 481 477 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 499 456 487 518 467 | 500 < 0.00009 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 511 498 520 527 499 | 500 < 0.0001 2 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 455 480 494 510 441 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 465 480 510 493 498 | 500 < 0.0001 4 6 2 7 8 | 5 | 0 0 0 0 0 > 0.9999 || = 0.53 466 491 499 505 489 | 500 < 0.0002 3 6 3 11 3 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 517 505 512 507 511 | 500 < 0.0003 4 4 3 7 3 | 5 | 0 0 0 0 0 > 0.9997 || = 0.51 503 483 548 508 503 | 500 < 0.0004 5 4 4 3 6 | 5 | 0 0 0 0 0 > 0.9996 || = 0.50 479 508 469 506 479 | 500 < 0.0005 6 7 6 5 8 | 5 | 0 0 0 0 0 > 0.9995 || = 0.49 526 490 517 475 499 | 500 < 0.0006 3 7 4 6 5 | 5 | 0 0 0 0 0 > 0.9994 || = 0.48 525 498 485 540 537 | 500 < 0.0007 2 3 2 7 3 | 5 | 0 0 1 0 1 > 0.9993 || = 0.47 531 474 499 517 534 | 500 < 0.0008 10 5 7 7 9 | 5 | 0 1 1 0 1 > 0.9992 || = 0.46 490 502 542 523 506 | 500 < 0.0009 5 2 5 2 6 | 5 | 2 1 1 0 1 > 0.9991 || = 0.45 494 535 511 496 498 | 500 < 0.001 7 1 9 2 6 | 5 | 0 1 2 2 1 > 0.999 || = 0.44 480 454 522 425 490 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 485 523 518 461 516 | 500 < 0.001 49 45 45 57 57 | 50 | 2 3 5 2 4 > 0.999 || = 0.42 506 509 528 497 499 | 500 < 0.002 64 38 45 48 51 | 50 | 24 31 26 41 35 > 0.998 || = 0.41 502 522 525 488 499 | 500 < 0.003 42 51 41 57 49 | 50 | 22 38 37 49 38 > 0.997 || = 0.40 534 492 461 534 484 | 500 < 0.004 56 44 48 55 63 | 50 | 40 44 34 43 38 > 0.996 || = 0.39 464 521 507 470 508 | 500 < 0.005 55 43 45 47 48 | 50 | 67 39 48 49 40 > 0.995 || = 0.38 525 525 521 499 483 | 500 < 0.006 52 56 52 42 59 | 50 | 47 52 40 55 41 > 0.994 || = 0.37 516 491 492 468 494 | 500 < 0.007 69 42 49 52 55 | 50 | 55 33 51 45 52 > 0.993 || = 0.36 498 491 513 464 508 | 500 < 0.008 65 32 47 47 51 | 50 | 60 43 54 46 40 > 0.992 || = 0.35 489 479 498 519 520 | 500 < 0.009 59 49 60 40 54 | 50 | 49 54 51 37 47 > 0.991 || = 0.34 478 541 494 475 487 | 500 < 0.01 42 39 41 56 49 | 50 | 61 48 36 45 58 > 0.99 || = 0.33 540 502 487 497 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 481 501 534 479 495 | 500 < 0.01 553 439 473 501 536 | 497.5 | 427 385 382 412 393 > 0.99 || = 0.31 512 498 482 500 521 | 500 = 0.01 244 252 226 260 242 | 252.5 | 242 214 257 238 265 = 0.99 || = 0.30 487 522 500 468 550 | 500 = 0.02 473 504 492 485 524 | 500 | 509 527 600 573 536 = 0.98 || = 0.29 489 543 500 476 507 | 500 =================================================================| 500 | 527 519 510 502 488 = 0.97 || = 0.28 527 494 491 481 497 | 500 sknuth_Gap test: | 500 | 493 506 501 472 463 = 0.96 || = 0.27 535 479 496 479 481 | 500 ----------------------------------------------- | 500 | 525 516 471 501 506 = 0.95 || = 0.26 512 486 455 496 502 | 500 N = 1, n = 10000000, r = 20, Alpha = 0, Beta = 0.000976562 | 500 | 515 520 519 534 538 = 0.94 || = 0.25 494 500 497 504 528 | 500 Anderson-Darling statistic = A2 | 500 | 546 499 481 504 499 = 0.93 || = 0.24 431 496 480 495 482 | 500 | 500 | 484 508 466 549 501 = 0.92 || = 0.23 514 503 520 506 508 | 500 =================================================================| 500 | 512 485 475 480 494 = 0.91 || = 0.22 499 499 518 539 516 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 477 510 520 498 495 = 0.90 || = 0.21 493 516 525 503 472 | 500 -----------------------------------------------------------------| 500 | 496 510 486 519 471 = 0.89 || = 0.20 507 519 446 470 467 | 500 SD Bern.: d 1.18381 1.45468 2.97099 | 500 | 504 478 497 526 516 = 0.88 || = 0.19 496 495 497 510 527 | 500 s 1.05953 1.26632 2.54409 | 500 | 535 497 526 488 507 = 0.87 || = 0.18 498 506 514 488 519 | 500 t 1.18768 0.84303 2.58740 | 500 | 513 475 494 528 476 = 0.86 || = 0.17 503 551 464 514 507 | 500 m 1.16630 0.83587 2.32322 | 500 | 512 494 450 505 533 = 0.85 || = 0.16 529 474 501 544 494 | 500 x 1.11598 0.83467 2.44539 | 500 | 467 525 495 520 537 = 0.84 || = 0.15 495 499 498 479 485 | 500 | 500 | 487 505 492 529 539 = 0.83 || = 0.14 497 493 487 520 517 | 500 Changes: d 49 4 5 | 500 | 531 528 506 509 485 = 0.82 || = 0.13 458 506 549 511 491 | 500 s 44 4 4 | 500 | 499 532 473 509 509 = 0.81 || = 0.12 486 491 505 472 487 | 500 t 54 4 2 | 500 | 477 488 487 509 511 = 0.80 || = 0.11 459 519 477 467 539 | 500 m 39 6 2 | 500 | 495 521 487 469 475 = 0.79 || = 0.10 458 486 521 484 502 | 500 x 45 5 3 | 500 | 459 538 544 533 477 = 0.78 || = 0.09 461 482 493 437 503 | 500 -----------------------------------------------------------------| 500 | 556 484 482 515 473 = 0.77 || = 0.08 529 512 482 499 472 | 500 Aver./ d 0.50066 499 > 500: 5 2 5 4 6 5 6 4 5 6 | 500 | 443 482 501 438 490 = 0.76 || = 0.07 486 510 506 501 500 | 500 median s 0.49900 499 ----- 6 4 4 6 5 3 3 4 6 6 | 500 | 478 522 524 485 513 = 0.75 || = 0.06 511 509 490 506 449 | 500 t 0.50004 499 2 5 3 4 7 7 4 6 3 5 | 500 | 525 533 508 505 526 = 0.74 || = 0.05 491 527 485 517 505 | 500 m 0.50222 504 7 5 4 1 4 8 8 6 8 6 | 500 | 530 472 519 542 483 = 0.73 || = 0.04 520 520 541 524 487 | 500 x 0.49927 500 4 6 5 5 4 4 7 3 6 5 | 500 | 521 484 494 473 420 = 0.72 || = 0.03 533 490 482 506 484 | 500 -----------------------------------------------------------------| 500 | 476 494 521 523 487 = 0.71 || = 0.02 473 504 492 485 524 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 486 476 477 525 518 = 0.70 || = 0.01 244 252 226 260 242 | 252.5 d 0 2 2 14 59 20 4 0 0 | 500 | 505 465 485 505 515 = 0.69 || < 0.01 553 439 473 501 536 | 497.5 s 1 0 3 7 75 14 1 0 0 | 500 | 530 481 529 525 500 = 0.68 ||========================================================================= t 1 0 3 12 69 13 2 0 1 | 500 | 536 507 500 507 495 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 2 2 15 63 17 1 1 0 | 500 | 497 527 526 514 495 = 0.66 ||========================================================================= x 1 1 2 11 69 16 1 0 0 | 500 | 478 531 476 502 530 = 0.65 || sknuth_Gap test: no 60 test no 61 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Gap test: test no 61 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 2 0 | 0.5 | 0 0 1 0 1 > 0.99999 || = 0.64 511 477 509 487 519 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 0 2 0 0 2 > 0.99998 || = 0.63 511 543 502 481 507 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 0 0 1 1 0 > 0.99997 || = 0.62 484 510 497 541 495 | 500 < 0.00004 0 1 2 0 2 | 0.5 | 1 1 1 1 2 > 0.99996 || = 0.61 514 502 516 496 499 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 2 0 0 1 0 > 0.99995 || = 0.60 525 491 480 543 501 | 500 < 0.00006 0 0 1 1 0 | 0.5 | 1 0 0 1 1 > 0.99994 || = 0.59 485 482 526 523 511 | 500 < 0.00007 1 1 0 0 1 | 0.5 | 0 1 0 1 1 > 0.99993 || = 0.58 528 488 511 551 486 | 500 < 0.00008 0 2 1 1 1 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 508 516 499 479 497 | 500 < 0.00009 0 0 0 2 0 | 0.5 | 0 2 0 1 2 > 0.99991 || = 0.56 490 519 454 522 514 | 500 < 0.0001 1 2 0 1 0 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 492 463 519 499 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 493 480 481 503 498 | 500 < 0.0001 2 6 4 10 4 | 5 | 5 8 3 6 9 > 0.9999 || = 0.53 512 459 512 518 494 | 500 < 0.0002 2 2 0 8 5 | 5 | 2 3 3 0 4 > 0.9998 || = 0.52 498 531 510 492 519 | 500 < 0.0003 6 3 2 4 3 | 5 | 3 3 3 6 4 > 0.9997 || = 0.51 501 492 497 506 484 | 500 < 0.0004 2 3 11 7 4 | 5 | 2 4 6 4 4 > 0.9996 || = 0.50 480 514 523 499 486 | 500 < 0.0005 6 4 5 5 8 | 5 | 12 5 4 6 4 > 0.9995 || = 0.49 509 490 482 529 469 | 500 < 0.0006 10 3 5 4 4 | 5 | 5 4 6 7 4 > 0.9994 || = 0.48 483 512 485 477 497 | 500 < 0.0007 6 6 3 8 5 | 5 | 2 8 5 4 7 > 0.9993 || = 0.47 494 506 533 498 488 | 500 < 0.0008 7 8 2 4 9 | 5 | 6 8 7 6 5 > 0.9992 || = 0.46 534 511 502 516 470 | 500 < 0.0009 6 3 0 8 7 | 5 | 5 7 3 9 3 > 0.9991 || = 0.45 523 449 475 493 510 | 500 < 0.001 6 4 1 4 5 | 5 | 2 4 2 7 5 > 0.999 || = 0.44 499 514 484 480 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 480 504 512 525 476 | 500 < 0.001 53 42 33 62 54 | 50 | 44 54 42 55 49 > 0.999 || = 0.42 503 536 481 535 502 | 500 < 0.002 56 46 43 52 49 | 50 | 58 45 40 54 62 > 0.998 || = 0.41 542 479 532 515 493 | 500 < 0.003 60 46 60 47 53 | 50 | 53 47 56 47 50 > 0.997 || = 0.40 500 501 508 507 479 | 500 < 0.004 48 35 40 46 57 | 50 | 54 41 41 42 49 > 0.996 || = 0.39 469 447 477 490 481 | 500 < 0.005 46 37 47 47 42 | 50 | 60 40 52 52 51 > 0.995 || = 0.38 481 517 489 457 471 | 500 < 0.006 60 34 61 36 46 | 50 | 43 50 38 52 55 > 0.994 || = 0.37 484 472 510 519 453 | 500 < 0.007 52 51 54 45 46 | 50 | 54 44 57 50 49 > 0.993 || = 0.36 513 525 507 490 527 | 500 < 0.008 47 58 41 44 52 | 50 | 37 40 44 61 49 > 0.992 || = 0.35 530 486 490 543 514 | 500 < 0.009 51 58 57 52 49 | 50 | 62 52 54 59 66 > 0.991 || = 0.34 471 504 509 499 510 | 500 < 0.01 49 41 39 45 56 | 50 | 48 41 58 50 47 > 0.99 || = 0.33 483 490 468 473 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 508 498 517 508 479 | 500 < 0.01 522 448 475 476 504 | 497.5 | 513 454 482 522 527 > 0.99 || = 0.31 499 488 511 443 536 | 500 = 0.01 278 270 239 226 259 | 252.5 | 256 271 244 263 239 = 0.99 || = 0.30 498 476 494 497 488 | 500 = 0.02 493 524 475 492 467 | 500 | 505 496 465 537 517 = 0.98 || = 0.29 517 542 511 514 499 | 500 =================================================================| 500 | 476 517 495 500 485 = 0.97 || = 0.28 489 484 536 468 505 | 500 sknuth_Gap test: | 500 | 498 494 495 505 513 = 0.96 || = 0.27 505 508 459 497 510 | 500 ----------------------------------------------- | 500 | 522 504 492 500 496 = 0.95 || = 0.26 512 498 481 539 514 | 500 N = 1, n = 10000000, r = 20, Alpha = 0, Beta = 0.000976562 | 500 | 498 476 468 489 517 = 0.94 || = 0.25 508 512 501 497 495 | 500 Test on the sum of all N observations | 500 | 489 484 529 492 526 = 0.93 || = 0.24 493 523 496 522 507 | 500 | 500 | 468 516 505 467 489 = 0.92 || = 0.23 501 509 494 473 533 | 500 =================================================================| 500 | 535 489 532 514 518 = 0.91 || = 0.22 491 485 478 550 496 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 494 508 565 505 508 = 0.90 || = 0.21 460 513 533 511 478 | 500 -----------------------------------------------------------------| 500 | 494 476 508 495 545 = 0.89 || = 0.20 475 518 502 462 502 | 500 SD Bern.: d 0.89403 0.74869 1.10236 | 500 | 476 486 515 519 518 = 0.88 || = 0.19 518 495 505 502 527 | 500 s 0.98437 1.38343 0.95125 | 500 | 478 529 503 520 515 = 0.87 || = 0.18 515 529 497 538 475 | 500 t 0.98565 1.36815 1.09049 | 500 | 463 490 520 503 494 = 0.86 || = 0.17 508 513 527 468 528 | 500 m 1.05264 0.96795 0.80537 | 500 | 496 475 521 483 489 = 0.85 || = 0.16 519 508 519 496 496 | 500 x 0.86878 0.65146 0.93747 | 500 | 531 485 521 523 493 = 0.84 || = 0.15 523 462 488 503 540 | 500 | 500 | 504 484 485 497 485 = 0.83 || = 0.14 493 499 503 528 466 | 500 Changes: d 46 5 6 | 500 | 487 498 474 516 520 = 0.82 || = 0.13 457 535 482 483 492 | 500 s 60 2 3 | 500 | 481 499 510 496 538 = 0.81 || = 0.12 509 527 514 485 494 | 500 t 46 6 7 | 500 | 481 495 505 489 490 = 0.80 || = 0.11 511 475 502 511 514 | 500 m 63 3 5 | 500 | 519 499 494 500 509 = 0.79 || = 0.10 507 507 528 457 472 | 500 x 52 6 6 | 500 | 533 514 458 532 516 = 0.78 || = 0.09 511 477 493 507 492 | 500 -----------------------------------------------------------------| 500 | 494 516 505 494 498 = 0.77 || = 0.08 507 502 506 447 490 | 500 Aver./ d 0.49999 498 > 500: 4 8 5 3 5 5 5 4 2 5 | 500 | 550 504 533 505 485 = 0.76 || = 0.07 488 502 513 524 499 | 500 median s 0.49912 501 ----- 5 6 7 3 7 3 7 6 2 4 | 500 | 545 548 517 478 525 = 0.75 || = 0.06 481 496 476 452 523 | 500 t 0.50170 502 3 7 5 5 5 5 6 7 8 3 | 500 | 490 492 510 505 489 = 0.74 || = 0.05 498 549 431 465 463 | 500 m 0.50276 499 2 5 5 3 6 7 4 4 6 5 | 500 | 480 531 548 475 479 = 0.73 || = 0.04 485 487 477 488 536 | 500 x 0.50161 498 4 4 6 4 3 5 4 3 6 6 | 500 | 466 519 526 459 476 = 0.72 || = 0.03 469 488 507 491 486 | 500 -----------------------------------------------------------------| 500 | 498 467 461 527 499 = 0.71 || = 0.02 493 524 475 492 467 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 484 506 466 516 486 = 0.70 || = 0.01 278 270 239 226 259 | 252.5 d 0 0 0 11 74 14 2 0 0 | 500 | 530 474 477 479 510 = 0.69 || < 0.01 522 448 475 476 504 | 497.5 s 0 0 3 14 67 15 2 0 0 | 500 | 495 511 488 503 476 = 0.68 ||========================================================================= t 0 1 1 15 70 12 2 0 0 | 500 | 478 526 509 494 525 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 13 67 16 2 0 0 | 500 | 526 513 508 508 496 = 0.66 ||========================================================================= x 0 0 1 12 74 13 1 0 0 | 500 | 489 497 516 484 473 = 0.65 || sknuth_Gap test: no 61 test no 62 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Run test: test no 62 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 531 513 520 560 520 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 2 1 1 1 1 > 0.99998 || = 0.63 503 519 522 491 508 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 2 0 1 0 1 > 0.99997 || = 0.62 501 544 534 506 481 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 0 1 0 0 2 > 0.99996 || = 0.61 505 492 532 457 537 | 500 < 0.00005 0 1 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99995 || = 0.60 496 487 524 495 510 | 500 < 0.00006 0 1 0 1 0 | 0.5 | 0 2 1 0 1 > 0.99994 || = 0.59 520 468 483 498 461 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 2 0 1 4 0 > 0.99993 || = 0.58 552 478 493 510 538 | 500 < 0.00008 0 0 1 0 1 | 0.5 | 1 2 2 0 0 > 0.99992 || = 0.57 470 485 508 517 492 | 500 < 0.00009 2 0 0 0 1 | 0.5 | 2 1 3 0 1 > 0.99991 || = 0.56 520 495 482 491 476 | 500 < 0.0001 3 0 0 0 1 | 0.5 | 4 0 1 2 1 > 0.9999 || = 0.55 490 492 552 487 542 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 508 483 490 533 487 | 500 < 0.0001 5 4 1 1 4 | 5 | 14 8 11 7 7 > 0.9999 || = 0.53 466 495 532 496 523 | 500 < 0.0002 4 3 0 3 3 | 5 | 4 6 5 3 1 > 0.9998 || = 0.52 515 494 451 479 487 | 500 < 0.0003 3 7 3 4 5 | 5 | 9 6 8 6 7 > 0.9997 || = 0.51 467 508 510 503 492 | 500 < 0.0004 3 1 3 5 3 | 5 | 6 14 14 6 7 > 0.9996 || = 0.50 478 499 470 477 486 | 500 < 0.0005 1 5 1 1 2 | 5 | 9 12 5 10 8 > 0.9995 || = 0.49 466 506 462 495 459 | 500 < 0.0006 4 1 4 3 3 | 5 | 6 13 6 6 10 > 0.9994 || = 0.48 502 500 456 458 479 | 500 < 0.0007 1 9 4 6 4 | 5 | 13 13 8 12 8 > 0.9993 || = 0.47 522 507 458 528 515 | 500 < 0.0008 5 1 3 6 2 | 5 | 5 8 14 3 3 > 0.9992 || = 0.46 453 480 484 467 510 | 500 < 0.0009 1 6 3 4 2 | 5 | 4 6 10 8 9 > 0.9991 || = 0.45 504 487 483 484 505 | 500 < 0.001 6 2 4 3 5 | 5 | 11 11 5 9 10 > 0.999 || = 0.44 485 443 450 495 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 458 516 505 479 487 | 500 < 0.001 33 39 26 36 33 | 50 | 81 97 86 70 70 > 0.999 || = 0.42 479 496 422 466 464 | 500 < 0.002 43 32 38 42 32 | 50 | 83 69 84 95 79 > 0.998 || = 0.41 461 510 520 473 435 | 500 < 0.003 30 27 32 39 25 | 50 | 72 71 85 79 78 > 0.997 || = 0.40 465 457 500 489 454 | 500 < 0.004 35 39 42 42 38 | 50 | 65 68 65 84 74 > 0.996 || = 0.39 461 485 511 477 439 | 500 < 0.005 39 31 46 41 40 | 50 | 80 78 74 64 61 > 0.995 || = 0.38 449 465 449 448 484 | 500 < 0.006 38 29 37 37 28 | 50 | 80 69 68 68 77 > 0.994 || = 0.37 492 456 434 500 465 | 500 < 0.007 32 25 38 30 37 | 50 | 62 74 77 82 89 > 0.993 || = 0.36 468 440 485 476 469 | 500 < 0.008 33 34 32 45 47 | 50 | 72 65 64 76 80 > 0.992 || = 0.35 470 459 466 477 463 | 500 < 0.009 51 41 32 43 29 | 50 | 76 63 74 77 71 > 0.991 || = 0.34 473 483 470 491 495 | 500 < 0.01 36 28 47 31 41 | 50 | 61 62 65 64 66 > 0.99 || = 0.33 463 454 465 452 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 458 456 461 497 485 | 500 < 0.01 370 325 370 386 350 | 497.5 | 732 716 742 759 745 > 0.99 || = 0.31 481 451 450 461 478 | 500 = 0.01 186 197 205 171 195 | 252.5 | 333 355 346 347 350 = 0.99 || = 0.30 446 451 467 490 475 | 500 = 0.02 379 328 383 387 370 | 500 | 697 648 699 681 640 = 0.98 || = 0.29 437 459 468 487 433 | 500 =================================================================| 500 | 651 624 626 654 641 = 0.97 || = 0.28 443 438 464 477 470 | 500 sknuth_Run test: | 500 | 644 640 640 664 656 = 0.96 || = 0.27 466 496 501 457 474 | 500 ----------------------------------------------- | 500 | 576 672 610 618 603 = 0.95 || = 0.26 419 465 483 463 433 | 500 N = 10, n = 1000000000, r = 15, Up = TRUE | 500 | 628 621 625 601 592 = 0.94 || = 0.25 488 455 449 457 450 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 585 654 606 616 616 = 0.93 || = 0.24 460 463 404 454 468 | 500 | 500 | 613 614 616 643 630 = 0.92 || = 0.23 417 454 453 427 437 | 500 =================================================================| 500 | 578 575 600 565 546 = 0.91 || = 0.22 403 448 417 418 435 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 621 598 558 574 579 = 0.90 || = 0.21 458 491 409 429 401 | 500 -----------------------------------------------------------------| 500 | 567 614 566 640 589 = 0.89 || = 0.20 442 440 420 440 457 | 500 SD Bern.: d 3.25766 2.01991 3.46120 | 500 | 577 550 613 567 561 = 0.88 || = 0.19 416 447 453 440 474 | 500 s 3.37534 2.58702 3.34651 | 500 | 609 586 548 598 577 = 0.87 || = 0.18 449 404 418 429 399 | 500 t 3.26534 2.04748 3.61511 | 500 | 514 612 582 573 573 = 0.86 || = 0.17 409 422 447 447 456 | 500 m 3.16100 1.75015 3.89218 | 500 | 602 598 614 579 578 = 0.85 || = 0.16 433 420 452 449 411 | 500 x 3.11761 2.31026 3.62644 | 500 | 585 548 588 545 572 = 0.84 || = 0.15 446 439 468 478 448 | 500 | 500 | 593 531 568 567 578 = 0.83 || = 0.14 461 434 436 426 459 | 500 Changes: d 17 2 0 | 500 | 506 533 543 550 587 = 0.82 || = 0.13 397 422 431 454 440 | 500 s 11 0 0 | 500 | 589 592 572 541 553 = 0.81 || = 0.12 435 395 432 414 421 | 500 t 21 0 0 | 500 | 604 597 555 526 520 = 0.80 || = 0.11 454 417 422 396 413 | 500 m 15 0 0 | 500 | 576 532 530 518 583 = 0.79 || = 0.10 436 393 430 418 409 | 500 x 17 0 0 | 500 | 506 556 569 557 562 = 0.78 || = 0.09 429 409 413 432 439 | 500 -----------------------------------------------------------------| 500 | 575 544 540 540 554 = 0.77 || = 0.08 427 415 404 428 415 | 500 Aver./ d 0.53828 488 > 500: 0 0 0 0 3 5 8 10 10 10 | 500 | 559 574 553 512 493 = 0.76 || = 0.07 416 392 394 406 437 | 500 median s 0.54062 494 ----- 0 0 0 0 4 1 9 10 10 10 | 500 | 532 545 534 509 555 = 0.75 || = 0.06 447 383 412 397 415 | 500 t 0.53860 490 0 0 1 1 2 5 8 10 10 10 | 500 | 554 568 557 556 565 = 0.74 || = 0.05 403 404 377 453 426 | 500 m 0.53631 491 0 0 0 0 1 4 6 10 10 10 | 500 | 527 547 540 520 519 = 0.73 || = 0.04 396 420 382 399 425 | 500 x 0.53655 487 0 0 0 0 3 4 8 8 10 10 | 500 | 539 565 544 532 539 = 0.72 || = 0.03 355 387 396 387 383 | 500 -----------------------------------------------------------------| 500 | 504 523 534 503 497 = 0.71 || = 0.02 379 328 383 387 370 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 555 515 495 480 519 = 0.70 || = 0.01 186 197 205 171 195 | 252.5 d 9 7 12 17 25 5 4 9 13 | 500 | 513 527 515 525 497 = 0.69 || < 0.01 370 325 370 386 350 | 497.5 s 10 7 13 9 27 10 6 4 15 | 500 | 544 540 554 507 561 = 0.68 ||========================================================================= t 9 10 12 12 21 12 8 5 12 | 500 | 496 527 525 528 518 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 8 9 9 15 29 9 6 5 11 | 500 | 573 501 483 531 516 = 0.66 ||========================================================================= x 7 9 10 15 29 5 8 8 10 | 500 | 488 542 516 465 516 = 0.65 || sknuth_Run test: no 62 test no 63 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Run test: test no 63 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 3 1 1 0 0 | 0.5 | 0 1 1 0 1 > 0.99999 || = 0.64 444 472 467 471 489 | 500 < 0.00002 0 2 2 2 2 | 0.5 | 0 0 0 0 2 > 0.99998 || = 0.63 481 500 469 504 489 | 500 < 0.00003 0 1 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 500 470 457 455 434 | 500 < 0.00004 0 1 1 2 2 | 0.5 | 0 1 0 1 0 > 0.99996 || = 0.61 498 461 467 490 468 | 500 < 0.00005 2 0 0 2 0 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 483 474 448 460 486 | 500 < 0.00006 0 0 1 1 1 | 0.5 | 2 0 1 0 0 > 0.99994 || = 0.59 528 436 496 483 501 | 500 < 0.00007 2 1 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 469 502 506 510 452 | 500 < 0.00008 0 2 0 1 0 | 0.5 | 0 0 0 1 0 > 0.99992 || = 0.57 484 469 472 466 492 | 500 < 0.00009 0 0 0 0 4 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 497 481 483 472 490 | 500 < 0.0001 0 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 503 466 504 500 494 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 499 480 469 478 490 | 500 < 0.0001 7 8 6 10 11 | 5 | 2 3 3 3 3 > 0.9999 || = 0.53 494 496 495 484 472 | 500 < 0.0002 8 7 12 8 4 | 5 | 3 0 1 1 1 > 0.9998 || = 0.52 473 494 478 514 493 | 500 < 0.0003 13 13 9 7 6 | 5 | 4 3 4 4 1 > 0.9997 || = 0.51 495 457 512 481 524 | 500 < 0.0004 8 9 6 4 8 | 5 | 5 4 4 2 7 > 0.9996 || = 0.50 480 495 478 530 451 | 500 < 0.0005 7 11 6 9 9 | 5 | 4 4 10 1 3 > 0.9995 || = 0.49 513 536 505 475 516 | 500 < 0.0006 9 6 16 6 4 | 5 | 4 4 3 2 2 > 0.9994 || = 0.48 476 496 520 525 469 | 500 < 0.0007 8 6 13 13 9 | 5 | 6 6 4 1 5 > 0.9993 || = 0.47 500 485 541 474 470 | 500 < 0.0008 6 6 9 6 12 | 5 | 2 6 6 2 6 > 0.9992 || = 0.46 506 555 483 511 516 | 500 < 0.0009 3 5 6 5 11 | 5 | 1 6 5 3 7 > 0.9991 || = 0.45 452 508 508 521 493 | 500 < 0.001 8 9 7 6 8 | 5 | 2 1 5 3 8 > 0.999 || = 0.44 513 510 520 531 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 511 507 513 513 554 | 500 < 0.001 77 80 90 74 82 | 50 | 33 37 45 22 43 > 0.999 || = 0.42 529 508 501 519 513 | 500 < 0.002 69 54 61 61 67 | 50 | 35 42 31 41 41 > 0.998 || = 0.41 500 478 534 488 488 | 500 < 0.003 77 90 60 71 76 | 50 | 32 27 42 43 29 > 0.997 || = 0.40 477 499 521 542 497 | 500 < 0.004 77 87 56 66 92 | 50 | 43 35 41 45 40 > 0.996 || = 0.39 500 501 549 457 512 | 500 < 0.005 69 59 78 81 83 | 50 | 36 29 41 39 33 > 0.995 || = 0.38 534 531 506 502 510 | 500 < 0.006 66 71 79 68 80 | 50 | 50 38 37 40 48 > 0.994 || = 0.37 504 531 512 484 500 | 500 < 0.007 72 70 66 72 82 | 50 | 42 33 34 33 43 > 0.993 || = 0.36 513 541 501 506 534 | 500 < 0.008 64 79 66 73 50 | 50 | 44 32 44 37 35 > 0.992 || = 0.35 508 501 526 558 517 | 500 < 0.009 69 67 70 75 67 | 50 | 41 42 32 40 45 > 0.991 || = 0.34 541 511 550 511 529 | 500 < 0.01 67 81 63 68 57 | 50 | 41 27 34 45 32 > 0.99 || = 0.33 522 505 532 556 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 531 557 519 543 540 | 500 < 0.01 707 738 689 709 736 | 497.5 | 397 342 381 385 389 > 0.99 || = 0.31 499 537 522 494 546 | 500 = 0.01 334 324 344 335 359 | 252.5 | 168 159 215 203 195 = 0.99 || = 0.30 522 543 549 524 540 | 500 = 0.02 680 667 647 661 659 | 500 | 377 367 361 390 431 = 0.98 || = 0.29 556 519 516 482 514 | 500 =================================================================| 500 | 371 388 393 389 350 = 0.97 || = 0.28 551 501 582 539 526 | 500 sknuth_Run test: | 500 | 389 386 359 403 395 = 0.96 || = 0.27 532 576 566 505 524 | 500 ----------------------------------------------- | 500 | 389 378 384 429 396 = 0.95 || = 0.26 538 560 548 560 524 | 500 N = 10, n = 1000000000, r = 15, Up = TRUE | 500 | 409 406 422 393 443 = 0.94 || = 0.25 508 560 562 565 545 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 392 363 380 403 424 = 0.93 || = 0.24 563 548 531 536 549 | 500 | 500 | 393 418 404 430 391 = 0.92 || = 0.23 580 549 545 528 531 | 500 =================================================================| 500 | 392 433 399 411 422 = 0.91 || = 0.22 536 553 537 488 587 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 417 393 448 424 408 = 0.90 || = 0.21 549 545 571 575 570 | 500 -----------------------------------------------------------------| 500 | 420 458 414 418 416 = 0.89 || = 0.20 561 568 536 553 573 | 500 SD Bern.: d 3.13715 2.99983 1.64093 | 500 | 411 416 421 401 420 = 0.88 || = 0.19 547 574 613 553 584 | 500 s 3.28772 3.71615 2.35828 | 500 | 480 408 431 424 433 = 0.87 || = 0.18 545 570 565 573 556 | 500 t 3.18989 3.02243 1.81914 | 500 | 431 452 429 425 412 = 0.86 || = 0.17 605 549 530 602 548 | 500 m 3.13718 3.04816 1.86800 | 500 | 452 428 426 462 462 = 0.85 || = 0.16 578 537 524 537 583 | 500 x 3.14599 3.77123 1.78245 | 500 | 448 420 439 458 411 = 0.84 || = 0.15 594 601 561 586 575 | 500 | 500 | 427 460 381 431 433 = 0.83 || = 0.14 591 549 571 553 589 | 500 Changes: d 13 0 0 | 500 | 420 422 381 417 442 = 0.82 || = 0.13 555 559 548 592 576 | 500 s 7 0 0 | 500 | 463 430 463 454 443 = 0.81 || = 0.12 559 550 598 577 609 | 500 t 11 0 0 | 500 | 411 463 441 463 446 = 0.80 || = 0.11 563 624 594 630 601 | 500 m 23 0 0 | 500 | 453 466 469 436 446 = 0.79 || = 0.10 601 591 644 602 563 | 500 x 15 2 0 | 500 | 438 456 488 413 435 = 0.78 || = 0.09 618 625 563 574 580 | 500 -----------------------------------------------------------------| 500 | 458 454 436 450 461 = 0.77 || = 0.08 615 573 573 618 600 | 500 Aver./ d 0.46207 499 > 500:10 10 10 8 5 2 0 0 0 0 | 500 | 455 429 413 449 449 = 0.76 || = 0.07 583 623 606 637 593 | 500 median s 0.46072 496 ----- 10 10 10 10 6 1 0 0 0 0 | 500 | 417 436 457 444 443 = 0.75 || = 0.06 595 592 614 619 625 | 500 t 0.46157 504 10 10 10 10 9 3 1 0 0 0 | 500 | 451 424 435 440 424 = 0.74 || = 0.05 620 587 634 604 582 | 500 m 0.46250 488 10 10 8 7 7 2 1 0 0 0 | 500 | 468 453 454 443 408 = 0.73 || = 0.04 636 630 667 634 603 | 500 x 0.46218 492 10 10 10 8 4 2 0 0 0 0 | 500 | 446 452 471 478 447 = 0.72 || = 0.03 623 690 582 639 652 | 500 -----------------------------------------------------------------| 500 | 460 448 443 432 479 = 0.71 || = 0.02 680 667 647 661 659 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 453 481 514 451 442 = 0.70 || = 0.01 334 324 344 335 359 | 252.5 d 12 6 11 10 28 8 10 3 13 | 500 | 436 457 448 445 465 = 0.69 || < 0.01 707 738 689 709 736 | 497.5 s 10 9 8 13 25 7 12 6 11 | 500 | 485 491 454 460 459 = 0.68 ||========================================================================= t 10 7 12 12 24 9 11 5 11 | 500 | 473 492 475 449 475 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 8 11 12 12 23 10 7 5 13 | 500 | 470 453 460 460 472 = 0.66 ||========================================================================= x 8 10 13 11 23 9 7 9 11 | 500 | 478 493 437 439 462 = 0.65 || sknuth_Run test: no 63 test no 64 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Run test: test no 64 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 2 1 2 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 511 477 522 504 478 | 500 < 0.00002 0 1 1 0 1 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 513 503 469 499 514 | 500 < 0.00003 0 2 1 0 0 | 0.5 | 0 2 0 0 0 > 0.99997 || = 0.62 459 500 451 513 507 | 500 < 0.00004 0 0 0 0 2 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 507 453 446 528 503 | 500 < 0.00005 0 1 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 496 480 531 461 515 | 500 < 0.00006 0 1 0 3 0 | 0.5 | 0 1 0 0 1 > 0.99994 || = 0.59 474 497 504 466 476 | 500 < 0.00007 1 1 0 1 1 | 0.5 | 0 1 0 0 1 > 0.99993 || = 0.58 501 466 493 491 503 | 500 < 0.00008 0 0 1 1 0 | 0.5 | 0 0 0 1 1 > 0.99992 || = 0.57 493 472 496 479 473 | 500 < 0.00009 1 1 0 0 2 | 0.5 | 0 1 0 0 1 > 0.99991 || = 0.56 477 521 505 516 469 | 500 < 0.0001 0 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 498 484 474 495 464 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 513 475 519 491 484 | 500 < 0.0001 2 10 7 8 8 | 5 | 0 5 1 1 4 > 0.9999 || = 0.53 523 464 464 500 533 | 500 < 0.0002 9 3 8 4 7 | 5 | 2 3 3 2 0 > 0.9998 || = 0.52 519 470 531 495 495 | 500 < 0.0003 4 5 4 1 4 | 5 | 4 1 2 4 2 > 0.9997 || = 0.51 530 485 484 506 473 | 500 < 0.0004 14 7 7 6 5 | 5 | 4 5 6 3 3 > 0.9996 || = 0.50 469 478 467 478 522 | 500 < 0.0005 9 8 4 8 6 | 5 | 1 3 2 4 2 > 0.9995 || = 0.49 481 503 512 504 481 | 500 < 0.0006 8 5 4 1 6 | 5 | 3 3 4 1 2 > 0.9994 || = 0.48 496 493 505 470 491 | 500 < 0.0007 3 8 8 10 6 | 5 | 3 1 2 4 2 > 0.9993 || = 0.47 508 497 490 504 514 | 500 < 0.0008 4 7 6 10 2 | 5 | 3 6 4 1 1 > 0.9992 || = 0.46 510 528 475 525 464 | 500 < 0.0009 7 4 9 2 9 | 5 | 2 6 5 2 4 > 0.9991 || = 0.45 493 509 451 498 492 | 500 < 0.001 7 6 4 5 5 | 5 | 6 5 0 6 6 > 0.999 || = 0.44 515 493 514 447 497 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 488 516 492 522 465 | 500 < 0.001 67 63 61 55 58 | 50 | 28 38 29 28 26 > 0.999 || = 0.42 449 496 505 525 493 | 500 < 0.002 58 75 54 59 56 | 50 | 44 48 40 38 42 > 0.998 || = 0.41 485 480 500 564 510 | 500 < 0.003 68 53 45 49 55 | 50 | 51 43 44 30 47 > 0.997 || = 0.40 478 533 503 487 512 | 500 < 0.004 57 58 62 65 53 | 50 | 56 52 51 43 41 > 0.996 || = 0.39 523 521 500 491 507 | 500 < 0.005 55 43 52 62 63 | 50 | 51 53 41 54 46 > 0.995 || = 0.38 538 500 535 497 490 | 500 < 0.006 61 49 55 57 53 | 50 | 49 46 51 41 43 > 0.994 || = 0.37 451 464 501 511 535 | 500 < 0.007 63 41 47 58 52 | 50 | 36 51 45 51 41 > 0.993 || = 0.36 526 528 504 486 473 | 500 < 0.008 49 52 59 61 54 | 50 | 48 48 43 50 48 > 0.992 || = 0.35 531 504 506 501 516 | 500 < 0.009 59 61 60 51 74 | 50 | 43 62 42 57 57 > 0.991 || = 0.34 528 536 490 486 503 | 500 < 0.01 63 69 62 67 54 | 50 | 40 53 56 49 44 > 0.99 || = 0.33 513 498 465 490 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 490 516 526 513 473 | 500 < 0.01 600 564 557 584 572 | 497.5 | 446 494 442 441 435 > 0.99 || = 0.31 487 471 489 508 553 | 500 = 0.01 267 282 284 284 262 | 252.5 | 272 256 267 237 214 = 0.99 || = 0.30 509 529 478 506 549 | 500 = 0.02 517 489 521 557 585 | 500 | 507 544 484 491 515 = 0.98 || = 0.29 476 520 495 540 505 | 500 =================================================================| 500 | 507 482 522 475 504 = 0.97 || = 0.28 502 504 506 528 524 | 500 sknuth_Run test: | 500 | 507 487 487 487 492 = 0.96 || = 0.27 504 486 465 493 509 | 500 ----------------------------------------------- | 500 | 513 468 487 441 465 = 0.95 || = 0.26 485 487 526 542 505 | 500 N = 10, n = 1000000000, r = 15, Up = TRUE | 500 | 494 486 503 474 515 = 0.94 || = 0.25 515 462 458 526 533 | 500 Anderson-Darling statistic = A2 | 500 | 496 535 467 489 518 = 0.93 || = 0.24 512 484 510 519 505 | 500 | 500 | 496 528 440 498 477 = 0.92 || = 0.23 478 538 523 524 495 | 500 =================================================================| 500 | 468 495 536 474 525 = 0.91 || = 0.22 501 497 504 470 507 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 490 487 479 489 473 = 0.90 || = 0.21 514 489 480 496 522 | 500 -----------------------------------------------------------------| 500 | 464 545 485 492 446 = 0.89 || = 0.20 494 489 534 504 508 | 500 SD Bern.: d 1.19824 1.60828 1.34825 | 500 | 517 485 441 487 472 = 0.88 || = 0.19 486 550 536 522 497 | 500 s 1.14365 1.72364 0.87678 | 500 | 492 494 497 456 486 = 0.87 || = 0.18 547 486 496 466 487 | 500 t 1.34229 1.15729 1.29214 | 500 | 438 490 481 471 468 = 0.86 || = 0.17 514 467 511 505 534 | 500 m 1.29214 1.41491 1.56602 | 500 | 500 469 469 501 461 = 0.85 || = 0.16 551 528 504 546 494 | 500 x 1.25668 1.36008 1.38993 | 500 | 484 504 516 474 498 = 0.84 || = 0.15 541 485 457 523 520 | 500 | 500 | 521 501 472 473 477 = 0.83 || = 0.14 483 522 516 493 485 | 500 Changes: d 41 2 2 | 500 | 471 460 512 450 489 = 0.82 || = 0.13 527 478 531 547 528 | 500 s 45 2 5 | 500 | 492 465 489 462 460 = 0.81 || = 0.12 506 546 529 503 544 | 500 t 55 4 5 | 500 | 461 516 479 464 462 = 0.80 || = 0.11 508 553 541 533 549 | 500 m 37 2 6 | 500 | 509 511 491 468 454 = 0.79 || = 0.10 524 493 489 527 489 | 500 x 41 0 2 | 500 | 508 529 518 461 502 = 0.78 || = 0.09 515 551 577 536 553 | 500 -----------------------------------------------------------------| 500 | 480 460 510 482 503 = 0.77 || = 0.08 526 528 526 527 521 | 500 Aver./ d 0.49310 502 > 500: 9 8 6 7 3 5 5 4 2 5 | 500 | 448 495 447 535 509 = 0.76 || = 0.07 493 510 509 534 507 | 500 median s 0.49536 496 ----- 9 5 3 6 5 1 1 5 3 4 | 500 | 488 506 426 445 490 = 0.75 || = 0.06 533 521 552 542 541 | 500 t 0.49241 503 10 7 6 5 5 5 4 4 2 4 | 500 | 437 500 473 504 487 = 0.74 || = 0.05 520 538 526 538 531 | 500 m 0.48889 497 10 8 7 5 6 2 5 2 1 0 | 500 | 464 473 520 474 484 = 0.73 || = 0.04 552 517 562 529 562 | 500 x 0.49061 501 10 5 9 6 3 3 5 4 0 5 | 500 | 510 462 532 481 501 = 0.72 || = 0.03 533 538 572 556 520 | 500 -----------------------------------------------------------------| 500 | 516 522 490 476 477 = 0.71 || = 0.02 517 489 521 557 585 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 511 472 482 492 506 = 0.70 || = 0.01 267 282 284 284 262 | 252.5 d 0 0 6 14 63 14 3 0 1 | 500 | 468 487 549 486 473 = 0.69 || < 0.01 600 564 557 584 572 | 497.5 s 0 0 1 18 61 15 6 0 0 | 500 | 473 494 494 531 500 = 0.68 ||========================================================================= t 0 1 7 13 58 16 4 2 0 | 500 | 470 487 515 487 473 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 5 18 52 20 5 1 0 | 500 | 502 483 511 504 514 = 0.66 ||========================================================================= x 0 0 4 22 58 10 5 2 0 | 500 | 474 486 493 497 467 = 0.65 || sknuth_Run test: no 64 test no 65 TestU01 250000 runs BigCrush Test smarsa_S sknuth_Run test: test no 65 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 3 1 1 2 | 0.5 | 0 2 1 0 0 > 0.99999 || = 0.64 415 507 447 461 425 | 500 < 0.00002 1 0 1 1 2 | 0.5 | 0 1 0 0 1 > 0.99998 || = 0.63 501 468 446 459 449 | 500 < 0.00003 0 2 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99997 || = 0.62 479 450 450 448 428 | 500 < 0.00004 1 2 0 1 1 | 0.5 | 3 0 0 0 0 > 0.99996 || = 0.61 448 477 476 437 434 | 500 < 0.00005 0 1 2 1 0 | 0.5 | 1 0 0 0 0 > 0.99995 || = 0.60 487 499 431 459 492 | 500 < 0.00006 0 2 1 0 0 | 0.5 | 0 0 1 0 1 > 0.99994 || = 0.59 489 474 485 460 481 | 500 < 0.00007 1 2 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 461 458 484 460 480 | 500 < 0.00008 0 0 1 3 1 | 0.5 | 0 0 1 1 0 > 0.99992 || = 0.57 488 486 420 503 491 | 500 < 0.00009 2 0 2 1 2 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 461 441 491 490 500 | 500 < 0.0001 1 1 3 0 1 | 0.5 | 0 0 0 0 1 > 0.9999 || = 0.55 488 475 498 474 482 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 493 470 462 489 460 | 500 < 0.0001 6 13 12 9 10 | 5 | 4 4 3 1 4 > 0.9999 || = 0.53 474 461 479 456 486 | 500 < 0.0002 14 5 7 7 11 | 5 | 3 2 0 0 1 > 0.9998 || = 0.52 498 496 472 474 480 | 500 < 0.0003 18 9 16 13 5 | 5 | 1 6 4 4 2 > 0.9997 || = 0.51 486 504 520 509 458 | 500 < 0.0004 9 11 3 9 16 | 5 | 4 6 4 4 4 > 0.9996 || = 0.50 514 499 509 478 499 | 500 < 0.0005 10 9 8 7 11 | 5 | 5 3 1 3 3 > 0.9995 || = 0.49 513 509 500 512 473 | 500 < 0.0006 11 10 5 9 7 | 5 | 2 3 4 3 2 > 0.9994 || = 0.48 490 503 508 453 507 | 500 < 0.0007 10 13 5 4 6 | 5 | 2 9 3 6 2 > 0.9993 || = 0.47 501 512 494 487 475 | 500 < 0.0008 9 9 8 14 9 | 5 | 6 5 2 2 4 > 0.9992 || = 0.46 489 498 487 481 452 | 500 < 0.0009 11 10 10 8 8 | 5 | 5 3 4 4 0 > 0.9991 || = 0.45 503 523 509 473 504 | 500 < 0.001 6 8 11 5 10 | 5 | 5 0 2 6 2 > 0.999 || = 0.44 472 495 488 518 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 496 488 491 491 498 | 500 < 0.001 104 97 85 85 93 | 50 | 37 41 27 33 24 > 0.999 || = 0.42 500 506 501 458 538 | 500 < 0.002 78 79 62 67 61 | 50 | 32 18 34 27 24 > 0.998 || = 0.41 505 528 533 466 501 | 500 < 0.003 78 94 85 86 86 | 50 | 37 31 22 30 40 > 0.997 || = 0.40 481 496 507 487 476 | 500 < 0.004 78 75 84 85 77 | 50 | 26 25 47 42 22 > 0.996 || = 0.39 554 517 508 510 521 | 500 < 0.005 75 85 81 90 74 | 50 | 38 21 43 37 38 > 0.995 || = 0.38 509 480 490 518 532 | 500 < 0.006 78 72 81 73 86 | 50 | 29 34 35 41 38 > 0.994 || = 0.37 530 448 534 504 525 | 500 < 0.007 65 70 98 97 87 | 50 | 32 30 36 45 36 > 0.993 || = 0.36 504 512 571 537 538 | 500 < 0.008 68 80 62 80 84 | 50 | 29 32 38 39 33 > 0.992 || = 0.35 554 574 531 539 557 | 500 < 0.009 77 80 70 74 69 | 50 | 34 34 32 37 32 > 0.991 || = 0.34 514 499 529 513 489 | 500 < 0.01 84 65 71 72 76 | 50 | 28 42 47 42 39 > 0.99 || = 0.33 535 559 501 509 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 521 540 538 541 476 | 500 < 0.01 785 797 779 809 793 | 497.5 | 322 308 361 373 326 > 0.99 || = 0.31 550 522 494 556 537 | 500 = 0.01 330 351 373 398 391 | 252.5 | 184 158 178 174 199 = 0.99 || = 0.30 533 515 538 529 542 | 500 = 0.02 712 712 722 679 711 | 500 | 370 335 353 392 366 = 0.98 || = 0.29 535 523 534 546 538 | 500 =================================================================| 500 | 383 376 381 383 382 = 0.97 || = 0.28 540 550 501 548 515 | 500 sknuth_Run test: | 500 | 370 358 420 387 406 = 0.96 || = 0.27 537 548 517 531 550 | 500 ----------------------------------------------- | 500 | 401 372 397 421 397 = 0.95 || = 0.26 527 539 539 553 517 | 500 N = 10, n = 1000000000, r = 15, Up = TRUE | 500 | 380 389 399 399 388 = 0.94 || = 0.25 545 544 551 526 536 | 500 Test on the sum of all N observations | 500 | 417 376 408 411 423 = 0.93 || = 0.24 550 551 522 533 551 | 500 | 500 | 381 402 389 399 375 = 0.92 || = 0.23 578 563 547 539 575 | 500 =================================================================| 500 | 401 386 373 383 420 = 0.91 || = 0.22 594 543 549 553 558 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 399 395 413 432 418 = 0.90 || = 0.21 564 568 609 590 579 | 500 -----------------------------------------------------------------| 500 | 407 422 415 410 401 = 0.89 || = 0.20 522 567 586 574 555 | 500 SD Bern.: d 3.67092 4.27085 2.58120 | 500 | 416 417 404 409 453 = 0.88 || = 0.19 557 570 599 547 600 | 500 s 3.84493 4.41695 2.91074 | 500 | 442 396 447 411 415 = 0.87 || = 0.18 608 548 548 550 565 | 500 t 3.70859 4.23555 2.24833 | 500 | 416 407 414 401 469 = 0.86 || = 0.17 584 521 550 582 564 | 500 m 3.70957 4.54826 1.95596 | 500 | 430 432 382 440 486 = 0.85 || = 0.16 558 613 541 556 596 | 500 x 3.67448 4.34475 2.62961 | 500 | 442 415 415 408 386 = 0.84 || = 0.15 587 622 540 604 583 | 500 | 500 | 402 407 433 465 366 = 0.83 || = 0.14 574 510 574 589 586 | 500 Changes: d 11 0 0 | 500 | 427 427 420 425 442 = 0.82 || = 0.13 613 602 590 575 582 | 500 s 15 0 0 | 500 | 442 433 429 428 435 = 0.81 || = 0.12 565 599 608 622 591 | 500 t 11 0 0 | 500 | 439 448 446 425 450 = 0.80 || = 0.11 589 611 609 633 588 | 500 m 11 0 0 | 500 | 437 429 446 424 431 = 0.79 || = 0.10 538 630 608 611 587 | 500 x 13 0 0 | 500 | 440 477 421 460 452 = 0.78 || = 0.09 596 639 606 581 596 | 500 -----------------------------------------------------------------| 500 | 436 443 448 486 425 = 0.77 || = 0.08 642 628 613 618 609 | 500 Aver./ d 0.45587 493 > 500:10 10 10 10 4 0 1 0 0 0 | 500 | 447 440 456 420 410 = 0.76 || = 0.07 616 624 636 610 653 | 500 median s 0.45417 496 ----- 10 10 10 7 6 1 1 0 0 0 | 500 | 415 454 421 424 478 = 0.75 || = 0.06 644 625 652 671 610 | 500 t 0.45593 491 10 10 10 8 5 1 0 0 0 0 | 500 | 421 420 443 430 479 = 0.74 || = 0.05 651 678 639 664 644 | 500 m 0.45619 486 10 10 10 10 2 2 1 0 0 0 | 500 | 411 426 486 462 457 = 0.73 || = 0.04 663 650 699 677 659 | 500 x 0.45693 486 10 10 10 8 4 0 1 0 0 0 | 500 | 467 466 478 458 445 = 0.72 || = 0.03 695 669 671 651 649 | 500 -----------------------------------------------------------------| 500 | 495 471 474 436 447 = 0.71 || = 0.02 712 712 722 679 711 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 446 493 459 427 454 = 0.70 || = 0.01 330 351 373 398 391 | 252.5 d 13 9 12 7 25 8 9 4 14 | 500 | 454 472 456 460 465 = 0.69 || < 0.01 785 797 779 809 793 | 497.5 s 14 9 8 13 24 7 6 4 16 | 500 | 431 449 468 502 426 = 0.68 ||========================================================================= t 11 13 9 9 25 10 5 3 16 | 500 | 449 458 423 442 441 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 14 10 6 18 18 8 8 4 15 | 500 | 470 493 465 470 436 = 0.66 ||========================================================================= x 11 10 13 9 22 9 7 7 13 | 500 | 475 466 445 464 515 = 0.65 || sknuth_Run test: no 65 test no 66 TestU01 250000 runs BigCrush Test smarsa_S Test sknuth_Permutation calling smultin_Multinomial test no 66 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 2 1 2 1 0 > 0.99999 || = 0.64 455 522 533 495 517 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 3 1 0 0 0 > 0.99998 || = 0.63 501 473 513 501 485 | 500 < 0.00003 0 0 1 1 0 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 491 499 488 515 481 | 500 < 0.00004 0 2 2 2 1 | 0.5 | 1 0 1 0 0 > 0.99996 || = 0.61 510 514 493 456 510 | 500 < 0.00005 0 1 0 0 2 | 0.5 | 1 0 0 0 0 > 0.99995 || = 0.60 491 491 481 520 527 | 500 < 0.00006 0 1 0 1 1 | 0.5 | 0 1 0 1 0 > 0.99994 || = 0.59 451 511 513 519 475 | 500 < 0.00007 0 1 0 1 0 | 0.5 | 2 0 1 0 1 > 0.99993 || = 0.58 520 502 509 498 516 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 526 511 484 484 485 | 500 < 0.00009 0 2 0 0 0 | 0.5 | 0 1 0 0 1 > 0.99991 || = 0.56 506 513 466 505 504 | 500 < 0.0001 0 1 0 2 2 | 0.5 | 0 3 0 0 0 > 0.9999 || = 0.55 476 516 508 463 463 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 524 494 510 483 519 | 500 < 0.0001 0 8 3 8 6 | 5 | 10 7 4 2 2 > 0.9999 || = 0.53 547 489 486 486 511 | 500 < 0.0002 7 8 3 5 4 | 5 | 2 2 3 1 3 > 0.9998 || = 0.52 499 482 501 443 498 | 500 < 0.0003 3 9 3 4 3 | 5 | 7 7 2 3 4 > 0.9997 || = 0.51 528 537 502 516 474 | 500 < 0.0004 7 5 6 4 5 | 5 | 3 2 3 3 5 > 0.9996 || = 0.50 484 476 537 524 497 | 500 < 0.0005 7 1 3 2 3 | 5 | 7 5 6 7 5 > 0.9995 || = 0.49 480 535 480 479 526 | 500 < 0.0006 5 6 9 8 10 | 5 | 5 5 4 1 6 > 0.9994 || = 0.48 470 524 512 497 548 | 500 < 0.0007 4 4 4 7 4 | 5 | 3 5 8 3 3 > 0.9993 || = 0.47 475 478 524 513 484 | 500 < 0.0008 5 5 9 5 6 | 5 | 4 6 5 5 0 > 0.9992 || = 0.46 507 492 505 538 492 | 500 < 0.0009 4 6 2 4 3 | 5 | 8 6 2 8 6 > 0.9991 || = 0.45 467 497 508 510 532 | 500 < 0.001 4 4 6 4 5 | 5 | 5 9 7 2 3 > 0.999 || = 0.44 508 458 498 521 503 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 518 466 484 448 522 | 500 < 0.001 46 56 48 51 49 | 50 | 54 54 44 35 37 > 0.999 || = 0.42 516 478 504 534 508 | 500 < 0.002 40 52 43 54 36 | 50 | 40 43 53 33 58 > 0.998 || = 0.41 514 539 491 490 491 | 500 < 0.003 38 53 46 66 44 | 50 | 60 56 49 43 47 > 0.997 || = 0.40 514 493 514 500 520 | 500 < 0.004 50 46 56 45 52 | 50 | 46 52 53 49 51 > 0.996 || = 0.39 521 513 469 546 509 | 500 < 0.005 46 43 53 48 43 | 50 | 40 53 54 47 39 > 0.995 || = 0.38 523 506 525 488 500 | 500 < 0.006 48 43 50 45 51 | 50 | 44 55 49 62 48 > 0.994 || = 0.37 501 518 488 513 455 | 500 < 0.007 52 52 56 49 58 | 50 | 55 47 48 54 50 > 0.993 || = 0.36 462 491 490 533 461 | 500 < 0.008 63 50 60 48 58 | 50 | 69 47 53 50 49 > 0.992 || = 0.35 462 518 453 480 513 | 500 < 0.009 43 42 40 36 49 | 50 | 56 45 40 51 65 > 0.991 || = 0.34 483 485 523 524 498 | 500 < 0.01 54 58 63 62 53 | 50 | 44 61 44 36 51 > 0.99 || = 0.33 515 502 531 506 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 498 497 498 507 504 | 500 < 0.01 480 495 515 504 493 | 497.5 | 508 513 487 460 495 > 0.99 || = 0.31 540 485 514 504 488 | 500 = 0.01 259 245 241 284 213 | 252.5 | 278 249 247 246 253 = 0.99 || = 0.30 486 492 520 517 522 | 500 = 0.02 521 506 449 511 496 | 500 | 487 534 456 445 464 = 0.98 || = 0.29 522 459 518 507 511 | 500 =================================================================| 500 | 546 523 504 517 468 = 0.97 || = 0.28 514 489 468 478 520 | 500 Test sknuth_Permutation calling smultin_Multinomial | 500 | 520 486 478 522 513 = 0.96 || = 0.27 469 491 483 516 513 | 500 smultin_Multinomial test: | 500 | 510 477 508 509 526 = 0.95 || = 0.26 504 476 526 477 480 | 500 ----------------------------------------------- | 500 | 511 486 534 477 539 = 0.94 || = 0.25 508 502 488 519 479 | 500 N = 1, n = 1000000000, r = 5, t = 3, | 500 | 482 507 489 506 494 = 0.93 || = 0.24 469 511 495 533 535 | 500 | 500 | 497 489 468 528 496 = 0.92 || = 0.23 526 506 491 521 522 | 500 =================================================================| 500 | 494 481 537 505 533 = 0.91 || = 0.22 514 509 481 479 477 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 501 478 497 479 503 = 0.90 || = 0.21 475 484 497 498 493 | 500 -----------------------------------------------------------------| 500 | 534 506 496 481 488 = 0.89 || = 0.20 503 532 444 478 487 | 500 SD Bern.: d 1.06121 1.01834 1.28593 | 500 | 494 505 469 535 468 = 0.88 || = 0.19 483 485 516 512 480 | 500 s 0.90280 0.76849 0.77883 | 500 | 511 547 506 540 459 = 0.87 || = 0.18 449 497 494 481 516 | 500 t 0.94274 1.01932 0.66515 | 500 | 506 494 520 501 519 = 0.86 || = 0.17 550 498 494 508 506 | 500 m 0.99422 1.15988 1.36449 | 500 | 495 502 524 516 465 = 0.85 || = 0.16 488 515 486 519 500 | 500 x 0.93561 0.92240 1.09140 | 500 | 557 467 517 486 483 = 0.84 || = 0.15 503 528 542 509 521 | 500 | 500 | 513 510 491 467 546 = 0.83 || = 0.14 478 505 490 506 466 | 500 Changes: d 51 3 5 | 500 | 544 506 512 520 490 = 0.82 || = 0.13 463 511 519 480 522 | 500 s 45 4 4 | 500 | 539 530 511 513 495 = 0.81 || = 0.12 498 525 477 496 509 | 500 t 55 5 6 | 500 | 459 526 498 490 489 = 0.80 || = 0.11 492 480 454 497 491 | 500 m 45 2 4 | 500 | 507 499 492 496 505 = 0.79 || = 0.10 505 491 483 479 479 | 500 x 52 5 5 | 500 | 525 474 499 529 499 = 0.78 || = 0.09 476 521 510 484 505 | 500 -----------------------------------------------------------------| 500 | 523 466 523 501 492 = 0.77 || = 0.08 514 492 504 520 502 | 500 Aver./ d 0.50289 503 > 500: 5 3 7 5 6 6 3 6 8 6 | 500 | 490 486 502 523 498 = 0.76 || = 0.07 471 494 498 479 489 | 500 median s 0.50102 498 ----- 3 5 5 5 3 6 6 4 7 4 | 500 | 492 532 481 523 516 = 0.75 || = 0.06 507 471 514 498 496 | 500 t 0.50099 499 6 3 2 5 6 6 5 5 6 4 | 500 | 476 504 528 502 492 = 0.74 || = 0.05 509 470 519 482 491 | 500 m 0.49931 501 5 5 5 8 5 4 3 6 6 6 | 500 | 525 539 486 492 519 = 0.73 || = 0.04 470 487 490 501 518 | 500 x 0.50018 499 4 5 5 4 7 5 5 5 3 5 | 500 | 503 472 505 483 524 = 0.72 || = 0.03 475 504 522 492 514 | 500 -----------------------------------------------------------------| 500 | 514 464 540 517 508 = 0.71 || = 0.02 521 506 449 511 496 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 508 513 481 471 462 = 0.70 || = 0.01 259 245 241 284 213 | 252.5 d 0 0 3 18 63 13 4 0 0 | 500 | 472 487 507 490 534 = 0.69 || < 0.01 480 495 515 504 493 | 497.5 s 0 0 0 14 71 15 1 0 0 | 500 | 478 522 499 468 514 = 0.68 ||========================================================================= t 0 0 4 7 75 15 0 0 0 | 500 | 475 525 541 491 507 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 9 75 13 1 0 0 | 500 | 482 492 486 510 496 = 0.66 ||========================================================================= x 0 0 2 12 76 9 2 0 0 | 500 | 480 533 518 457 498 = 0.65 || Test sknuth_Permutation calling smultin_Multinomial no 66 test no 67 TestU01 250000 runs BigCrush Test smarsa_S Test sknuth_Permutation calling smultin_Multinomial test no 67 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 1 0 | 0.5 | 1 0 1 0 0 > 0.99999 || = 0.64 467 530 478 474 504 | 500 < 0.00002 0 1 0 0 1 | 0.5 | 0 0 1 0 1 > 0.99998 || = 0.63 493 498 471 484 538 | 500 < 0.00003 0 1 0 0 2 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 520 466 522 511 496 | 500 < 0.00004 1 1 0 0 1 | 0.5 | 0 2 0 0 0 > 0.99996 || = 0.61 479 474 479 529 525 | 500 < 0.00005 0 0 1 0 0 | 0.5 | 1 0 0 0 1 > 0.99995 || = 0.60 475 531 499 491 484 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 1 0 0 2 > 0.99994 || = 0.59 504 481 534 490 488 | 500 < 0.00007 0 0 0 0 1 | 0.5 | 0 0 1 0 0 > 0.99993 || = 0.58 453 487 502 426 521 | 500 < 0.00008 1 1 2 2 0 | 0.5 | 0 0 0 1 0 > 0.99992 || = 0.57 516 484 488 515 475 | 500 < 0.00009 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 528 526 497 483 501 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 0 0 2 1 1 > 0.9999 || = 0.55 483 503 507 500 456 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 521 507 501 524 487 | 500 < 0.0001 2 6 3 4 6 | 5 | 3 3 5 2 5 > 0.9999 || = 0.53 471 465 515 502 477 | 500 < 0.0002 3 5 1 5 6 | 5 | 3 4 1 2 2 > 0.9998 || = 0.52 450 483 521 511 495 | 500 < 0.0003 3 6 9 6 3 | 5 | 8 5 8 7 4 > 0.9997 || = 0.51 476 498 464 527 503 | 500 < 0.0004 5 4 2 7 6 | 5 | 7 3 8 8 2 > 0.9996 || = 0.50 554 528 522 497 482 | 500 < 0.0005 3 5 8 0 6 | 5 | 9 1 5 5 1 > 0.9995 || = 0.49 529 537 532 518 492 | 500 < 0.0006 9 3 5 1 5 | 5 | 3 3 8 5 3 > 0.9994 || = 0.48 480 508 487 481 479 | 500 < 0.0007 4 7 6 3 3 | 5 | 2 6 6 1 4 > 0.9993 || = 0.47 498 506 466 474 476 | 500 < 0.0008 5 2 11 5 1 | 5 | 2 4 4 6 6 > 0.9992 || = 0.46 469 518 500 482 512 | 500 < 0.0009 3 4 2 9 8 | 5 | 4 4 5 6 5 > 0.9991 || = 0.45 477 516 520 497 540 | 500 < 0.001 4 5 4 4 5 | 5 | 6 6 7 4 3 > 0.999 || = 0.44 516 535 482 506 536 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 461 479 489 524 486 | 500 < 0.001 41 47 51 44 49 | 50 | 47 39 57 46 35 > 0.999 || = 0.42 479 484 499 536 534 | 500 < 0.002 49 53 54 55 52 | 50 | 47 49 39 31 69 > 0.998 || = 0.41 489 558 499 495 504 | 500 < 0.003 44 59 48 51 48 | 50 | 55 42 63 47 46 > 0.997 || = 0.40 506 496 527 510 471 | 500 < 0.004 58 54 54 47 39 | 50 | 38 56 45 38 60 > 0.996 || = 0.39 526 512 504 492 561 | 500 < 0.005 49 52 55 58 45 | 50 | 53 56 45 56 45 > 0.995 || = 0.38 523 511 503 547 527 | 500 < 0.006 57 58 58 48 45 | 50 | 44 48 45 48 53 > 0.994 || = 0.37 489 500 496 505 480 | 500 < 0.007 56 48 50 48 51 | 50 | 50 63 64 50 45 > 0.993 || = 0.36 531 517 450 494 523 | 500 < 0.008 52 44 63 59 56 | 50 | 44 50 47 55 57 > 0.992 || = 0.35 489 506 499 495 486 | 500 < 0.009 47 54 44 55 54 | 50 | 44 39 50 49 71 > 0.991 || = 0.34 514 504 498 468 504 | 500 < 0.01 45 38 56 44 51 | 50 | 60 47 51 55 50 > 0.99 || = 0.33 508 541 526 519 507 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 514 532 548 460 513 | 500 < 0.01 498 507 533 509 490 | 497.5 | 482 489 506 475 531 > 0.99 || = 0.31 446 482 523 498 492 | 500 = 0.01 259 243 241 281 258 | 252.5 | 232 227 230 255 260 = 0.99 || = 0.30 496 465 519 524 482 | 500 = 0.02 534 534 518 466 527 | 500 | 500 505 509 519 504 = 0.98 || = 0.29 495 499 515 480 512 | 500 =================================================================| 500 | 502 498 494 504 492 = 0.97 || = 0.28 504 502 443 492 495 | 500 Test sknuth_Permutation calling smultin_Multinomial | 500 | 509 489 497 505 500 = 0.96 || = 0.27 518 472 495 522 476 | 500 smultin_Multinomial test: | 500 | 483 504 526 519 470 = 0.95 || = 0.26 506 498 470 498 479 | 500 ----------------------------------------------- | 500 | 484 508 508 515 515 = 0.94 || = 0.25 497 496 475 517 453 | 500 N = 1, n = 1000000000, r = 5, t = 5, | 500 | 510 486 533 531 524 = 0.93 || = 0.24 501 488 502 506 483 | 500 | 500 | 508 541 539 517 533 = 0.92 || = 0.23 521 504 489 528 489 | 500 =================================================================| 500 | 519 492 474 496 461 = 0.91 || = 0.22 488 494 467 523 505 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 496 489 474 489 512 = 0.90 || = 0.21 502 561 520 516 523 | 500 -----------------------------------------------------------------| 500 | 521 454 478 499 521 = 0.89 || = 0.20 463 475 472 481 525 | 500 SD Bern.: d 0.99565 0.78268 0.89932 | 500 | 510 479 524 498 486 = 0.88 || = 0.19 505 516 495 509 462 | 500 s 0.98283 0.87564 1.05976 | 500 | 498 480 473 507 516 = 0.87 || = 0.18 511 459 492 480 504 | 500 t 0.99861 0.85716 1.11410 | 500 | 461 502 493 525 502 = 0.86 || = 0.17 478 528 522 505 517 | 500 m 0.97030 0.75535 1.11499 | 500 | 493 523 486 565 494 = 0.85 || = 0.16 529 494 509 470 495 | 500 x 0.91163 0.68443 1.58255 | 500 | 526 514 511 469 509 = 0.84 || = 0.15 508 497 523 475 525 | 500 | 500 | 526 473 516 517 490 = 0.83 || = 0.14 463 484 513 503 489 | 500 Changes: d 52 4 5 | 500 | 440 490 467 482 499 = 0.82 || = 0.13 512 503 536 486 500 | 500 s 51 4 4 | 500 | 517 516 503 467 486 = 0.81 || = 0.12 547 529 485 516 473 | 500 t 44 6 6 | 500 | 503 503 496 492 497 = 0.80 || = 0.11 503 487 510 507 506 | 500 m 45 6 5 | 500 | 494 465 505 509 499 = 0.79 || = 0.10 498 502 522 466 485 | 500 x 49 3 8 | 500 | 504 519 508 529 489 = 0.78 || = 0.09 481 540 461 491 485 | 500 -----------------------------------------------------------------| 500 | 503 482 537 508 494 = 0.77 || = 0.08 511 491 486 495 484 | 500 Aver./ d 0.49901 503 > 500: 8 7 6 6 3 4 5 7 5 5 | 500 | 511 484 510 513 478 = 0.76 || = 0.07 518 529 482 513 519 | 500 median s 0.49763 498 ----- 6 5 3 7 7 4 1 5 4 4 | 500 | 475 510 536 480 516 = 0.75 || = 0.06 511 482 479 465 515 | 500 t 0.50083 500 2 7 3 6 3 6 5 7 4 6 | 500 | 503 526 523 490 519 = 0.74 || = 0.05 505 517 491 483 510 | 500 m 0.50176 500 3 5 6 4 5 5 4 6 4 8 | 500 | 499 469 461 510 487 = 0.73 || = 0.04 486 503 500 497 517 | 500 x 0.50036 499 6 4 4 6 5 3 6 2 5 6 | 500 | 530 502 481 522 484 = 0.72 || = 0.03 510 480 462 470 486 | 500 -----------------------------------------------------------------| 500 | 536 490 506 485 500 = 0.71 || = 0.02 534 534 518 466 527 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 475 475 472 492 508 = 0.70 || = 0.01 259 243 241 281 258 | 252.5 d 0 0 4 13 69 13 2 0 0 | 500 | 526 488 501 490 473 = 0.69 || < 0.01 498 507 533 509 490 | 497.5 s 0 0 1 13 69 16 2 0 0 | 500 | 512 474 525 521 501 = 0.68 ||========================================================================= t 0 0 2 16 66 16 1 0 0 | 500 | 524 491 492 508 494 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 0 14 72 12 2 0 0 | 500 | 513 485 511 458 490 = 0.66 ||========================================================================= x 0 0 1 11 73 15 1 0 0 | 500 | 483 496 520 500 542 = 0.65 || Test sknuth_Permutation calling smultin_Multinomial no 67 test no 68 TestU01 250000 runs BigCrush Test smarsa_S Test sknuth_Permutation calling smultin_Multinomial test no 68 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 2 0 0 > 0.99999 || = 0.64 519 478 481 503 532 | 500 < 0.00002 2 2 1 0 0 | 0.5 | 1 0 0 1 0 > 0.99998 || = 0.63 537 522 496 496 482 | 500 < 0.00003 1 1 0 0 0 | 0.5 | 1 1 0 1 1 > 0.99997 || = 0.62 494 517 490 491 474 | 500 < 0.00004 0 0 2 0 0 | 0.5 | 0 1 0 1 0 > 0.99996 || = 0.61 486 489 495 506 508 | 500 < 0.00005 1 0 1 0 0 | 0.5 | 0 0 1 1 0 > 0.99995 || = 0.60 489 499 489 525 509 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 482 516 489 500 514 | 500 < 0.00007 0 1 1 0 0 | 0.5 | 0 0 0 1 1 > 0.99993 || = 0.58 503 514 510 498 555 | 500 < 0.00008 0 0 1 0 0 | 0.5 | 2 0 0 0 1 > 0.99992 || = 0.57 524 443 523 494 471 | 500 < 0.00009 3 1 0 1 1 | 0.5 | 0 2 0 1 0 > 0.99991 || = 0.56 507 480 509 506 500 | 500 < 0.0001 1 0 1 0 2 | 0.5 | 0 0 2 1 0 > 0.9999 || = 0.55 506 515 513 472 476 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 516 479 509 529 482 | 500 < 0.0001 8 5 7 1 3 | 5 | 4 4 5 8 3 > 0.9999 || = 0.53 495 502 541 514 499 | 500 < 0.0002 6 4 4 5 3 | 5 | 3 3 3 0 1 > 0.9998 || = 0.52 511 493 493 493 486 | 500 < 0.0003 2 3 5 0 7 | 5 | 12 2 5 2 2 > 0.9997 || = 0.51 476 524 462 477 507 | 500 < 0.0004 3 6 9 6 6 | 5 | 3 7 9 7 4 > 0.9996 || = 0.50 512 483 489 519 536 | 500 < 0.0005 4 3 3 6 6 | 5 | 6 5 1 8 5 > 0.9995 || = 0.49 491 451 506 495 508 | 500 < 0.0006 4 5 7 8 6 | 5 | 4 6 6 4 3 > 0.9994 || = 0.48 495 492 513 539 538 | 500 < 0.0007 4 3 5 3 8 | 5 | 4 4 5 9 4 > 0.9993 || = 0.47 480 510 516 510 477 | 500 < 0.0008 3 10 9 6 2 | 5 | 6 8 1 6 9 > 0.9992 || = 0.46 516 499 544 541 528 | 500 < 0.0009 4 8 3 10 6 | 5 | 3 2 7 9 4 > 0.9991 || = 0.45 413 502 484 506 475 | 500 < 0.001 4 4 5 6 6 | 5 | 8 3 7 5 5 > 0.999 || = 0.44 489 519 506 523 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 484 504 486 472 497 | 500 < 0.001 42 51 57 51 53 | 50 | 53 44 49 58 40 > 0.999 || = 0.42 477 526 495 450 488 | 500 < 0.002 47 61 41 43 45 | 50 | 42 42 43 51 51 > 0.998 || = 0.41 502 509 466 509 491 | 500 < 0.003 51 47 58 56 63 | 50 | 45 60 47 46 41 > 0.997 || = 0.40 525 494 526 518 499 | 500 < 0.004 55 54 60 49 66 | 50 | 62 40 44 39 43 > 0.996 || = 0.39 544 498 499 516 480 | 500 < 0.005 58 44 44 44 45 | 50 | 55 56 48 55 59 > 0.995 || = 0.38 510 465 495 519 537 | 500 < 0.006 53 62 54 41 53 | 50 | 54 60 53 44 57 > 0.994 || = 0.37 489 497 508 543 508 | 500 < 0.007 55 52 50 45 59 | 50 | 44 55 35 51 47 > 0.993 || = 0.36 453 488 479 505 504 | 500 < 0.008 37 53 58 66 42 | 50 | 46 56 31 54 36 > 0.992 || = 0.35 495 477 495 473 480 | 500 < 0.009 47 41 40 50 51 | 50 | 61 56 55 51 41 > 0.991 || = 0.34 503 532 474 515 463 | 500 < 0.01 54 56 52 45 40 | 50 | 49 44 49 53 50 > 0.99 || = 0.33 485 495 518 472 502 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 477 464 479 446 533 | 500 < 0.01 499 521 514 490 517 | 497.5 | 511 513 454 502 465 > 0.99 || = 0.31 479 506 503 489 514 | 500 = 0.01 256 251 226 242 272 | 252.5 | 241 262 263 248 245 = 0.99 || = 0.30 462 492 481 470 475 | 500 = 0.02 502 517 492 502 499 | 500 | 481 509 521 530 492 = 0.98 || = 0.29 508 469 521 479 487 | 500 =================================================================| 500 | 541 541 504 489 481 = 0.97 || = 0.28 507 494 485 502 516 | 500 Test sknuth_Permutation calling smultin_Multinomial | 500 | 536 494 484 504 487 = 0.96 || = 0.27 483 509 491 456 501 | 500 smultin_Multinomial test: | 500 | 529 511 449 521 488 = 0.95 || = 0.26 520 486 505 513 505 | 500 ----------------------------------------------- | 500 | 503 473 497 528 498 = 0.94 || = 0.25 478 442 479 444 468 | 500 N = 1, n = 500000000, r = 5, t = 7, | 500 | 505 515 515 494 503 = 0.93 || = 0.24 478 509 523 528 489 | 500 | 500 | 542 508 498 541 506 = 0.92 || = 0.23 487 510 496 460 461 | 500 =================================================================| 500 | 473 504 514 489 493 = 0.91 || = 0.22 470 530 513 502 512 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 476 473 479 492 511 = 0.90 || = 0.21 514 483 512 494 518 | 500 -----------------------------------------------------------------| 500 | 518 500 496 479 524 = 0.89 || = 0.20 499 499 537 499 478 | 500 SD Bern.: d 1.01927 0.88474 0.95650 | 500 | 492 501 494 491 490 = 0.88 || = 0.19 533 481 526 465 501 | 500 s 0.93536 0.95650 1.06729 | 500 | 489 504 525 514 491 = 0.87 || = 0.18 462 464 493 493 501 | 500 t 0.84152 1.01440 1.20059 | 500 | 478 527 482 539 471 = 0.86 || = 0.17 481 525 504 498 494 | 500 m 0.99112 1.01045 0.76194 | 500 | 506 490 514 487 505 = 0.85 || = 0.16 534 504 507 505 495 | 500 x 0.92065 1.21633 1.13809 | 500 | 477 499 498 487 532 = 0.84 || = 0.15 503 484 536 500 546 | 500 | 500 | 490 515 481 529 514 = 0.83 || = 0.14 505 485 524 520 499 | 500 Changes: d 46 3 5 | 500 | 494 492 500 502 535 = 0.82 || = 0.13 495 497 478 523 498 | 500 s 46 6 4 | 500 | 529 496 484 523 477 = 0.81 || = 0.12 496 499 528 466 479 | 500 t 49 8 4 | 500 | 505 525 490 480 489 = 0.80 || = 0.11 531 482 502 500 519 | 500 m 53 5 4 | 500 | 566 495 494 486 510 = 0.79 || = 0.10 513 468 512 509 507 | 500 x 41 7 4 | 500 | 507 498 475 505 500 = 0.78 || = 0.09 483 453 500 513 495 | 500 -----------------------------------------------------------------| 500 | 494 521 495 505 501 = 0.77 || = 0.08 518 514 499 537 478 | 500 Aver./ d 0.50132 500 > 500: 6 6 4 3 3 6 4 7 3 7 | 500 | 508 478 499 478 485 = 0.76 || = 0.07 520 506 512 495 490 | 500 median s 0.50176 501 ----- 7 2 4 2 6 5 7 6 4 8 | 500 | 498 519 503 470 494 = 0.75 || = 0.06 530 519 505 497 529 | 500 t 0.49816 499 5 8 6 3 6 6 5 2 2 5 | 500 | 510 485 474 520 497 = 0.74 || = 0.05 500 536 501 515 520 | 500 m 0.50158 502 5 4 4 5 7 4 6 4 5 6 | 500 | 506 512 508 489 498 = 0.73 || = 0.04 492 474 467 512 493 | 500 x 0.49849 499 5 5 5 6 3 4 4 3 6 2 | 500 | 497 515 476 464 502 = 0.72 || = 0.03 488 544 517 473 557 | 500 -----------------------------------------------------------------| 500 | 523 528 493 520 486 = 0.71 || = 0.02 502 517 492 502 499 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 463 516 518 481 500 = 0.70 || = 0.01 256 251 226 242 272 | 252.5 d 0 1 1 11 72 14 2 0 0 | 500 | 511 518 510 515 541 = 0.69 || < 0.01 499 521 514 490 517 | 497.5 s 0 0 4 10 74 13 0 0 0 | 500 | 546 520 502 520 511 = 0.68 ||========================================================================= t 0 0 1 9 78 13 0 0 0 | 500 | 486 511 487 509 474 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 68 16 0 0 0 | 500 | 490 526 528 472 494 = 0.66 ||========================================================================= x 0 0 0 14 72 12 3 0 0 | 500 | 468 477 529 531 467 = 0.65 || Test sknuth_Permutation calling smultin_Multinomial no 68 test no 69 TestU01 250000 runs BigCrush Test smarsa_S Test sknuth_Permutation calling smultin_Multinomial test no 69 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 0 | 0.5 | 1 0 0 2 0 > 0.99999 || = 0.64 525 490 467 495 508 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 521 503 524 508 502 | 500 < 0.00003 0 1 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 491 501 455 498 503 | 500 < 0.00004 1 0 0 0 1 | 0.5 | 2 0 1 0 0 > 0.99996 || = 0.61 548 534 497 505 530 | 500 < 0.00005 0 0 1 0 1 | 0.5 | 0 1 0 0 0 > 0.99995 || = 0.60 514 471 505 510 473 | 500 < 0.00006 1 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 461 486 484 490 484 | 500 < 0.00007 0 0 2 1 1 | 0.5 | 0 3 1 0 0 > 0.99993 || = 0.58 512 474 501 536 481 | 500 < 0.00008 0 1 0 0 1 | 0.5 | 1 1 1 1 0 > 0.99992 || = 0.57 467 509 533 526 542 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 1 0 1 0 > 0.99991 || = 0.56 502 483 498 492 513 | 500 < 0.0001 0 0 0 2 2 | 0.5 | 1 0 1 1 0 > 0.9999 || = 0.55 537 519 475 472 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 502 484 500 494 469 | 500 < 0.0001 2 3 5 4 7 | 5 | 5 6 4 5 0 > 0.9999 || = 0.53 474 505 523 500 454 | 500 < 0.0002 2 7 4 5 1 | 5 | 5 1 2 7 2 > 0.9998 || = 0.52 509 501 529 534 474 | 500 < 0.0003 5 5 9 5 6 | 5 | 5 4 2 2 5 > 0.9997 || = 0.51 499 478 499 477 487 | 500 < 0.0004 5 5 11 2 5 | 5 | 6 6 7 5 6 > 0.9996 || = 0.50 516 544 545 478 511 | 500 < 0.0005 7 5 4 6 6 | 5 | 7 3 5 8 4 > 0.9995 || = 0.49 494 516 491 504 525 | 500 < 0.0006 5 3 15 8 5 | 5 | 7 6 1 5 6 > 0.9994 || = 0.48 475 500 520 500 473 | 500 < 0.0007 8 3 6 8 2 | 5 | 3 6 8 7 7 > 0.9993 || = 0.47 483 512 491 510 499 | 500 < 0.0008 7 5 8 5 3 | 5 | 3 4 6 3 3 > 0.9992 || = 0.46 529 508 533 475 496 | 500 < 0.0009 9 8 5 3 5 | 5 | 6 5 6 5 3 > 0.9991 || = 0.45 488 481 524 504 487 | 500 < 0.001 10 2 5 5 3 | 5 | 6 5 4 4 4 > 0.999 || = 0.44 522 505 510 513 462 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 511 528 457 502 485 | 500 < 0.001 60 46 72 51 43 | 50 | 53 46 45 51 40 > 0.999 || = 0.42 507 520 510 475 488 | 500 < 0.002 49 44 47 60 39 | 50 | 35 58 42 37 49 > 0.998 || = 0.41 530 455 533 512 480 | 500 < 0.003 45 50 51 42 52 | 50 | 45 43 66 58 60 > 0.997 || = 0.40 483 463 484 464 491 | 500 < 0.004 62 59 59 48 44 | 50 | 61 49 62 27 52 > 0.996 || = 0.39 518 494 501 515 493 | 500 < 0.005 47 50 52 59 46 | 50 | 46 42 41 49 49 > 0.995 || = 0.38 482 515 454 485 461 | 500 < 0.006 58 43 38 45 36 | 50 | 55 48 53 37 36 > 0.994 || = 0.37 468 480 501 489 478 | 500 < 0.007 64 49 57 41 59 | 50 | 51 48 53 52 48 > 0.993 || = 0.36 495 506 512 514 525 | 500 < 0.008 42 49 53 45 37 | 50 | 50 42 30 43 45 > 0.992 || = 0.35 472 481 488 484 527 | 500 < 0.009 59 45 55 53 63 | 50 | 48 43 55 45 52 > 0.991 || = 0.34 529 499 507 501 501 | 500 < 0.01 62 53 44 54 47 | 50 | 49 51 51 50 49 > 0.99 || = 0.33 495 485 525 499 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 505 483 534 491 463 | 500 < 0.01 548 488 528 498 466 | 497.5 | 493 470 498 449 480 > 0.99 || = 0.31 461 502 491 515 485 | 500 = 0.01 267 255 257 259 259 | 252.5 | 266 230 248 264 259 = 0.99 || = 0.30 512 500 537 526 489 | 500 = 0.02 487 523 509 511 514 | 500 | 480 504 485 494 548 = 0.98 || = 0.29 562 500 484 506 499 | 500 =================================================================| 500 | 473 484 508 509 521 = 0.97 || = 0.28 478 501 479 509 484 | 500 Test sknuth_Permutation calling smultin_Multinomial | 500 | 507 500 494 478 483 = 0.96 || = 0.27 463 531 489 470 487 | 500 smultin_Multinomial test: | 500 | 535 501 489 528 493 = 0.95 || = 0.26 499 505 462 472 535 | 500 ----------------------------------------------- | 500 | 535 522 478 535 507 = 0.94 || = 0.25 481 504 508 492 501 | 500 N = 1, n = 500000000, r = 10, t = 10, | 500 | 487 515 507 480 482 = 0.93 || = 0.24 515 514 447 504 493 | 500 | 500 | 513 502 530 502 522 = 0.92 || = 0.23 495 520 498 484 529 | 500 =================================================================| 500 | 483 516 507 457 510 = 0.91 || = 0.22 516 501 522 491 514 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 474 503 488 528 516 = 0.90 || = 0.21 493 495 465 514 501 | 500 -----------------------------------------------------------------| 500 | 483 501 516 503 550 = 0.89 || = 0.20 491 535 486 530 501 | 500 SD Bern.: d 1.11683 1.28749 0.92457 | 500 | 495 493 495 493 476 = 0.88 || = 0.19 548 498 489 491 511 | 500 s 0.88621 0.66062 0.79536 | 500 | 507 514 514 520 510 = 0.87 || = 0.18 480 519 491 508 525 | 500 t 1.01747 1.29833 1.42478 | 500 | 475 510 474 494 514 = 0.86 || = 0.17 548 530 543 503 486 | 500 m 0.95970 0.90155 1.42267 | 500 | 496 501 508 514 530 = 0.85 || = 0.16 515 506 489 512 474 | 500 x 0.97666 1.30448 0.93426 | 500 | 478 471 500 511 490 = 0.84 || = 0.15 497 525 508 523 490 | 500 | 500 | 483 548 499 454 529 = 0.83 || = 0.14 467 500 508 514 499 | 500 Changes: d 55 6 5 | 500 | 529 486 507 505 501 = 0.82 || = 0.13 483 479 558 489 469 | 500 s 46 3 3 | 500 | 500 516 502 501 525 = 0.81 || = 0.12 529 518 510 491 480 | 500 t 54 5 5 | 500 | 499 519 520 476 544 = 0.80 || = 0.11 497 497 532 480 506 | 500 m 62 4 5 | 500 | 518 521 553 482 504 = 0.79 || = 0.10 446 483 508 481 478 | 500 x 32 6 4 | 500 | 464 489 482 528 518 = 0.78 || = 0.09 510 502 446 501 516 | 500 -----------------------------------------------------------------| 500 | 466 476 500 455 518 = 0.77 || = 0.08 519 500 520 475 496 | 500 Aver./ d 0.49875 497 > 500: 6 4 3 4 5 6 6 2 2 5 | 500 | 528 489 445 556 512 = 0.76 || = 0.07 523 523 476 487 517 | 500 median s 0.49811 501 ----- 7 5 8 3 6 4 4 2 7 6 | 500 | 476 460 490 498 532 = 0.75 || = 0.06 490 501 501 492 524 | 500 t 0.49915 500 6 7 2 7 6 5 2 3 5 5 | 500 | 470 471 486 522 490 = 0.74 || = 0.05 492 550 511 472 511 | 500 m 0.50026 501 5 5 5 5 6 4 5 6 7 5 | 500 | 455 490 518 538 514 = 0.73 || = 0.04 514 506 483 558 472 | 500 x 0.50288 501 6 3 6 3 1 3 6 9 8 6 | 500 | 457 495 480 528 503 = 0.72 || = 0.03 483 470 494 498 485 | 500 -----------------------------------------------------------------| 500 | 495 487 483 506 531 = 0.71 || = 0.02 487 523 509 511 514 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 557 463 477 474 449 = 0.70 || = 0.01 267 255 257 259 259 | 252.5 d 0 0 2 17 64 11 7 0 0 | 500 | 494 497 497 515 467 = 0.69 || < 0.01 548 488 528 498 466 | 497.5 s 0 0 1 12 76 10 2 0 0 | 500 | 491 525 492 536 480 = 0.68 ||========================================================================= t 0 0 5 8 71 14 3 0 0 | 500 | 500 497 490 472 499 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 69 13 2 0 0 | 500 | 549 458 493 519 521 = 0.66 ||========================================================================= x 0 0 2 13 69 15 2 0 0 | 500 | 516 482 508 468 512 = 0.65 || Test sknuth_Permutation calling smultin_Multinomial no 69 test no 70 TestU01 250000 runs BigCrush Test smarsa_S Test sknuth_CollisionPermut calling smultin_Multinomial test no 70 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 1 0 0 | 0.5 | 1 1 0 0 0 > 0.99999 || = 0.64 416 414 430 450 421 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 516 521 539 533 560 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 2 1 > 0.99997 || = 0.62 536 494 511 528 509 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 0 1 0 0 0 > 0.99996 || = 0.61 442 474 464 447 445 | 500 < 0.00005 0 0 1 0 1 | 0.5 | 1 0 0 1 2 > 0.99995 || = 0.60 575 535 533 550 579 | 500 < 0.00006 0 3 1 1 0 | 0.5 | 0 1 1 0 0 > 0.99994 || = 0.59 454 459 497 479 452 | 500 < 0.00007 0 1 0 0 1 | 0.5 | 0 0 1 2 0 > 0.99993 || = 0.58 534 576 557 524 545 | 500 < 0.00008 0 2 0 0 1 | 0.5 | 1 0 0 2 0 > 0.99992 || = 0.57 476 488 446 442 458 | 500 < 0.00009 1 0 1 0 0 | 0.5 | 0 0 0 0 2 > 0.99991 || = 0.56 524 542 567 539 537 | 500 < 0.0001 0 1 0 1 1 | 0.5 | 0 0 0 1 0 > 0.9999 || = 0.55 441 430 446 492 457 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 436 463 450 437 454 | 500 < 0.0001 3 7 5 2 5 | 5 | 4 3 2 8 5 > 0.9999 || = 0.53 552 534 586 581 591 | 500 < 0.0002 6 6 6 7 7 | 5 | 1 4 2 2 6 > 0.9998 || = 0.52 480 454 460 485 481 | 500 < 0.0003 3 4 3 7 5 | 5 | 3 0 6 3 7 > 0.9997 || = 0.51 513 584 547 579 544 | 500 < 0.0004 5 6 4 3 2 | 5 | 6 2 3 5 5 > 0.9996 || = 0.50 563 558 571 513 548 | 500 < 0.0005 2 3 7 7 5 | 5 | 6 3 4 5 3 > 0.9995 || = 0.49 453 500 502 471 475 | 500 < 0.0006 3 8 4 8 6 | 5 | 6 3 5 2 2 > 0.9994 || = 0.48 553 582 569 571 574 | 500 < 0.0007 3 6 3 5 7 | 5 | 3 3 4 4 4 > 0.9993 || = 0.47 430 460 454 479 480 | 500 < 0.0008 5 6 3 7 7 | 5 | 5 7 4 2 4 > 0.9992 || = 0.46 564 518 560 554 556 | 500 < 0.0009 8 4 4 2 2 | 5 | 3 5 6 8 3 > 0.9991 || = 0.45 442 439 470 489 469 | 500 < 0.001 5 5 3 3 6 | 5 | 3 4 9 4 5 > 0.999 || = 0.44 439 482 467 440 414 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 562 525 532 518 543 | 500 < 0.001 43 55 42 51 52 | 50 | 40 34 45 43 44 > 0.999 || = 0.42 422 459 478 426 441 | 500 < 0.002 53 51 47 42 37 | 50 | 54 57 42 54 45 > 0.998 || = 0.41 538 567 547 559 530 | 500 < 0.003 56 39 47 64 57 | 50 | 27 68 41 57 45 > 0.997 || = 0.40 467 417 447 430 429 | 500 < 0.004 51 61 54 51 52 | 50 | 54 48 57 50 54 > 0.996 || = 0.39 542 536 588 521 547 | 500 < 0.005 50 44 62 40 41 | 50 | 50 52 51 50 44 > 0.995 || = 0.38 539 509 549 560 526 | 500 < 0.006 50 65 59 39 43 | 50 | 40 50 56 48 47 > 0.994 || = 0.37 461 448 494 415 432 | 500 < 0.007 45 56 52 57 50 | 50 | 49 48 47 44 43 > 0.993 || = 0.36 544 536 503 505 528 | 500 < 0.008 47 42 47 59 48 | 50 | 42 50 59 68 49 > 0.992 || = 0.35 503 470 532 514 531 | 500 < 0.009 59 50 65 50 57 | 50 | 39 48 49 51 51 > 0.991 || = 0.34 472 520 520 483 504 | 500 < 0.01 51 46 40 33 44 | 50 | 53 56 49 44 50 > 0.99 || = 0.33 540 501 486 516 497 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 519 468 497 470 490 | 500 < 0.01 505 509 515 486 481 | 497.5 | 448 511 496 509 472 > 0.99 || = 0.31 490 506 490 522 534 | 500 = 0.01 249 247 227 237 248 | 252.5 | 241 262 255 240 268 = 0.99 || = 0.30 490 541 479 523 476 | 500 = 0.02 509 515 508 517 472 | 500 | 501 484 481 470 459 = 0.98 || = 0.29 459 473 468 429 457 | 500 =================================================================| 500 | 454 603 519 473 499 = 0.97 || = 0.28 443 495 493 476 496 | 500 Test sknuth_CollisionPermut calling smultin_Multinomial | 500 | 497 518 522 526 509 = 0.96 || = 0.27 534 559 551 537 529 | 500 smultin_Multinomial test: | 500 | 493 468 462 468 476 = 0.95 || = 0.26 452 447 432 426 439 | 500 ----------------------------------------------- | 500 | 488 523 511 482 480 = 0.94 || = 0.25 560 480 533 541 496 | 500 N = 20, n = 20000000, r = 0, t = 14, | 500 | 475 507 472 509 493 = 0.93 || = 0.24 499 504 485 491 516 | 500 | 500 | 512 507 521 503 546 = 0.92 || = 0.23 531 512 486 502 484 | 500 =================================================================| 500 | 547 464 461 539 528 = 0.91 || = 0.22 536 475 474 495 466 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 488 510 494 525 482 = 0.90 || = 0.21 563 545 555 566 516 | 500 -----------------------------------------------------------------| 500 | 494 457 471 482 471 = 0.89 || = 0.20 538 482 537 520 540 | 500 SD Bern.: d 1.81059 0.64993 1.38343 | 500 | 509 549 512 528 462 = 0.88 || = 0.19 420 437 414 428 436 | 500 s 1.71700 1.13634 1.16762 | 500 | 528 508 508 515 488 = 0.87 || = 0.18 499 519 586 581 561 | 500 t 1.70708 1.15035 0.83467 | 500 | 508 498 526 562 524 = 0.86 || = 0.17 476 464 468 447 464 | 500 m 1.70572 1.34380 1.01538 | 500 | 464 475 498 496 494 = 0.85 || = 0.16 517 512 496 462 525 | 500 x 1.73619 0.94386 0.62958 | 500 | 550 520 520 506 496 = 0.84 || = 0.15 504 493 474 487 500 | 500 | 500 | 434 462 461 462 498 = 0.83 || = 0.14 530 533 510 521 541 | 500 Changes: d 61 3 5 | 500 | 515 471 463 460 419 = 0.82 || = 0.13 475 470 469 521 530 | 500 s 70 5 5 | 500 | 501 475 482 520 521 = 0.81 || = 0.12 516 515 483 521 556 | 500 t 67 4 4 | 500 | 540 508 503 524 520 = 0.80 || = 0.11 436 442 502 499 509 | 500 m 65 5 4 | 500 | 509 482 452 464 506 = 0.79 || = 0.10 489 503 441 458 485 | 500 x 60 5 4 | 500 | 551 570 539 543 550 = 0.78 || = 0.09 517 544 539 530 570 | 500 -----------------------------------------------------------------| 500 | 538 498 450 474 504 = 0.77 || = 0.08 479 483 495 494 463 | 500 Aver./ d 0.49911 501 > 500: 5 4 6 6 4 5 4 7 6 3 | 500 | 495 493 505 532 499 = 0.76 || = 0.07 491 525 484 520 495 | 500 median s 0.50026 501 ----- 6 5 4 7 4 5 5 4 4 7 | 500 | 415 432 430 433 444 = 0.75 || = 0.06 487 542 506 519 494 | 500 t 0.49839 499 6 3 4 5 5 5 5 5 4 5 | 500 | 548 534 516 467 532 = 0.74 || = 0.05 518 500 532 502 522 | 500 m 0.49934 503 7 4 5 7 4 5 5 4 6 5 | 500 | 443 478 445 477 446 = 0.73 || = 0.04 562 475 500 507 512 | 500 x 0.49853 499 3 6 4 6 4 5 6 6 2 4 | 500 | 581 556 554 519 564 = 0.72 || = 0.03 486 518 542 540 489 | 500 -----------------------------------------------------------------| 500 | 504 442 499 477 499 = 0.71 || = 0.02 509 515 508 517 472 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 495 486 500 495 471 = 0.70 || = 0.01 249 247 227 237 248 | 252.5 d 0 5 14 9 42 17 12 2 0 | 500 | 514 457 506 518 506 = 0.69 || < 0.01 505 509 515 486 481 | 497.5 s 0 4 7 20 44 15 5 5 1 | 500 | 490 530 484 497 486 = 0.68 ||========================================================================= t 0 4 9 17 45 12 8 6 0 | 500 | 478 510 470 512 513 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 7 6 16 46 16 6 4 0 | 500 | 544 501 508 517 516 = 0.66 ||========================================================================= x 0 5 8 16 42 16 10 3 1 | 500 | 500 523 531 471 510 = 0.65 || Test sknuth_CollisionPermut calling smultin_Multinomial no 70 test no 71 TestU01 250000 runs BigCrush Test smarsa_S Test sknuth_CollisionPermut calling smultin_Multinomial test no 71 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 1 1 0 0 > 0.99999 || = 0.64 466 420 431 444 429 | 500 < 0.00002 0 1 1 0 2 | 0.5 | 0 0 0 0 2 > 0.99998 || = 0.63 516 545 498 522 530 | 500 < 0.00003 1 0 1 0 0 | 0.5 | 1 1 0 0 1 > 0.99997 || = 0.62 551 529 522 557 533 | 500 < 0.00004 0 0 3 1 0 | 0.5 | 0 0 0 1 0 > 0.99996 || = 0.61 427 462 452 436 443 | 500 < 0.00005 0 1 0 0 2 | 0.5 | 1 1 0 0 1 > 0.99995 || = 0.60 535 534 569 542 543 | 500 < 0.00006 0 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 449 460 423 423 447 | 500 < 0.00007 0 2 1 0 0 | 0.5 | 1 1 0 1 0 > 0.99993 || = 0.58 537 520 536 536 555 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99992 || = 0.57 458 472 451 416 456 | 500 < 0.00009 0 0 0 0 1 | 0.5 | 1 0 1 1 1 > 0.99991 || = 0.56 537 540 532 580 537 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 1 1 0 > 0.9999 || = 0.55 453 435 513 511 416 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 425 509 491 491 425 | 500 < 0.0001 1 6 6 1 5 | 5 | 4 4 4 4 5 > 0.9999 || = 0.53 581 563 581 552 554 | 500 < 0.0002 7 4 5 3 3 | 5 | 3 2 0 2 4 > 0.9998 || = 0.52 447 456 458 448 439 | 500 < 0.0003 3 4 3 4 5 | 5 | 3 4 4 4 2 > 0.9997 || = 0.51 597 527 515 560 557 | 500 < 0.0004 1 6 9 1 5 | 5 | 6 4 8 4 2 > 0.9996 || = 0.50 538 542 547 547 572 | 500 < 0.0005 2 3 2 1 6 | 5 | 2 2 8 4 5 > 0.9995 || = 0.49 479 479 455 463 516 | 500 < 0.0006 4 5 7 5 7 | 5 | 4 6 2 2 3 > 0.9994 || = 0.48 582 570 601 542 572 | 500 < 0.0007 1 6 2 3 8 | 5 | 2 9 5 5 11 > 0.9993 || = 0.47 431 502 480 441 489 | 500 < 0.0008 6 2 10 5 3 | 5 | 3 0 4 10 4 > 0.9992 || = 0.46 565 547 566 545 551 | 500 < 0.0009 5 0 8 2 8 | 5 | 7 8 7 4 6 > 0.9991 || = 0.45 473 455 468 428 481 | 500 < 0.001 5 2 7 12 4 | 5 | 3 3 7 6 8 > 0.999 || = 0.44 498 442 429 468 432 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 562 531 530 563 559 | 500 < 0.001 35 38 59 37 54 | 50 | 37 42 49 45 50 > 0.999 || = 0.42 456 486 475 433 450 | 500 < 0.002 51 47 47 45 45 | 50 | 40 56 46 49 45 > 0.998 || = 0.41 588 553 527 503 555 | 500 < 0.003 63 49 61 39 57 | 50 | 51 39 60 53 51 > 0.997 || = 0.40 451 459 437 398 450 | 500 < 0.004 58 35 51 39 45 | 50 | 54 48 52 43 40 > 0.996 || = 0.39 538 551 552 531 529 | 500 < 0.005 46 53 50 42 45 | 50 | 62 46 63 47 49 > 0.995 || = 0.38 501 532 517 567 548 | 500 < 0.006 59 64 44 47 58 | 50 | 56 57 58 50 43 > 0.994 || = 0.37 479 419 434 474 427 | 500 < 0.007 53 56 43 42 56 | 50 | 65 44 41 40 57 > 0.993 || = 0.36 478 541 509 514 494 | 500 < 0.008 42 43 55 50 38 | 50 | 45 49 58 51 49 > 0.992 || = 0.35 523 499 487 517 552 | 500 < 0.009 47 60 59 42 49 | 50 | 49 53 42 39 45 > 0.991 || = 0.34 516 488 520 545 505 | 500 < 0.01 46 54 43 38 55 | 50 | 50 59 62 54 51 > 0.99 || = 0.33 558 520 509 485 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 501 513 510 522 508 | 500 < 0.01 500 499 512 421 502 | 497.5 | 509 493 531 471 480 > 0.99 || = 0.31 453 457 498 509 492 | 500 = 0.01 221 273 244 244 264 | 252.5 | 244 267 243 275 268 = 0.99 || = 0.30 446 475 493 502 493 | 500 = 0.02 500 483 516 514 485 | 500 | 530 497 511 463 482 = 0.98 || = 0.29 455 495 475 478 495 | 500 =================================================================| 500 | 535 510 534 493 517 = 0.97 || = 0.28 460 478 484 508 482 | 500 Test sknuth_CollisionPermut calling smultin_Multinomial | 500 | 486 501 515 542 523 = 0.96 || = 0.27 538 522 521 550 546 | 500 smultin_Multinomial test: | 500 | 441 457 450 439 489 = 0.95 || = 0.26 439 450 457 455 446 | 500 ----------------------------------------------- | 500 | 481 474 500 510 550 = 0.94 || = 0.25 513 500 534 491 547 | 500 N = 20, n = 20000000, r = 10, t = 14, | 500 | 503 512 499 472 483 = 0.93 || = 0.24 508 519 538 541 505 | 500 | 500 | 512 515 465 525 504 = 0.92 || = 0.23 504 498 481 525 484 | 500 =================================================================| 500 | 517 527 515 510 455 = 0.91 || = 0.22 472 541 523 494 497 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 465 463 502 498 485 = 0.90 || = 0.21 531 531 537 529 494 | 500 -----------------------------------------------------------------| 500 | 454 471 512 485 495 = 0.89 || = 0.20 500 540 507 509 525 | 500 SD Bern.: d 1.76643 1.14424 1.19809 | 500 | 515 546 518 540 518 = 0.88 || = 0.19 429 432 405 456 447 | 500 s 1.58334 1.25361 0.91368 | 500 | 466 495 488 485 493 = 0.87 || = 0.18 534 549 533 524 550 | 500 t 1.66253 0.95125 1.18970 | 500 | 551 550 524 535 527 = 0.86 || = 0.17 506 455 487 496 514 | 500 m 1.74998 1.25042 0.81403 | 500 | 462 461 452 491 474 = 0.85 || = 0.16 543 480 457 508 474 | 500 x 1.72052 0.90598 0.71027 | 500 | 539 506 479 484 524 = 0.84 || = 0.15 505 480 462 500 469 | 500 | 500 | 462 478 456 480 487 = 0.83 || = 0.14 511 499 509 556 511 | 500 Changes: d 62 4 2 | 500 | 492 518 489 498 542 = 0.82 || = 0.13 493 483 474 496 511 | 500 s 61 3 5 | 500 | 531 513 492 477 480 = 0.81 || = 0.12 530 548 516 492 528 | 500 t 64 5 5 | 500 | 557 566 546 569 526 = 0.80 || = 0.11 464 440 505 473 463 | 500 m 66 0 5 | 500 | 469 479 483 527 483 = 0.79 || = 0.10 488 541 498 480 540 | 500 x 69 6 5 | 500 | 541 531 544 538 605 = 0.78 || = 0.09 520 528 536 552 510 | 500 -----------------------------------------------------------------| 500 | 502 496 485 493 476 = 0.77 || = 0.08 474 451 518 485 498 | 500 Aver./ d 0.50060 501 > 500: 4 6 5 6 4 5 5 6 4 6 | 500 | 522 482 493 481 503 = 0.76 || = 0.07 472 489 520 492 506 | 500 median s 0.50094 499 ----- 4 3 5 5 5 6 5 4 5 6 | 500 | 434 434 459 445 473 = 0.75 || = 0.06 513 487 496 519 491 | 500 t 0.49999 502 6 4 6 6 4 6 6 4 4 5 | 500 | 555 560 548 535 510 = 0.74 || = 0.05 520 502 566 482 497 | 500 m 0.49889 500 5 3 6 8 4 6 5 5 2 5 | 500 | 466 476 434 451 465 = 0.73 || = 0.04 500 480 450 505 483 | 500 x 0.50048 497 4 6 4 5 5 5 5 5 4 5 | 500 | 556 532 548 546 526 = 0.72 || = 0.03 487 490 458 552 438 | 500 -----------------------------------------------------------------| 500 | 463 463 474 444 422 = 0.71 || = 0.02 500 483 516 514 485 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 483 498 511 511 479 = 0.70 || = 0.01 221 273 244 244 264 | 252.5 d 0 4 11 17 41 16 8 3 1 | 500 | 515 487 505 514 454 = 0.69 || < 0.01 500 499 512 421 502 | 497.5 s 0 3 8 14 46 18 11 1 0 | 500 | 512 498 559 454 520 = 0.68 ||========================================================================= t 1 3 9 13 50 14 8 2 1 | 500 | 498 509 502 478 496 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 1 5 10 9 45 16 12 3 0 | 500 | 511 530 486 489 542 = 0.66 ||========================================================================= x 0 6 10 8 47 15 12 2 1 | 500 | 496 509 513 510 516 = 0.65 || Test sknuth_CollisionPermut calling smultin_Multinomial no 71 test no 72 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 72 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 0 | 0.5 | 1 1 1 1 0 > 0.99999 || = 0.64 507 486 515 505 504 | 500 < 0.00002 0 1 2 0 0 | 0.5 | 1 2 1 0 0 > 0.99998 || = 0.63 500 505 493 515 464 | 500 < 0.00003 1 1 0 1 1 | 0.5 | 1 1 0 1 0 > 0.99997 || = 0.62 482 517 482 465 491 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 1 1 1 0 1 > 0.99996 || = 0.61 558 484 489 526 477 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 503 495 437 488 495 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 1 3 1 0 0 > 0.99994 || = 0.59 477 498 512 522 483 | 500 < 0.00007 0 0 0 0 3 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 528 463 524 502 481 | 500 < 0.00008 2 0 0 0 0 | 0.5 | 0 0 0 1 1 > 0.99992 || = 0.57 470 501 543 460 517 | 500 < 0.00009 1 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99991 || = 0.56 505 479 469 512 489 | 500 < 0.0001 0 1 1 0 1 | 0.5 | 1 0 1 0 0 > 0.9999 || = 0.55 508 483 503 526 472 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 515 488 492 488 492 | 500 < 0.0001 5 4 3 3 6 | 5 | 6 9 6 3 2 > 0.9999 || = 0.53 465 530 495 489 542 | 500 < 0.0002 3 3 3 2 3 | 5 | 3 2 4 2 1 > 0.9998 || = 0.52 486 441 554 526 488 | 500 < 0.0003 7 7 7 1 1 | 5 | 10 10 5 8 3 > 0.9997 || = 0.51 476 450 470 472 503 | 500 < 0.0004 9 8 5 3 8 | 5 | 9 6 4 2 3 > 0.9996 || = 0.50 473 486 493 466 528 | 500 < 0.0005 4 6 3 2 8 | 5 | 5 4 3 5 7 > 0.9995 || = 0.49 509 523 489 477 520 | 500 < 0.0006 3 5 6 2 4 | 5 | 5 6 5 4 7 > 0.9994 || = 0.48 506 478 522 512 463 | 500 < 0.0007 7 3 8 7 6 | 5 | 4 4 9 11 5 > 0.9993 || = 0.47 498 519 480 523 457 | 500 < 0.0008 6 3 5 5 4 | 5 | 6 4 6 6 5 > 0.9992 || = 0.46 535 520 501 498 511 | 500 < 0.0009 3 2 2 5 6 | 5 | 6 7 7 4 6 > 0.9991 || = 0.45 516 497 543 540 482 | 500 < 0.001 7 6 7 3 4 | 5 | 4 6 4 6 1 > 0.999 || = 0.44 473 472 466 495 475 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 490 537 475 512 485 | 500 < 0.001 54 47 49 33 50 | 50 | 58 58 53 51 40 > 0.999 || = 0.42 500 514 514 493 481 | 500 < 0.002 48 53 48 40 51 | 50 | 40 39 63 45 52 > 0.998 || = 0.41 482 501 489 481 479 | 500 < 0.003 69 51 33 54 39 | 50 | 46 49 51 45 52 > 0.997 || = 0.40 519 453 524 487 528 | 500 < 0.004 49 44 55 46 49 | 50 | 46 43 41 44 53 > 0.996 || = 0.39 478 514 489 495 533 | 500 < 0.005 56 65 39 41 48 | 50 | 59 42 39 49 50 > 0.995 || = 0.38 494 530 482 497 521 | 500 < 0.006 46 39 55 50 52 | 50 | 50 54 47 52 42 > 0.994 || = 0.37 508 469 506 500 498 | 500 < 0.007 55 48 65 37 54 | 50 | 50 50 49 58 58 > 0.993 || = 0.36 512 504 488 494 528 | 500 < 0.008 54 36 43 54 44 | 50 | 52 53 56 39 44 > 0.992 || = 0.35 480 512 518 478 490 | 500 < 0.009 43 49 47 46 47 | 50 | 55 58 56 42 45 > 0.991 || = 0.34 521 488 495 526 498 | 500 < 0.01 57 52 50 55 41 | 50 | 70 59 54 51 68 > 0.99 || = 0.33 486 478 455 525 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 486 488 516 510 507 | 500 < 0.01 531 484 484 456 475 | 497.5 | 526 505 509 476 504 > 0.99 || = 0.31 501 494 520 493 480 | 500 = 0.01 277 244 268 272 255 | 252.5 | 267 231 301 233 245 = 0.99 || = 0.30 518 529 510 460 525 | 500 = 0.02 463 446 514 489 531 | 500 | 524 516 480 493 524 = 0.98 || = 0.29 513 490 523 490 508 | 500 =================================================================| 500 | 535 514 517 478 463 = 0.97 || = 0.28 505 508 501 533 537 | 500 sknuth_MaxOft test: | 500 | 522 520 487 487 483 = 0.96 || = 0.27 493 526 463 500 493 | 500 ----------------------------------------------- | 500 | 515 482 497 508 475 = 0.95 || = 0.26 474 504 501 527 485 | 500 N = 40, n = 10000000, r = 0, d = 100000, t = 8 | 500 | 508 491 515 511 543 = 0.94 || = 0.25 521 487 500 509 525 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 523 529 506 479 462 = 0.93 || = 0.24 484 486 445 522 482 | 500 | 500 | 488 488 493 477 527 = 0.92 || = 0.23 447 469 478 479 522 | 500 =================================================================| 500 | 515 506 510 542 476 = 0.91 || = 0.22 524 490 490 489 488 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 497 501 521 538 529 = 0.90 || = 0.21 465 492 451 500 514 | 500 -----------------------------------------------------------------| 500 | 499 502 487 553 505 = 0.89 || = 0.20 512 526 501 486 510 | 500 SD Bern.: d 0.96426 1.07104 1.18886 | 500 | 495 456 507 519 503 = 0.88 || = 0.19 500 523 457 520 483 | 500 s 0.99381 1.10145 0.96897 | 500 | 473 517 502 484 525 = 0.87 || = 0.18 519 536 467 482 500 | 500 t 1.08857 1.22371 0.97925 | 500 | 510 496 524 464 468 = 0.86 || = 0.17 513 492 514 532 510 | 500 m 1.03463 1.20724 0.82744 | 500 | 524 505 485 460 475 = 0.85 || = 0.16 492 514 499 483 484 | 500 x 0.99146 0.73928 1.12304 | 500 | 483 531 481 516 533 = 0.84 || = 0.15 493 518 495 502 540 | 500 | 500 | 500 483 565 475 484 = 0.83 || = 0.14 471 490 499 521 495 | 500 Changes: d 50 8 4 | 500 | 541 509 485 482 519 = 0.82 || = 0.13 521 508 490 511 467 | 500 s 49 5 4 | 500 | 490 473 507 514 455 = 0.81 || = 0.12 498 481 459 464 505 | 500 t 51 4 2 | 500 | 520 500 496 519 517 = 0.80 || = 0.11 484 479 515 553 497 | 500 m 48 5 4 | 500 | 471 479 511 487 501 = 0.79 || = 0.10 523 511 524 501 527 | 500 x 59 4 5 | 500 | 510 511 469 504 483 = 0.78 || = 0.09 502 510 512 534 508 | 500 -----------------------------------------------------------------| 500 | 483 521 505 493 527 = 0.77 || = 0.08 530 497 534 495 489 | 500 Aver./ d 0.50157 501 > 500: 5 4 5 5 5 5 3 7 3 9 | 500 | 502 492 522 482 535 = 0.76 || = 0.07 485 493 540 469 503 | 500 median s 0.50003 500 ----- 5 6 4 5 6 2 6 4 6 6 | 500 | 509 514 508 438 484 = 0.75 || = 0.06 481 530 487 511 517 | 500 t 0.50145 501 7 3 4 5 5 5 4 7 6 6 | 500 | 509 485 515 495 500 = 0.74 || = 0.05 528 516 472 495 526 | 500 m 0.49888 498 5 7 4 3 4 5 6 5 5 3 | 500 | 503 499 498 521 492 = 0.73 || = 0.04 486 526 520 528 504 | 500 x 0.49874 500 7 4 6 5 3 3 5 5 6 4 | 500 | 509 478 505 530 518 = 0.72 || = 0.03 473 528 537 506 490 | 500 -----------------------------------------------------------------| 500 | 471 529 530 519 464 = 0.71 || = 0.02 463 446 514 489 531 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 477 515 508 525 538 = 0.70 || = 0.01 277 244 268 272 255 | 252.5 d 0 0 1 17 67 15 1 0 0 | 500 | 493 537 520 515 513 = 0.69 || < 0.01 531 484 484 456 475 | 497.5 s 0 0 4 8 71 17 1 0 0 | 500 | 494 530 513 514 477 = 0.68 ||========================================================================= t 0 0 4 11 72 11 2 1 0 | 500 | 528 555 468 470 522 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 15 66 17 2 0 0 | 500 | 456 476 480 488 477 = 0.66 ||========================================================================= x 0 0 1 17 62 21 0 0 0 | 500 | 457 494 480 494 501 = 0.65 || sknuth_MaxOft test: no 72 test no 73 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 73 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 1 1 1 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 489 499 506 501 489 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 0 3 0 0 1 > 0.99998 || = 0.63 511 545 440 474 528 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 496 560 493 463 485 | 500 < 0.00004 1 0 0 1 2 | 0.5 | 0 1 1 0 0 > 0.99996 || = 0.61 538 503 512 489 523 | 500 < 0.00005 0 0 2 1 1 | 0.5 | 0 1 0 1 0 > 0.99995 || = 0.60 479 464 494 495 496 | 500 < 0.00006 0 0 1 0 1 | 0.5 | 1 1 0 1 1 > 0.99994 || = 0.59 517 494 468 529 504 | 500 < 0.00007 1 2 0 0 0 | 0.5 | 0 1 1 0 0 > 0.99993 || = 0.58 522 467 477 548 539 | 500 < 0.00008 0 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 539 469 452 503 471 | 500 < 0.00009 0 1 1 1 0 | 0.5 | 0 0 0 0 1 > 0.99991 || = 0.56 488 462 557 496 473 | 500 < 0.0001 1 0 0 0 1 | 0.5 | 2 0 2 1 1 > 0.9999 || = 0.55 499 502 496 501 478 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 521 458 474 527 508 | 500 < 0.0001 3 5 6 4 6 | 5 | 3 7 4 5 4 > 0.9999 || = 0.53 478 466 468 562 507 | 500 < 0.0002 2 2 6 5 6 | 5 | 3 0 1 0 1 > 0.9998 || = 0.52 493 507 489 505 521 | 500 < 0.0003 5 4 7 5 7 | 5 | 5 4 2 3 4 > 0.9997 || = 0.51 462 525 487 482 510 | 500 < 0.0004 3 4 4 6 4 | 5 | 7 4 9 4 9 > 0.9996 || = 0.50 508 523 494 442 488 | 500 < 0.0005 2 6 9 6 6 | 5 | 7 3 8 6 10 > 0.9995 || = 0.49 527 526 484 491 498 | 500 < 0.0006 5 4 6 6 9 | 5 | 4 2 6 5 3 > 0.9994 || = 0.48 487 499 526 569 494 | 500 < 0.0007 3 6 8 5 6 | 5 | 7 3 8 14 2 > 0.9993 || = 0.47 525 519 537 537 471 | 500 < 0.0008 11 6 1 7 4 | 5 | 4 2 2 10 1 > 0.9992 || = 0.46 513 520 498 508 523 | 500 < 0.0009 8 5 7 8 8 | 5 | 3 2 7 6 4 > 0.9991 || = 0.45 496 457 476 517 507 | 500 < 0.001 3 4 3 4 1 | 5 | 6 2 5 2 7 > 0.999 || = 0.44 491 498 510 472 509 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 486 484 477 465 492 | 500 < 0.001 45 46 57 56 57 | 50 | 49 29 52 55 45 > 0.999 || = 0.42 487 499 497 527 524 | 500 < 0.002 47 54 35 56 56 | 50 | 42 48 57 47 61 > 0.998 || = 0.41 513 550 513 448 476 | 500 < 0.003 50 34 62 53 50 | 50 | 47 44 51 47 48 > 0.997 || = 0.40 502 503 507 501 539 | 500 < 0.004 57 47 56 52 47 | 50 | 60 42 56 62 65 > 0.996 || = 0.39 507 515 515 504 512 | 500 < 0.005 55 48 50 40 41 | 50 | 48 44 53 49 50 > 0.995 || = 0.38 502 491 499 524 507 | 500 < 0.006 60 50 51 52 51 | 50 | 50 46 37 49 51 > 0.994 || = 0.37 500 482 459 489 485 | 500 < 0.007 55 40 54 52 43 | 50 | 48 48 61 49 34 > 0.993 || = 0.36 473 517 455 499 508 | 500 < 0.008 52 44 68 44 50 | 50 | 56 49 51 47 57 > 0.992 || = 0.35 485 531 503 492 491 | 500 < 0.009 51 64 70 40 49 | 50 | 44 50 63 41 52 > 0.991 || = 0.34 494 491 537 512 503 | 500 < 0.01 52 42 52 56 33 | 50 | 38 54 75 52 57 > 0.99 || = 0.33 476 483 515 505 466 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 510 533 531 505 498 | 500 < 0.01 524 469 555 501 477 | 497.5 | 482 454 556 498 520 > 0.99 || = 0.31 473 486 499 520 503 | 500 = 0.01 272 210 272 241 259 | 252.5 | 285 253 269 262 234 = 0.99 || = 0.30 470 541 494 505 510 | 500 = 0.02 483 529 482 476 524 | 500 | 473 506 509 505 505 = 0.98 || = 0.29 522 475 527 502 514 | 500 =================================================================| 500 | 497 512 477 501 526 = 0.97 || = 0.28 532 506 469 523 509 | 500 sknuth_MaxOft test: | 500 | 464 508 497 494 506 = 0.96 || = 0.27 461 498 535 488 542 | 500 ----------------------------------------------- | 500 | 516 478 493 529 510 = 0.95 || = 0.26 515 505 473 506 498 | 500 N = 40, n = 10000000, r = 0, d = 100000, t = 8 | 500 | 505 493 488 499 537 = 0.94 || = 0.25 485 497 474 477 486 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 496 495 496 515 475 = 0.93 || = 0.24 510 471 476 506 499 | 500 | 500 | 524 550 491 536 486 = 0.92 || = 0.23 518 489 505 516 473 | 500 =================================================================| 500 | 523 507 498 485 474 = 0.91 || = 0.22 490 526 487 515 519 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 474 505 500 507 513 = 0.90 || = 0.21 519 538 483 480 505 | 500 -----------------------------------------------------------------| 500 | 503 465 492 504 552 = 0.89 || = 0.20 567 520 523 516 532 | 500 SD Bern.: d 1.03448 0.69603 0.89262 | 500 | 510 470 519 507 529 = 0.88 || = 0.19 494 501 450 521 478 | 500 s 1.17584 1.18126 1.11230 | 500 | 457 546 536 488 471 = 0.87 || = 0.18 493 507 495 522 488 | 500 t 1.07947 1.54931 1.53959 | 500 | 541 528 506 505 514 = 0.86 || = 0.17 484 492 509 503 507 | 500 m 0.99875 0.85482 0.75402 | 500 | 518 448 491 468 496 = 0.85 || = 0.16 496 483 538 500 522 | 500 x 1.02122 1.01539 1.21220 | 500 | 487 492 481 491 513 = 0.84 || = 0.15 438 507 524 491 515 | 500 | 500 | 489 530 507 483 495 = 0.83 || = 0.14 488 486 500 539 436 | 500 Changes: d 47 1 4 | 500 | 525 504 509 500 485 = 0.82 || = 0.13 493 501 474 462 511 | 500 s 49 4 1 | 500 | 551 475 490 542 527 = 0.81 || = 0.12 496 484 505 491 516 | 500 t 42 4 2 | 500 | 510 486 514 483 464 = 0.80 || = 0.11 484 513 503 535 462 | 500 m 45 4 4 | 500 | 495 497 501 500 498 = 0.79 || = 0.10 523 478 512 460 526 | 500 x 49 3 7 | 500 | 480 498 527 467 496 = 0.78 || = 0.09 518 522 474 488 508 | 500 -----------------------------------------------------------------| 500 | 455 468 454 510 526 = 0.77 || = 0.08 495 584 546 483 494 | 500 Aver./ d 0.49981 496 > 500: 6 1 7 3 5 4 5 4 6 5 | 500 | 505 506 490 486 451 = 0.76 || = 0.07 485 462 547 488 489 | 500 median s 0.49812 499 ----- 7 5 5 5 5 3 5 2 5 6 | 500 | 465 495 533 512 466 = 0.75 || = 0.06 530 511 468 481 469 | 500 t 0.49967 498 5 6 4 5 5 1 5 7 5 3 | 500 | 502 521 524 520 463 = 0.74 || = 0.05 540 539 487 464 481 | 500 m 0.50088 501 2 5 7 7 6 7 3 3 5 7 | 500 | 518 494 502 491 490 = 0.73 || = 0.04 504 524 521 494 513 | 500 x 0.50002 503 5 6 6 6 5 6 4 2 6 6 | 500 | 483 479 506 486 516 = 0.72 || = 0.03 472 508 492 509 531 | 500 -----------------------------------------------------------------| 500 | 475 497 492 482 489 = 0.71 || = 0.02 483 529 482 476 524 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 495 449 496 504 503 = 0.70 || = 0.01 272 210 272 241 259 | 252.5 d 0 0 2 14 67 15 2 1 0 | 500 | 485 495 497 513 499 = 0.69 || < 0.01 524 469 555 501 477 | 497.5 s 0 0 3 17 61 14 5 1 0 | 500 | 511 489 510 480 534 = 0.68 ||========================================================================= t 0 0 5 15 61 15 5 0 0 | 500 | 509 501 507 478 484 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 11 74 11 2 1 0 | 500 | 531 474 505 496 435 = 0.66 ||========================================================================= x 0 0 3 15 64 18 1 0 0 | 500 | 473 528 492 488 499 = 0.65 || sknuth_MaxOft test: no 73 test no 74 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 74 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 1 0 0 0 | 0.5 | 0 0 0 0 2 > 0.99999 || = 0.64 467 514 525 498 488 | 500 < 0.00002 1 1 3 1 1 | 0.5 | 0 0 1 2 1 > 0.99998 || = 0.63 478 492 519 486 431 | 500 < 0.00003 0 1 1 0 2 | 0.5 | 0 2 0 0 0 > 0.99997 || = 0.62 516 478 531 508 508 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 1 0 1 0 0 > 0.99996 || = 0.61 505 464 484 538 540 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 1 0 0 0 1 > 0.99995 || = 0.60 529 487 475 498 519 | 500 < 0.00006 0 1 0 1 0 | 0.5 | 0 1 1 1 3 > 0.99994 || = 0.59 490 493 494 503 493 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 482 490 451 497 544 | 500 < 0.00008 1 1 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 484 471 537 486 501 | 500 < 0.00009 0 0 0 0 1 | 0.5 | 1 1 1 0 1 > 0.99991 || = 0.56 519 494 502 514 513 | 500 < 0.0001 1 1 1 0 1 | 0.5 | 0 0 0 1 1 > 0.9999 || = 0.55 462 495 499 480 469 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 487 486 501 475 547 | 500 < 0.0001 5 6 6 2 7 | 5 | 3 5 4 4 10 > 0.9999 || = 0.53 484 557 460 549 518 | 500 < 0.0002 4 4 4 4 7 | 5 | 2 2 3 2 2 > 0.9998 || = 0.52 485 525 496 491 501 | 500 < 0.0003 4 4 7 5 4 | 5 | 4 8 3 2 3 > 0.9997 || = 0.51 488 548 489 540 501 | 500 < 0.0004 7 6 5 7 4 | 5 | 4 5 9 7 3 > 0.9996 || = 0.50 501 517 502 527 494 | 500 < 0.0005 7 4 6 7 4 | 5 | 4 1 3 5 5 > 0.9995 || = 0.49 487 474 478 530 472 | 500 < 0.0006 3 3 4 4 2 | 5 | 6 1 4 3 1 > 0.9994 || = 0.48 504 492 473 512 499 | 500 < 0.0007 4 5 1 2 9 | 5 | 6 4 5 6 8 > 0.9993 || = 0.47 522 481 474 480 544 | 500 < 0.0008 7 6 4 2 4 | 5 | 2 3 6 2 7 > 0.9992 || = 0.46 480 493 450 510 497 | 500 < 0.0009 2 4 8 1 3 | 5 | 6 3 6 5 4 > 0.9991 || = 0.45 510 491 536 483 501 | 500 < 0.001 1 5 8 5 6 | 5 | 4 3 4 6 6 > 0.999 || = 0.44 520 500 508 527 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 472 527 497 516 488 | 500 < 0.001 44 47 53 39 50 | 50 | 41 35 47 42 49 > 0.999 || = 0.42 527 514 466 527 525 | 500 < 0.002 48 41 56 45 51 | 50 | 48 46 62 52 44 > 0.998 || = 0.41 470 501 516 507 488 | 500 < 0.003 57 59 45 58 35 | 50 | 51 29 51 45 46 > 0.997 || = 0.40 503 506 481 507 526 | 500 < 0.004 49 40 48 43 43 | 50 | 49 44 52 54 39 > 0.996 || = 0.39 514 483 492 496 493 | 500 < 0.005 53 46 63 46 47 | 50 | 48 45 38 55 45 > 0.995 || = 0.38 471 528 513 485 500 | 500 < 0.006 54 33 52 62 52 | 50 | 58 55 36 48 46 > 0.994 || = 0.37 490 510 506 488 522 | 500 < 0.007 50 57 51 39 50 | 50 | 53 60 59 56 48 > 0.993 || = 0.36 513 543 485 484 473 | 500 < 0.008 52 50 53 50 49 | 50 | 54 48 38 50 50 > 0.992 || = 0.35 544 514 479 517 494 | 500 < 0.009 47 55 51 45 42 | 50 | 57 47 55 55 55 > 0.991 || = 0.34 529 498 505 491 518 | 500 < 0.01 51 54 57 57 64 | 50 | 50 63 48 56 54 > 0.99 || = 0.33 474 515 497 497 473 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 471 473 505 497 489 | 500 < 0.01 505 482 529 484 483 | 497.5 | 509 472 486 513 476 > 0.99 || = 0.31 516 528 505 508 523 | 500 = 0.01 271 254 261 251 220 | 252.5 | 262 253 251 254 219 = 0.99 || = 0.30 502 503 463 507 479 | 500 = 0.02 494 496 510 489 511 | 500 | 494 503 499 496 502 = 0.98 || = 0.29 526 518 512 485 529 | 500 =================================================================| 500 | 472 513 468 494 484 = 0.97 || = 0.28 505 480 521 512 510 | 500 sknuth_MaxOft test: | 500 | 510 530 498 489 488 = 0.96 || = 0.27 486 467 530 499 519 | 500 ----------------------------------------------- | 500 | 467 465 496 462 502 = 0.95 || = 0.26 461 515 487 476 489 | 500 N = 40, n = 10000000, r = 0, d = 100000, t = 8 | 500 | 509 499 492 484 517 = 0.94 || = 0.25 459 487 502 521 502 | 500 Anderson-Darling statistic = A2 | 500 | 475 517 521 565 485 = 0.93 || = 0.24 502 535 479 519 503 | 500 | 500 | 471 461 517 474 514 = 0.92 || = 0.23 501 541 493 499 481 | 500 =================================================================| 500 | 520 487 499 476 504 = 0.91 || = 0.22 515 490 495 554 488 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 499 475 504 529 523 = 0.90 || = 0.21 503 543 489 495 488 | 500 -----------------------------------------------------------------| 500 | 516 499 518 552 497 = 0.89 || = 0.20 515 488 484 492 488 | 500 SD Bern.: d 0.97226 0.50818 0.67708 | 500 | 500 496 511 473 477 = 0.88 || = 0.19 499 529 518 490 511 | 500 s 0.97144 1.15469 1.44985 | 500 | 505 485 491 475 473 = 0.87 || = 0.18 471 483 515 447 518 | 500 t 1.04904 0.78396 1.22698 | 500 | 532 485 463 510 453 = 0.86 || = 0.17 511 469 462 526 488 | 500 m 1.00043 1.10870 0.68590 | 500 | 522 502 529 464 516 = 0.85 || = 0.16 519 529 531 470 496 | 500 x 0.93383 1.04837 0.72146 | 500 | 512 480 539 526 518 = 0.84 || = 0.15 554 521 493 503 474 | 500 | 500 | 482 494 472 505 486 = 0.83 || = 0.14 505 453 493 514 489 | 500 Changes: d 50 7 4 | 500 | 536 487 497 499 484 = 0.82 || = 0.13 514 538 542 461 489 | 500 s 51 5 3 | 500 | 468 507 531 497 485 = 0.81 || = 0.12 513 500 470 479 488 | 500 t 47 2 6 | 500 | 481 499 461 520 469 = 0.80 || = 0.11 482 493 522 517 513 | 500 m 55 5 7 | 500 | 478 511 531 490 519 = 0.79 || = 0.10 540 519 531 489 516 | 500 x 50 5 1 | 500 | 505 491 579 496 495 = 0.78 || = 0.09 524 505 526 475 501 | 500 -----------------------------------------------------------------| 500 | 505 502 485 511 504 = 0.77 || = 0.08 513 500 488 512 497 | 500 Aver./ d 0.49859 502 > 500: 5 7 7 6 6 2 4 6 6 5 | 500 | 508 497 500 517 498 = 0.76 || = 0.07 495 512 517 507 526 | 500 median s 0.49839 499 ----- 4 5 5 7 4 3 3 5 2 5 | 500 | 499 474 514 492 519 = 0.75 || = 0.06 487 456 486 492 524 | 500 t 0.49925 500 8 6 4 5 3 3 6 6 6 2 | 500 | 519 510 516 524 518 = 0.74 || = 0.05 482 488 513 490 480 | 500 m 0.50078 498 3 4 4 3 8 4 6 5 5 3 | 500 | 525 486 516 458 487 = 0.73 || = 0.04 485 524 517 536 477 | 500 x 0.49951 500 5 4 5 3 5 8 5 6 3 5 | 500 | 453 531 492 506 530 = 0.72 || = 0.03 534 476 503 453 527 | 500 -----------------------------------------------------------------| 500 | 502 540 503 470 517 = 0.71 || = 0.02 494 496 510 489 511 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 495 488 517 506 498 = 0.70 || = 0.01 271 254 261 251 220 | 252.5 d 0 0 1 16 70 12 2 0 0 | 500 | 547 514 492 501 521 = 0.69 || < 0.01 505 482 529 484 483 | 497.5 s 0 0 1 13 70 15 2 0 0 | 500 | 493 513 441 485 518 = 0.68 ||========================================================================= t 0 0 4 12 70 14 0 1 0 | 500 | 460 478 451 466 507 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 14 70 11 4 0 0 | 500 | 498 481 505 506 500 = 0.66 ||========================================================================= x 0 1 3 9 75 12 1 0 0 | 500 | 504 499 502 519 489 = 0.65 || sknuth_MaxOft test: no 74 test no 75 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 75 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 3 1 0 | 0.5 | 1 1 0 0 1 > 0.99999 || = 0.64 474 485 485 472 516 | 500 < 0.00002 0 0 1 0 1 | 0.5 | 0 1 1 0 1 > 0.99998 || = 0.63 501 490 469 491 510 | 500 < 0.00003 1 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 501 525 522 542 476 | 500 < 0.00004 0 0 0 1 1 | 0.5 | 2 0 1 0 1 > 0.99996 || = 0.61 508 478 479 504 475 | 500 < 0.00005 1 2 0 0 1 | 0.5 | 0 0 0 1 0 > 0.99995 || = 0.60 539 499 530 547 493 | 500 < 0.00006 1 0 0 0 0 | 0.5 | 0 1 0 1 1 > 0.99994 || = 0.59 487 489 467 479 473 | 500 < 0.00007 1 0 1 2 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 472 498 499 489 519 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 556 529 482 502 489 | 500 < 0.00009 0 0 1 0 0 | 0.5 | 3 2 2 0 0 > 0.99991 || = 0.56 522 510 465 506 490 | 500 < 0.0001 1 0 0 1 0 | 0.5 | 1 0 1 0 1 > 0.9999 || = 0.55 489 490 496 471 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 495 524 490 528 500 | 500 < 0.0001 6 5 6 5 4 | 5 | 7 5 5 2 6 > 0.9999 || = 0.53 494 522 515 507 522 | 500 < 0.0002 3 9 4 1 6 | 5 | 2 4 5 2 0 > 0.9998 || = 0.52 501 518 478 482 515 | 500 < 0.0003 5 4 5 6 7 | 5 | 6 4 2 5 4 > 0.9997 || = 0.51 499 495 539 508 526 | 500 < 0.0004 6 4 9 1 5 | 5 | 6 7 6 5 6 > 0.9996 || = 0.50 475 480 464 512 492 | 500 < 0.0005 5 1 7 9 6 | 5 | 7 5 2 0 3 > 0.9995 || = 0.49 494 508 442 553 482 | 500 < 0.0006 2 6 11 4 4 | 5 | 5 5 3 5 5 > 0.9994 || = 0.48 488 477 485 449 480 | 500 < 0.0007 7 5 3 5 2 | 5 | 7 9 4 4 2 > 0.9993 || = 0.47 497 480 504 486 491 | 500 < 0.0008 6 4 6 8 1 | 5 | 8 4 5 5 10 > 0.9992 || = 0.46 519 490 495 483 532 | 500 < 0.0009 2 3 10 3 7 | 5 | 5 5 2 1 3 > 0.9991 || = 0.45 514 531 482 521 493 | 500 < 0.001 9 5 9 8 5 | 5 | 4 2 5 6 5 > 0.999 || = 0.44 524 509 506 485 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 468 466 512 539 517 | 500 < 0.001 51 46 70 50 47 | 50 | 57 50 39 35 44 > 0.999 || = 0.42 500 511 496 478 482 | 500 < 0.002 47 47 54 44 46 | 50 | 35 44 55 45 47 > 0.998 || = 0.41 474 535 568 515 461 | 500 < 0.003 42 59 63 56 48 | 50 | 63 39 39 53 45 > 0.997 || = 0.40 491 477 479 502 510 | 500 < 0.004 63 49 59 41 59 | 50 | 45 51 53 43 39 > 0.996 || = 0.39 496 481 491 525 507 | 500 < 0.005 42 49 53 52 46 | 50 | 47 63 46 45 56 > 0.995 || = 0.38 516 526 508 498 486 | 500 < 0.006 56 43 43 40 44 | 50 | 56 61 61 45 47 > 0.994 || = 0.37 524 475 527 487 506 | 500 < 0.007 57 55 63 51 47 | 50 | 55 49 52 53 55 > 0.993 || = 0.36 472 496 492 553 521 | 500 < 0.008 49 44 59 53 41 | 50 | 46 36 48 67 52 > 0.992 || = 0.35 479 445 480 519 496 | 500 < 0.009 52 39 44 51 44 | 50 | 57 40 45 40 48 > 0.991 || = 0.34 506 460 479 505 483 | 500 < 0.01 48 60 61 43 47 | 50 | 46 46 40 46 49 > 0.99 || = 0.33 476 509 496 474 480 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 497 540 530 493 472 | 500 < 0.01 507 491 569 481 469 | 497.5 | 507 479 478 472 482 > 0.99 || = 0.31 485 508 514 491 529 | 500 = 0.01 251 247 243 238 240 | 252.5 | 256 232 300 258 271 = 0.99 || = 0.30 462 497 494 478 509 | 500 = 0.02 515 523 468 539 520 | 500 | 483 490 525 522 520 = 0.98 || = 0.29 517 503 488 545 516 | 500 =================================================================| 500 | 489 518 474 512 453 = 0.97 || = 0.28 509 516 499 493 532 | 500 sknuth_MaxOft test: | 500 | 518 519 517 507 541 = 0.96 || = 0.27 488 492 472 463 503 | 500 ----------------------------------------------- | 500 | 484 513 494 493 484 = 0.95 || = 0.26 492 487 483 494 502 | 500 N = 40, n = 10000000, r = 0, d = 100000, t = 8 | 500 | 521 478 527 539 487 = 0.94 || = 0.25 508 536 521 539 507 | 500 Test on the sum of all N observations | 500 | 513 518 498 498 492 = 0.93 || = 0.24 491 490 485 501 518 | 500 | 500 | 523 465 500 524 502 = 0.92 || = 0.23 507 506 495 493 478 | 500 =================================================================| 500 | 503 505 475 528 500 = 0.91 || = 0.22 513 483 526 469 474 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 519 509 517 507 542 = 0.90 || = 0.21 465 533 489 472 503 | 500 -----------------------------------------------------------------| 500 | 517 474 500 499 534 = 0.89 || = 0.20 496 557 513 514 517 | 500 SD Bern.: d 0.93206 0.89598 1.11320 | 500 | 494 509 485 470 454 = 0.88 || = 0.19 473 505 490 541 531 | 500 s 0.99111 0.93748 1.23430 | 500 | 516 477 504 487 513 = 0.87 || = 0.18 531 491 494 497 501 | 500 t 1.05317 1.50474 1.04550 | 500 | 502 490 506 519 516 = 0.86 || = 0.17 525 486 492 508 513 | 500 m 1.08803 0.79663 1.24319 | 500 | 449 463 478 508 472 = 0.85 || = 0.16 513 512 501 485 501 | 500 x 0.88337 0.77109 0.73520 | 500 | 492 493 475 497 492 = 0.84 || = 0.15 455 493 521 510 496 | 500 | 500 | 513 502 497 503 509 = 0.83 || = 0.14 523 498 503 505 479 | 500 Changes: d 46 7 7 | 500 | 472 462 529 505 511 = 0.82 || = 0.13 535 523 521 509 503 | 500 s 52 5 2 | 500 | 504 469 495 542 512 = 0.81 || = 0.12 496 518 524 525 495 | 500 t 57 4 6 | 500 | 490 530 489 480 501 = 0.80 || = 0.11 480 518 490 508 505 | 500 m 42 6 4 | 500 | 513 492 531 495 485 = 0.79 || = 0.10 470 469 498 532 504 | 500 x 46 2 4 | 500 | 492 492 490 472 468 = 0.78 || = 0.09 513 498 493 498 477 | 500 -----------------------------------------------------------------| 500 | 508 524 496 451 465 = 0.77 || = 0.08 514 449 520 490 493 | 500 Aver./ d 0.49929 499 > 500: 8 5 5 3 3 4 4 4 6 7 | 500 | 523 506 530 490 509 = 0.76 || = 0.07 542 505 493 461 512 | 500 median s 0.49889 499 ----- 5 5 6 4 5 5 5 7 3 5 | 500 | 488 501 493 500 514 = 0.75 || = 0.06 539 511 540 464 497 | 500 t 0.49892 496 5 5 3 4 4 3 3 5 4 4 | 500 | 535 523 542 544 536 = 0.74 || = 0.05 538 503 501 490 513 | 500 m 0.50140 499 1 8 4 4 5 6 3 3 6 7 | 500 | 482 503 489 488 500 = 0.73 || = 0.04 501 492 496 462 493 | 500 x 0.50024 501 3 7 8 5 3 4 6 4 7 4 | 500 | 484 514 514 507 497 = 0.72 || = 0.03 489 512 539 445 494 | 500 -----------------------------------------------------------------| 500 | 497 481 513 525 479 = 0.71 || = 0.02 515 523 468 539 520 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 495 520 493 504 528 = 0.70 || = 0.01 251 247 243 238 240 | 252.5 d 0 0 2 14 71 13 1 0 0 | 500 | 499 537 504 499 479 = 0.69 || < 0.01 507 491 569 481 469 | 497.5 s 0 0 2 15 67 15 2 0 0 | 500 | 518 477 470 491 528 = 0.68 ||========================================================================= t 0 0 2 10 72 14 1 2 0 | 500 | 457 558 508 465 519 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 65 15 4 0 0 | 500 | 478 472 440 464 521 = 0.66 ||========================================================================= x 0 0 2 11 76 12 0 0 0 | 500 | 475 505 497 490 485 = 0.65 || sknuth_MaxOft test: no 75 test no 76 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 76 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 0 0 2 > 0.99999 || = 0.64 496 521 522 521 540 | 500 < 0.00002 1 1 2 0 1 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 489 522 493 499 503 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 495 486 502 528 492 | 500 < 0.00004 0 0 0 1 1 | 0.5 | 1 1 0 0 1 > 0.99996 || = 0.61 538 491 529 527 487 | 500 < 0.00005 1 0 0 0 0 | 0.5 | 1 1 0 1 1 > 0.99995 || = 0.60 479 502 493 514 504 | 500 < 0.00006 0 0 0 1 0 | 0.5 | 1 1 0 0 1 > 0.99994 || = 0.59 536 508 494 488 532 | 500 < 0.00007 1 0 3 0 0 | 0.5 | 1 0 1 2 0 > 0.99993 || = 0.58 514 489 454 546 503 | 500 < 0.00008 0 1 1 0 0 | 0.5 | 1 0 0 1 0 > 0.99992 || = 0.57 487 492 494 499 493 | 500 < 0.00009 1 1 0 0 0 | 0.5 | 0 0 2 1 2 > 0.99991 || = 0.56 495 505 491 464 502 | 500 < 0.0001 3 1 0 0 0 | 0.5 | 0 1 3 0 2 > 0.9999 || = 0.55 496 496 490 533 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 506 481 503 512 527 | 500 < 0.0001 7 4 6 3 2 | 5 | 5 4 6 6 10 > 0.9999 || = 0.53 499 472 512 472 497 | 500 < 0.0002 3 5 2 6 7 | 5 | 5 4 3 4 5 > 0.9998 || = 0.52 526 509 504 476 518 | 500 < 0.0003 6 4 5 8 7 | 5 | 2 4 6 8 6 > 0.9997 || = 0.51 465 496 506 505 514 | 500 < 0.0004 3 4 4 2 6 | 5 | 2 7 5 6 5 > 0.9996 || = 0.50 487 493 471 500 522 | 500 < 0.0005 8 7 7 2 6 | 5 | 3 3 4 2 4 > 0.9995 || = 0.49 530 542 485 494 492 | 500 < 0.0006 5 3 3 1 4 | 5 | 6 2 0 6 6 > 0.9994 || = 0.48 526 516 472 443 487 | 500 < 0.0007 3 6 4 7 1 | 5 | 7 8 4 5 5 > 0.9993 || = 0.47 468 487 509 494 479 | 500 < 0.0008 6 5 3 2 2 | 5 | 6 6 6 3 7 > 0.9992 || = 0.46 507 481 489 488 520 | 500 < 0.0009 5 5 2 5 1 | 5 | 7 7 4 6 5 > 0.9991 || = 0.45 496 477 504 492 487 | 500 < 0.001 4 6 6 3 6 | 5 | 6 6 3 3 7 > 0.999 || = 0.44 494 483 511 525 486 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 541 489 501 465 491 | 500 < 0.001 50 49 42 39 42 | 50 | 49 51 41 49 60 > 0.999 || = 0.42 536 490 519 511 469 | 500 < 0.002 51 41 55 53 52 | 50 | 41 58 54 49 52 > 0.998 || = 0.41 472 480 471 488 506 | 500 < 0.003 29 51 57 48 60 | 50 | 47 50 38 57 54 > 0.997 || = 0.40 496 496 504 509 486 | 500 < 0.004 45 61 57 50 53 | 50 | 56 47 59 49 58 > 0.996 || = 0.39 481 494 492 489 483 | 500 < 0.005 61 45 43 46 50 | 50 | 52 54 49 52 55 > 0.995 || = 0.38 517 488 508 484 507 | 500 < 0.006 51 49 50 38 51 | 50 | 56 54 50 51 45 > 0.994 || = 0.37 467 519 521 471 538 | 500 < 0.007 48 49 45 47 50 | 50 | 58 43 53 44 52 > 0.993 || = 0.36 494 514 482 495 477 | 500 < 0.008 49 46 61 47 48 | 50 | 52 50 38 44 57 > 0.992 || = 0.35 479 485 474 484 518 | 500 < 0.009 44 41 46 58 44 | 50 | 53 48 51 55 53 > 0.991 || = 0.34 540 538 540 497 489 | 500 < 0.01 60 50 47 45 51 | 50 | 54 52 53 59 50 > 0.99 || = 0.33 478 499 492 514 516 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 492 482 508 512 520 | 500 < 0.01 488 482 503 471 501 | 497.5 | 518 507 486 509 536 > 0.99 || = 0.31 497 463 482 520 498 | 500 = 0.01 237 264 261 253 242 | 252.5 | 247 265 260 248 252 = 0.99 || = 0.30 505 523 490 501 509 | 500 = 0.02 490 497 490 498 490 | 500 | 518 490 468 505 491 = 0.98 || = 0.29 494 539 491 490 456 | 500 =================================================================| 500 | 500 523 513 531 478 = 0.97 || = 0.28 493 524 443 491 486 | 500 sknuth_MaxOft test: | 500 | 507 467 492 508 524 = 0.96 || = 0.27 543 525 461 517 526 | 500 ----------------------------------------------- | 500 | 501 501 542 520 462 = 0.95 || = 0.26 488 524 481 523 482 | 500 N = 40, n = 10000000, r = 0, d = 100000, t = 8 | 500 | 525 503 501 492 536 = 0.94 || = 0.25 519 550 492 479 481 | 500 Test results for Anderson-Darling: | 500 | 503 485 502 530 497 = 0.93 || = 0.24 507 494 507 443 491 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 533 557 517 500 464 = 0.92 || = 0.23 516 522 534 493 497 | 500 =================================================================| 500 | 533 475 507 501 479 = 0.91 || = 0.22 503 512 519 501 484 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 511 516 496 517 459 = 0.90 || = 0.21 503 487 488 504 528 | 500 -----------------------------------------------------------------| 500 | 486 471 474 509 485 = 0.89 || = 0.20 493 487 525 471 493 | 500 SD Bern.: d 0.95586 1.20890 0.72145 | 500 | 457 503 492 490 531 = 0.88 || = 0.19 486 475 526 509 510 | 500 s 0.99660 0.81033 0.57123 | 500 | 478 485 493 509 537 = 0.87 || = 0.18 506 510 510 499 516 | 500 t 0.95900 0.90266 0.98638 | 500 | 477 464 514 508 475 = 0.86 || = 0.17 470 493 491 534 492 | 500 m 0.90338 0.89599 0.68589 | 500 | 486 454 537 536 498 = 0.85 || = 0.16 540 478 479 533 507 | 500 x 0.90106 0.66214 0.76979 | 500 | 468 480 484 478 510 = 0.84 || = 0.15 479 506 518 510 496 | 500 | 500 | 509 481 504 497 491 = 0.83 || = 0.14 474 527 517 496 508 | 500 Changes: d 53 5 1 | 500 | 483 448 474 510 513 = 0.82 || = 0.13 517 507 494 486 525 | 500 s 47 2 4 | 500 | 527 512 536 508 487 = 0.81 || = 0.12 514 486 528 502 495 | 500 t 49 4 7 | 500 | 476 505 511 457 527 = 0.80 || = 0.11 501 530 509 470 493 | 500 m 53 4 5 | 500 | 477 489 456 516 474 = 0.79 || = 0.10 482 535 493 499 500 | 500 x 58 5 3 | 500 | 515 534 488 509 507 = 0.78 || = 0.09 453 531 501 482 494 | 500 -----------------------------------------------------------------| 500 | 489 523 456 463 523 = 0.77 || = 0.08 531 473 532 484 533 | 500 Aver./ d 0.50035 496 > 500: 4 5 6 3 5 4 3 5 3 8 | 500 | 506 487 531 503 471 = 0.76 || = 0.07 521 503 486 491 511 | 500 median s 0.49817 499 ----- 6 6 7 4 2 4 6 6 3 6 | 500 | 461 487 500 490 506 = 0.75 || = 0.06 524 503 459 496 485 | 500 t 0.49996 501 7 6 4 4 6 4 7 4 4 7 | 500 | 519 504 465 523 518 = 0.74 || = 0.05 506 512 502 505 487 | 500 m 0.50206 500 3 5 4 4 3 5 8 5 7 7 | 500 | 509 442 533 494 516 = 0.73 || = 0.04 494 509 519 486 517 | 500 x 0.49977 497 4 5 2 6 2 7 4 7 4 3 | 500 | 490 506 488 505 470 = 0.72 || = 0.03 483 473 509 540 498 | 500 -----------------------------------------------------------------| 500 | 529 522 521 480 519 = 0.71 || = 0.02 490 497 490 498 490 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 485 522 559 471 472 = 0.70 || = 0.01 237 264 261 253 242 | 252.5 d 0 0 1 13 68 19 0 0 0 | 500 | 524 522 516 505 535 = 0.69 || < 0.01 488 482 503 471 501 | 497.5 s 0 0 3 11 70 15 2 0 0 | 500 | 476 530 494 504 483 = 0.68 ||========================================================================= t 0 0 2 12 74 12 1 0 0 | 500 | 528 497 482 509 480 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 11 74 13 1 0 0 | 500 | 478 465 519 534 469 = 0.66 ||========================================================================= x 0 0 0 12 73 16 0 0 0 | 500 | 492 511 509 515 522 = 0.65 || sknuth_MaxOft test: no 76 test no 77 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 77 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 3 | 0.5 | 2 1 0 1 1 > 0.99999 || = 0.64 496 495 475 488 476 | 500 < 0.00002 0 0 1 0 2 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 517 505 510 498 472 | 500 < 0.00003 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 492 510 492 516 524 | 500 < 0.00004 0 0 1 1 0 | 0.5 | 0 1 1 0 0 > 0.99996 || = 0.61 488 517 486 494 514 | 500 < 0.00005 0 0 0 1 1 | 0.5 | 2 1 0 0 1 > 0.99995 || = 0.60 528 501 488 503 521 | 500 < 0.00006 0 2 0 2 0 | 0.5 | 0 0 0 3 0 > 0.99994 || = 0.59 513 517 512 457 496 | 500 < 0.00007 1 0 1 1 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 519 509 505 489 516 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 498 520 489 484 481 | 500 < 0.00009 0 1 0 1 1 | 0.5 | 0 2 0 0 0 > 0.99991 || = 0.56 580 557 502 499 520 | 500 < 0.0001 2 1 1 1 0 | 0.5 | 0 1 0 0 1 > 0.9999 || = 0.55 483 521 512 470 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 502 532 521 482 526 | 500 < 0.0001 3 6 4 7 9 | 5 | 4 7 1 4 3 > 0.9999 || = 0.53 512 502 518 517 476 | 500 < 0.0002 6 5 0 9 4 | 5 | 2 2 1 1 3 > 0.9998 || = 0.52 486 476 468 522 463 | 500 < 0.0003 5 4 5 4 6 | 5 | 7 8 2 2 4 > 0.9997 || = 0.51 496 509 520 528 533 | 500 < 0.0004 10 7 2 6 5 | 5 | 5 5 7 7 5 > 0.9996 || = 0.50 498 522 502 484 515 | 500 < 0.0005 2 3 6 3 6 | 5 | 2 2 3 6 10 > 0.9995 || = 0.49 483 493 541 490 486 | 500 < 0.0006 5 1 4 3 4 | 5 | 9 10 5 6 7 > 0.9994 || = 0.48 463 496 504 493 456 | 500 < 0.0007 2 7 4 3 6 | 5 | 5 4 4 5 5 > 0.9993 || = 0.47 498 498 519 464 501 | 500 < 0.0008 7 4 3 8 3 | 5 | 5 5 1 3 5 > 0.9992 || = 0.46 472 496 476 501 477 | 500 < 0.0009 2 5 7 4 2 | 5 | 6 5 3 1 5 > 0.9991 || = 0.45 481 482 487 488 486 | 500 < 0.001 3 10 3 5 6 | 5 | 4 3 1 4 5 > 0.999 || = 0.44 464 458 529 524 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 496 540 515 533 514 | 500 < 0.001 45 52 38 52 51 | 50 | 49 51 28 39 52 > 0.999 || = 0.42 512 488 510 500 505 | 500 < 0.002 63 50 53 49 57 | 50 | 51 55 43 46 62 > 0.998 || = 0.41 499 520 508 504 477 | 500 < 0.003 65 47 42 44 39 | 50 | 47 57 46 57 46 > 0.997 || = 0.40 475 504 462 495 493 | 500 < 0.004 50 50 63 67 58 | 50 | 51 50 56 60 38 > 0.996 || = 0.39 530 485 487 489 469 | 500 < 0.005 52 40 45 44 53 | 50 | 60 55 54 34 46 > 0.995 || = 0.38 482 492 502 555 453 | 500 < 0.006 56 52 62 62 51 | 50 | 39 46 56 57 60 > 0.994 || = 0.37 490 472 501 494 490 | 500 < 0.007 40 43 50 44 54 | 50 | 39 59 53 49 53 > 0.993 || = 0.36 495 497 521 515 490 | 500 < 0.008 54 45 55 61 42 | 50 | 48 47 63 53 46 > 0.992 || = 0.35 491 457 535 495 502 | 500 < 0.009 51 61 51 58 62 | 50 | 44 45 48 54 48 > 0.991 || = 0.34 477 513 537 508 446 | 500 < 0.01 58 47 54 49 49 | 50 | 54 49 38 49 44 > 0.99 || = 0.33 471 503 513 462 475 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 529 512 486 496 504 | 500 < 0.01 534 487 513 530 516 | 497.5 | 482 514 485 498 495 > 0.99 || = 0.31 524 508 461 503 491 | 500 = 0.01 256 257 234 259 251 | 252.5 | 219 258 247 251 262 = 0.99 || = 0.30 489 498 526 510 513 | 500 = 0.02 500 466 527 520 530 | 500 | 518 529 493 495 446 = 0.98 || = 0.29 529 481 513 509 469 | 500 =================================================================| 500 | 518 539 537 507 517 = 0.97 || = 0.28 520 499 511 521 544 | 500 sknuth_MaxOft test: | 500 | 461 536 497 495 502 = 0.96 || = 0.27 508 475 515 511 494 | 500 ----------------------------------------------- | 500 | 519 478 484 490 491 = 0.95 || = 0.26 534 489 517 517 517 | 500 N = 40, n = 10000000, r = 0, d = 100000, t = 8 | 500 | 504 516 477 511 503 = 0.94 || = 0.25 494 530 506 539 487 | 500 Test results for Anderson-Darling: | 500 | 489 490 498 461 534 = 0.93 || = 0.24 514 443 521 529 498 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 486 501 503 461 496 = 0.92 || = 0.23 482 485 465 530 493 | 500 =================================================================| 500 | 514 508 512 459 517 = 0.91 || = 0.22 492 516 513 462 520 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 473 517 480 544 494 = 0.90 || = 0.21 475 509 472 505 442 | 500 -----------------------------------------------------------------| 500 | 491 516 512 472 462 = 0.89 || = 0.20 537 436 501 541 522 | 500 SD Bern.: d 0.97992 1.13193 0.90598 | 500 | 517 466 497 507 514 = 0.88 || = 0.19 503 497 495 552 491 | 500 s 0.97073 0.80164 0.68150 | 500 | 502 495 470 489 510 = 0.87 || = 0.18 500 476 502 506 499 | 500 t 0.89486 1.09324 1.38849 | 500 | 443 484 501 456 557 = 0.86 || = 0.17 476 495 470 502 522 | 500 m 1.01240 1.21056 1.11230 | 500 | 501 497 510 516 497 = 0.85 || = 0.16 485 539 490 485 515 | 500 x 1.05498 0.97001 0.98942 | 500 | 500 482 485 472 496 = 0.84 || = 0.15 493 517 468 476 492 | 500 | 500 | 517 495 506 503 523 = 0.83 || = 0.14 489 510 527 499 552 | 500 Changes: d 45 5 5 | 500 | 510 494 536 473 484 = 0.82 || = 0.13 515 494 497 493 501 | 500 s 43 5 5 | 500 | 527 488 548 447 507 = 0.81 || = 0.12 537 542 492 488 508 | 500 t 45 7 2 | 500 | 501 518 466 503 504 = 0.80 || = 0.11 499 485 490 492 459 | 500 m 54 7 6 | 500 | 513 502 458 485 479 = 0.79 || = 0.10 497 482 481 507 468 | 500 x 59 5 3 | 500 | 516 479 532 519 479 = 0.78 || = 0.09 473 505 486 528 504 | 500 -----------------------------------------------------------------| 500 | 490 506 480 514 512 = 0.77 || = 0.08 518 488 514 484 523 | 500 Aver./ d 0.49930 499 > 500: 6 3 6 3 1 6 4 7 6 5 | 500 | 492 492 471 499 502 = 0.76 || = 0.07 480 497 477 543 475 | 500 median s 0.50214 501 ----- 5 4 3 4 3 9 6 6 2 8 | 500 | 515 501 489 525 537 = 0.75 || = 0.06 543 501 520 493 533 | 500 t 0.49937 501 6 2 8 7 7 7 3 3 6 3 | 500 | 504 476 509 452 481 = 0.74 || = 0.05 503 516 517 505 492 | 500 m 0.49590 500 8 4 9 5 4 4 4 5 4 3 | 500 | 509 522 510 474 493 = 0.73 || = 0.04 445 444 487 520 538 | 500 x 0.50001 501 7 5 4 3 4 6 5 5 5 6 | 500 | 507 482 496 521 477 = 0.72 || = 0.03 526 527 506 504 507 | 500 -----------------------------------------------------------------| 500 | 498 535 495 485 515 = 0.71 || = 0.02 500 466 527 520 530 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 499 509 497 502 493 = 0.70 || = 0.01 256 257 234 259 251 | 252.5 d 0 0 3 13 71 13 0 1 0 | 500 | 524 506 514 487 512 = 0.69 || < 0.01 534 487 513 530 516 | 497.5 s 0 0 3 10 77 10 1 0 0 | 500 | 505 499 508 532 493 = 0.68 ||========================================================================= t 0 0 0 17 73 10 1 0 0 | 500 | 501 470 489 496 495 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 14 70 13 2 0 0 | 500 | 472 509 488 487 536 = 0.66 ||========================================================================= x 0 0 4 15 67 12 3 0 0 | 500 | 477 498 473 512 545 = 0.65 || sknuth_MaxOft test: no 77 test no 78 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 78 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 1 | 0.5 | 0 1 1 0 0 > 0.99999 || = 0.64 491 542 529 462 504 | 500 < 0.00002 0 0 0 1 1 | 0.5 | 0 0 1 0 2 > 0.99998 || = 0.63 491 502 498 498 471 | 500 < 0.00003 1 2 2 0 1 | 0.5 | 0 0 2 0 1 > 0.99997 || = 0.62 451 489 496 523 506 | 500 < 0.00004 1 0 0 1 0 | 0.5 | 1 0 0 0 1 > 0.99996 || = 0.61 492 520 455 480 517 | 500 < 0.00005 0 0 1 1 1 | 0.5 | 2 1 0 0 1 > 0.99995 || = 0.60 480 493 484 495 504 | 500 < 0.00006 2 0 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99994 || = 0.59 481 464 496 474 470 | 500 < 0.00007 1 1 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99993 || = 0.58 559 495 503 498 480 | 500 < 0.00008 1 1 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 488 499 530 491 492 | 500 < 0.00009 0 0 1 0 0 | 0.5 | 0 2 0 0 0 > 0.99991 || = 0.56 489 502 507 516 478 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 517 521 506 486 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 494 513 509 535 499 | 500 < 0.0001 6 5 5 4 5 | 5 | 4 4 5 0 6 > 0.9999 || = 0.53 502 499 516 510 445 | 500 < 0.0002 5 5 3 9 7 | 5 | 3 3 2 3 3 > 0.9998 || = 0.52 470 516 511 521 531 | 500 < 0.0003 10 3 4 2 5 | 5 | 5 2 5 7 6 > 0.9997 || = 0.51 499 468 510 505 544 | 500 < 0.0004 4 4 1 3 7 | 5 | 5 4 3 5 4 > 0.9996 || = 0.50 479 535 524 532 506 | 500 < 0.0005 6 3 7 6 6 | 5 | 6 6 8 2 3 > 0.9995 || = 0.49 505 528 536 472 543 | 500 < 0.0006 5 8 3 4 3 | 5 | 8 2 6 5 8 > 0.9994 || = 0.48 523 501 482 512 530 | 500 < 0.0007 10 1 6 3 6 | 5 | 4 4 3 6 4 > 0.9993 || = 0.47 527 475 458 501 501 | 500 < 0.0008 6 5 3 9 5 | 5 | 6 5 6 7 6 > 0.9992 || = 0.46 477 511 522 480 529 | 500 < 0.0009 5 5 5 7 6 | 5 | 4 5 4 4 4 > 0.9991 || = 0.45 527 507 483 507 505 | 500 < 0.001 9 4 4 3 5 | 5 | 2 6 2 5 5 > 0.999 || = 0.44 530 511 468 482 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 504 548 455 514 487 | 500 < 0.001 66 43 41 50 55 | 50 | 47 41 44 44 49 > 0.999 || = 0.42 493 516 539 463 478 | 500 < 0.002 39 46 43 45 51 | 50 | 58 47 49 53 53 > 0.998 || = 0.41 500 518 488 500 516 | 500 < 0.003 49 48 56 52 52 | 50 | 54 58 46 44 42 > 0.997 || = 0.40 489 496 494 524 498 | 500 < 0.004 54 46 49 46 49 | 50 | 46 69 58 51 42 > 0.996 || = 0.39 493 529 511 515 535 | 500 < 0.005 48 50 61 47 42 | 50 | 41 44 63 51 55 > 0.995 || = 0.38 493 478 469 500 456 | 500 < 0.006 40 50 58 49 50 | 50 | 57 35 57 57 57 > 0.994 || = 0.37 498 492 519 510 483 | 500 < 0.007 44 54 63 64 49 | 50 | 54 61 53 54 44 > 0.993 || = 0.36 552 510 494 485 519 | 500 < 0.008 58 43 50 47 48 | 50 | 54 50 59 53 46 > 0.992 || = 0.35 495 472 460 502 552 | 500 < 0.009 50 58 56 45 49 | 50 | 57 45 45 52 62 > 0.991 || = 0.34 468 488 521 529 510 | 500 < 0.01 43 61 35 47 54 | 50 | 56 55 56 38 46 > 0.99 || = 0.33 487 465 491 472 531 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 533 491 469 536 509 | 500 < 0.01 491 499 512 492 499 | 497.5 | 524 505 530 497 496 > 0.99 || = 0.31 539 539 518 482 483 | 500 = 0.01 255 238 249 256 236 | 252.5 | 241 247 254 253 229 = 0.99 || = 0.30 502 510 541 481 492 | 500 = 0.02 474 507 496 503 522 | 500 | 522 463 501 523 504 = 0.98 || = 0.29 519 469 517 504 472 | 500 =================================================================| 500 | 508 507 527 495 507 = 0.97 || = 0.28 493 477 503 499 492 | 500 sknuth_MaxOft test: | 500 | 503 571 501 537 460 = 0.96 || = 0.27 475 469 488 515 491 | 500 ----------------------------------------------- | 500 | 490 488 494 485 533 = 0.95 || = 0.26 509 517 483 484 465 | 500 N = 40, n = 10000000, r = 0, d = 100000, t = 8 | 500 | 487 519 434 525 524 = 0.94 || = 0.25 460 495 522 530 501 | 500 Test results for Anderson-Darling: | 500 | 488 511 475 506 485 = 0.93 || = 0.24 511 512 438 507 498 | 500 Anderson-Darling statistic = A2 | 500 | 513 474 499 481 504 = 0.92 || = 0.23 535 487 497 542 478 | 500 =================================================================| 500 | 487 486 496 504 526 = 0.91 || = 0.22 516 529 515 490 455 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 459 523 523 499 506 = 0.90 || = 0.21 520 513 482 508 521 | 500 -----------------------------------------------------------------| 500 | 499 490 529 478 509 = 0.89 || = 0.20 517 510 507 507 459 | 500 SD Bern.: d 0.96995 1.13810 0.83945 | 500 | 470 507 481 497 502 = 0.88 || = 0.19 495 498 505 486 538 | 500 s 1.07453 0.81893 1.37690 | 500 | 541 496 492 473 490 = 0.87 || = 0.18 489 497 515 496 516 | 500 t 1.00507 1.25121 0.98638 | 500 | 480 463 498 488 514 = 0.86 || = 0.17 500 513 500 483 513 | 500 m 0.92931 0.76718 0.78140 | 500 | 488 506 527 520 478 = 0.85 || = 0.16 505 500 483 498 505 | 500 x 1.05451 0.48396 0.92131 | 500 | 514 517 508 514 492 = 0.84 || = 0.15 495 490 516 536 523 | 500 | 500 | 512 518 520 495 494 = 0.83 || = 0.14 477 534 550 475 504 | 500 Changes: d 45 5 3 | 500 | 538 510 500 523 538 = 0.82 || = 0.13 480 465 515 505 496 | 500 s 54 3 5 | 500 | 462 477 461 496 463 = 0.81 || = 0.12 527 498 489 493 489 | 500 t 44 6 3 | 500 | 482 499 486 487 495 = 0.80 || = 0.11 457 464 494 517 535 | 500 m 59 4 4 | 500 | 505 508 521 508 486 = 0.79 || = 0.10 506 509 536 498 536 | 500 x 43 2 6 | 500 | 490 473 512 516 479 = 0.78 || = 0.09 508 555 515 539 484 | 500 -----------------------------------------------------------------| 500 | 514 513 483 483 519 = 0.77 || = 0.08 487 545 464 550 467 | 500 Aver./ d 0.49990 499 > 500: 5 3 7 4 6 3 4 6 4 5 | 500 | 510 485 489 467 467 = 0.76 || = 0.07 520 467 471 458 491 | 500 median s 0.49982 501 ----- 7 3 5 4 8 4 4 4 6 5 | 500 | 479 461 491 496 492 = 0.75 || = 0.06 548 515 500 513 508 | 500 t 0.49977 500 5 6 5 5 3 8 3 4 5 5 | 500 | 521 493 473 438 509 = 0.74 || = 0.05 505 527 502 490 559 | 500 m 0.49878 499 6 3 7 5 5 5 5 2 3 6 | 500 | 514 492 511 487 503 = 0.73 || = 0.04 477 506 501 457 525 | 500 x 0.49865 501 5 8 2 6 7 3 6 3 5 6 | 500 | 527 503 497 479 496 = 0.72 || = 0.03 468 416 510 537 479 | 500 -----------------------------------------------------------------| 500 | 480 502 502 471 482 = 0.71 || = 0.02 474 507 496 503 522 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 483 472 496 509 507 = 0.70 || = 0.01 255 238 249 256 236 | 252.5 d 0 0 1 13 72 12 3 0 0 | 500 | 514 463 516 502 473 = 0.69 || < 0.01 491 499 512 492 499 | 497.5 s 0 1 0 20 66 10 3 1 0 | 500 | 513 532 481 511 498 = 0.68 ||========================================================================= t 0 0 4 10 73 12 2 0 0 | 500 | 501 496 545 496 509 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 11 73 15 1 0 0 | 500 | 507 476 485 506 452 = 0.66 ||========================================================================= x 0 0 3 13 67 16 2 0 0 | 500 | 497 490 495 494 506 = 0.65 || sknuth_MaxOft test: no 78 test no 79 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 79 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 0 | 0.5 | 1 1 1 0 0 > 0.99999 || = 0.64 492 509 530 486 482 | 500 < 0.00002 0 1 1 1 0 | 0.5 | 0 1 0 1 1 > 0.99998 || = 0.63 492 529 437 513 454 | 500 < 0.00003 1 2 0 1 0 | 0.5 | 1 3 1 0 0 > 0.99997 || = 0.62 508 513 470 499 546 | 500 < 0.00004 1 0 0 1 2 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 487 517 482 513 503 | 500 < 0.00005 0 0 1 0 0 | 0.5 | 1 0 2 0 0 > 0.99995 || = 0.60 496 460 491 503 495 | 500 < 0.00006 0 2 0 1 1 | 0.5 | 0 0 0 1 1 > 0.99994 || = 0.59 500 475 513 482 551 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 488 497 513 496 493 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 1 1 0 1 > 0.99992 || = 0.57 472 500 544 517 534 | 500 < 0.00009 0 1 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99991 || = 0.56 545 488 512 518 494 | 500 < 0.0001 2 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 517 503 510 509 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 531 506 510 503 453 | 500 < 0.0001 4 6 2 6 3 | 5 | 4 7 7 2 3 > 0.9999 || = 0.53 464 498 529 553 515 | 500 < 0.0002 4 4 1 2 3 | 5 | 2 2 1 3 2 > 0.9998 || = 0.52 538 498 534 517 511 | 500 < 0.0003 3 10 4 5 8 | 5 | 6 3 4 3 5 > 0.9997 || = 0.51 509 482 504 524 478 | 500 < 0.0004 5 6 5 3 7 | 5 | 4 8 4 3 5 > 0.9996 || = 0.50 516 534 537 494 563 | 500 < 0.0005 7 5 3 1 6 | 5 | 5 5 5 8 6 > 0.9995 || = 0.49 498 501 487 514 502 | 500 < 0.0006 6 4 8 7 4 | 5 | 5 4 3 8 8 > 0.9994 || = 0.48 508 489 491 494 433 | 500 < 0.0007 5 7 5 8 8 | 5 | 7 4 8 7 7 > 0.9993 || = 0.47 532 486 470 522 467 | 500 < 0.0008 3 3 5 6 1 | 5 | 6 4 3 4 4 > 0.9992 || = 0.46 541 484 473 458 518 | 500 < 0.0009 4 3 4 3 1 | 5 | 8 4 8 5 5 > 0.9991 || = 0.45 495 484 484 531 479 | 500 < 0.001 8 8 3 3 4 | 5 | 5 2 7 6 3 > 0.999 || = 0.44 505 541 490 517 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 537 495 550 512 500 | 500 < 0.001 49 56 40 44 45 | 50 | 52 43 50 49 48 > 0.999 || = 0.42 496 473 533 517 501 | 500 < 0.002 40 34 47 53 51 | 50 | 46 61 47 47 50 > 0.998 || = 0.41 494 480 519 484 435 | 500 < 0.003 41 53 59 52 38 | 50 | 47 40 42 38 41 > 0.997 || = 0.40 545 478 488 472 528 | 500 < 0.004 41 50 42 56 60 | 50 | 38 42 52 38 62 > 0.996 || = 0.39 481 543 477 476 490 | 500 < 0.005 49 51 52 39 49 | 50 | 46 57 55 59 52 > 0.995 || = 0.38 524 546 502 482 524 | 500 < 0.006 61 44 44 55 47 | 50 | 37 59 57 50 52 > 0.994 || = 0.37 528 474 496 496 551 | 500 < 0.007 48 55 50 59 41 | 50 | 58 51 68 50 54 > 0.993 || = 0.36 491 498 485 495 556 | 500 < 0.008 61 42 50 49 45 | 50 | 59 51 40 48 45 > 0.992 || = 0.35 520 471 502 538 506 | 500 < 0.009 54 47 40 52 45 | 50 | 51 48 57 45 38 > 0.991 || = 0.34 501 488 505 491 567 | 500 < 0.01 48 48 38 47 53 | 50 | 51 55 64 51 50 > 0.99 || = 0.33 472 470 504 524 469 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 493 492 510 476 469 | 500 < 0.01 492 480 462 506 474 | 497.5 | 485 507 532 475 492 > 0.99 || = 0.31 520 547 503 503 464 | 500 = 0.01 240 266 271 239 238 | 252.5 | 259 259 246 229 243 = 0.99 || = 0.30 508 506 525 481 516 | 500 = 0.02 499 516 515 464 501 | 500 | 449 505 451 505 509 = 0.98 || = 0.29 527 495 492 512 581 | 500 =================================================================| 500 | 517 525 500 510 485 = 0.97 || = 0.28 499 535 465 484 527 | 500 sknuth_MaxOft test: | 500 | 498 496 473 514 503 = 0.96 || = 0.27 496 495 497 493 490 | 500 ----------------------------------------------- | 500 | 487 500 491 489 509 = 0.95 || = 0.26 475 537 526 444 476 | 500 N = 30, n = 10000000, r = 0, d = 100000, t = 16 | 500 | 469 532 498 522 491 = 0.94 || = 0.25 493 483 519 490 496 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 486 511 488 466 466 = 0.93 || = 0.24 512 497 493 506 503 | 500 | 500 | 464 524 493 543 463 = 0.92 || = 0.23 453 474 540 495 506 | 500 =================================================================| 500 | 500 488 527 513 531 = 0.91 || = 0.22 501 492 506 513 522 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 545 494 430 510 497 = 0.90 || = 0.21 521 491 485 486 458 | 500 -----------------------------------------------------------------| 500 | 468 490 469 509 531 = 0.89 || = 0.20 482 509 476 460 498 | 500 SD Bern.: d 1.00511 1.03007 1.00547 | 500 | 478 535 500 487 487 = 0.88 || = 0.19 523 495 530 450 536 | 500 s 0.91021 0.93854 0.99547 | 500 | 503 459 526 504 506 = 0.87 || = 0.18 502 493 488 512 531 | 500 t 1.07499 1.03781 1.28125 | 500 | 471 479 510 515 479 = 0.86 || = 0.17 510 517 535 492 475 | 500 m 0.99504 0.80786 0.90487 | 500 | 462 519 506 532 517 = 0.85 || = 0.16 472 479 541 486 494 | 500 x 1.20687 0.91696 0.91914 | 500 | 509 485 458 486 514 = 0.84 || = 0.15 519 496 482 499 480 | 500 | 500 | 486 474 514 482 485 = 0.83 || = 0.14 491 503 515 545 475 | 500 Changes: d 52 4 2 | 500 | 517 485 507 513 537 = 0.82 || = 0.13 502 495 477 523 486 | 500 s 47 7 5 | 500 | 544 522 505 535 505 = 0.81 || = 0.12 529 481 480 538 487 | 500 t 41 4 3 | 500 | 501 503 519 453 490 = 0.80 || = 0.11 517 496 483 481 512 | 500 m 53 6 3 | 500 | 451 495 472 513 490 = 0.79 || = 0.10 488 512 512 518 504 | 500 x 54 5 2 | 500 | 508 510 535 541 519 = 0.78 || = 0.09 480 491 488 495 546 | 500 -----------------------------------------------------------------| 500 | 469 490 520 464 488 = 0.77 || = 0.08 465 511 515 487 496 | 500 Aver./ d 0.49890 500 > 500: 1 7 4 6 6 5 6 5 5 2 | 500 | 514 517 501 501 483 = 0.76 || = 0.07 500 456 525 503 508 | 500 median s 0.50095 497 ----- 6 3 3 4 2 2 8 4 3 7 | 500 | 484 522 453 523 527 = 0.75 || = 0.06 475 534 532 524 507 | 500 t 0.49777 502 7 5 4 7 3 9 3 5 6 2 | 500 | 514 497 513 515 511 = 0.74 || = 0.05 526 514 480 477 485 | 500 m 0.50140 501 3 5 3 3 6 8 4 6 7 6 | 500 | 532 495 476 494 478 = 0.73 || = 0.04 482 502 502 497 503 | 500 x 0.49934 496 5 4 5 6 5 4 4 3 6 4 | 500 | 469 474 489 504 474 = 0.72 || = 0.03 490 475 511 493 491 | 500 -----------------------------------------------------------------| 500 | 486 493 485 486 483 = 0.71 || = 0.02 499 516 515 464 501 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 504 505 504 527 476 = 0.70 || = 0.01 240 266 271 239 238 | 252.5 d 0 0 3 14 67 14 3 0 0 | 500 | 499 495 479 468 492 = 0.69 || < 0.01 492 480 462 506 474 | 497.5 s 0 0 0 13 74 12 2 0 0 | 500 | 513 514 496 491 486 = 0.68 ||========================================================================= t 0 1 3 14 63 19 1 0 0 | 500 | 513 539 519 507 511 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 69 13 2 0 0 | 500 | 530 470 464 477 506 = 0.66 ||========================================================================= x 0 1 3 13 65 11 6 2 0 | 500 | 511 517 498 475 482 = 0.65 || sknuth_MaxOft test: no 79 test no 80 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 80 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 1 1 1 | 0.5 | 1 2 1 1 0 > 0.99999 || = 0.64 487 482 536 495 490 | 500 < 0.00002 1 1 1 1 0 | 0.5 | 1 0 1 0 1 > 0.99998 || = 0.63 500 472 472 536 561 | 500 < 0.00003 0 0 1 0 1 | 0.5 | 0 1 1 0 0 > 0.99997 || = 0.62 460 544 478 465 518 | 500 < 0.00004 0 1 2 0 0 | 0.5 | 0 0 1 1 2 > 0.99996 || = 0.61 495 529 501 495 480 | 500 < 0.00005 1 0 2 2 1 | 0.5 | 0 1 2 1 1 > 0.99995 || = 0.60 508 495 513 478 532 | 500 < 0.00006 0 1 0 2 1 | 0.5 | 0 2 0 0 1 > 0.99994 || = 0.59 498 491 480 495 487 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 1 0 1 1 2 > 0.99993 || = 0.58 483 526 504 480 495 | 500 < 0.00008 0 0 1 0 1 | 0.5 | 2 0 0 0 0 > 0.99992 || = 0.57 536 532 477 514 503 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99991 || = 0.56 513 482 552 531 478 | 500 < 0.0001 0 1 0 0 1 | 0.5 | 0 1 2 1 0 > 0.9999 || = 0.55 496 487 490 509 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 473 479 498 474 476 | 500 < 0.0001 4 4 8 7 6 | 5 | 5 7 10 5 8 > 0.9999 || = 0.53 487 527 501 500 523 | 500 < 0.0002 5 5 10 4 4 | 5 | 4 3 3 3 1 > 0.9998 || = 0.52 486 505 480 542 515 | 500 < 0.0003 5 5 6 7 3 | 5 | 7 2 9 2 7 > 0.9997 || = 0.51 470 487 462 548 471 | 500 < 0.0004 5 9 8 3 5 | 5 | 6 4 7 4 3 > 0.9996 || = 0.50 497 487 520 507 500 | 500 < 0.0005 8 5 8 5 10 | 5 | 5 7 2 2 3 > 0.9995 || = 0.49 501 513 449 493 510 | 500 < 0.0006 5 3 6 4 4 | 5 | 5 7 4 4 2 > 0.9994 || = 0.48 492 471 492 518 492 | 500 < 0.0007 4 3 7 3 4 | 5 | 6 3 6 5 1 > 0.9993 || = 0.47 490 479 526 521 502 | 500 < 0.0008 5 6 2 3 6 | 5 | 7 7 7 1 7 > 0.9992 || = 0.46 529 490 507 484 498 | 500 < 0.0009 9 5 4 7 3 | 5 | 7 5 8 4 5 > 0.9991 || = 0.45 506 542 505 511 525 | 500 < 0.001 9 4 5 5 6 | 5 | 5 4 4 6 9 > 0.999 || = 0.44 505 516 503 466 511 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 517 515 495 486 468 | 500 < 0.001 59 49 64 48 51 | 50 | 57 49 60 36 46 > 0.999 || = 0.42 471 498 520 503 513 | 500 < 0.002 43 61 43 31 44 | 50 | 42 50 37 43 44 > 0.998 || = 0.41 494 479 465 501 516 | 500 < 0.003 49 52 60 70 70 | 50 | 46 50 40 53 70 > 0.997 || = 0.40 511 477 476 519 470 | 500 < 0.004 53 41 49 47 58 | 50 | 65 56 48 61 57 > 0.996 || = 0.39 496 522 525 511 529 | 500 < 0.005 60 42 39 46 49 | 50 | 37 51 53 53 48 > 0.995 || = 0.38 495 483 557 505 525 | 500 < 0.006 38 57 53 33 53 | 50 | 43 47 45 55 53 > 0.994 || = 0.37 477 479 514 515 515 | 500 < 0.007 58 52 47 50 63 | 50 | 44 55 60 59 50 > 0.993 || = 0.36 492 537 493 479 516 | 500 < 0.008 50 48 50 50 48 | 50 | 52 48 59 45 52 > 0.992 || = 0.35 508 497 488 542 444 | 500 < 0.009 35 53 59 39 34 | 50 | 55 47 37 53 50 > 0.991 || = 0.34 484 508 499 496 528 | 500 < 0.01 36 62 34 61 54 | 50 | 58 40 42 41 46 > 0.99 || = 0.33 495 469 502 505 473 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 512 484 529 533 509 | 500 < 0.01 481 517 498 475 524 | 497.5 | 499 493 481 499 516 > 0.99 || = 0.31 506 482 503 522 511 | 500 = 0.01 232 247 247 242 262 | 252.5 | 250 203 275 220 264 = 0.99 || = 0.30 504 481 489 507 504 | 500 = 0.02 505 500 533 500 487 | 500 | 475 527 475 513 496 = 0.98 || = 0.29 518 489 512 509 522 | 500 =================================================================| 500 | 517 516 512 482 515 = 0.97 || = 0.28 492 529 504 517 510 | 500 sknuth_MaxOft test: | 500 | 507 488 549 488 490 = 0.96 || = 0.27 516 481 498 536 490 | 500 ----------------------------------------------- | 500 | 512 498 463 494 559 = 0.95 || = 0.26 471 482 492 502 519 | 500 N = 30, n = 10000000, r = 0, d = 100000, t = 16 | 500 | 490 538 483 485 482 = 0.94 || = 0.25 513 480 502 489 465 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 473 468 526 474 487 = 0.93 || = 0.24 546 484 509 516 481 | 500 | 500 | 508 491 457 545 543 = 0.92 || = 0.23 509 496 474 490 511 | 500 =================================================================| 500 | 480 500 532 496 487 = 0.91 || = 0.22 511 501 518 513 507 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 520 495 474 493 482 = 0.90 || = 0.21 512 498 510 495 483 | 500 -----------------------------------------------------------------| 500 | 483 518 541 500 483 = 0.89 || = 0.20 455 490 535 477 498 | 500 SD Bern.: d 0.94650 1.31898 1.18464 | 500 | 499 507 507 480 500 = 0.88 || = 0.19 507 511 513 504 497 | 500 s 0.90597 0.98130 0.60857 | 500 | 510 463 484 484 507 = 0.87 || = 0.18 509 493 529 489 476 | 500 t 1.02278 1.28282 1.28203 | 500 | 514 498 500 524 508 = 0.86 || = 0.17 475 481 469 539 543 | 500 m 0.96045 1.62623 1.10054 | 500 | 489 498 495 452 534 = 0.85 || = 0.16 552 468 526 538 488 | 500 x 1.09194 1.38343 1.03395 | 500 | 482 487 505 483 501 = 0.84 || = 0.15 518 515 511 496 535 | 500 | 500 | 509 538 483 469 478 = 0.83 || = 0.14 495 520 486 494 484 | 500 Changes: d 53 5 4 | 500 | 506 511 544 497 450 = 0.82 || = 0.13 481 512 492 476 483 | 500 s 45 5 4 | 500 | 513 489 519 516 462 = 0.81 || = 0.12 541 493 503 461 472 | 500 t 57 7 5 | 500 | 524 514 466 513 485 = 0.80 || = 0.11 458 493 484 514 492 | 500 m 47 3 4 | 500 | 492 530 511 473 489 = 0.79 || = 0.10 487 501 492 485 518 | 500 x 56 6 6 | 500 | 535 478 505 488 491 = 0.78 || = 0.09 547 491 517 491 480 | 500 -----------------------------------------------------------------| 500 | 473 500 500 465 516 = 0.77 || = 0.08 486 532 451 544 489 | 500 Aver./ d 0.50036 500 > 500: 4 5 7 4 6 3 4 6 6 5 | 500 | 515 501 481 516 511 = 0.76 || = 0.07 524 528 489 530 465 | 500 median s 0.50058 498 ----- 3 5 2 3 4 4 7 5 4 3 | 500 | 486 488 522 477 453 = 0.75 || = 0.06 473 500 482 511 516 | 500 t 0.49947 500 5 5 7 6 5 4 3 4 5 5 | 500 | 545 529 497 464 549 = 0.74 || = 0.05 510 491 529 497 445 | 500 m 0.49707 500 4 4 6 8 6 5 4 4 2 3 | 500 | 510 498 488 504 511 = 0.73 || = 0.04 495 496 521 527 498 | 500 x 0.50103 500 4 3 5 8 6 5 4 5 4 5 | 500 | 503 491 488 489 492 = 0.72 || = 0.03 461 498 473 500 513 | 500 -----------------------------------------------------------------| 500 | 489 522 508 507 535 = 0.71 || = 0.02 505 500 533 500 487 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 515 522 496 509 505 = 0.70 || = 0.01 232 247 247 242 262 | 252.5 d 0 0 1 16 72 8 4 0 0 | 500 | 456 502 489 506 471 = 0.69 || < 0.01 481 517 498 475 524 | 497.5 s 0 1 0 7 77 16 0 0 0 | 500 | 528 527 476 483 554 = 0.68 ||========================================================================= t 0 0 2 15 67 14 3 0 0 | 500 | 544 506 493 482 493 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 13 72 12 2 0 0 | 500 | 519 510 457 482 486 = 0.66 ||========================================================================= x 0 0 4 12 69 12 4 0 0 | 500 | 476 492 518 505 457 = 0.65 || sknuth_MaxOft test: no 80 test no 81 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 81 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 1 1 0 1 | 0.5 | 0 0 0 1 1 > 0.99999 || = 0.64 541 529 490 497 518 | 500 < 0.00002 1 0 0 0 0 | 0.5 | 1 1 0 0 0 > 0.99998 || = 0.63 534 489 522 518 467 | 500 < 0.00003 0 2 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 490 501 458 509 501 | 500 < 0.00004 0 2 0 2 0 | 0.5 | 0 1 0 0 2 > 0.99996 || = 0.61 518 532 536 520 506 | 500 < 0.00005 0 0 1 1 0 | 0.5 | 0 0 3 0 0 > 0.99995 || = 0.60 511 507 485 496 493 | 500 < 0.00006 0 1 0 0 1 | 0.5 | 0 2 0 0 0 > 0.99994 || = 0.59 498 486 484 477 529 | 500 < 0.00007 1 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 496 513 468 503 517 | 500 < 0.00008 1 0 2 0 0 | 0.5 | 1 0 0 0 1 > 0.99992 || = 0.57 520 467 505 534 517 | 500 < 0.00009 0 2 2 0 0 | 0.5 | 0 1 2 1 0 > 0.99991 || = 0.56 475 494 473 491 470 | 500 < 0.0001 0 0 1 1 0 | 0.5 | 0 2 0 2 1 > 0.9999 || = 0.55 497 498 534 463 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 503 489 564 491 520 | 500 < 0.0001 5 8 9 4 3 | 5 | 2 7 5 4 5 > 0.9999 || = 0.53 472 493 530 511 513 | 500 < 0.0002 6 7 6 6 2 | 5 | 2 0 1 2 1 > 0.9998 || = 0.52 493 504 522 489 473 | 500 < 0.0003 5 5 7 6 2 | 5 | 8 5 3 7 4 > 0.9997 || = 0.51 537 490 521 516 512 | 500 < 0.0004 6 4 2 5 7 | 5 | 3 5 5 5 4 > 0.9996 || = 0.50 504 474 500 533 475 | 500 < 0.0005 4 3 7 9 1 | 5 | 4 2 6 1 5 > 0.9995 || = 0.49 510 542 514 520 483 | 500 < 0.0006 2 7 9 3 6 | 5 | 5 5 7 4 7 > 0.9994 || = 0.48 493 460 507 503 559 | 500 < 0.0007 7 7 6 3 6 | 5 | 2 5 7 4 5 > 0.9993 || = 0.47 524 473 542 514 487 | 500 < 0.0008 4 8 2 1 4 | 5 | 8 5 6 3 1 > 0.9992 || = 0.46 550 518 489 470 507 | 500 < 0.0009 3 8 4 1 3 | 5 | 2 5 3 4 4 > 0.9991 || = 0.45 526 454 475 477 496 | 500 < 0.001 6 9 5 6 3 | 5 | 2 2 4 6 6 > 0.999 || = 0.44 506 506 483 484 519 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 519 524 511 542 490 | 500 < 0.001 48 66 57 44 37 | 50 | 38 41 47 40 42 > 0.999 || = 0.42 516 490 503 556 487 | 500 < 0.002 41 50 59 59 63 | 50 | 54 55 54 48 43 > 0.998 || = 0.41 459 473 550 482 469 | 500 < 0.003 41 47 61 40 53 | 50 | 41 54 50 44 51 > 0.997 || = 0.40 472 487 480 525 517 | 500 < 0.004 50 49 48 47 54 | 50 | 52 57 44 52 49 > 0.996 || = 0.39 517 475 519 518 492 | 500 < 0.005 50 46 47 52 41 | 50 | 59 52 52 66 58 > 0.995 || = 0.38 516 499 484 472 521 | 500 < 0.006 53 57 43 51 51 | 50 | 43 48 44 55 44 > 0.994 || = 0.37 540 543 519 509 507 | 500 < 0.007 54 62 55 50 57 | 50 | 52 52 52 47 50 > 0.993 || = 0.36 464 491 550 497 541 | 500 < 0.008 45 41 51 52 51 | 50 | 62 50 41 46 42 > 0.992 || = 0.35 473 507 487 501 538 | 500 < 0.009 44 37 58 48 43 | 50 | 53 40 58 56 50 > 0.991 || = 0.34 504 462 514 496 508 | 500 < 0.01 60 49 53 50 57 | 50 | 61 64 55 47 59 > 0.99 || = 0.33 502 490 479 537 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 495 516 521 524 505 | 500 < 0.01 486 504 532 493 507 | 497.5 | 515 513 497 501 488 > 0.99 || = 0.31 524 513 477 533 516 | 500 = 0.01 245 253 218 229 253 | 252.5 | 225 255 234 257 250 = 0.99 || = 0.30 532 509 499 485 505 | 500 = 0.02 480 515 472 482 533 | 500 | 485 516 498 507 531 = 0.98 || = 0.29 475 509 500 501 537 | 500 =================================================================| 500 | 497 524 465 463 495 = 0.97 || = 0.28 474 491 528 481 473 | 500 sknuth_MaxOft test: | 500 | 508 483 471 538 506 = 0.96 || = 0.27 500 451 489 515 514 | 500 ----------------------------------------------- | 500 | 488 535 467 493 510 = 0.95 || = 0.26 479 502 458 477 488 | 500 N = 30, n = 10000000, r = 0, d = 100000, t = 16 | 500 | 479 458 458 506 461 = 0.94 || = 0.25 523 493 497 521 463 | 500 Anderson-Darling statistic = A2 | 500 | 554 485 482 538 500 = 0.93 || = 0.24 511 513 509 520 515 | 500 | 500 | 528 490 489 460 489 = 0.92 || = 0.23 478 445 516 497 469 | 500 =================================================================| 500 | 478 527 491 494 490 = 0.91 || = 0.22 495 493 526 489 481 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 501 467 482 481 482 = 0.90 || = 0.21 514 494 488 505 516 | 500 -----------------------------------------------------------------| 500 | 486 537 516 506 522 = 0.89 || = 0.20 485 459 506 501 478 | 500 SD Bern.: d 0.97440 0.83946 1.14336 | 500 | 537 474 479 531 524 = 0.88 || = 0.19 497 541 495 485 500 | 500 s 1.00014 1.20558 0.97925 | 500 | 505 494 489 477 517 = 0.87 || = 0.18 512 532 496 496 453 | 500 t 1.06126 0.90819 0.74197 | 500 | 490 476 473 533 486 = 0.86 || = 0.17 490 502 459 447 483 | 500 m 1.00310 0.69171 0.99547 | 500 | 498 474 481 465 515 = 0.85 || = 0.16 537 504 510 490 468 | 500 x 0.97910 1.08957 0.84894 | 500 | 489 524 513 483 501 = 0.84 || = 0.15 491 489 527 524 482 | 500 | 500 | 499 512 507 540 454 = 0.83 || = 0.14 492 528 504 471 477 | 500 Changes: d 51 3 5 | 500 | 489 518 498 484 489 = 0.82 || = 0.13 506 518 463 497 504 | 500 s 50 3 5 | 500 | 515 530 523 480 489 = 0.81 || = 0.12 495 490 525 477 470 | 500 t 49 2 7 | 500 | 508 545 544 481 486 = 0.80 || = 0.11 480 489 517 499 514 | 500 m 55 6 4 | 500 | 484 484 484 506 551 = 0.79 || = 0.10 483 497 495 541 515 | 500 x 53 5 5 | 500 | 538 515 482 501 497 = 0.78 || = 0.09 485 502 522 495 501 | 500 -----------------------------------------------------------------| 500 | 506 479 502 504 490 = 0.77 || = 0.08 478 498 487 516 513 | 500 Aver./ d 0.50206 498 > 500: 2 3 3 7 7 4 5 6 4 4 | 500 | 488 481 492 467 476 = 0.76 || = 0.07 517 482 519 513 491 | 500 median s 0.50073 501 ----- 7 6 3 5 4 3 7 6 5 6 | 500 | 507 501 470 469 472 = 0.75 || = 0.06 460 488 509 480 539 | 500 t 0.49817 498 4 5 5 5 6 6 5 4 4 0 | 500 | 505 470 500 532 522 = 0.74 || = 0.05 443 529 490 492 529 | 500 m 0.50039 497 3 2 6 6 6 4 6 5 4 6 | 500 | 496 504 492 456 488 = 0.73 || = 0.04 523 502 492 474 465 | 500 x 0.49990 501 8 3 4 8 4 6 7 4 5 3 | 500 | 508 525 510 481 511 = 0.72 || = 0.03 475 506 480 509 507 | 500 -----------------------------------------------------------------| 500 | 477 508 538 518 512 = 0.71 || = 0.02 480 515 472 482 533 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 508 491 495 497 468 = 0.70 || = 0.01 245 253 218 229 253 | 252.5 d 0 0 1 13 70 15 2 0 0 | 500 | 529 516 534 510 526 = 0.69 || < 0.01 486 504 532 493 507 | 497.5 s 0 0 3 14 65 18 1 0 0 | 500 | 498 495 487 526 502 = 0.68 ||========================================================================= t 0 0 1 16 67 14 3 0 0 | 500 | 500 539 486 492 527 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 17 66 16 1 0 0 | 500 | 460 523 509 497 492 = 0.66 ||========================================================================= x 0 0 2 16 70 11 2 0 0 | 500 | 482 515 538 516 501 = 0.65 || sknuth_MaxOft test: no 81 test no 82 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 82 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 2 2 0 1 | 0.5 | 0 0 1 1 1 > 0.99999 || = 0.64 516 512 505 483 487 | 500 < 0.00002 0 2 0 0 1 | 0.5 | 0 1 0 2 0 > 0.99998 || = 0.63 541 483 523 479 432 | 500 < 0.00003 0 0 1 0 0 | 0.5 | 0 1 2 1 0 > 0.99997 || = 0.62 459 492 495 498 540 | 500 < 0.00004 0 1 0 0 1 | 0.5 | 1 1 1 1 0 > 0.99996 || = 0.61 505 516 464 496 535 | 500 < 0.00005 1 0 2 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 510 483 499 513 491 | 500 < 0.00006 0 2 2 0 0 | 0.5 | 1 2 0 0 0 > 0.99994 || = 0.59 495 504 490 523 510 | 500 < 0.00007 0 1 2 2 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 524 506 457 494 520 | 500 < 0.00008 0 1 2 0 1 | 0.5 | 1 0 0 1 1 > 0.99992 || = 0.57 523 509 489 493 499 | 500 < 0.00009 2 1 1 0 0 | 0.5 | 1 0 1 0 1 > 0.99991 || = 0.56 496 469 479 501 501 | 500 < 0.0001 0 0 1 0 0 | 0.5 | 2 0 0 0 1 > 0.9999 || = 0.55 514 476 476 469 467 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 490 532 534 495 496 | 500 < 0.0001 5 10 13 2 4 | 5 | 6 5 5 7 4 > 0.9999 || = 0.53 536 487 501 527 514 | 500 < 0.0002 9 9 10 4 5 | 5 | 3 4 2 2 4 > 0.9998 || = 0.52 503 459 485 516 532 | 500 < 0.0003 5 4 5 5 2 | 5 | 3 4 5 4 5 > 0.9997 || = 0.51 481 534 501 476 538 | 500 < 0.0004 4 6 3 6 4 | 5 | 4 5 4 1 0 > 0.9996 || = 0.50 459 473 464 454 519 | 500 < 0.0005 2 6 5 5 3 | 5 | 3 8 8 4 8 > 0.9995 || = 0.49 503 480 502 489 527 | 500 < 0.0006 3 2 5 7 5 | 5 | 5 4 3 0 5 > 0.9994 || = 0.48 471 495 522 526 498 | 500 < 0.0007 4 8 4 8 6 | 5 | 3 4 4 4 5 > 0.9993 || = 0.47 487 508 490 489 498 | 500 < 0.0008 5 7 6 6 7 | 5 | 5 2 6 7 1 > 0.9992 || = 0.46 478 497 500 512 484 | 500 < 0.0009 3 6 7 6 8 | 5 | 5 4 5 3 6 > 0.9991 || = 0.45 483 494 496 508 506 | 500 < 0.001 6 4 8 7 4 | 5 | 7 7 5 4 5 > 0.999 || = 0.44 495 509 469 482 502 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 538 508 525 469 484 | 500 < 0.001 46 62 66 56 48 | 50 | 44 47 47 36 43 > 0.999 || = 0.42 513 472 505 506 482 | 500 < 0.002 51 49 52 50 62 | 50 | 47 49 51 53 41 > 0.998 || = 0.41 488 511 459 474 517 | 500 < 0.003 54 53 42 43 51 | 50 | 57 55 49 41 54 > 0.997 || = 0.40 526 512 503 511 492 | 500 < 0.004 43 51 46 51 47 | 50 | 40 53 44 62 46 > 0.996 || = 0.39 532 510 523 537 457 | 500 < 0.005 53 41 56 38 52 | 50 | 37 45 47 40 44 > 0.995 || = 0.38 498 529 499 501 512 | 500 < 0.006 48 56 54 51 53 | 50 | 49 51 42 47 69 > 0.994 || = 0.37 524 491 514 534 489 | 500 < 0.007 37 43 43 62 58 | 50 | 57 44 50 45 50 > 0.993 || = 0.36 541 490 501 553 494 | 500 < 0.008 52 46 40 49 46 | 50 | 51 46 42 56 44 > 0.992 || = 0.35 501 506 536 495 507 | 500 < 0.009 44 50 54 48 35 | 50 | 51 39 43 57 63 > 0.991 || = 0.34 461 500 505 523 485 | 500 < 0.01 57 37 46 48 46 | 50 | 56 49 57 47 53 > 0.99 || = 0.33 509 494 526 507 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 532 511 475 534 496 | 500 < 0.01 485 488 499 496 498 | 497.5 | 489 478 472 484 507 > 0.99 || = 0.31 452 500 498 481 447 | 500 = 0.01 255 265 229 223 283 | 252.5 | 213 281 259 253 252 = 0.99 || = 0.30 547 510 522 501 469 | 500 = 0.02 459 512 524 477 509 | 500 | 455 518 511 500 528 = 0.98 || = 0.29 498 519 510 454 521 | 500 =================================================================| 500 | 517 519 489 473 478 = 0.97 || = 0.28 478 505 564 514 500 | 500 sknuth_MaxOft test: | 500 | 495 471 472 484 491 = 0.96 || = 0.27 494 506 523 531 482 | 500 ----------------------------------------------- | 500 | 526 510 515 493 511 = 0.95 || = 0.26 531 501 471 502 525 | 500 N = 30, n = 10000000, r = 0, d = 100000, t = 16 | 500 | 527 463 512 491 488 = 0.94 || = 0.25 495 490 499 509 513 | 500 Test on the sum of all N observations | 500 | 494 481 524 495 503 = 0.93 || = 0.24 473 487 490 486 516 | 500 | 500 | 463 487 523 503 529 = 0.92 || = 0.23 490 479 473 521 534 | 500 =================================================================| 500 | 509 505 481 490 497 = 0.91 || = 0.22 513 535 508 484 550 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 498 503 501 520 521 = 0.90 || = 0.21 474 505 476 485 488 | 500 -----------------------------------------------------------------| 500 | 523 494 510 473 540 = 0.89 || = 0.20 512 509 508 522 477 | 500 SD Bern.: d 1.06470 0.84065 0.95020 | 500 | 529 496 496 501 477 = 0.88 || = 0.19 512 481 469 516 464 | 500 s 0.79611 1.00648 0.69890 | 500 | 521 528 525 494 489 = 0.87 || = 0.18 544 484 516 475 500 | 500 t 0.97822 1.07104 0.75136 | 500 | 494 508 456 493 519 = 0.86 || = 0.17 526 512 501 545 511 | 500 m 1.01182 0.87678 1.14773 | 500 | 466 482 532 503 498 = 0.85 || = 0.16 484 525 500 518 517 | 500 x 1.04783 0.99246 1.24399 | 500 | 450 514 494 495 516 = 0.84 || = 0.15 502 502 463 473 542 | 500 | 500 | 498 504 497 502 494 = 0.83 || = 0.14 458 496 521 516 477 | 500 Changes: d 48 7 3 | 500 | 496 509 506 495 502 = 0.82 || = 0.13 491 462 510 503 478 | 500 s 52 5 4 | 500 | 500 485 514 493 473 = 0.81 || = 0.12 491 484 521 508 469 | 500 t 49 5 3 | 500 | 488 490 499 495 511 = 0.80 || = 0.11 506 514 479 518 474 | 500 m 52 5 6 | 500 | 514 509 525 478 486 = 0.79 || = 0.10 474 506 515 493 490 | 500 x 51 4 5 | 500 | 536 495 526 496 505 = 0.78 || = 0.09 496 467 502 521 482 | 500 -----------------------------------------------------------------| 500 | 505 488 507 499 517 = 0.77 || = 0.08 488 514 490 564 524 | 500 Aver./ d 0.50141 498 > 500: 1 5 3 7 4 6 8 5 3 4 | 500 | 554 494 505 478 479 = 0.76 || = 0.07 488 490 499 466 461 | 500 median s 0.49949 503 ----- 6 5 7 5 5 5 6 3 6 5 | 500 | 495 481 460 491 472 = 0.75 || = 0.06 471 530 479 541 481 | 500 t 0.50082 501 4 6 5 7 5 3 4 6 6 6 | 500 | 497 506 564 546 527 = 0.74 || = 0.05 498 494 500 456 482 | 500 m 0.49810 498 4 7 6 8 5 5 3 3 4 2 | 500 | 490 551 503 507 471 = 0.73 || = 0.04 486 514 466 527 480 | 500 x 0.50109 498 5 3 6 2 4 6 4 5 5 5 | 500 | 532 488 498 497 490 = 0.72 || = 0.03 489 505 501 475 545 | 500 -----------------------------------------------------------------| 500 | 488 481 488 527 501 = 0.71 || = 0.02 459 512 524 477 509 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 515 508 543 516 494 = 0.70 || = 0.01 255 265 229 223 283 | 252.5 d 0 0 4 12 63 20 2 0 0 | 500 | 502 488 483 525 497 = 0.69 || < 0.01 485 488 499 496 498 | 497.5 s 0 0 0 9 83 8 1 0 0 | 500 | 483 515 511 458 474 = 0.68 ||========================================================================= t 0 0 0 19 65 15 2 0 0 | 500 | 506 522 493 459 499 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 67 13 4 0 0 | 500 | 524 496 492 499 548 = 0.66 ||========================================================================= x 0 1 1 14 67 15 3 0 0 | 500 | 516 509 476 526 533 = 0.65 || sknuth_MaxOft test: no 82 test no 83 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 83 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 541 452 444 487 553 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 0 1 1 0 3 > 0.99998 || = 0.63 499 486 469 502 502 | 500 < 0.00003 0 1 0 0 0 | 0.5 | 1 1 0 1 0 > 0.99997 || = 0.62 483 500 499 485 497 | 500 < 0.00004 0 1 1 1 2 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 525 500 573 506 518 | 500 < 0.00005 0 0 1 0 2 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 473 495 495 483 503 | 500 < 0.00006 1 1 1 0 0 | 0.5 | 0 0 0 0 1 > 0.99994 || = 0.59 488 497 494 519 507 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 1 0 0 0 1 > 0.99993 || = 0.58 515 495 463 502 479 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99992 || = 0.57 555 493 503 500 516 | 500 < 0.00009 0 0 2 1 1 | 0.5 | 1 0 0 0 0 > 0.99991 || = 0.56 506 481 509 474 507 | 500 < 0.0001 1 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.9999 || = 0.55 493 492 493 482 526 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 497 470 472 507 526 | 500 < 0.0001 3 3 7 3 7 | 5 | 4 2 2 1 6 > 0.9999 || = 0.53 489 526 497 489 509 | 500 < 0.0002 5 7 9 2 5 | 5 | 2 3 0 3 2 > 0.9998 || = 0.52 538 490 518 506 531 | 500 < 0.0003 5 1 1 11 1 | 5 | 5 5 1 4 2 > 0.9997 || = 0.51 473 491 514 508 491 | 500 < 0.0004 2 11 4 5 5 | 5 | 3 6 5 4 4 > 0.9996 || = 0.50 490 539 519 471 508 | 500 < 0.0005 5 2 6 6 7 | 5 | 4 7 4 3 7 > 0.9995 || = 0.49 505 481 510 510 493 | 500 < 0.0006 4 4 3 3 9 | 5 | 4 2 4 3 5 > 0.9994 || = 0.48 462 523 478 506 517 | 500 < 0.0007 5 6 4 5 5 | 5 | 4 2 2 2 11 > 0.9993 || = 0.47 503 509 461 525 487 | 500 < 0.0008 6 10 4 3 2 | 5 | 5 4 3 4 6 > 0.9992 || = 0.46 473 508 507 515 456 | 500 < 0.0009 9 5 7 4 4 | 5 | 2 2 5 9 6 > 0.9991 || = 0.45 522 471 518 498 499 | 500 < 0.001 8 3 2 7 7 | 5 | 4 6 3 7 5 > 0.999 || = 0.44 473 473 509 499 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 534 517 497 496 504 | 500 < 0.001 52 52 47 49 52 | 50 | 37 39 29 40 54 > 0.999 || = 0.42 542 512 538 497 469 | 500 < 0.002 40 47 49 44 45 | 50 | 48 47 43 40 40 > 0.998 || = 0.41 512 475 502 477 461 | 500 < 0.003 53 58 41 56 41 | 50 | 46 39 45 42 48 > 0.997 || = 0.40 492 455 500 515 515 | 500 < 0.004 47 43 59 49 53 | 50 | 53 51 50 39 54 > 0.996 || = 0.39 475 500 457 497 517 | 500 < 0.005 51 50 45 45 56 | 50 | 45 49 48 50 42 > 0.995 || = 0.38 484 475 510 533 464 | 500 < 0.006 60 57 46 31 48 | 50 | 62 45 44 46 53 > 0.994 || = 0.37 524 504 498 510 505 | 500 < 0.007 45 51 57 47 42 | 50 | 47 55 44 34 47 > 0.993 || = 0.36 493 576 452 514 495 | 500 < 0.008 49 55 45 48 47 | 50 | 38 39 46 46 52 > 0.992 || = 0.35 485 488 490 506 534 | 500 < 0.009 55 53 41 39 48 | 50 | 52 49 56 55 57 > 0.991 || = 0.34 500 498 498 537 491 | 500 < 0.01 52 55 55 64 55 | 50 | 68 62 44 46 55 > 0.99 || = 0.33 469 504 509 499 540 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 504 499 490 479 488 | 500 < 0.01 504 521 485 472 487 | 497.5 | 496 475 449 438 502 > 0.99 || = 0.31 492 504 506 472 488 | 500 = 0.01 248 265 262 265 245 | 252.5 | 282 258 238 245 238 = 0.99 || = 0.30 513 506 491 491 489 | 500 = 0.02 488 522 498 478 511 | 500 | 467 515 502 524 476 = 0.98 || = 0.29 532 499 518 541 469 | 500 =================================================================| 500 | 529 507 512 499 504 = 0.97 || = 0.28 495 567 499 537 458 | 500 sknuth_MaxOft test: | 500 | 481 505 515 491 524 = 0.96 || = 0.27 493 526 503 516 490 | 500 ----------------------------------------------- | 500 | 495 452 524 527 531 = 0.95 || = 0.26 452 486 505 529 524 | 500 N = 30, n = 10000000, r = 0, d = 100000, t = 16 | 500 | 511 455 505 507 503 = 0.94 || = 0.25 479 530 501 457 508 | 500 Test results for Anderson-Darling: | 500 | 495 486 492 491 512 = 0.93 || = 0.24 503 523 529 495 497 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 491 482 541 507 500 = 0.92 || = 0.23 530 502 511 510 466 | 500 =================================================================| 500 | 517 522 530 538 500 = 0.91 || = 0.22 503 505 458 493 468 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 482 481 515 480 501 = 0.90 || = 0.21 513 515 501 504 512 | 500 -----------------------------------------------------------------| 500 | 530 490 521 489 500 = 0.89 || = 0.20 518 521 480 481 503 | 500 SD Bern.: d 0.98034 0.74601 1.30294 | 500 | 498 552 497 492 473 = 0.88 || = 0.19 479 481 465 517 478 | 500 s 1.05048 0.68590 1.06729 | 500 | 504 469 485 501 506 = 0.87 || = 0.18 523 504 550 506 558 | 500 t 1.02430 0.88700 1.16590 | 500 | 485 528 542 474 496 = 0.86 || = 0.17 500 534 499 492 483 | 500 m 0.87924 1.25760 1.19557 | 500 | 537 485 513 504 502 = 0.85 || = 0.16 503 501 513 491 501 | 500 x 1.04528 0.72284 0.76979 | 500 | 529 514 468 507 471 = 0.84 || = 0.15 461 489 497 501 543 | 500 | 500 | 516 474 528 473 497 = 0.83 || = 0.14 487 490 508 502 533 | 500 Changes: d 53 6 5 | 500 | 524 462 500 525 521 = 0.82 || = 0.13 512 511 517 493 496 | 500 s 49 4 5 | 500 | 519 532 442 483 501 = 0.81 || = 0.12 462 495 486 506 510 | 500 t 52 5 2 | 500 | 507 501 524 525 457 = 0.80 || = 0.11 486 509 510 494 472 | 500 m 54 3 2 | 500 | 475 465 477 493 512 = 0.79 || = 0.10 484 474 482 480 489 | 500 x 57 4 6 | 500 | 499 497 480 468 466 = 0.78 || = 0.09 501 524 503 514 500 | 500 -----------------------------------------------------------------| 500 | 482 506 499 499 545 = 0.77 || = 0.08 507 483 504 489 500 | 500 Aver./ d 0.50079 499 > 500: 6 3 6 3 6 4 5 2 7 4 | 500 | 498 491 513 518 509 = 0.76 || = 0.07 514 491 524 508 508 | 500 median s 0.49822 499 ----- 4 5 8 5 5 1 3 5 4 5 | 500 | 473 499 506 523 472 = 0.75 || = 0.06 475 490 531 483 502 | 500 t 0.49987 501 6 5 7 3 6 4 3 5 5 7 | 500 | 476 505 510 525 557 = 0.74 || = 0.05 522 498 487 528 506 | 500 m 0.49990 500 4 5 6 5 5 5 6 5 4 5 | 500 | 511 529 480 489 535 = 0.73 || = 0.04 499 483 530 499 510 | 500 x 0.50088 501 5 5 4 4 4 8 6 5 5 6 | 500 | 490 494 497 475 478 = 0.72 || = 0.03 538 467 481 482 441 | 500 -----------------------------------------------------------------| 500 | 461 535 528 509 481 = 0.71 || = 0.02 488 522 498 478 511 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 493 489 504 545 508 = 0.70 || = 0.01 248 265 262 265 245 | 252.5 d 0 0 1 16 66 17 1 0 0 | 500 | 463 505 466 510 483 = 0.69 || < 0.01 504 521 485 472 487 | 497.5 s 0 0 4 13 67 13 2 2 0 | 500 | 491 498 498 520 524 = 0.68 ||========================================================================= t 0 0 4 10 73 12 1 1 0 | 500 | 512 476 514 502 460 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 10 74 14 1 0 0 | 500 | 517 516 479 495 526 = 0.66 ||========================================================================= x 0 0 1 17 66 13 4 0 0 | 500 | 531 559 486 449 472 = 0.65 || sknuth_MaxOft test: no 83 test no 84 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 84 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 2 1 | 0.5 | 1 0 0 0 1 > 0.99999 || = 0.64 505 491 499 510 525 | 500 < 0.00002 0 1 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 509 507 507 546 464 | 500 < 0.00003 1 0 0 0 4 | 0.5 | 1 0 2 1 0 > 0.99997 || = 0.62 497 486 474 491 509 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 485 465 534 489 515 | 500 < 0.00005 1 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 486 485 508 522 502 | 500 < 0.00006 0 0 1 0 0 | 0.5 | 0 0 0 0 1 > 0.99994 || = 0.59 488 488 490 481 529 | 500 < 0.00007 0 2 0 0 2 | 0.5 | 0 1 0 2 1 > 0.99993 || = 0.58 494 465 518 511 457 | 500 < 0.00008 1 0 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 479 497 479 496 486 | 500 < 0.00009 0 1 2 0 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 530 483 543 511 515 | 500 < 0.0001 0 0 2 0 0 | 0.5 | 0 0 1 0 2 > 0.9999 || = 0.55 485 528 468 501 522 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 510 511 476 528 511 | 500 < 0.0001 4 4 7 5 10 | 5 | 2 1 3 3 5 > 0.9999 || = 0.53 518 500 478 487 477 | 500 < 0.0002 5 9 5 8 5 | 5 | 2 1 3 1 2 > 0.9998 || = 0.52 481 482 496 531 522 | 500 < 0.0003 5 4 4 4 7 | 5 | 11 7 10 4 4 > 0.9997 || = 0.51 558 496 494 515 494 | 500 < 0.0004 4 8 6 3 7 | 5 | 7 5 5 8 6 > 0.9996 || = 0.50 513 483 481 515 491 | 500 < 0.0005 4 5 1 5 4 | 5 | 3 3 6 5 4 > 0.9995 || = 0.49 501 488 506 495 550 | 500 < 0.0006 2 4 5 7 2 | 5 | 2 7 4 3 7 > 0.9994 || = 0.48 533 486 470 479 511 | 500 < 0.0007 10 4 4 3 3 | 5 | 6 5 8 3 5 > 0.9993 || = 0.47 490 555 504 487 523 | 500 < 0.0008 7 6 2 8 5 | 5 | 6 5 3 8 6 > 0.9992 || = 0.46 534 493 536 515 508 | 500 < 0.0009 6 6 2 5 4 | 5 | 8 2 6 5 4 > 0.9991 || = 0.45 469 529 492 459 479 | 500 < 0.001 7 3 2 6 7 | 5 | 4 8 5 4 6 > 0.999 || = 0.44 439 500 506 486 526 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 492 479 494 484 482 | 500 < 0.001 54 53 38 54 54 | 50 | 51 44 53 44 49 > 0.999 || = 0.42 486 519 470 443 462 | 500 < 0.002 49 49 58 49 51 | 50 | 39 56 40 53 52 > 0.998 || = 0.41 497 465 477 497 472 | 500 < 0.003 47 52 63 48 53 | 50 | 60 52 65 49 47 > 0.997 || = 0.40 489 476 510 520 507 | 500 < 0.004 42 40 49 47 61 | 50 | 56 49 52 54 60 > 0.996 || = 0.39 524 505 492 468 508 | 500 < 0.005 58 58 53 57 46 | 50 | 56 60 43 46 52 > 0.995 || = 0.38 497 488 533 507 524 | 500 < 0.006 46 57 46 47 53 | 50 | 55 59 46 47 52 > 0.994 || = 0.37 550 500 490 508 541 | 500 < 0.007 57 60 45 52 54 | 50 | 66 44 48 55 48 > 0.993 || = 0.36 477 498 497 515 491 | 500 < 0.008 52 59 57 52 50 | 50 | 61 34 47 43 60 > 0.992 || = 0.35 501 497 477 475 516 | 500 < 0.009 50 42 54 43 41 | 50 | 47 40 34 45 58 > 0.991 || = 0.34 460 518 498 502 472 | 500 < 0.01 61 51 53 42 57 | 50 | 46 57 62 62 54 > 0.99 || = 0.33 493 485 514 511 474 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 483 495 534 517 530 | 500 < 0.01 516 521 516 491 520 | 497.5 | 537 495 490 498 532 > 0.99 || = 0.31 500 497 504 508 490 | 500 = 0.01 230 245 257 252 245 | 252.5 | 265 269 253 255 259 = 0.99 || = 0.30 517 503 491 497 500 | 500 = 0.02 545 425 527 467 499 | 500 | 484 523 525 490 505 = 0.98 || = 0.29 511 501 470 526 517 | 500 =================================================================| 500 | 507 514 501 499 476 = 0.97 || = 0.28 472 512 505 505 512 | 500 sknuth_MaxOft test: | 500 | 472 477 505 509 502 = 0.96 || = 0.27 494 513 495 446 493 | 500 ----------------------------------------------- | 500 | 502 538 522 471 511 = 0.95 || = 0.26 498 497 503 465 516 | 500 N = 30, n = 10000000, r = 0, d = 100000, t = 16 | 500 | 504 514 499 508 493 = 0.94 || = 0.25 467 475 507 522 524 | 500 Test results for Anderson-Darling: | 500 | 500 460 481 480 486 = 0.93 || = 0.24 483 540 508 521 505 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 491 481 502 523 519 = 0.92 || = 0.23 510 504 493 523 499 | 500 =================================================================| 500 | 500 486 485 529 471 = 0.91 || = 0.22 508 502 511 501 461 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 463 528 489 513 483 = 0.90 || = 0.21 498 478 493 500 452 | 500 -----------------------------------------------------------------| 500 | 491 484 521 502 501 = 0.89 || = 0.20 497 516 532 478 526 | 500 SD Bern.: d 1.01984 0.82986 1.20142 | 500 | 508 492 511 522 517 = 0.88 || = 0.19 500 488 515 498 522 | 500 s 0.92347 0.97310 1.18295 | 500 | 503 472 507 495 464 = 0.87 || = 0.18 524 538 488 525 472 | 500 t 0.90907 1.00249 1.27813 | 500 | 507 506 440 483 490 = 0.86 || = 0.17 437 490 517 501 510 | 500 m 0.87757 0.64684 0.81279 | 500 | 512 525 511 511 529 = 0.85 || = 0.16 493 505 485 495 508 | 500 x 0.97405 0.79789 0.78268 | 500 | 500 503 509 502 486 = 0.84 || = 0.15 499 508 459 479 485 | 500 | 500 | 490 480 512 488 490 = 0.83 || = 0.14 505 490 484 496 557 | 500 Changes: d 46 6 3 | 500 | 488 497 518 498 499 = 0.82 || = 0.13 499 526 528 518 492 | 500 s 51 6 5 | 500 | 497 501 456 500 498 = 0.81 || = 0.12 508 532 502 509 500 | 500 t 58 5 4 | 500 | 519 496 492 484 470 = 0.80 || = 0.11 458 498 491 498 489 | 500 m 46 5 7 | 500 | 464 517 518 497 510 = 0.79 || = 0.10 486 487 507 506 533 | 500 x 52 4 5 | 500 | 555 487 467 512 470 = 0.78 || = 0.09 512 552 447 468 475 | 500 -----------------------------------------------------------------| 500 | 508 501 495 492 495 = 0.77 || = 0.08 540 511 508 455 455 | 500 Aver./ d 0.49947 500 > 500: 7 3 3 4 3 4 4 7 4 5 | 500 | 482 494 508 473 490 = 0.76 || = 0.07 548 514 497 502 511 | 500 median s 0.49982 500 ----- 6 5 7 3 3 2 5 7 5 5 | 500 | 468 510 531 473 494 = 0.75 || = 0.06 528 509 518 482 521 | 500 t 0.49957 501 7 5 6 4 5 3 6 5 7 6 | 500 | 503 508 475 493 497 = 0.74 || = 0.05 526 494 531 531 486 | 500 m 0.50089 501 4 5 6 7 2 7 7 3 5 6 | 500 | 513 523 537 492 514 = 0.73 || = 0.04 500 505 491 530 489 | 500 x 0.49926 500 4 5 6 5 6 6 6 3 3 6 | 500 | 509 516 501 507 466 = 0.72 || = 0.03 487 464 505 504 505 | 500 -----------------------------------------------------------------| 500 | 530 520 486 518 517 = 0.71 || = 0.02 545 425 527 467 499 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 491 502 474 522 519 = 0.70 || = 0.01 230 245 257 252 245 | 252.5 d 0 0 2 11 72 11 5 0 0 | 500 | 482 478 501 534 497 = 0.69 || < 0.01 516 521 516 491 520 | 497.5 s 0 1 0 9 75 14 2 0 0 | 500 | 480 528 488 519 499 = 0.68 ||========================================================================= t 0 0 2 13 73 13 0 0 0 | 500 | 501 479 528 492 517 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 9 78 10 1 0 0 | 500 | 529 506 518 513 466 = 0.66 ||========================================================================= x 0 0 2 17 67 13 2 0 0 | 500 | 496 507 514 502 504 = 0.65 || sknuth_MaxOft test: no 84 test no 85 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 85 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 1 0 1 | 0.5 | 0 0 1 0 0 > 0.99999 || = 0.64 501 496 519 528 474 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 1 0 0 2 0 > 0.99998 || = 0.63 515 516 478 506 522 | 500 < 0.00003 0 0 1 0 0 | 0.5 | 0 0 2 1 0 > 0.99997 || = 0.62 455 508 492 518 441 | 500 < 0.00004 0 0 2 0 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 487 530 495 472 505 | 500 < 0.00005 1 1 0 1 1 | 0.5 | 0 1 1 0 0 > 0.99995 || = 0.60 537 500 444 480 501 | 500 < 0.00006 1 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 463 493 481 512 504 | 500 < 0.00007 1 0 0 2 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 489 516 521 559 490 | 500 < 0.00008 1 2 1 1 0 | 0.5 | 0 1 1 0 1 > 0.99992 || = 0.57 471 494 463 517 514 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 1 0 1 0 1 > 0.99991 || = 0.56 534 510 545 438 516 | 500 < 0.0001 0 0 0 1 1 | 0.5 | 0 1 1 0 2 > 0.9999 || = 0.55 479 482 486 471 449 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 466 523 519 509 510 | 500 < 0.0001 4 5 6 5 5 | 5 | 2 3 7 3 4 > 0.9999 || = 0.53 496 529 465 512 521 | 500 < 0.0002 4 1 3 5 10 | 5 | 1 2 1 0 3 > 0.9998 || = 0.52 510 506 487 498 511 | 500 < 0.0003 6 5 6 6 4 | 5 | 5 9 3 2 4 > 0.9997 || = 0.51 514 519 508 498 461 | 500 < 0.0004 2 3 4 7 7 | 5 | 5 2 4 3 4 > 0.9996 || = 0.50 504 469 479 546 516 | 500 < 0.0005 5 5 2 4 7 | 5 | 8 6 4 6 6 > 0.9995 || = 0.49 512 476 512 510 497 | 500 < 0.0006 6 4 5 8 7 | 5 | 6 6 4 5 8 > 0.9994 || = 0.48 504 499 497 457 518 | 500 < 0.0007 4 2 6 4 1 | 5 | 5 2 3 8 7 > 0.9993 || = 0.47 516 514 502 477 501 | 500 < 0.0008 3 5 6 4 4 | 5 | 5 5 4 2 1 > 0.9992 || = 0.46 544 466 483 520 479 | 500 < 0.0009 4 7 4 8 8 | 5 | 5 12 2 2 8 > 0.9991 || = 0.45 508 562 550 529 492 | 500 < 0.001 5 8 3 5 5 | 5 | 9 6 5 6 2 > 0.999 || = 0.44 498 502 477 484 486 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 485 536 485 531 478 | 500 < 0.001 43 45 45 56 58 | 50 | 51 53 37 37 47 > 0.999 || = 0.42 518 509 490 520 482 | 500 < 0.002 60 47 46 51 45 | 50 | 39 51 53 44 52 > 0.998 || = 0.41 494 555 463 452 492 | 500 < 0.003 55 64 65 53 58 | 50 | 46 47 53 44 57 > 0.997 || = 0.40 456 509 524 509 506 | 500 < 0.004 53 46 66 51 49 | 50 | 43 57 46 56 46 > 0.996 || = 0.39 486 491 492 515 528 | 500 < 0.005 56 50 47 48 60 | 50 | 49 49 60 44 45 > 0.995 || = 0.38 478 500 465 516 503 | 500 < 0.006 46 53 54 42 47 | 50 | 53 45 59 56 60 > 0.994 || = 0.37 525 497 490 491 479 | 500 < 0.007 43 57 51 53 53 | 50 | 58 56 50 42 62 > 0.993 || = 0.36 519 500 513 517 468 | 500 < 0.008 47 55 48 48 41 | 50 | 54 59 61 48 48 > 0.992 || = 0.35 524 533 519 462 484 | 500 < 0.009 53 47 43 51 53 | 50 | 44 43 48 52 40 > 0.991 || = 0.34 504 520 495 510 461 | 500 < 0.01 60 51 59 50 54 | 50 | 63 52 55 42 48 > 0.99 || = 0.33 499 490 511 483 471 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 516 540 464 515 484 | 500 < 0.01 516 515 524 503 518 | 497.5 | 500 512 522 465 505 > 0.99 || = 0.31 469 526 526 510 480 | 500 = 0.01 246 253 245 241 244 | 252.5 | 262 243 250 274 271 = 0.99 || = 0.30 499 512 523 520 523 | 500 = 0.02 480 514 524 502 485 | 500 | 514 492 518 528 490 = 0.98 || = 0.29 482 488 480 501 490 | 500 =================================================================| 500 | 506 441 499 521 481 = 0.97 || = 0.28 516 455 513 511 539 | 500 sknuth_MaxOft test: | 500 | 482 492 500 496 462 = 0.96 || = 0.27 487 514 535 479 514 | 500 ----------------------------------------------- | 500 | 507 483 480 506 522 = 0.95 || = 0.26 492 512 488 478 500 | 500 N = 30, n = 10000000, r = 0, d = 100000, t = 16 | 500 | 503 509 449 463 514 = 0.94 || = 0.25 489 488 475 492 512 | 500 Test results for Anderson-Darling: | 500 | 520 493 521 515 502 = 0.93 || = 0.24 477 503 539 533 535 | 500 Anderson-Darling statistic = A2 | 500 | 546 459 504 492 516 = 0.92 || = 0.23 484 508 499 472 527 | 500 =================================================================| 500 | 511 492 507 461 492 = 0.91 || = 0.22 516 513 480 520 521 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 499 468 509 494 466 = 0.90 || = 0.21 507 492 517 476 525 | 500 -----------------------------------------------------------------| 500 | 501 491 492 512 497 = 0.89 || = 0.20 500 463 477 501 535 | 500 SD Bern.: d 0.95072 0.89710 0.98231 | 500 | 508 491 531 520 494 = 0.88 || = 0.19 511 498 531 509 486 | 500 s 0.97568 0.82381 0.72698 | 500 | 483 515 478 519 487 = 0.87 || = 0.18 495 515 436 492 499 | 500 t 1.05765 1.16848 1.03394 | 500 | 481 507 511 526 493 = 0.86 || = 0.17 494 507 499 459 484 | 500 m 1.04578 0.50818 0.98536 | 500 | 505 465 482 486 473 = 0.85 || = 0.16 511 475 519 484 489 | 500 x 1.00241 0.86991 0.95440 | 500 | 500 483 495 538 524 = 0.84 || = 0.15 529 522 491 540 480 | 500 | 500 | 494 512 477 482 521 = 0.83 || = 0.14 505 467 503 510 514 | 500 Changes: d 42 3 4 | 500 | 506 492 497 498 518 = 0.82 || = 0.13 515 501 487 509 504 | 500 s 42 5 6 | 500 | 469 457 499 541 534 = 0.81 || = 0.12 502 476 517 489 492 | 500 t 60 5 7 | 500 | 464 495 508 507 527 = 0.80 || = 0.11 507 504 505 496 515 | 500 m 53 5 6 | 500 | 481 537 517 479 569 = 0.79 || = 0.10 508 488 489 485 493 | 500 x 42 8 4 | 500 | 516 515 482 497 475 = 0.78 || = 0.09 509 490 532 482 475 | 500 -----------------------------------------------------------------| 500 | 487 520 447 527 480 = 0.77 || = 0.08 487 477 525 495 485 | 500 Aver./ d 0.49841 502 > 500: 6 8 3 5 6 4 4 4 4 9 | 500 | 485 512 483 475 527 = 0.76 || = 0.07 476 490 474 515 484 | 500 median s 0.49895 500 ----- 5 5 5 5 7 6 5 8 3 2 | 500 | 518 517 472 485 481 = 0.75 || = 0.06 505 486 538 504 497 | 500 t 0.49885 499 7 5 4 5 4 4 6 4 3 5 | 500 | 470 506 499 507 520 = 0.74 || = 0.05 545 462 513 523 525 | 500 m 0.50107 504 5 4 5 7 6 5 6 4 6 5 | 500 | 526 533 537 483 484 = 0.73 || = 0.04 536 514 484 458 499 | 500 x 0.50055 497 2 3 8 3 3 7 5 5 4 6 | 500 | 507 490 484 509 540 = 0.72 || = 0.03 549 514 513 479 494 | 500 -----------------------------------------------------------------| 500 | 440 504 536 493 487 = 0.71 || = 0.02 480 514 524 502 485 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 498 518 508 479 531 = 0.70 || = 0.01 246 253 245 241 244 | 252.5 d 0 0 2 12 75 9 3 0 0 | 500 | 467 512 530 459 485 = 0.69 || < 0.01 516 515 524 503 518 | 497.5 s 0 0 2 14 74 9 2 0 0 | 500 | 506 484 505 533 481 = 0.68 ||========================================================================= t 0 0 4 11 66 18 2 0 0 | 500 | 494 461 530 512 490 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 69 13 2 0 0 | 500 | 462 487 491 514 516 = 0.66 ||========================================================================= x 0 0 2 10 72 16 0 1 0 | 500 | 531 480 535 474 538 = 0.65 || sknuth_MaxOft test: no 85 test no 86 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 86 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 0 | 0.5 | 0 2 0 0 1 > 0.99999 || = 0.64 526 500 509 459 506 | 500 < 0.00002 0 1 0 0 2 | 0.5 | 0 1 1 0 0 > 0.99998 || = 0.63 481 514 487 518 510 | 500 < 0.00003 2 0 0 0 1 | 0.5 | 1 0 3 0 0 > 0.99997 || = 0.62 539 519 489 503 512 | 500 < 0.00004 2 1 0 1 0 | 0.5 | 1 1 0 0 0 > 0.99996 || = 0.61 491 504 514 521 512 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 495 488 508 515 480 | 500 < 0.00006 1 1 0 1 0 | 0.5 | 0 0 0 1 1 > 0.99994 || = 0.59 459 477 505 505 533 | 500 < 0.00007 1 0 0 0 0 | 0.5 | 0 1 2 0 0 > 0.99993 || = 0.58 513 505 468 520 481 | 500 < 0.00008 1 3 0 2 0 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 512 489 485 471 463 | 500 < 0.00009 0 1 0 3 0 | 0.5 | 0 0 0 1 2 > 0.99991 || = 0.56 492 507 516 498 464 | 500 < 0.0001 0 1 0 1 0 | 0.5 | 2 1 0 2 1 > 0.9999 || = 0.55 530 481 499 475 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 503 482 514 466 487 | 500 < 0.0001 7 8 1 8 4 | 5 | 4 7 6 4 5 > 0.9999 || = 0.53 507 486 514 523 518 | 500 < 0.0002 4 5 4 2 7 | 5 | 4 2 1 1 3 > 0.9998 || = 0.52 485 510 473 473 529 | 500 < 0.0003 5 2 2 4 12 | 5 | 9 2 3 2 7 > 0.9997 || = 0.51 490 477 484 531 530 | 500 < 0.0004 8 5 7 4 3 | 5 | 6 2 4 6 2 > 0.9996 || = 0.50 458 500 513 496 467 | 500 < 0.0005 7 6 8 5 6 | 5 | 3 9 5 5 7 > 0.9995 || = 0.49 509 479 490 479 494 | 500 < 0.0006 6 3 1 4 4 | 5 | 1 4 5 6 6 > 0.9994 || = 0.48 479 512 521 518 470 | 500 < 0.0007 4 1 5 3 2 | 5 | 4 3 10 4 2 > 0.9993 || = 0.47 528 494 518 481 497 | 500 < 0.0008 9 7 4 6 3 | 5 | 8 6 4 2 5 > 0.9992 || = 0.46 497 496 517 514 510 | 500 < 0.0009 8 7 5 10 9 | 5 | 5 3 4 8 6 > 0.9991 || = 0.45 478 511 447 563 524 | 500 < 0.001 4 5 5 5 7 | 5 | 3 8 1 5 5 > 0.999 || = 0.44 478 540 543 516 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 506 530 464 511 494 | 500 < 0.001 62 49 42 51 57 | 50 | 47 46 43 43 48 > 0.999 || = 0.42 521 523 513 510 456 | 500 < 0.002 47 53 44 53 45 | 50 | 64 43 51 55 36 > 0.998 || = 0.41 513 477 495 519 462 | 500 < 0.003 48 61 52 54 62 | 50 | 38 49 49 55 51 > 0.997 || = 0.40 448 460 484 509 495 | 500 < 0.004 46 56 46 43 47 | 50 | 53 48 56 47 46 > 0.996 || = 0.39 487 483 503 532 504 | 500 < 0.005 39 48 49 49 41 | 50 | 58 50 52 45 64 > 0.995 || = 0.38 481 505 479 472 480 | 500 < 0.006 45 51 38 44 64 | 50 | 50 42 58 45 53 > 0.994 || = 0.37 494 528 495 522 477 | 500 < 0.007 68 50 55 51 42 | 50 | 47 46 41 50 44 > 0.993 || = 0.36 496 457 506 494 535 | 500 < 0.008 52 40 50 59 62 | 50 | 49 60 34 47 36 > 0.992 || = 0.35 513 552 495 543 556 | 500 < 0.009 52 47 58 53 51 | 50 | 50 54 52 57 47 > 0.991 || = 0.34 473 494 495 479 512 | 500 < 0.01 58 42 45 46 47 | 50 | 43 50 61 51 52 > 0.99 || = 0.33 496 501 499 515 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 495 495 477 475 507 | 500 < 0.01 517 497 479 503 518 | 497.5 | 499 488 497 495 477 > 0.99 || = 0.31 490 512 523 499 494 | 500 = 0.01 249 269 225 240 261 | 252.5 | 272 236 233 244 273 = 0.99 || = 0.30 466 476 490 518 508 | 500 = 0.02 467 493 452 509 521 | 500 | 554 509 508 481 523 = 0.98 || = 0.29 505 501 497 488 516 | 500 =================================================================| 500 | 509 508 520 486 510 = 0.97 || = 0.28 514 519 500 488 461 | 500 sknuth_MaxOft test: | 500 | 510 518 460 538 516 = 0.96 || = 0.27 491 475 513 500 491 | 500 ----------------------------------------------- | 500 | 498 516 493 482 505 = 0.95 || = 0.26 503 501 521 486 544 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 24 | 500 | 491 503 477 502 510 = 0.94 || = 0.25 508 517 471 512 498 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 496 490 523 502 483 = 0.93 || = 0.24 486 485 519 452 498 | 500 | 500 | 502 514 521 570 503 = 0.92 || = 0.23 525 521 486 507 494 | 500 =================================================================| 500 | 482 496 511 530 469 = 0.91 || = 0.22 454 494 504 504 441 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 523 491 478 489 459 = 0.90 || = 0.21 460 504 517 515 501 | 500 -----------------------------------------------------------------| 500 | 502 527 513 475 482 = 0.89 || = 0.20 518 527 490 509 456 | 500 SD Bern.: d 0.95727 1.19641 0.98129 | 500 | 492 485 471 479 496 = 0.88 || = 0.19 524 499 530 462 476 | 500 s 0.82724 0.83107 0.72973 | 500 | 485 473 504 496 512 = 0.87 || = 0.18 528 495 520 513 526 | 500 t 0.93769 0.87106 1.11140 | 500 | 494 508 526 472 515 = 0.86 || = 0.17 506 483 504 532 498 | 500 m 0.98905 0.66214 0.65910 | 500 | 491 484 487 516 487 = 0.85 || = 0.16 474 526 487 484 486 | 500 x 1.01665 1.20226 1.15555 | 500 | 515 520 497 503 478 = 0.84 || = 0.15 502 501 484 496 501 | 500 | 500 | 510 520 467 489 511 = 0.83 || = 0.14 507 470 499 502 474 | 500 Changes: d 44 2 4 | 500 | 464 492 508 510 509 = 0.82 || = 0.13 515 502 516 510 490 | 500 s 58 4 2 | 500 | 476 502 513 516 498 = 0.81 || = 0.12 459 492 555 492 489 | 500 t 52 6 5 | 500 | 496 526 490 501 503 = 0.80 || = 0.11 511 509 497 527 506 | 500 m 47 3 3 | 500 | 472 488 474 484 516 = 0.79 || = 0.10 513 499 508 538 495 | 500 x 47 7 5 | 500 | 552 489 507 486 526 = 0.78 || = 0.09 527 469 530 518 484 | 500 -----------------------------------------------------------------| 500 | 520 484 530 493 549 = 0.77 || = 0.08 495 480 503 485 503 | 500 Aver./ d 0.50179 501 > 500: 3 8 6 1 5 5 5 8 4 6 | 500 | 516 467 497 454 490 = 0.76 || = 0.07 482 503 497 477 504 | 500 median s 0.49968 500 ----- 5 4 7 5 5 3 5 5 5 6 | 500 | 532 503 504 487 502 = 0.75 || = 0.06 499 514 507 487 494 | 500 t 0.49894 499 5 6 5 3 5 5 5 4 5 5 | 500 | 512 505 512 490 469 = 0.74 || = 0.05 497 498 502 459 490 | 500 m 0.50015 500 3 6 5 5 8 5 7 2 4 5 | 500 | 502 508 498 508 516 = 0.73 || = 0.04 477 520 563 477 552 | 500 x 0.50060 501 6 3 3 6 3 5 10 6 4 7 | 500 | 506 514 486 486 461 = 0.72 || = 0.03 522 528 494 480 493 | 500 -----------------------------------------------------------------| 500 | 522 480 484 489 490 = 0.71 || = 0.02 467 493 452 509 521 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 493 492 485 522 509 = 0.70 || = 0.01 249 269 225 240 261 | 252.5 d 0 0 2 12 72 12 3 0 0 | 500 | 505 479 520 497 501 = 0.69 || < 0.01 517 497 479 503 518 | 497.5 s 0 0 0 13 75 12 1 0 0 | 500 | 526 492 482 526 532 = 0.68 ||========================================================================= t 0 0 2 13 75 9 2 0 0 | 500 | 491 528 465 509 533 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 13 74 10 1 1 0 | 500 | 545 475 532 482 522 = 0.66 ||========================================================================= x 0 0 1 15 69 13 3 0 0 | 500 | 481 535 525 516 516 = 0.65 || sknuth_MaxOft test: no 86 test no 87 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 87 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 1 2 | 0.5 | 0 1 0 1 0 > 0.99999 || = 0.64 468 492 505 495 496 | 500 < 0.00002 0 0 1 1 0 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 501 503 479 472 514 | 500 < 0.00003 1 1 0 1 0 | 0.5 | 0 1 0 2 0 > 0.99997 || = 0.62 484 526 524 519 448 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 0 1 1 > 0.99996 || = 0.61 452 515 523 437 502 | 500 < 0.00005 1 0 0 2 0 | 0.5 | 0 1 0 0 1 > 0.99995 || = 0.60 523 507 530 509 480 | 500 < 0.00006 1 0 1 0 0 | 0.5 | 1 1 1 0 0 > 0.99994 || = 0.59 499 533 475 514 497 | 500 < 0.00007 0 0 1 0 1 | 0.5 | 0 0 2 1 1 > 0.99993 || = 0.58 493 502 459 537 494 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 0 1 0 2 1 > 0.99992 || = 0.57 544 517 489 501 531 | 500 < 0.00009 0 0 1 0 0 | 0.5 | 0 2 1 2 0 > 0.99991 || = 0.56 492 494 495 510 505 | 500 < 0.0001 0 0 1 0 0 | 0.5 | 0 0 0 0 1 > 0.9999 || = 0.55 513 537 478 502 525 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 490 431 520 507 527 | 500 < 0.0001 3 2 6 5 3 | 5 | 1 7 4 9 6 > 0.9999 || = 0.53 519 463 479 511 499 | 500 < 0.0002 3 5 7 2 4 | 5 | 4 2 3 3 2 > 0.9998 || = 0.52 462 474 483 504 505 | 500 < 0.0003 5 5 5 8 8 | 5 | 4 1 1 3 5 > 0.9997 || = 0.51 483 497 500 496 491 | 500 < 0.0004 6 2 4 4 7 | 5 | 5 10 0 4 6 > 0.9996 || = 0.50 498 507 525 502 507 | 500 < 0.0005 3 3 4 7 9 | 5 | 6 2 8 9 0 > 0.9995 || = 0.49 467 500 507 474 502 | 500 < 0.0006 5 5 3 5 4 | 5 | 5 8 7 6 6 > 0.9994 || = 0.48 468 493 505 510 487 | 500 < 0.0007 3 5 5 5 2 | 5 | 8 2 1 4 5 > 0.9993 || = 0.47 482 526 509 494 493 | 500 < 0.0008 8 5 6 4 7 | 5 | 3 5 5 7 4 > 0.9992 || = 0.46 519 484 460 555 532 | 500 < 0.0009 4 4 7 6 4 | 5 | 7 6 0 5 3 > 0.9991 || = 0.45 487 491 521 477 538 | 500 < 0.001 3 4 6 6 3 | 5 | 7 3 6 4 2 > 0.999 || = 0.44 536 475 524 525 540 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 487 496 532 501 452 | 500 < 0.001 43 40 53 52 51 | 50 | 50 46 35 54 39 > 0.999 || = 0.42 498 491 533 509 481 | 500 < 0.002 50 36 48 52 56 | 50 | 55 52 41 39 58 > 0.998 || = 0.41 525 500 502 467 519 | 500 < 0.003 61 51 44 36 43 | 50 | 47 46 44 40 52 > 0.997 || = 0.40 501 492 495 483 480 | 500 < 0.004 58 54 49 53 47 | 50 | 48 45 48 43 51 > 0.996 || = 0.39 552 498 451 507 473 | 500 < 0.005 48 38 54 38 53 | 50 | 57 68 50 42 62 > 0.995 || = 0.38 515 524 496 500 519 | 500 < 0.006 55 58 42 47 46 | 50 | 57 51 47 51 46 > 0.994 || = 0.37 521 528 483 500 560 | 500 < 0.007 43 61 33 35 59 | 50 | 42 40 48 48 53 > 0.993 || = 0.36 509 475 495 498 514 | 500 < 0.008 54 59 60 53 55 | 50 | 55 53 47 50 54 > 0.992 || = 0.35 505 509 464 493 499 | 500 < 0.009 63 55 41 48 48 | 50 | 52 44 58 63 48 > 0.991 || = 0.34 487 527 502 502 537 | 500 < 0.01 68 55 47 51 53 | 50 | 52 41 60 44 44 > 0.99 || = 0.33 513 488 493 500 471 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 491 541 506 507 525 | 500 < 0.01 543 507 471 465 511 | 497.5 | 515 486 478 474 507 > 0.99 || = 0.31 500 466 507 498 517 | 500 = 0.01 244 280 268 253 252 | 252.5 | 253 263 291 242 241 = 0.99 || = 0.30 501 468 520 533 511 | 500 = 0.02 520 512 453 510 522 | 500 | 491 508 533 494 535 = 0.98 || = 0.29 501 494 502 522 495 | 500 =================================================================| 500 | 523 487 518 473 506 = 0.97 || = 0.28 538 533 505 518 522 | 500 sknuth_MaxOft test: | 500 | 481 524 480 460 476 = 0.96 || = 0.27 483 521 489 545 537 | 500 ----------------------------------------------- | 500 | 471 524 512 519 531 = 0.95 || = 0.26 517 468 518 460 507 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 24 | 500 | 476 504 477 518 536 = 0.94 || = 0.25 493 468 510 491 483 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 511 520 491 494 465 = 0.93 || = 0.24 509 473 496 524 525 | 500 | 500 | 509 489 505 459 529 = 0.92 || = 0.23 535 476 475 498 453 | 500 =================================================================| 500 | 472 506 519 522 531 = 0.91 || = 0.22 507 535 513 496 488 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 499 476 525 498 522 = 0.90 || = 0.21 533 514 470 531 490 | 500 -----------------------------------------------------------------| 500 | 508 508 504 501 498 = 0.89 || = 0.20 453 510 505 494 489 | 500 SD Bern.: d 1.01363 1.28204 0.68297 | 500 | 449 437 469 483 482 = 0.88 || = 0.19 495 517 474 471 461 | 500 s 0.97432 1.24400 1.10688 | 500 | 493 494 515 484 507 = 0.87 || = 0.18 489 522 515 479 486 | 500 t 0.98928 1.10417 1.03201 | 500 | 510 482 503 466 472 = 0.86 || = 0.17 503 496 492 486 500 | 500 m 1.00750 1.10054 1.05882 | 500 | 484 506 471 475 440 = 0.85 || = 0.16 504 503 471 493 479 | 500 x 1.09392 0.69171 0.91148 | 500 | 487 470 521 556 502 = 0.84 || = 0.15 541 485 483 492 508 | 500 | 500 | 460 509 458 494 494 = 0.83 || = 0.14 515 517 507 513 502 | 500 Changes: d 55 5 5 | 500 | 464 491 483 492 467 = 0.82 || = 0.13 536 454 531 492 483 | 500 s 45 3 6 | 500 | 470 500 485 498 496 = 0.81 || = 0.12 486 494 522 496 489 | 500 t 46 5 1 | 500 | 489 488 528 493 483 = 0.80 || = 0.11 531 495 496 499 521 | 500 m 53 6 5 | 500 | 514 496 467 551 501 = 0.79 || = 0.10 488 486 497 517 532 | 500 x 48 6 4 | 500 | 485 512 504 490 570 = 0.78 || = 0.09 491 511 504 515 494 | 500 -----------------------------------------------------------------| 500 | 487 496 512 502 461 = 0.77 || = 0.08 514 520 506 492 461 | 500 Aver./ d 0.49648 499 > 500: 5 6 7 7 4 4 4 4 2 5 | 500 | 497 492 507 497 486 = 0.76 || = 0.07 486 516 512 521 473 | 500 median s 0.49979 500 ----- 8 4 5 5 1 5 7 3 3 7 | 500 | 522 493 555 494 491 = 0.75 || = 0.06 524 503 527 490 473 | 500 t 0.50070 503 8 4 6 4 8 2 7 6 5 6 | 500 | 531 497 463 531 467 = 0.74 || = 0.05 495 471 502 492 515 | 500 m 0.49960 498 5 2 5 4 5 9 4 5 2 3 | 500 | 522 529 540 480 482 = 0.73 || = 0.04 491 509 502 535 514 | 500 x 0.49987 499 5 4 4 7 5 5 5 3 3 7 | 500 | 454 481 486 525 516 = 0.72 || = 0.03 504 484 503 429 502 | 500 -----------------------------------------------------------------| 500 | 500 514 485 505 486 = 0.71 || = 0.02 520 512 453 510 522 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 502 526 489 531 490 = 0.70 || = 0.01 244 280 268 253 252 | 252.5 d 0 0 4 12 68 15 2 0 0 | 500 | 498 533 504 498 474 = 0.69 || < 0.01 543 507 471 465 511 | 497.5 s 0 1 2 14 66 18 0 0 0 | 500 | 477 526 507 480 482 = 0.68 ||========================================================================= t 0 0 2 15 68 14 2 0 0 | 500 | 529 525 536 537 510 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 1 13 72 10 4 0 0 | 500 | 477 496 509 516 502 = 0.66 ||========================================================================= x 0 0 4 13 65 17 1 1 0 | 500 | 536 468 482 500 524 = 0.65 || sknuth_MaxOft test: no 87 test no 88 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 88 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 0 | 0.5 | 0 2 0 2 0 > 0.99999 || = 0.64 520 486 493 496 502 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 0 1 1 1 1 > 0.99998 || = 0.63 484 502 531 475 473 | 500 < 0.00003 0 0 0 1 1 | 0.5 | 0 0 1 0 0 > 0.99997 || = 0.62 433 451 496 447 544 | 500 < 0.00004 2 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 533 508 517 512 479 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 1 1 1 1 > 0.99995 || = 0.60 460 500 510 513 488 | 500 < 0.00006 0 1 0 0 2 | 0.5 | 1 0 1 0 2 > 0.99994 || = 0.59 522 533 516 518 520 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 1 0 0 0 0 > 0.99993 || = 0.58 520 485 501 495 520 | 500 < 0.00008 0 0 1 0 0 | 0.5 | 2 0 0 0 0 > 0.99992 || = 0.57 503 527 510 511 522 | 500 < 0.00009 0 1 1 1 0 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 512 529 478 513 484 | 500 < 0.0001 2 0 1 0 0 | 0.5 | 0 0 0 1 0 > 0.9999 || = 0.55 473 486 479 518 523 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 509 488 493 541 493 | 500 < 0.0001 4 2 5 4 3 | 5 | 4 4 4 6 4 > 0.9999 || = 0.53 516 534 472 499 492 | 500 < 0.0002 5 4 7 3 4 | 5 | 2 1 1 1 2 > 0.9998 || = 0.52 490 504 490 489 501 | 500 < 0.0003 4 5 1 3 4 | 5 | 6 6 1 5 7 > 0.9997 || = 0.51 514 494 507 458 500 | 500 < 0.0004 5 3 5 7 5 | 5 | 5 10 3 5 8 > 0.9996 || = 0.50 459 463 501 472 498 | 500 < 0.0005 3 5 6 6 8 | 5 | 5 9 7 6 3 > 0.9995 || = 0.49 486 502 470 492 499 | 500 < 0.0006 6 9 4 7 8 | 5 | 4 5 1 7 5 > 0.9994 || = 0.48 492 497 485 460 543 | 500 < 0.0007 6 4 7 7 6 | 5 | 3 7 4 6 1 > 0.9993 || = 0.47 495 499 484 524 495 | 500 < 0.0008 5 4 5 5 3 | 5 | 10 5 7 3 6 > 0.9992 || = 0.46 539 488 521 533 499 | 500 < 0.0009 5 2 4 6 3 | 5 | 2 7 3 4 5 > 0.9991 || = 0.45 497 499 498 525 502 | 500 < 0.001 7 6 3 9 7 | 5 | 9 6 8 2 3 > 0.999 || = 0.44 473 514 497 512 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 521 488 502 509 504 | 500 < 0.001 50 44 47 57 51 | 50 | 50 60 39 45 44 > 0.999 || = 0.42 503 495 492 493 469 | 500 < 0.002 46 44 37 48 47 | 50 | 43 42 45 38 50 > 0.998 || = 0.41 521 489 527 496 485 | 500 < 0.003 54 51 54 40 67 | 50 | 47 53 60 54 48 > 0.997 || = 0.40 492 496 503 503 508 | 500 < 0.004 42 64 54 39 48 | 50 | 53 49 45 40 44 > 0.996 || = 0.39 500 496 512 466 508 | 500 < 0.005 65 53 45 70 68 | 50 | 41 52 46 41 55 > 0.995 || = 0.38 502 491 506 519 549 | 500 < 0.006 58 50 55 40 43 | 50 | 57 47 48 51 46 > 0.994 || = 0.37 496 496 514 517 500 | 500 < 0.007 49 44 37 40 48 | 50 | 43 60 48 40 54 > 0.993 || = 0.36 536 457 486 459 485 | 500 < 0.008 59 52 48 56 57 | 50 | 50 46 52 40 46 > 0.992 || = 0.35 524 476 500 488 481 | 500 < 0.009 54 66 43 45 49 | 50 | 40 55 60 54 47 > 0.991 || = 0.34 488 503 515 515 492 | 500 < 0.01 54 58 46 48 54 | 50 | 53 44 35 48 45 > 0.99 || = 0.33 498 494 523 495 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 539 517 526 478 508 | 500 < 0.01 531 526 466 483 532 | 497.5 | 477 508 478 451 479 > 0.99 || = 0.31 514 531 476 490 487 | 500 = 0.01 245 243 214 245 254 | 252.5 | 253 273 246 246 267 = 0.99 || = 0.30 473 471 500 545 493 | 500 = 0.02 496 478 492 494 539 | 500 | 488 492 496 500 510 = 0.98 || = 0.29 495 499 510 528 493 | 500 =================================================================| 500 | 509 528 510 540 500 = 0.97 || = 0.28 505 503 490 500 466 | 500 sknuth_MaxOft test: | 500 | 473 523 506 497 489 = 0.96 || = 0.27 561 516 495 480 476 | 500 ----------------------------------------------- | 500 | 526 505 531 459 494 = 0.95 || = 0.26 486 487 516 488 487 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 24 | 500 | 466 487 511 486 483 = 0.94 || = 0.25 508 564 530 501 508 | 500 Anderson-Darling statistic = A2 | 500 | 484 552 513 496 513 = 0.93 || = 0.24 471 477 479 475 476 | 500 | 500 | 480 506 525 523 460 = 0.92 || = 0.23 522 478 524 525 532 | 500 =================================================================| 500 | 503 512 473 494 522 = 0.91 || = 0.22 520 495 488 507 454 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 482 475 491 514 494 = 0.90 || = 0.21 500 475 502 516 553 | 500 -----------------------------------------------------------------| 500 | 515 497 481 545 562 = 0.89 || = 0.20 510 508 508 455 507 | 500 SD Bern.: d 0.94139 0.99949 0.84303 | 500 | 469 507 509 510 501 = 0.88 || = 0.19 502 492 487 471 511 | 500 s 0.98826 1.13015 0.85364 | 500 | 452 531 463 491 519 = 0.87 || = 0.18 529 504 546 478 492 | 500 t 0.86077 0.99849 1.11768 | 500 | 486 454 510 518 474 = 0.86 || = 0.17 490 526 479 506 497 | 500 m 1.02958 1.37107 1.08404 | 500 | 517 472 468 490 483 = 0.85 || = 0.16 482 509 502 525 464 | 500 x 0.93548 1.22208 0.60526 | 500 | 509 493 516 525 484 = 0.84 || = 0.15 500 484 510 527 493 | 500 | 500 | 485 478 482 537 491 = 0.83 || = 0.14 520 550 509 507 497 | 500 Changes: d 53 5 5 | 500 | 501 472 492 493 528 = 0.82 || = 0.13 508 533 490 483 484 | 500 s 48 3 9 | 500 | 471 487 514 503 490 = 0.81 || = 0.12 498 491 477 541 498 | 500 t 50 4 4 | 500 | 496 515 528 486 507 = 0.80 || = 0.11 515 527 516 533 493 | 500 m 48 5 6 | 500 | 488 515 487 549 507 = 0.79 || = 0.10 509 510 504 485 496 | 500 x 45 8 4 | 500 | 474 482 471 514 493 = 0.78 || = 0.09 516 469 507 469 483 | 500 -----------------------------------------------------------------| 500 | 502 482 486 498 519 = 0.77 || = 0.08 508 533 503 495 483 | 500 Aver./ d 0.49717 501 > 500: 5 6 6 5 4 7 7 4 4 4 | 500 | 504 495 501 516 494 = 0.76 || = 0.07 479 511 476 477 468 | 500 median s 0.49913 498 ----- 6 7 4 3 2 5 3 3 2 8 | 500 | 509 481 500 499 507 = 0.75 || = 0.06 519 530 512 487 512 | 500 t 0.50016 501 4 6 6 6 4 5 7 4 4 6 | 500 | 467 549 528 547 512 = 0.74 || = 0.05 501 478 487 507 508 | 500 m 0.50106 497 2 6 5 4 6 6 3 4 7 2 | 500 | 500 500 454 494 494 = 0.73 || = 0.04 487 507 507 495 549 | 500 x 0.50002 497 7 1 4 3 4 5 2 6 4 4 | 500 | 498 498 520 494 495 = 0.72 || = 0.03 476 509 499 503 506 | 500 -----------------------------------------------------------------| 500 | 508 500 470 494 548 = 0.71 || = 0.02 496 478 492 494 539 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 491 493 478 502 494 = 0.70 || = 0.01 245 243 214 245 254 | 252.5 d 0 1 1 13 75 10 1 0 0 | 500 | 526 471 509 476 477 = 0.69 || < 0.01 531 526 466 483 532 | 497.5 s 0 0 2 12 68 15 4 0 0 | 500 | 514 481 506 470 482 = 0.68 ||========================================================================= t 0 0 2 11 74 13 1 0 0 | 500 | 507 499 530 481 492 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 65 15 4 0 0 | 500 | 523 467 523 471 497 = 0.66 ||========================================================================= x 0 0 1 10 78 7 5 0 0 | 500 | 521 519 538 529 483 = 0.65 || sknuth_MaxOft test: no 88 test no 89 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 89 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99999 || = 0.64 471 476 484 475 502 | 500 < 0.00002 0 0 0 2 0 | 0.5 | 0 0 0 1 0 > 0.99998 || = 0.63 494 503 484 502 474 | 500 < 0.00003 1 0 0 3 1 | 0.5 | 0 1 1 0 0 > 0.99997 || = 0.62 497 477 487 487 544 | 500 < 0.00004 0 0 3 0 0 | 0.5 | 1 0 1 0 0 > 0.99996 || = 0.61 498 504 481 496 521 | 500 < 0.00005 0 0 0 1 1 | 0.5 | 0 0 2 0 0 > 0.99995 || = 0.60 517 492 458 497 475 | 500 < 0.00006 0 0 1 0 0 | 0.5 | 0 1 1 0 0 > 0.99994 || = 0.59 518 482 522 461 475 | 500 < 0.00007 0 1 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 500 507 517 467 484 | 500 < 0.00008 0 0 0 0 2 | 0.5 | 2 0 1 0 2 > 0.99992 || = 0.57 458 508 448 515 503 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 2 0 0 1 0 > 0.99991 || = 0.56 488 529 487 504 516 | 500 < 0.0001 1 1 1 1 0 | 0.5 | 2 1 0 0 1 > 0.9999 || = 0.55 466 533 555 518 523 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 458 493 514 494 506 | 500 < 0.0001 3 2 5 7 5 | 5 | 8 4 6 2 3 > 0.9999 || = 0.53 496 518 473 488 539 | 500 < 0.0002 4 2 9 2 4 | 5 | 2 1 2 3 3 > 0.9998 || = 0.52 491 501 536 468 498 | 500 < 0.0003 4 6 6 6 4 | 5 | 5 6 4 3 8 > 0.9997 || = 0.51 464 493 455 508 484 | 500 < 0.0004 5 3 8 8 5 | 5 | 3 8 2 8 8 > 0.9996 || = 0.50 503 499 522 475 504 | 500 < 0.0005 7 3 4 3 4 | 5 | 7 4 2 9 6 > 0.9995 || = 0.49 473 534 518 489 482 | 500 < 0.0006 6 6 2 1 4 | 5 | 3 5 5 6 5 > 0.9994 || = 0.48 510 522 526 515 538 | 500 < 0.0007 5 3 3 6 3 | 5 | 5 5 9 5 3 > 0.9993 || = 0.47 495 497 462 542 472 | 500 < 0.0008 6 4 11 7 7 | 5 | 4 3 3 4 10 > 0.9992 || = 0.46 489 448 486 515 506 | 500 < 0.0009 6 6 1 5 1 | 5 | 6 3 4 5 4 > 0.9991 || = 0.45 484 551 492 489 517 | 500 < 0.001 4 3 1 4 7 | 5 | 7 5 2 7 4 > 0.999 || = 0.44 531 483 537 522 521 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 503 505 495 492 487 | 500 < 0.001 50 38 50 49 44 | 50 | 50 44 39 52 54 > 0.999 || = 0.42 508 483 496 495 528 | 500 < 0.002 70 51 45 52 54 | 50 | 47 73 43 41 54 > 0.998 || = 0.41 474 484 526 504 490 | 500 < 0.003 62 49 47 37 62 | 50 | 46 61 43 43 49 > 0.997 || = 0.40 468 498 505 498 507 | 500 < 0.004 33 54 55 51 60 | 50 | 44 55 44 45 45 > 0.996 || = 0.39 543 500 498 521 506 | 500 < 0.005 51 63 38 42 44 | 50 | 52 44 42 50 57 > 0.995 || = 0.38 503 520 494 500 532 | 500 < 0.006 49 50 58 47 47 | 50 | 37 51 43 52 52 > 0.994 || = 0.37 514 464 503 513 497 | 500 < 0.007 45 51 48 54 54 | 50 | 53 44 60 54 47 > 0.993 || = 0.36 507 508 456 499 472 | 500 < 0.008 48 52 41 56 46 | 50 | 64 42 44 51 61 > 0.992 || = 0.35 464 521 533 507 479 | 500 < 0.009 46 56 46 57 62 | 50 | 66 53 53 61 55 > 0.991 || = 0.34 507 499 486 535 470 | 500 < 0.01 52 49 49 59 58 | 50 | 41 41 68 42 65 > 0.99 || = 0.33 521 521 467 487 521 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 498 468 503 506 534 | 500 < 0.01 506 513 477 504 531 | 497.5 | 500 508 479 491 539 > 0.99 || = 0.31 493 499 521 496 496 | 500 = 0.01 273 236 253 233 285 | 252.5 | 244 236 243 259 274 = 0.99 || = 0.30 505 481 483 525 490 | 500 = 0.02 506 502 463 497 531 | 500 | 505 523 515 471 497 = 0.98 || = 0.29 508 455 528 473 501 | 500 =================================================================| 500 | 534 528 455 516 495 = 0.97 || = 0.28 503 507 478 492 462 | 500 sknuth_MaxOft test: | 500 | 462 476 481 509 488 = 0.96 || = 0.27 508 496 501 499 498 | 500 ----------------------------------------------- | 500 | 519 532 499 460 523 = 0.95 || = 0.26 496 514 492 482 519 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 24 | 500 | 515 513 475 527 487 = 0.94 || = 0.25 530 513 511 525 550 | 500 Test on the sum of all N observations | 500 | 483 493 533 471 479 = 0.93 || = 0.24 474 495 521 493 469 | 500 | 500 | 470 530 514 448 521 = 0.92 || = 0.23 509 479 483 515 468 | 500 =================================================================| 500 | 514 474 532 469 481 = 0.91 || = 0.22 502 500 514 531 492 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 485 497 508 504 475 = 0.90 || = 0.21 525 507 490 512 474 | 500 -----------------------------------------------------------------| 500 | 526 501 513 465 522 = 0.89 || = 0.20 525 525 526 483 506 | 500 SD Bern.: d 1.00314 1.33032 1.24640 | 500 | 487 466 554 496 514 = 0.88 || = 0.19 513 500 483 468 502 | 500 s 0.92321 0.86414 1.37034 | 500 | 515 512 527 529 470 = 0.87 || = 0.18 493 527 528 522 531 | 500 t 1.05932 0.85949 1.29447 | 500 | 501 488 508 505 499 = 0.86 || = 0.17 477 483 510 510 465 | 500 m 0.89420 0.92782 0.85481 | 500 | 491 465 455 528 464 = 0.85 || = 0.16 526 481 481 498 523 | 500 x 1.05550 1.07849 0.99144 | 500 | 488 475 504 500 483 = 0.84 || = 0.15 520 491 496 491 518 | 500 | 500 | 466 515 487 509 473 = 0.83 || = 0.14 573 506 478 464 517 | 500 Changes: d 44 5 4 | 500 | 488 524 528 477 545 = 0.82 || = 0.13 502 488 500 472 499 | 500 s 60 6 6 | 500 | 491 486 506 509 486 = 0.81 || = 0.12 531 515 485 509 512 | 500 t 54 4 3 | 500 | 506 474 476 514 499 = 0.80 || = 0.11 512 512 506 494 467 | 500 m 55 5 3 | 500 | 486 475 466 490 482 = 0.79 || = 0.10 510 501 478 505 522 | 500 x 50 5 4 | 500 | 456 490 558 513 508 = 0.78 || = 0.09 490 524 506 506 484 | 500 -----------------------------------------------------------------| 500 | 497 499 512 507 526 = 0.77 || = 0.08 546 463 487 485 482 | 500 Aver./ d 0.49750 502 > 500: 7 8 8 7 4 2 2 6 3 6 | 500 | 553 542 500 477 526 = 0.76 || = 0.07 509 510 489 493 508 | 500 median s 0.49989 500 ----- 7 5 5 4 4 6 6 3 4 6 | 500 | 515 493 493 542 504 = 0.75 || = 0.06 487 511 513 529 468 | 500 t 0.50075 500 6 3 6 4 5 5 5 3 8 4 | 500 | 509 509 475 511 468 = 0.74 || = 0.05 511 505 511 502 490 | 500 m 0.49988 502 5 4 4 6 5 4 5 8 6 4 | 500 | 467 493 484 541 456 = 0.73 || = 0.04 502 484 512 503 464 | 500 x 0.50003 499 4 7 4 4 6 5 5 5 3 4 | 500 | 531 510 513 527 548 = 0.72 || = 0.03 450 514 524 482 469 | 500 -----------------------------------------------------------------| 500 | 515 490 486 513 497 = 0.71 || = 0.02 506 502 463 497 531 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 509 452 529 502 496 = 0.70 || = 0.01 273 236 253 233 285 | 252.5 d 0 0 1 17 69 11 2 1 0 | 500 | 495 522 515 537 493 = 0.69 || < 0.01 506 513 477 504 531 | 497.5 s 0 0 3 14 69 14 1 0 0 | 500 | 518 527 487 496 503 = 0.68 ||========================================================================= t 0 0 4 10 69 14 4 0 0 | 500 | 479 488 545 500 486 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 17 70 13 0 0 0 | 500 | 482 529 509 503 501 = 0.66 ||========================================================================= x 0 0 0 21 60 16 4 0 0 | 500 | 472 507 502 507 492 = 0.65 || sknuth_MaxOft test: no 89 test no 90 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 90 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 1 0 1 | 0.5 | 0 1 1 1 0 > 0.99999 || = 0.64 511 499 525 486 515 | 500 < 0.00002 1 1 0 0 0 | 0.5 | 0 0 2 0 0 > 0.99998 || = 0.63 487 519 470 523 519 | 500 < 0.00003 1 1 0 0 0 | 0.5 | 1 0 2 1 0 > 0.99997 || = 0.62 469 529 473 483 444 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 461 521 514 481 476 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 1 0 2 0 > 0.99995 || = 0.60 492 551 529 562 520 | 500 < 0.00006 1 1 1 0 0 | 0.5 | 1 0 0 1 0 > 0.99994 || = 0.59 515 502 475 513 495 | 500 < 0.00007 1 0 0 1 0 | 0.5 | 1 0 0 1 1 > 0.99993 || = 0.58 503 505 484 490 509 | 500 < 0.00008 0 1 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 542 514 477 504 529 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 1 0 2 0 > 0.99991 || = 0.56 488 497 568 478 495 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 452 502 513 515 501 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 481 508 505 552 502 | 500 < 0.0001 6 5 3 1 2 | 5 | 3 3 6 8 1 > 0.9999 || = 0.53 514 493 497 499 500 | 500 < 0.0002 4 5 7 5 5 | 5 | 5 4 3 2 2 > 0.9998 || = 0.52 507 491 470 471 504 | 500 < 0.0003 5 9 8 2 3 | 5 | 3 4 4 3 2 > 0.9997 || = 0.51 489 465 470 496 501 | 500 < 0.0004 4 7 6 2 3 | 5 | 3 2 6 6 8 > 0.9996 || = 0.50 502 543 495 467 513 | 500 < 0.0005 5 3 4 4 10 | 5 | 2 6 5 1 7 > 0.9995 || = 0.49 480 506 488 507 527 | 500 < 0.0006 4 2 6 3 6 | 5 | 3 5 8 5 8 > 0.9994 || = 0.48 500 475 479 481 501 | 500 < 0.0007 6 4 6 6 5 | 5 | 4 6 3 3 4 > 0.9993 || = 0.47 471 532 514 521 503 | 500 < 0.0008 7 7 5 4 4 | 5 | 9 9 8 2 4 > 0.9992 || = 0.46 466 515 469 505 481 | 500 < 0.0009 5 4 2 7 7 | 5 | 4 7 6 6 3 > 0.9991 || = 0.45 504 499 502 508 516 | 500 < 0.001 3 8 6 6 8 | 5 | 9 9 3 5 4 > 0.999 || = 0.44 498 517 495 503 478 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 490 469 527 495 495 | 500 < 0.001 49 54 53 40 53 | 50 | 45 55 52 41 43 > 0.999 || = 0.42 518 460 541 494 504 | 500 < 0.002 51 50 50 39 43 | 50 | 49 57 51 50 34 > 0.998 || = 0.41 496 511 489 438 469 | 500 < 0.003 55 42 59 37 52 | 50 | 51 46 43 52 46 > 0.997 || = 0.40 477 498 524 505 514 | 500 < 0.004 49 58 62 51 38 | 50 | 63 52 39 44 53 > 0.996 || = 0.39 526 467 484 480 512 | 500 < 0.005 63 38 51 70 41 | 50 | 52 55 37 56 51 > 0.995 || = 0.38 513 501 495 468 494 | 500 < 0.006 54 46 61 47 42 | 50 | 49 48 39 42 52 > 0.994 || = 0.37 465 478 502 476 510 | 500 < 0.007 41 43 50 53 51 | 50 | 45 41 56 63 56 > 0.993 || = 0.36 466 521 456 482 506 | 500 < 0.008 47 61 50 51 44 | 50 | 48 70 46 45 46 > 0.992 || = 0.35 496 469 530 499 506 | 500 < 0.009 47 52 40 62 49 | 50 | 61 39 51 53 49 > 0.991 || = 0.34 536 509 521 520 491 | 500 < 0.01 51 42 50 51 47 | 50 | 49 53 53 44 43 > 0.99 || = 0.33 511 499 504 508 494 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 502 527 498 487 481 | 500 < 0.01 507 486 526 501 460 | 497.5 | 512 516 467 490 473 > 0.99 || = 0.31 517 453 461 493 468 | 500 = 0.01 236 258 236 270 272 | 252.5 | 271 252 248 259 222 = 0.99 || = 0.30 487 461 511 498 506 | 500 = 0.02 531 468 553 502 498 | 500 | 486 485 488 491 510 = 0.98 || = 0.29 532 547 510 515 491 | 500 =================================================================| 500 | 514 527 482 464 473 = 0.97 || = 0.28 545 497 506 519 499 | 500 sknuth_MaxOft test: | 500 | 527 511 490 482 499 = 0.96 || = 0.27 466 496 494 468 542 | 500 ----------------------------------------------- | 500 | 510 490 515 470 501 = 0.95 || = 0.26 530 521 529 482 507 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 24 | 500 | 509 519 469 491 509 = 0.94 || = 0.25 443 525 543 516 498 | 500 Test results for Anderson-Darling: | 500 | 472 469 549 540 517 = 0.93 || = 0.24 522 499 472 513 464 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 495 487 492 484 509 = 0.92 || = 0.23 492 476 471 495 488 | 500 =================================================================| 500 | 487 509 492 534 489 = 0.91 || = 0.22 508 527 529 462 516 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 482 511 500 459 522 = 0.90 || = 0.21 529 455 540 524 485 | 500 -----------------------------------------------------------------| 500 | 482 464 533 474 498 = 0.89 || = 0.20 464 482 515 510 528 | 500 SD Bern.: d 0.97585 0.79159 0.83945 | 500 | 527 495 482 501 515 = 0.88 || = 0.19 491 480 512 476 500 | 500 s 0.98692 1.04167 1.21220 | 500 | 498 495 490 524 469 = 0.87 || = 0.18 489 502 461 491 486 | 500 t 1.06248 0.95546 1.02715 | 500 | 504 475 501 550 515 = 0.86 || = 0.17 492 487 489 492 510 | 500 m 1.02602 1.38271 0.95963 | 500 | 493 543 505 473 490 = 0.85 || = 0.16 501 501 490 505 477 | 500 x 0.81481 0.89263 0.93533 | 500 | 502 488 478 503 474 = 0.84 || = 0.15 467 512 523 521 543 | 500 | 500 | 521 525 534 516 503 = 0.83 || = 0.14 492 531 473 483 504 | 500 Changes: d 50 5 4 | 500 | 526 530 494 554 508 = 0.82 || = 0.13 469 502 498 494 515 | 500 s 55 5 6 | 500 | 480 487 525 488 503 = 0.81 || = 0.12 505 540 460 515 520 | 500 t 55 3 4 | 500 | 494 500 475 548 483 = 0.80 || = 0.11 503 478 503 499 474 | 500 m 55 3 8 | 500 | 531 490 500 529 488 = 0.79 || = 0.10 488 518 494 502 500 | 500 x 56 5 2 | 500 | 492 494 506 500 495 = 0.78 || = 0.09 532 521 484 486 500 | 500 -----------------------------------------------------------------| 500 | 516 506 476 516 488 = 0.77 || = 0.08 507 523 511 491 518 | 500 Aver./ d 0.50074 502 > 500: 8 3 6 6 2 5 6 5 5 6 | 500 | 509 504 522 498 473 = 0.76 || = 0.07 461 481 496 516 511 | 500 median s 0.49998 501 ----- 6 7 4 4 5 6 5 5 4 5 | 500 | 522 482 497 555 514 = 0.75 || = 0.06 514 486 468 457 487 | 500 t 0.49915 497 5 3 7 5 5 4 5 3 5 2 | 500 | 488 503 520 512 512 = 0.74 || = 0.05 504 507 503 486 533 | 500 m 0.50147 499 5 4 6 2 6 5 4 6 6 3 | 500 | 470 475 490 477 493 = 0.73 || = 0.04 515 516 535 503 496 | 500 x 0.49902 501 5 5 4 5 6 7 5 4 6 5 | 500 | 521 510 496 492 514 = 0.72 || = 0.03 519 512 494 499 504 | 500 -----------------------------------------------------------------| 500 | 490 513 500 524 503 = 0.71 || = 0.02 531 468 553 502 498 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 527 478 479 495 493 = 0.70 || = 0.01 236 258 236 270 272 | 252.5 d 0 0 2 15 68 15 1 0 0 | 500 | 520 472 473 482 513 = 0.69 || < 0.01 507 486 526 501 460 | 497.5 s 0 0 3 14 69 13 2 0 0 | 500 | 528 507 511 512 500 = 0.68 ||========================================================================= t 0 0 0 22 58 17 3 1 0 | 500 | 516 509 548 492 488 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 14 72 8 6 0 0 | 500 | 514 450 475 519 531 = 0.66 ||========================================================================= x 0 0 1 13 79 8 0 0 0 | 500 | 478 489 525 521 508 = 0.65 || sknuth_MaxOft test: no 90 test no 91 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 91 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 1 0 | 0.5 | 0 2 1 2 1 > 0.99999 || = 0.64 498 506 496 487 485 | 500 < 0.00002 1 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 518 502 517 517 487 | 500 < 0.00003 2 0 0 0 1 | 0.5 | 1 0 1 1 0 > 0.99997 || = 0.62 501 517 491 521 474 | 500 < 0.00004 1 1 0 1 1 | 0.5 | 1 0 0 0 1 > 0.99996 || = 0.61 516 483 481 511 509 | 500 < 0.00005 0 0 0 2 0 | 0.5 | 0 0 1 0 1 > 0.99995 || = 0.60 503 495 503 497 496 | 500 < 0.00006 1 0 0 1 0 | 0.5 | 1 0 0 1 0 > 0.99994 || = 0.59 502 462 513 509 499 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 2 0 1 1 > 0.99993 || = 0.58 520 491 525 483 511 | 500 < 0.00008 1 0 0 0 1 | 0.5 | 1 0 1 0 0 > 0.99992 || = 0.57 521 516 486 465 472 | 500 < 0.00009 0 1 0 0 1 | 0.5 | 0 2 1 0 0 > 0.99991 || = 0.56 504 498 499 471 508 | 500 < 0.0001 0 1 0 1 0 | 0.5 | 0 1 0 1 1 > 0.9999 || = 0.55 468 476 470 483 511 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 531 501 476 467 499 | 500 < 0.0001 6 4 1 6 5 | 5 | 4 7 5 6 5 > 0.9999 || = 0.53 478 466 506 485 523 | 500 < 0.0002 3 4 2 3 2 | 5 | 4 2 3 4 7 > 0.9998 || = 0.52 548 493 510 529 501 | 500 < 0.0003 4 3 6 3 6 | 5 | 5 5 9 2 1 > 0.9997 || = 0.51 452 494 518 513 496 | 500 < 0.0004 4 4 3 4 6 | 5 | 5 4 8 4 9 > 0.9996 || = 0.50 494 506 476 522 517 | 500 < 0.0005 8 7 2 7 4 | 5 | 4 5 5 4 4 > 0.9995 || = 0.49 451 449 487 488 501 | 500 < 0.0006 6 4 3 5 3 | 5 | 5 8 9 3 4 > 0.9994 || = 0.48 522 495 515 534 482 | 500 < 0.0007 7 4 4 3 7 | 5 | 8 3 6 4 6 > 0.9993 || = 0.47 479 538 514 484 529 | 500 < 0.0008 8 5 3 5 6 | 5 | 5 7 10 3 5 > 0.9992 || = 0.46 510 504 504 510 470 | 500 < 0.0009 5 2 4 12 5 | 5 | 6 4 7 2 5 > 0.9991 || = 0.45 511 476 494 493 465 | 500 < 0.001 4 1 7 4 6 | 5 | 3 5 2 2 8 > 0.999 || = 0.44 438 524 484 505 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 515 475 500 484 488 | 500 < 0.001 55 38 35 52 50 | 50 | 49 50 64 34 54 > 0.999 || = 0.42 470 549 505 518 559 | 500 < 0.002 44 57 59 47 50 | 50 | 52 59 66 43 42 > 0.998 || = 0.41 514 506 490 501 505 | 500 < 0.003 40 52 50 54 50 | 50 | 46 57 53 54 53 > 0.997 || = 0.40 508 503 514 474 497 | 500 < 0.004 53 41 39 43 49 | 50 | 54 52 57 54 46 > 0.996 || = 0.39 521 523 439 504 522 | 500 < 0.005 55 51 38 49 39 | 50 | 57 54 63 66 53 > 0.995 || = 0.38 488 459 529 508 488 | 500 < 0.006 51 44 54 53 51 | 50 | 43 42 51 56 52 > 0.994 || = 0.37 493 503 499 513 518 | 500 < 0.007 40 63 48 46 45 | 50 | 46 51 58 54 40 > 0.993 || = 0.36 480 477 501 531 499 | 500 < 0.008 53 50 45 53 59 | 50 | 55 51 55 39 44 > 0.992 || = 0.35 468 511 481 517 514 | 500 < 0.009 53 63 51 50 45 | 50 | 57 48 49 54 59 > 0.991 || = 0.34 447 485 493 483 460 | 500 < 0.01 55 51 53 56 45 | 50 | 48 61 52 58 51 > 0.99 || = 0.33 475 533 471 531 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 520 484 499 506 501 | 500 < 0.01 499 510 472 503 483 | 497.5 | 507 525 568 512 494 > 0.99 || = 0.31 524 528 514 473 494 | 500 = 0.01 281 246 268 232 248 | 252.5 | 226 269 246 248 253 = 0.99 || = 0.30 525 520 505 492 468 | 500 = 0.02 514 504 482 506 541 | 500 | 542 517 501 521 514 = 0.98 || = 0.29 495 487 514 517 535 | 500 =================================================================| 500 | 497 514 532 461 501 = 0.97 || = 0.28 470 510 508 483 510 | 500 sknuth_MaxOft test: | 500 | 484 534 529 493 514 = 0.96 || = 0.27 507 488 445 494 510 | 500 ----------------------------------------------- | 500 | 453 497 532 493 507 = 0.95 || = 0.26 527 542 483 543 459 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 24 | 500 | 511 493 463 502 540 = 0.94 || = 0.25 517 511 507 541 526 | 500 Test results for Anderson-Darling: | 500 | 479 498 491 500 521 = 0.93 || = 0.24 498 520 517 505 507 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 478 472 482 544 478 = 0.92 || = 0.23 544 531 517 494 544 | 500 =================================================================| 500 | 538 458 487 538 503 = 0.91 || = 0.22 513 496 493 515 476 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 490 517 488 518 488 = 0.90 || = 0.21 499 505 496 495 504 | 500 -----------------------------------------------------------------| 500 | 507 503 525 518 493 = 0.89 || = 0.20 514 548 476 478 462 | 500 SD Bern.: d 1.13784 0.82381 0.67708 | 500 | 527 443 525 503 500 = 0.88 || = 0.19 513 474 521 495 524 | 500 s 1.04089 1.14424 0.82623 | 500 | 480 486 535 498 525 = 0.87 || = 0.18 494 475 481 490 502 | 500 t 0.95667 1.11948 1.24480 | 500 | 451 507 497 476 495 = 0.86 || = 0.17 549 476 521 499 475 | 500 m 0.89016 0.54615 1.30141 | 500 | 484 491 499 492 526 = 0.85 || = 0.16 468 474 488 479 512 | 500 x 0.96411 0.74736 0.82015 | 500 | 490 501 494 496 493 = 0.84 || = 0.15 513 520 492 492 515 | 500 | 500 | 483 488 479 496 474 = 0.83 || = 0.14 509 507 509 486 503 | 500 Changes: d 52 4 6 | 500 | 537 536 501 529 486 = 0.82 || = 0.13 448 512 514 505 466 | 500 s 56 7 5 | 500 | 527 464 470 493 497 = 0.81 || = 0.12 478 466 514 503 438 | 500 t 51 5 2 | 500 | 500 510 467 514 507 = 0.80 || = 0.11 478 492 471 505 525 | 500 m 50 8 3 | 500 | 503 463 479 501 490 = 0.79 || = 0.10 508 521 501 518 496 | 500 x 57 4 6 | 500 | 509 510 480 471 512 = 0.78 || = 0.09 507 495 498 478 498 | 500 -----------------------------------------------------------------| 500 | 558 530 492 496 529 = 0.77 || = 0.08 498 500 526 517 494 | 500 Aver./ d 0.49954 502 > 500: 6 5 6 4 6 7 6 5 4 4 | 500 | 468 521 519 497 535 = 0.76 || = 0.07 472 534 471 489 516 | 500 median s 0.49937 501 ----- 5 4 7 6 6 2 5 6 5 5 | 500 | 519 560 478 466 511 = 0.75 || = 0.06 506 474 484 495 452 | 500 t 0.50103 499 5 6 5 4 5 6 4 2 4 5 | 500 | 473 484 492 550 504 = 0.74 || = 0.05 495 520 519 483 490 | 500 m 0.50076 498 3 4 5 7 5 3 6 4 4 5 | 500 | 488 508 541 489 464 = 0.73 || = 0.04 474 475 526 493 491 | 500 x 0.50098 501 3 6 7 4 5 5 4 7 2 8 | 500 | 514 478 495 499 480 = 0.72 || = 0.03 545 511 525 483 535 | 500 -----------------------------------------------------------------| 500 | 486 493 497 507 509 = 0.71 || = 0.02 514 504 482 506 541 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 490 498 533 483 475 = 0.70 || = 0.01 281 246 268 232 248 | 252.5 d 0 0 7 11 66 13 4 0 0 | 500 | 486 481 498 505 499 = 0.69 || < 0.01 499 510 472 503 483 | 497.5 s 0 0 2 19 64 13 3 0 0 | 500 | 531 505 541 492 478 = 0.68 ||========================================================================= t 0 0 2 11 73 14 0 1 0 | 500 | 512 517 492 437 519 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 10 79 10 1 0 0 | 500 | 497 459 517 524 502 = 0.66 ||========================================================================= x 0 0 2 14 70 14 1 0 0 | 500 | 529 498 491 513 503 = 0.65 || sknuth_MaxOft test: no 91 test no 92 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 92 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 2 0 0 | 0.5 | 0 0 1 1 1 > 0.99999 || = 0.64 502 462 516 523 506 | 500 < 0.00002 0 1 0 1 0 | 0.5 | 1 0 0 0 1 > 0.99998 || = 0.63 500 477 537 495 490 | 500 < 0.00003 0 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 525 496 459 486 446 | 500 < 0.00004 2 0 2 0 0 | 0.5 | 1 1 1 0 0 > 0.99996 || = 0.61 519 546 502 471 502 | 500 < 0.00005 0 2 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 487 487 490 497 525 | 500 < 0.00006 2 2 0 2 1 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 510 490 505 520 498 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 1 0 2 > 0.99993 || = 0.58 499 466 497 534 502 | 500 < 0.00008 0 1 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 538 494 525 482 524 | 500 < 0.00009 1 0 0 1 2 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 509 486 508 527 549 | 500 < 0.0001 0 0 0 0 1 | 0.5 | 1 0 0 1 0 > 0.9999 || = 0.55 486 488 475 534 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 447 540 481 499 531 | 500 < 0.0001 6 8 4 5 4 | 5 | 4 2 4 2 4 > 0.9999 || = 0.53 535 486 524 527 490 | 500 < 0.0002 7 4 5 4 4 | 5 | 3 2 3 0 2 > 0.9998 || = 0.52 452 485 489 499 484 | 500 < 0.0003 7 5 5 4 8 | 5 | 2 3 7 7 2 > 0.9997 || = 0.51 490 497 553 459 507 | 500 < 0.0004 5 3 2 3 5 | 5 | 4 3 3 5 5 > 0.9996 || = 0.50 468 518 515 506 490 | 500 < 0.0005 4 5 10 1 8 | 5 | 4 2 10 5 4 > 0.9995 || = 0.49 507 517 494 493 478 | 500 < 0.0006 6 2 4 7 4 | 5 | 1 2 3 4 8 > 0.9994 || = 0.48 439 477 479 479 506 | 500 < 0.0007 3 6 7 9 3 | 5 | 6 3 4 5 5 > 0.9993 || = 0.47 464 519 516 506 517 | 500 < 0.0008 7 4 4 5 7 | 5 | 3 3 4 6 7 > 0.9992 || = 0.46 501 504 513 475 485 | 500 < 0.0009 2 3 4 3 6 | 5 | 5 4 5 4 3 > 0.9991 || = 0.45 524 502 477 518 480 | 500 < 0.001 6 6 3 2 3 | 5 | 6 11 2 2 6 > 0.999 || = 0.44 533 536 491 477 508 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 480 496 498 503 498 | 500 < 0.001 53 46 48 43 52 | 50 | 38 35 45 40 46 > 0.999 || = 0.42 504 507 474 500 474 | 500 < 0.002 49 55 62 52 45 | 50 | 51 29 55 52 58 > 0.998 || = 0.41 454 486 518 494 480 | 500 < 0.003 43 51 55 35 41 | 50 | 48 52 50 57 54 > 0.997 || = 0.40 547 510 547 519 488 | 500 < 0.004 48 56 56 43 45 | 50 | 61 41 49 55 50 > 0.996 || = 0.39 485 491 523 511 517 | 500 < 0.005 48 48 43 51 34 | 50 | 43 54 46 46 57 > 0.995 || = 0.38 464 497 515 523 528 | 500 < 0.006 47 59 58 52 46 | 50 | 57 42 56 48 51 > 0.994 || = 0.37 523 516 487 531 495 | 500 < 0.007 51 52 42 52 49 | 50 | 47 59 48 50 59 > 0.993 || = 0.36 529 482 504 476 480 | 500 < 0.008 57 55 67 58 58 | 50 | 57 44 56 46 56 > 0.992 || = 0.35 537 478 494 481 482 | 500 < 0.009 50 41 53 44 50 | 50 | 49 50 46 46 45 > 0.991 || = 0.34 472 530 487 483 499 | 500 < 0.01 49 50 45 49 58 | 50 | 56 54 60 51 53 > 0.99 || = 0.33 510 543 525 468 482 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 467 484 486 533 511 | 500 < 0.01 495 513 529 479 478 | 497.5 | 507 460 511 491 529 > 0.99 || = 0.31 487 515 504 476 518 | 500 = 0.01 238 259 267 276 255 | 252.5 | 260 262 252 252 256 = 0.99 || = 0.30 563 470 499 505 509 | 500 = 0.02 503 452 491 497 506 | 500 | 511 486 507 486 534 = 0.98 || = 0.29 490 508 491 515 498 | 500 =================================================================| 500 | 497 524 501 497 528 = 0.97 || = 0.28 486 504 462 494 501 | 500 sknuth_MaxOft test: | 500 | 492 521 520 511 503 = 0.96 || = 0.27 513 537 453 504 526 | 500 ----------------------------------------------- | 500 | 499 472 507 497 501 = 0.95 || = 0.26 496 528 507 529 537 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 24 | 500 | 483 507 451 509 476 = 0.94 || = 0.25 512 506 534 507 465 | 500 Test results for Anderson-Darling: | 500 | 521 493 511 493 515 = 0.93 || = 0.24 475 512 467 487 476 | 500 Anderson-Darling statistic = A2 | 500 | 483 513 512 471 517 = 0.92 || = 0.23 483 503 534 504 473 | 500 =================================================================| 500 | 523 520 514 538 473 = 0.91 || = 0.22 509 509 510 496 493 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 454 464 466 459 474 = 0.90 || = 0.21 461 472 506 475 497 | 500 -----------------------------------------------------------------| 500 | 517 514 493 525 496 = 0.89 || = 0.20 511 501 502 468 529 | 500 SD Bern.: d 1.07979 0.50422 0.96276 | 500 | 514 487 461 486 544 = 0.88 || = 0.19 523 524 506 462 508 | 500 s 0.89600 0.73928 1.38921 | 500 | 473 498 522 488 466 = 0.87 || = 0.18 477 475 464 527 498 | 500 t 1.00489 1.19138 0.72006 | 500 | 496 500 481 488 493 = 0.86 || = 0.17 491 489 501 487 508 | 500 m 0.94837 0.93533 0.68003 | 500 | 499 495 464 502 468 = 0.85 || = 0.16 515 509 465 466 536 | 500 x 0.94254 1.03588 0.77109 | 500 | 501 485 490 494 506 = 0.84 || = 0.15 512 481 452 507 528 | 500 | 500 | 501 480 501 504 492 = 0.83 || = 0.14 487 493 494 496 474 | 500 Changes: d 57 3 9 | 500 | 513 549 500 491 482 = 0.82 || = 0.13 514 507 485 453 485 | 500 s 51 4 7 | 500 | 510 493 476 552 478 = 0.81 || = 0.12 529 498 491 490 507 | 500 t 46 6 7 | 500 | 493 500 513 506 485 = 0.80 || = 0.11 476 504 476 513 518 | 500 m 56 4 3 | 500 | 470 522 504 548 468 = 0.79 || = 0.10 530 499 519 502 509 | 500 x 43 4 5 | 500 | 537 523 495 509 476 = 0.78 || = 0.09 467 535 552 496 528 | 500 -----------------------------------------------------------------| 500 | 482 526 490 503 495 = 0.77 || = 0.08 518 496 507 528 505 | 500 Aver./ d 0.49897 501 > 500: 7 6 4 5 6 4 7 4 6 5 | 500 | 522 477 523 507 539 = 0.76 || = 0.07 548 469 529 479 510 | 500 median s 0.49951 499 ----- 5 4 9 4 7 1 2 6 2 6 | 500 | 527 486 506 464 451 = 0.75 || = 0.06 535 511 536 519 473 | 500 t 0.49944 501 7 3 6 5 4 5 5 6 2 8 | 500 | 478 488 541 522 511 = 0.74 || = 0.05 518 513 504 504 497 | 500 m 0.50096 499 5 4 5 5 4 5 6 7 4 3 | 500 | 503 504 534 516 497 = 0.73 || = 0.04 501 494 476 518 482 | 500 x 0.49981 499 5 7 4 5 3 6 6 4 2 8 | 500 | 500 530 484 499 520 = 0.72 || = 0.03 514 496 495 486 496 | 500 -----------------------------------------------------------------| 500 | 470 504 474 462 515 = 0.71 || = 0.02 503 452 491 497 506 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 503 483 488 503 474 = 0.70 || = 0.01 238 259 267 276 255 | 252.5 d 0 0 5 14 64 15 3 0 0 | 500 | 460 501 517 518 517 = 0.69 || < 0.01 495 513 529 479 478 | 497.5 s 0 0 1 12 74 12 2 0 0 | 500 | 496 500 493 477 519 = 0.68 ||========================================================================= t 0 0 3 15 67 13 3 0 0 | 500 | 502 485 497 528 514 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 16 67 15 2 0 0 | 500 | 514 488 485 521 499 = 0.66 ||========================================================================= x 0 0 2 14 68 16 1 0 0 | 500 | 505 485 504 509 526 = 0.65 || sknuth_MaxOft test: no 92 test no 93 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 93 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 1 0 0 | 0.5 | 0 0 0 0 1 > 0.99999 || = 0.64 519 510 473 497 505 | 500 < 0.00002 0 1 0 1 0 | 0.5 | 0 0 1 0 1 > 0.99998 || = 0.63 513 501 509 513 504 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 1 1 > 0.99997 || = 0.62 504 470 518 443 483 | 500 < 0.00004 1 0 0 0 1 | 0.5 | 2 2 2 1 0 > 0.99996 || = 0.61 484 489 522 536 505 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 2 0 > 0.99995 || = 0.60 500 514 487 481 484 | 500 < 0.00006 1 3 2 1 1 | 0.5 | 0 2 3 0 0 > 0.99994 || = 0.59 496 519 474 506 535 | 500 < 0.00007 2 0 1 1 1 | 0.5 | 1 0 1 0 0 > 0.99993 || = 0.58 460 472 483 510 521 | 500 < 0.00008 0 0 1 1 0 | 0.5 | 1 1 0 0 0 > 0.99992 || = 0.57 524 466 484 456 508 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99991 || = 0.56 478 494 506 491 509 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 1 2 0 2 0 > 0.9999 || = 0.55 493 501 501 529 526 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 496 521 503 481 475 | 500 < 0.0001 6 5 5 5 3 | 5 | 5 7 7 6 4 > 0.9999 || = 0.53 500 506 496 499 512 | 500 < 0.0002 6 11 5 1 2 | 5 | 2 4 3 3 2 > 0.9998 || = 0.52 477 532 465 460 550 | 500 < 0.0003 6 6 5 6 2 | 5 | 7 4 3 5 8 > 0.9997 || = 0.51 505 512 516 528 548 | 500 < 0.0004 5 6 4 6 7 | 5 | 5 5 5 6 5 > 0.9996 || = 0.50 529 491 479 488 539 | 500 < 0.0005 3 1 7 9 3 | 5 | 7 7 3 3 8 > 0.9995 || = 0.49 524 539 491 522 519 | 500 < 0.0006 1 6 4 7 5 | 5 | 5 4 3 9 8 > 0.9994 || = 0.48 500 458 514 466 507 | 500 < 0.0007 9 10 1 5 7 | 5 | 3 2 2 6 6 > 0.9993 || = 0.47 502 508 513 524 503 | 500 < 0.0008 8 3 5 4 3 | 5 | 8 4 2 9 4 > 0.9992 || = 0.46 532 506 491 488 486 | 500 < 0.0009 5 3 7 5 5 | 5 | 5 3 6 5 5 > 0.9991 || = 0.45 482 465 473 497 499 | 500 < 0.001 6 3 7 10 4 | 5 | 3 4 7 8 6 > 0.999 || = 0.44 510 518 522 527 490 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 515 459 491 509 486 | 500 < 0.001 55 54 50 58 41 | 50 | 50 44 41 60 56 > 0.999 || = 0.42 494 475 522 494 502 | 500 < 0.002 46 48 49 48 40 | 50 | 43 48 49 61 36 > 0.998 || = 0.41 504 497 463 490 507 | 500 < 0.003 65 63 55 57 55 | 50 | 33 55 44 47 59 > 0.997 || = 0.40 545 517 478 462 503 | 500 < 0.004 59 50 52 52 46 | 50 | 48 57 42 43 47 > 0.996 || = 0.39 494 491 513 521 517 | 500 < 0.005 54 47 44 51 42 | 50 | 47 51 52 55 54 > 0.995 || = 0.38 481 507 504 481 514 | 500 < 0.006 50 58 39 50 53 | 50 | 58 44 52 51 54 > 0.994 || = 0.37 493 489 495 498 462 | 500 < 0.007 47 41 43 44 56 | 50 | 37 48 52 57 52 > 0.993 || = 0.36 525 482 501 506 488 | 500 < 0.008 51 56 45 42 39 | 50 | 42 45 52 61 56 > 0.992 || = 0.35 489 501 483 486 478 | 500 < 0.009 44 49 45 39 52 | 50 | 45 57 43 50 56 > 0.991 || = 0.34 474 478 495 482 490 | 500 < 0.01 44 52 65 49 43 | 50 | 59 50 46 44 52 > 0.99 || = 0.33 480 533 504 468 529 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 486 524 485 495 534 | 500 < 0.01 515 518 487 490 467 | 497.5 | 462 499 473 529 522 > 0.99 || = 0.31 471 507 515 500 448 | 500 = 0.01 244 268 266 260 224 | 252.5 | 267 263 259 271 265 = 0.99 || = 0.30 547 463 504 504 509 | 500 = 0.02 490 475 457 519 499 | 500 | 493 492 519 465 481 = 0.98 || = 0.29 508 481 532 488 478 | 500 =================================================================| 500 | 507 526 517 560 524 = 0.97 || = 0.28 513 506 467 515 490 | 500 sknuth_MaxOft test: | 500 | 523 496 461 481 480 = 0.96 || = 0.27 562 511 561 470 518 | 500 ----------------------------------------------- | 500 | 473 465 496 493 528 = 0.95 || = 0.26 499 526 479 511 468 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 32 | 500 | 539 518 505 520 500 = 0.94 || = 0.25 508 522 486 530 477 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 496 517 534 462 500 = 0.93 || = 0.24 487 479 522 483 536 | 500 | 500 | 504 498 493 564 512 = 0.92 || = 0.23 499 536 471 491 493 | 500 =================================================================| 500 | 485 490 491 530 507 = 0.91 || = 0.22 501 480 505 460 493 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 511 519 516 520 491 = 0.90 || = 0.21 506 462 528 494 509 | 500 -----------------------------------------------------------------| 500 | 477 560 548 497 504 = 0.89 || = 0.20 514 477 521 457 519 | 500 SD Bern.: d 0.95149 0.94386 1.22861 | 500 | 512 513 495 512 458 = 0.88 || = 0.19 441 489 502 527 491 | 500 s 0.94822 0.87678 0.67708 | 500 | 466 516 478 526 475 = 0.87 || = 0.18 472 499 524 466 515 | 500 t 0.91475 1.01143 0.72561 | 500 | 514 525 481 505 506 = 0.86 || = 0.17 534 489 507 507 496 | 500 m 1.07762 0.82986 1.01143 | 500 | 483 502 525 547 491 = 0.85 || = 0.16 501 485 512 480 515 | 500 x 0.95066 1.00548 0.93212 | 500 | 456 525 513 476 491 = 0.84 || = 0.15 482 468 483 497 476 | 500 | 500 | 516 496 529 520 478 = 0.83 || = 0.14 517 506 478 494 500 | 500 Changes: d 57 5 3 | 500 | 490 517 529 518 494 = 0.82 || = 0.13 493 489 476 514 520 | 500 s 46 8 4 | 500 | 535 495 504 515 516 = 0.81 || = 0.12 516 490 513 521 465 | 500 t 52 3 2 | 500 | 530 516 495 486 502 = 0.80 || = 0.11 477 527 498 510 490 | 500 m 57 3 3 | 500 | 462 497 515 530 523 = 0.79 || = 0.10 507 521 498 517 513 | 500 x 51 6 4 | 500 | 493 496 493 532 488 = 0.78 || = 0.09 465 540 509 479 456 | 500 -----------------------------------------------------------------| 500 | 529 500 496 489 478 = 0.77 || = 0.08 502 506 462 442 519 | 500 Aver./ d 0.50009 500 > 500: 4 5 7 2 7 2 7 5 5 5 | 500 | 517 496 477 503 491 = 0.76 || = 0.07 503 536 516 497 488 | 500 median s 0.50072 500 ----- 7 3 5 5 5 7 2 3 8 5 | 500 | 514 502 487 503 486 = 0.75 || = 0.06 491 509 505 492 496 | 500 t 0.50105 501 6 5 6 6 4 4 6 4 7 5 | 500 | 508 500 525 545 511 = 0.74 || = 0.05 499 466 504 496 460 | 500 m 0.50340 498 3 6 3 3 4 4 4 6 8 6 | 500 | 476 518 492 478 483 = 0.73 || = 0.04 482 524 501 510 498 | 500 x 0.50131 500 2 4 4 5 6 8 6 5 3 6 | 500 | 488 482 514 505 525 = 0.72 || = 0.03 512 489 487 491 535 | 500 -----------------------------------------------------------------| 500 | 489 469 532 469 531 = 0.71 || = 0.02 490 475 457 519 499 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 509 480 457 519 505 = 0.70 || = 0.01 244 268 266 260 224 | 252.5 d 0 0 1 15 71 11 3 0 0 | 500 | 475 471 510 489 479 = 0.69 || < 0.01 515 518 487 490 467 | 497.5 s 0 0 0 16 71 13 1 0 0 | 500 | 510 489 508 496 504 = 0.68 ||========================================================================= t 0 0 0 14 75 10 2 0 0 | 500 | 495 497 484 498 481 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 13 69 13 4 0 0 | 500 | 513 478 526 520 491 = 0.66 ||========================================================================= x 0 0 1 12 73 13 2 0 0 | 500 | 517 488 493 481 520 = 0.65 || sknuth_MaxOft test: no 93 test no 94 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 94 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 3 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 504 498 507 499 534 | 500 < 0.00002 0 3 0 3 0 | 0.5 | 2 0 1 0 0 > 0.99998 || = 0.63 530 476 497 481 552 | 500 < 0.00003 1 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 503 465 501 497 479 | 500 < 0.00004 1 1 0 0 0 | 0.5 | 2 0 1 0 0 > 0.99996 || = 0.61 473 484 481 524 500 | 500 < 0.00005 2 0 1 0 1 | 0.5 | 1 1 0 1 0 > 0.99995 || = 0.60 513 483 503 470 504 | 500 < 0.00006 0 0 1 0 1 | 0.5 | 1 0 0 0 1 > 0.99994 || = 0.59 517 481 508 477 496 | 500 < 0.00007 0 1 1 1 0 | 0.5 | 0 1 1 0 0 > 0.99993 || = 0.58 488 449 512 477 506 | 500 < 0.00008 2 0 0 1 0 | 0.5 | 2 1 0 0 0 > 0.99992 || = 0.57 469 537 449 469 494 | 500 < 0.00009 0 1 0 1 0 | 0.5 | 0 0 1 1 0 > 0.99991 || = 0.56 511 533 497 529 476 | 500 < 0.0001 0 0 0 0 1 | 0.5 | 0 0 0 1 1 > 0.9999 || = 0.55 531 496 495 514 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 506 475 526 524 498 | 500 < 0.0001 7 9 3 8 4 | 5 | 8 3 4 3 2 > 0.9999 || = 0.53 514 456 483 512 462 | 500 < 0.0002 4 4 6 7 9 | 5 | 2 8 0 2 2 > 0.9998 || = 0.52 501 507 505 501 493 | 500 < 0.0003 4 4 6 6 6 | 5 | 6 5 3 3 5 > 0.9997 || = 0.51 487 526 504 466 511 | 500 < 0.0004 6 6 6 6 3 | 5 | 6 8 2 9 5 > 0.9996 || = 0.50 528 500 513 503 499 | 500 < 0.0005 7 4 5 4 6 | 5 | 5 1 4 8 6 > 0.9995 || = 0.49 505 500 504 510 486 | 500 < 0.0006 12 8 7 2 8 | 5 | 7 3 2 6 4 > 0.9994 || = 0.48 496 520 525 487 487 | 500 < 0.0007 9 3 1 5 6 | 5 | 3 4 7 4 6 > 0.9993 || = 0.47 508 499 521 498 528 | 500 < 0.0008 6 3 5 6 5 | 5 | 2 4 5 4 2 > 0.9992 || = 0.46 496 499 530 489 519 | 500 < 0.0009 1 1 2 5 4 | 5 | 11 4 4 4 5 > 0.9991 || = 0.45 504 488 495 522 469 | 500 < 0.001 10 10 5 3 7 | 5 | 6 4 5 8 8 > 0.999 || = 0.44 453 506 472 465 437 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 477 505 529 491 485 | 500 < 0.001 66 52 46 52 58 | 50 | 56 44 36 51 45 > 0.999 || = 0.42 479 505 537 504 500 | 500 < 0.002 46 47 42 40 45 | 50 | 52 53 46 52 52 > 0.998 || = 0.41 510 493 467 515 461 | 500 < 0.003 47 59 44 46 59 | 50 | 54 52 45 45 51 > 0.997 || = 0.40 540 492 521 515 521 | 500 < 0.004 37 45 60 59 38 | 50 | 58 62 56 45 60 > 0.996 || = 0.39 529 542 507 509 569 | 500 < 0.005 50 50 45 59 37 | 50 | 47 49 50 51 50 > 0.995 || = 0.38 506 465 539 535 513 | 500 < 0.006 41 50 59 54 58 | 50 | 52 43 52 47 48 > 0.994 || = 0.37 502 456 492 463 532 | 500 < 0.007 38 59 44 52 41 | 50 | 46 35 39 56 45 > 0.993 || = 0.36 490 466 524 469 493 | 500 < 0.008 42 57 48 56 55 | 50 | 56 50 57 48 48 > 0.992 || = 0.35 508 486 512 496 470 | 500 < 0.009 53 46 59 54 39 | 50 | 52 42 53 54 57 > 0.991 || = 0.34 468 525 475 479 510 | 500 < 0.01 53 59 36 64 46 | 50 | 45 57 51 57 37 > 0.99 || = 0.33 473 515 481 521 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 495 535 475 505 552 | 500 < 0.01 473 524 483 536 476 | 497.5 | 518 487 485 506 493 > 0.99 || = 0.31 488 521 486 508 461 | 500 = 0.01 256 219 252 266 233 | 252.5 | 252 268 252 255 278 = 0.99 || = 0.30 515 514 485 462 532 | 500 = 0.02 522 483 515 522 511 | 500 | 497 492 467 502 521 = 0.98 || = 0.29 469 499 476 482 474 | 500 =================================================================| 500 | 484 484 471 517 509 = 0.97 || = 0.28 486 535 514 529 489 | 500 sknuth_MaxOft test: | 500 | 506 510 485 472 499 = 0.96 || = 0.27 513 563 514 495 512 | 500 ----------------------------------------------- | 500 | 498 487 456 481 467 = 0.95 || = 0.26 553 503 471 536 539 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 32 | 500 | 497 485 518 520 513 = 0.94 || = 0.25 505 505 487 511 476 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 496 498 506 496 511 = 0.93 || = 0.24 482 531 486 519 485 | 500 | 500 | 505 499 512 502 517 = 0.92 || = 0.23 494 470 551 478 464 | 500 =================================================================| 500 | 492 515 521 473 461 = 0.91 || = 0.22 499 491 497 478 502 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 467 512 472 516 480 = 0.90 || = 0.21 508 486 512 507 521 | 500 -----------------------------------------------------------------| 500 | 535 475 516 525 501 = 0.89 || = 0.20 513 488 537 469 453 | 500 SD Bern.: d 0.98668 1.23106 0.65453 | 500 | 493 506 535 511 535 = 0.88 || = 0.19 506 501 488 511 514 | 500 s 0.98956 0.83227 1.07849 | 500 | 489 533 507 490 499 = 0.87 || = 0.18 510 510 540 495 462 | 500 t 1.01040 1.13104 0.95650 | 500 | 453 513 488 481 507 = 0.86 || = 0.17 481 514 503 485 510 | 500 m 0.98755 1.04932 0.58337 | 500 | 500 489 503 499 516 = 0.85 || = 0.16 499 509 549 512 478 | 500 x 1.04661 1.25760 0.87335 | 500 | 499 492 510 524 497 = 0.84 || = 0.15 533 491 503 526 490 | 500 | 500 | 525 477 500 517 522 = 0.83 || = 0.14 494 468 463 529 510 | 500 Changes: d 49 2 5 | 500 | 530 529 516 450 504 = 0.82 || = 0.13 526 493 501 464 506 | 500 s 41 6 3 | 500 | 526 522 535 491 482 = 0.81 || = 0.12 512 488 523 479 517 | 500 t 44 6 5 | 500 | 511 516 484 486 476 = 0.80 || = 0.11 497 500 511 553 519 | 500 m 48 2 6 | 500 | 502 492 466 503 511 = 0.79 || = 0.10 529 499 466 490 488 | 500 x 50 7 4 | 500 | 459 513 465 486 514 = 0.78 || = 0.09 465 545 486 509 482 | 500 -----------------------------------------------------------------| 500 | 470 500 525 518 493 = 0.77 || = 0.08 523 511 541 557 510 | 500 Aver./ d 0.50019 502 > 500: 4 6 5 5 5 7 6 6 4 3 | 500 | 537 497 461 520 497 = 0.76 || = 0.07 509 468 520 533 510 | 500 median s 0.49908 499 ----- 6 4 5 6 4 4 3 4 6 3 | 500 | 475 489 497 453 524 = 0.75 || = 0.06 476 512 498 519 528 | 500 t 0.49820 501 4 7 5 4 7 6 5 2 7 4 | 500 | 543 536 466 483 471 = 0.74 || = 0.05 474 498 489 498 514 | 500 m 0.49730 502 8 5 5 5 5 5 4 4 5 6 | 500 | 525 520 467 482 542 = 0.73 || = 0.04 489 530 473 520 488 | 500 x 0.50088 500 5 6 4 7 3 4 3 5 6 6 | 500 | 483 471 520 503 510 = 0.72 || = 0.03 466 517 510 493 494 | 500 -----------------------------------------------------------------| 500 | 536 463 488 473 488 = 0.71 || = 0.02 522 483 515 522 511 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 474 489 489 495 496 = 0.70 || = 0.01 256 219 252 266 233 | 252.5 d 0 0 3 17 63 17 1 0 0 | 500 | 508 487 507 486 472 = 0.69 || < 0.01 473 524 483 536 476 | 497.5 s 0 0 2 14 70 13 2 0 0 | 500 | 504 502 524 510 484 = 0.68 ||========================================================================= t 0 0 1 19 64 15 2 0 0 | 500 | 441 504 506 513 497 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 70 12 2 0 0 | 500 | 477 481 488 465 516 = 0.66 ||========================================================================= x 0 0 2 16 70 10 2 1 0 | 500 | 514 518 475 509 491 = 0.65 || sknuth_MaxOft test: no 94 test no 95 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 95 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 1 1 | 0.5 | 0 0 0 0 1 > 0.99999 || = 0.64 482 492 485 486 480 | 500 < 0.00002 0 1 0 2 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 478 487 501 502 518 | 500 < 0.00003 0 1 0 0 0 | 0.5 | 0 0 0 0 2 > 0.99997 || = 0.62 498 505 500 515 531 | 500 < 0.00004 0 0 0 1 1 | 0.5 | 0 0 0 0 1 > 0.99996 || = 0.61 509 510 492 469 475 | 500 < 0.00005 0 1 1 2 1 | 0.5 | 0 2 2 0 0 > 0.99995 || = 0.60 528 489 509 507 477 | 500 < 0.00006 0 1 0 2 1 | 0.5 | 0 0 0 1 1 > 0.99994 || = 0.59 505 515 524 490 517 | 500 < 0.00007 1 2 0 3 0 | 0.5 | 0 0 1 0 0 > 0.99993 || = 0.58 466 483 472 535 494 | 500 < 0.00008 0 1 0 1 0 | 0.5 | 1 0 0 1 1 > 0.99992 || = 0.57 513 553 455 502 485 | 500 < 0.00009 1 0 0 0 0 | 0.5 | 0 1 0 1 1 > 0.99991 || = 0.56 496 498 495 505 505 | 500 < 0.0001 1 1 1 0 0 | 0.5 | 0 0 0 2 0 > 0.9999 || = 0.55 529 521 479 529 505 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 487 539 505 517 512 | 500 < 0.0001 3 8 3 12 4 | 5 | 1 3 3 5 7 > 0.9999 || = 0.53 495 509 512 485 492 | 500 < 0.0002 4 3 6 4 7 | 5 | 2 2 2 2 1 > 0.9998 || = 0.52 526 525 477 528 508 | 500 < 0.0003 3 6 2 7 1 | 5 | 2 2 3 5 6 > 0.9997 || = 0.51 532 500 496 534 509 | 500 < 0.0004 5 4 6 7 6 | 5 | 5 1 5 5 9 > 0.9996 || = 0.50 497 472 513 505 491 | 500 < 0.0005 11 3 2 5 6 | 5 | 2 5 3 6 1 > 0.9995 || = 0.49 473 519 515 489 502 | 500 < 0.0006 5 4 7 2 8 | 5 | 3 4 4 2 2 > 0.9994 || = 0.48 496 517 567 482 531 | 500 < 0.0007 7 6 10 2 6 | 5 | 5 8 1 1 8 > 0.9993 || = 0.47 527 526 480 485 532 | 500 < 0.0008 4 8 5 6 5 | 5 | 3 4 3 8 1 > 0.9992 || = 0.46 518 477 489 493 498 | 500 < 0.0009 6 7 5 2 9 | 5 | 5 12 3 4 6 > 0.9991 || = 0.45 498 492 509 496 504 | 500 < 0.001 5 8 5 2 5 | 5 | 6 9 7 3 4 > 0.999 || = 0.44 485 482 472 493 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 545 486 537 498 493 | 500 < 0.001 53 57 51 49 57 | 50 | 34 50 34 41 45 > 0.999 || = 0.42 495 485 497 516 544 | 500 < 0.002 55 46 47 42 35 | 50 | 30 59 40 44 39 > 0.998 || = 0.41 484 487 523 473 485 | 500 < 0.003 67 45 42 44 50 | 50 | 51 46 59 49 50 > 0.997 || = 0.40 500 466 525 487 484 | 500 < 0.004 44 54 38 41 54 | 50 | 49 39 48 50 44 > 0.996 || = 0.39 497 478 513 476 534 | 500 < 0.005 45 55 45 50 52 | 50 | 55 55 42 41 42 > 0.995 || = 0.38 462 542 477 467 494 | 500 < 0.006 61 54 49 55 68 | 50 | 44 43 53 56 51 > 0.994 || = 0.37 490 463 503 471 506 | 500 < 0.007 52 52 51 58 37 | 50 | 51 61 49 55 56 > 0.993 || = 0.36 521 505 519 461 480 | 500 < 0.008 47 49 50 58 53 | 50 | 37 61 39 49 49 > 0.992 || = 0.35 524 523 491 526 497 | 500 < 0.009 45 55 52 41 49 | 50 | 38 47 44 60 53 > 0.991 || = 0.34 539 491 472 467 472 | 500 < 0.01 46 41 48 61 40 | 50 | 70 38 49 50 58 > 0.99 || = 0.33 458 510 487 501 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 475 491 557 520 487 | 500 < 0.01 515 508 473 499 495 | 497.5 | 459 499 457 495 487 > 0.99 || = 0.31 495 509 509 521 499 | 500 = 0.01 246 252 261 265 231 | 252.5 | 246 258 225 234 244 = 0.99 || = 0.30 479 472 491 501 489 | 500 = 0.02 513 520 487 502 515 | 500 | 532 464 516 495 532 = 0.98 || = 0.29 485 478 485 487 534 | 500 =================================================================| 500 | 521 532 522 531 498 = 0.97 || = 0.28 506 453 479 529 505 | 500 sknuth_MaxOft test: | 500 | 544 506 500 522 517 = 0.96 || = 0.27 528 518 499 480 481 | 500 ----------------------------------------------- | 500 | 503 522 494 473 475 = 0.95 || = 0.26 451 501 518 477 485 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 32 | 500 | 502 526 472 469 497 = 0.94 || = 0.25 497 542 529 513 509 | 500 Anderson-Darling statistic = A2 | 500 | 474 522 497 491 566 = 0.93 || = 0.24 504 468 509 500 510 | 500 | 500 | 514 475 497 568 540 = 0.92 || = 0.23 498 512 494 531 457 | 500 =================================================================| 500 | 497 465 492 461 522 = 0.91 || = 0.22 478 532 503 457 502 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 486 476 465 462 489 = 0.90 || = 0.21 525 487 497 490 505 | 500 -----------------------------------------------------------------| 500 | 520 503 532 508 498 = 0.89 || = 0.20 514 488 508 524 546 | 500 SD Bern.: d 0.97149 1.05787 1.69376 | 500 | 489 489 498 476 484 = 0.88 || = 0.19 503 484 483 493 494 | 500 s 0.95643 0.71868 1.17275 | 500 | 491 491 534 519 527 = 0.87 || = 0.18 519 488 499 499 503 | 500 t 0.93130 0.71168 1.16074 | 500 | 488 517 513 499 509 = 0.86 || = 0.17 465 472 504 515 486 | 500 m 0.94659 1.03685 0.85012 | 500 | 467 493 484 498 495 = 0.85 || = 0.16 494 526 514 481 510 | 500 x 1.02997 1.34007 0.84539 | 500 | 501 458 529 469 514 = 0.84 || = 0.15 520 480 463 514 510 | 500 | 500 | 506 509 503 502 532 = 0.83 || = 0.14 494 533 499 518 504 | 500 Changes: d 43 3 7 | 500 | 516 514 493 519 531 = 0.82 || = 0.13 465 518 497 509 482 | 500 s 48 5 6 | 500 | 512 508 499 528 507 = 0.81 || = 0.12 518 486 488 507 523 | 500 t 54 5 4 | 500 | 520 473 493 539 429 = 0.80 || = 0.11 517 512 517 534 494 | 500 m 45 3 4 | 500 | 537 508 489 486 450 = 0.79 || = 0.10 495 521 527 528 516 | 500 x 52 5 3 | 500 | 504 478 504 516 473 = 0.78 || = 0.09 482 501 499 472 494 | 500 -----------------------------------------------------------------| 500 | 507 526 500 486 506 = 0.77 || = 0.08 474 507 517 507 472 | 500 Aver./ d 0.50163 498 > 500: 4 5 5 3 3 6 3 7 5 6 | 500 | 485 490 516 500 499 = 0.76 || = 0.07 447 518 509 519 491 | 500 median s 0.49899 501 ----- 8 5 5 5 3 6 5 4 5 7 | 500 | 528 492 474 500 474 = 0.75 || = 0.06 497 470 517 516 474 | 500 t 0.49933 499 5 4 5 5 6 4 4 4 5 2 | 500 | 520 476 456 499 477 = 0.74 || = 0.05 465 518 455 513 489 | 500 m 0.49850 500 8 7 4 5 1 8 5 2 5 3 | 500 | 498 490 514 485 528 = 0.73 || = 0.04 519 522 496 499 476 | 500 x 0.50183 497 1 6 7 2 5 6 4 3 6 5 | 500 | 549 507 491 491 516 = 0.72 || = 0.03 509 512 512 526 478 | 500 -----------------------------------------------------------------| 500 | 495 516 528 479 496 = 0.71 || = 0.02 513 520 487 502 515 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 486 531 506 496 539 = 0.70 || = 0.01 246 252 261 265 231 | 252.5 d 0 0 2 13 71 13 2 0 0 | 500 | 505 501 491 479 477 = 0.69 || < 0.01 515 508 473 499 495 | 497.5 s 0 0 1 16 70 13 1 0 0 | 500 | 489 469 521 501 465 = 0.68 ||========================================================================= t 0 0 2 13 73 11 1 1 0 | 500 | 469 480 485 510 561 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 18 68 14 0 1 0 | 500 | 493 502 529 476 490 = 0.66 ||========================================================================= x 0 1 1 14 68 14 3 0 0 | 500 | 502 488 495 502 479 = 0.65 || sknuth_MaxOft test: no 95 test no 96 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 96 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 0 | 0.5 | 1 1 1 1 0 > 0.99999 || = 0.64 482 513 489 485 516 | 500 < 0.00002 0 1 0 1 0 | 0.5 | 0 0 0 2 0 > 0.99998 || = 0.63 534 502 465 483 474 | 500 < 0.00003 0 2 0 0 1 | 0.5 | 0 0 1 4 0 > 0.99997 || = 0.62 521 493 517 460 499 | 500 < 0.00004 1 1 0 0 2 | 0.5 | 0 2 0 1 0 > 0.99996 || = 0.61 465 470 504 453 505 | 500 < 0.00005 0 0 1 2 1 | 0.5 | 0 0 0 1 1 > 0.99995 || = 0.60 495 491 484 557 523 | 500 < 0.00006 0 0 0 1 1 | 0.5 | 1 0 1 0 1 > 0.99994 || = 0.59 490 505 487 497 510 | 500 < 0.00007 1 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 497 535 486 502 509 | 500 < 0.00008 0 1 0 1 1 | 0.5 | 0 0 1 0 0 > 0.99992 || = 0.57 511 503 503 518 509 | 500 < 0.00009 0 0 1 2 2 | 0.5 | 0 0 1 0 1 > 0.99991 || = 0.56 495 494 521 508 492 | 500 < 0.0001 0 0 1 0 1 | 0.5 | 0 1 0 0 0 > 0.9999 || = 0.55 509 512 515 495 463 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 508 483 502 474 481 | 500 < 0.0001 2 5 3 8 9 | 5 | 2 4 5 10 3 > 0.9999 || = 0.53 486 511 457 458 484 | 500 < 0.0002 6 3 8 7 6 | 5 | 2 4 3 3 1 > 0.9998 || = 0.52 526 471 496 471 473 | 500 < 0.0003 7 7 3 6 4 | 5 | 5 5 7 9 6 > 0.9997 || = 0.51 538 535 473 485 514 | 500 < 0.0004 7 4 3 6 4 | 5 | 3 9 7 6 3 > 0.9996 || = 0.50 493 508 533 483 519 | 500 < 0.0005 8 3 1 2 8 | 5 | 4 6 3 3 10 > 0.9995 || = 0.49 499 482 522 522 535 | 500 < 0.0006 8 3 3 4 4 | 5 | 6 2 3 4 3 > 0.9994 || = 0.48 499 531 476 470 492 | 500 < 0.0007 4 9 4 5 1 | 5 | 6 6 7 2 5 > 0.9993 || = 0.47 515 526 500 500 515 | 500 < 0.0008 3 3 2 4 7 | 5 | 3 3 4 5 3 > 0.9992 || = 0.46 506 493 501 539 482 | 500 < 0.0009 4 4 7 1 6 | 5 | 7 4 4 3 5 > 0.9991 || = 0.45 463 517 472 510 464 | 500 < 0.001 6 2 4 5 1 | 5 | 9 5 7 4 5 > 0.999 || = 0.44 531 483 516 503 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 509 470 518 519 507 | 500 < 0.001 55 43 38 48 50 | 50 | 47 48 50 49 44 > 0.999 || = 0.42 505 500 503 499 479 | 500 < 0.002 50 55 46 50 56 | 50 | 52 54 40 41 57 > 0.998 || = 0.41 458 473 543 508 489 | 500 < 0.003 41 49 28 47 62 | 50 | 47 65 50 40 45 > 0.997 || = 0.40 490 518 477 500 496 | 500 < 0.004 37 37 39 49 40 | 50 | 55 43 50 56 46 > 0.996 || = 0.39 488 513 485 498 489 | 500 < 0.005 48 57 46 47 47 | 50 | 67 61 46 45 54 > 0.995 || = 0.38 516 479 503 524 513 | 500 < 0.006 47 48 52 46 50 | 50 | 54 61 50 61 62 > 0.994 || = 0.37 506 454 500 503 484 | 500 < 0.007 60 50 64 48 44 | 50 | 50 33 57 47 43 > 0.993 || = 0.36 492 490 493 467 543 | 500 < 0.008 56 53 48 45 52 | 50 | 60 60 59 45 48 > 0.992 || = 0.35 506 498 528 525 484 | 500 < 0.009 43 49 46 62 37 | 50 | 63 41 57 47 36 > 0.991 || = 0.34 506 472 488 508 478 | 500 < 0.01 51 47 53 48 47 | 50 | 52 38 53 72 48 > 0.99 || = 0.33 497 520 495 497 530 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 514 487 508 517 488 | 500 < 0.01 488 488 460 490 485 | 497.5 | 547 504 512 503 483 > 0.99 || = 0.31 486 499 479 503 494 | 500 = 0.01 255 281 264 268 263 | 252.5 | 260 244 228 246 237 = 0.99 || = 0.30 512 526 502 496 550 | 500 = 0.02 495 489 512 543 508 | 500 | 514 509 449 512 490 = 0.98 || = 0.29 472 513 498 505 545 | 500 =================================================================| 500 | 476 529 498 506 508 = 0.97 || = 0.28 495 500 536 509 516 | 500 sknuth_MaxOft test: | 500 | 470 507 501 471 512 = 0.96 || = 0.27 500 493 506 507 546 | 500 ----------------------------------------------- | 500 | 464 545 507 455 484 = 0.95 || = 0.26 523 504 487 533 515 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 32 | 500 | 497 481 441 551 501 = 0.94 || = 0.25 488 495 491 520 471 | 500 Test on the sum of all N observations | 500 | 485 510 454 496 483 = 0.93 || = 0.24 476 522 504 508 515 | 500 | 500 | 518 464 501 508 509 = 0.92 || = 0.23 531 497 493 470 514 | 500 =================================================================| 500 | 479 500 510 534 514 = 0.91 || = 0.22 510 517 506 485 487 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 489 500 516 521 524 = 0.90 || = 0.21 525 494 479 492 485 | 500 -----------------------------------------------------------------| 500 | 522 486 523 489 497 = 0.89 || = 0.20 510 480 471 507 493 | 500 SD Bern.: d 0.91433 0.97413 1.11858 | 500 | 489 519 538 497 494 = 0.88 || = 0.19 505 504 514 513 471 | 500 s 0.94768 0.79537 1.51732 | 500 | 500 517 523 490 507 = 0.87 || = 0.18 461 516 492 485 494 | 500 t 1.05097 1.42197 0.78012 | 500 | 503 476 491 486 481 = 0.86 || = 0.17 500 520 524 515 482 | 500 m 0.99207 0.65758 1.33557 | 500 | 496 463 508 499 494 = 0.85 || = 0.16 491 521 543 491 502 | 500 x 0.90836 1.00747 1.03877 | 500 | 501 507 529 478 503 = 0.84 || = 0.15 519 521 538 545 464 | 500 | 500 | 492 498 485 487 516 = 0.83 || = 0.14 513 534 517 484 484 | 500 Changes: d 51 4 5 | 500 | 496 465 509 506 516 = 0.82 || = 0.13 497 529 472 480 509 | 500 s 55 6 6 | 500 | 530 521 472 505 495 = 0.81 || = 0.12 515 502 490 494 472 | 500 t 51 3 1 | 500 | 492 511 509 483 497 = 0.80 || = 0.11 527 457 494 496 497 | 500 m 45 2 5 | 500 | 508 494 468 527 453 = 0.79 || = 0.10 500 505 492 519 492 | 500 x 46 4 4 | 500 | 515 505 505 533 512 = 0.78 || = 0.09 490 520 518 476 522 | 500 -----------------------------------------------------------------| 500 | 514 504 516 474 465 = 0.77 || = 0.08 505 470 483 508 490 | 500 Aver./ d 0.50047 500 > 500: 3 5 5 6 5 5 5 6 4 4 | 500 | 507 489 507 526 493 = 0.76 || = 0.07 470 480 536 523 531 | 500 median s 0.49953 502 ----- 3 9 4 3 4 6 4 7 4 6 | 500 | 505 504 473 487 505 = 0.75 || = 0.06 462 489 521 511 475 | 500 t 0.49789 502 7 5 4 4 6 4 4 8 7 5 | 500 | 502 503 536 493 516 = 0.74 || = 0.05 506 491 491 520 503 | 500 m 0.49753 500 8 4 7 6 6 4 2 3 3 6 | 500 | 478 547 517 477 511 = 0.73 || = 0.04 500 522 540 543 510 | 500 x 0.49993 497 7 2 6 4 3 5 5 5 5 5 | 500 | 499 465 525 454 525 = 0.72 || = 0.03 471 497 538 507 512 | 500 -----------------------------------------------------------------| 500 | 484 515 527 478 496 = 0.71 || = 0.02 495 489 512 543 508 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 538 431 432 525 510 = 0.70 || = 0.01 255 281 264 268 263 | 252.5 d 0 0 1 13 75 10 2 0 0 | 500 | 566 506 503 496 542 = 0.69 || < 0.01 488 488 460 490 485 | 497.5 s 0 1 1 13 75 9 2 0 0 | 500 | 451 496 506 481 541 = 0.68 ||========================================================================= t 0 1 3 14 66 17 0 0 0 | 500 | 458 487 482 459 499 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 12 71 12 3 0 0 | 500 | 511 514 487 478 487 = 0.66 ||========================================================================= x 0 0 1 11 77 9 3 0 0 | 500 | 496 476 461 505 469 = 0.65 || sknuth_MaxOft test: no 96 test no 97 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 97 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 2 0 1 | 0.5 | 1 0 1 1 3 > 0.99999 || = 0.64 499 504 503 488 495 | 500 < 0.00002 1 2 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99998 || = 0.63 504 470 477 480 544 | 500 < 0.00003 0 1 1 0 0 | 0.5 | 0 0 1 0 0 > 0.99997 || = 0.62 510 481 501 508 496 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 1 0 1 1 0 > 0.99996 || = 0.61 508 489 496 500 520 | 500 < 0.00005 1 2 0 0 2 | 0.5 | 1 0 2 0 0 > 0.99995 || = 0.60 534 521 506 494 488 | 500 < 0.00006 1 0 0 0 1 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 492 497 495 533 477 | 500 < 0.00007 0 1 0 3 0 | 0.5 | 3 0 1 0 1 > 0.99993 || = 0.58 479 511 470 516 490 | 500 < 0.00008 1 0 1 0 0 | 0.5 | 0 0 3 3 0 > 0.99992 || = 0.57 527 500 485 494 519 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 512 489 511 462 511 | 500 < 0.0001 0 0 1 3 0 | 0.5 | 0 2 0 1 2 > 0.9999 || = 0.55 493 489 519 534 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 447 480 463 486 544 | 500 < 0.0001 5 6 6 6 5 | 5 | 8 2 10 7 6 > 0.9999 || = 0.53 504 487 537 486 508 | 500 < 0.0002 2 6 8 3 8 | 5 | 4 3 2 2 2 > 0.9998 || = 0.52 526 464 533 511 451 | 500 < 0.0003 4 7 7 5 6 | 5 | 6 7 5 4 9 > 0.9997 || = 0.51 460 481 482 543 483 | 500 < 0.0004 2 4 3 4 5 | 5 | 4 7 6 2 4 > 0.9996 || = 0.50 483 526 487 500 479 | 500 < 0.0005 4 1 4 3 2 | 5 | 5 3 7 3 3 > 0.9995 || = 0.49 480 496 470 485 500 | 500 < 0.0006 6 6 9 9 3 | 5 | 6 4 4 8 9 > 0.9994 || = 0.48 487 511 503 480 499 | 500 < 0.0007 5 3 5 2 2 | 5 | 6 7 6 2 3 > 0.9993 || = 0.47 470 453 492 506 485 | 500 < 0.0008 7 7 3 2 6 | 5 | 10 6 7 5 6 > 0.9992 || = 0.46 481 503 513 519 538 | 500 < 0.0009 3 4 5 6 5 | 5 | 7 4 3 6 8 > 0.9991 || = 0.45 488 509 509 479 495 | 500 < 0.001 6 5 4 6 5 | 5 | 6 6 8 6 1 > 0.999 || = 0.44 512 534 474 490 475 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 471 536 505 470 485 | 500 < 0.001 44 49 54 46 47 | 50 | 62 49 58 45 51 > 0.999 || = 0.42 530 497 498 490 500 | 500 < 0.002 46 48 44 56 43 | 50 | 38 36 49 39 62 > 0.998 || = 0.41 510 501 510 495 507 | 500 < 0.003 46 38 47 55 44 | 50 | 46 35 56 46 66 > 0.997 || = 0.40 484 512 512 458 532 | 500 < 0.004 53 45 49 47 60 | 50 | 50 65 56 44 37 > 0.996 || = 0.39 502 485 518 473 502 | 500 < 0.005 46 42 44 42 53 | 50 | 36 51 40 53 37 > 0.995 || = 0.38 492 494 504 477 485 | 500 < 0.006 36 56 41 56 52 | 50 | 64 37 48 43 52 > 0.994 || = 0.37 517 498 507 463 511 | 500 < 0.007 56 49 44 47 50 | 50 | 55 50 52 52 49 > 0.993 || = 0.36 516 487 493 498 502 | 500 < 0.008 42 65 49 51 61 | 50 | 51 47 29 54 57 > 0.992 || = 0.35 474 479 508 505 498 | 500 < 0.009 52 58 49 49 49 | 50 | 45 39 62 40 45 > 0.991 || = 0.34 484 533 518 467 492 | 500 < 0.01 50 55 55 43 58 | 50 | 54 53 51 52 63 > 0.99 || = 0.33 497 493 491 489 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 507 537 510 482 508 | 500 < 0.01 471 505 476 492 517 | 497.5 | 501 462 501 468 519 > 0.99 || = 0.31 507 502 481 485 498 | 500 = 0.01 254 266 263 249 249 | 252.5 | 245 240 236 253 253 = 0.99 || = 0.30 514 496 516 494 493 | 500 = 0.02 486 493 503 488 491 | 500 | 491 516 525 495 509 = 0.98 || = 0.29 462 513 465 477 521 | 500 =================================================================| 500 | 501 514 497 551 486 = 0.97 || = 0.28 542 529 528 535 527 | 500 sknuth_MaxOft test: | 500 | 512 522 503 530 516 = 0.96 || = 0.27 483 495 465 507 512 | 500 ----------------------------------------------- | 500 | 536 536 503 544 489 = 0.95 || = 0.26 493 475 499 520 520 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 32 | 500 | 513 489 540 504 477 = 0.94 || = 0.25 518 505 520 518 492 | 500 Test results for Anderson-Darling: | 500 | 499 501 502 489 518 = 0.93 || = 0.24 500 520 524 505 526 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 513 493 499 488 481 = 0.92 || = 0.23 557 502 510 476 539 | 500 =================================================================| 500 | 486 502 540 490 481 = 0.91 || = 0.22 491 499 505 481 505 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 545 536 489 523 451 = 0.90 || = 0.21 510 512 488 475 511 | 500 -----------------------------------------------------------------| 500 | 467 502 507 507 504 = 0.89 || = 0.20 486 491 490 512 491 | 500 SD Bern.: d 0.94249 0.88700 1.23592 | 500 | 454 460 463 532 487 = 0.88 || = 0.19 493 519 494 528 486 | 500 s 0.92972 1.08589 1.38343 | 500 | 517 504 475 478 480 = 0.87 || = 0.18 528 485 462 480 507 | 500 t 0.88049 0.69603 1.28982 | 500 | 507 468 498 507 481 = 0.86 || = 0.17 512 471 487 489 487 | 500 m 0.98089 0.70176 0.87220 | 500 | 521 505 524 548 483 = 0.85 || = 0.16 472 484 497 495 463 | 500 x 0.91359 0.88700 1.40568 | 500 | 527 470 480 505 502 = 0.84 || = 0.15 508 469 508 497 463 | 500 | 500 | 503 514 510 471 482 = 0.83 || = 0.14 496 517 511 507 455 | 500 Changes: d 51 6 4 | 500 | 524 512 527 468 501 = 0.82 || = 0.13 500 536 511 520 525 | 500 s 53 3 3 | 500 | 476 513 496 523 530 = 0.81 || = 0.12 497 503 474 492 540 | 500 t 61 2 6 | 500 | 490 496 541 504 475 = 0.80 || = 0.11 453 483 519 502 501 | 500 m 36 6 5 | 500 | 528 513 493 532 482 = 0.79 || = 0.10 523 473 494 506 531 | 500 x 50 5 6 | 500 | 509 536 497 544 521 = 0.78 || = 0.09 512 504 485 510 486 | 500 -----------------------------------------------------------------| 500 | 473 525 520 462 524 = 0.77 || = 0.08 464 483 511 514 505 | 500 Aver./ d 0.50128 502 > 500: 6 4 4 6 3 5 7 5 7 6 | 500 | 507 467 481 483 464 = 0.76 || = 0.07 480 521 480 514 491 | 500 median s 0.49949 501 ----- 7 4 6 3 7 2 4 6 7 6 | 500 | 485 509 506 513 535 = 0.75 || = 0.06 505 523 462 500 470 | 500 t 0.50126 502 5 4 5 7 6 5 6 3 4 7 | 500 | 502 508 496 551 527 = 0.74 || = 0.05 507 501 514 478 500 | 500 m 0.50213 498 4 5 6 1 2 5 5 7 7 5 | 500 | 508 523 491 517 483 = 0.73 || = 0.04 521 532 515 482 507 | 500 x 0.49918 500 3 5 8 4 3 5 5 5 4 5 | 500 | 487 495 494 482 506 = 0.72 || = 0.03 503 492 490 530 494 | 500 -----------------------------------------------------------------| 500 | 494 456 454 520 494 = 0.71 || = 0.02 486 493 503 488 491 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 540 483 550 501 503 = 0.70 || = 0.01 254 266 263 249 249 | 252.5 d 0 0 3 11 73 12 2 0 0 | 500 | 507 521 513 523 520 = 0.69 || < 0.01 471 505 476 492 517 | 497.5 s 0 0 2 12 73 14 0 0 0 | 500 | 515 493 493 505 498 = 0.68 ||========================================================================= t 0 0 1 14 74 11 1 0 0 | 500 | 516 522 526 511 524 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 15 69 14 3 0 0 | 500 | 490 501 510 489 490 = 0.66 ||========================================================================= x 0 0 3 8 75 15 0 0 0 | 500 | 483 447 473 470 490 = 0.65 || sknuth_MaxOft test: no 97 test no 98 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 98 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 505 518 473 478 504 | 500 < 0.00002 0 2 2 0 0 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 471 474 497 505 473 | 500 < 0.00003 0 3 0 0 1 | 0.5 | 1 0 1 0 0 > 0.99997 || = 0.62 492 527 529 511 517 | 500 < 0.00004 0 1 2 1 2 | 0.5 | 2 0 1 0 0 > 0.99996 || = 0.61 549 505 518 496 492 | 500 < 0.00005 2 1 0 0 0 | 0.5 | 1 1 1 0 1 > 0.99995 || = 0.60 509 478 478 532 493 | 500 < 0.00006 0 0 1 0 3 | 0.5 | 1 1 1 0 0 > 0.99994 || = 0.59 472 513 498 523 472 | 500 < 0.00007 0 1 1 1 0 | 0.5 | 0 0 0 0 1 > 0.99993 || = 0.58 498 524 515 493 514 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 479 480 523 530 511 | 500 < 0.00009 0 0 1 3 0 | 0.5 | 0 0 1 0 0 > 0.99991 || = 0.56 497 515 490 513 495 | 500 < 0.0001 1 0 0 1 0 | 0.5 | 2 0 0 0 0 > 0.9999 || = 0.55 486 500 493 502 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 495 484 489 502 488 | 500 < 0.0001 3 9 7 9 7 | 5 | 7 2 5 0 3 > 0.9999 || = 0.53 531 505 500 507 506 | 500 < 0.0002 4 2 5 3 5 | 5 | 3 1 2 3 3 > 0.9998 || = 0.52 502 524 468 537 481 | 500 < 0.0003 8 4 3 5 6 | 5 | 7 3 5 5 7 > 0.9997 || = 0.51 518 464 505 502 486 | 500 < 0.0004 5 6 3 5 10 | 5 | 4 5 9 6 5 > 0.9996 || = 0.50 503 480 535 504 508 | 500 < 0.0005 7 9 6 2 4 | 5 | 6 7 4 2 4 > 0.9995 || = 0.49 496 484 488 496 512 | 500 < 0.0006 3 5 5 5 6 | 5 | 4 2 4 3 4 > 0.9994 || = 0.48 498 503 511 462 496 | 500 < 0.0007 6 5 9 4 7 | 5 | 6 5 5 9 1 > 0.9993 || = 0.47 519 525 512 478 530 | 500 < 0.0008 7 5 6 3 6 | 5 | 4 10 10 2 2 > 0.9992 || = 0.46 492 463 500 526 498 | 500 < 0.0009 5 5 6 5 3 | 5 | 6 5 0 4 6 > 0.9991 || = 0.45 467 544 544 525 470 | 500 < 0.001 4 2 6 7 3 | 5 | 3 7 5 5 2 > 0.999 || = 0.44 502 512 531 512 476 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 492 465 552 544 510 | 500 < 0.001 52 52 56 48 57 | 50 | 50 47 49 39 37 > 0.999 || = 0.42 521 486 524 500 509 | 500 < 0.002 41 45 42 56 51 | 50 | 50 46 51 55 64 > 0.998 || = 0.41 532 494 511 506 484 | 500 < 0.003 54 39 46 56 42 | 50 | 49 60 47 53 46 > 0.997 || = 0.40 510 502 543 554 483 | 500 < 0.004 64 54 41 43 41 | 50 | 49 32 41 34 45 > 0.996 || = 0.39 503 483 545 490 481 | 500 < 0.005 41 46 46 56 59 | 50 | 59 57 60 38 42 > 0.995 || = 0.38 507 493 494 434 495 | 500 < 0.006 45 36 55 59 54 | 50 | 52 58 54 41 46 > 0.994 || = 0.37 472 486 533 511 517 | 500 < 0.007 52 52 61 53 30 | 50 | 47 44 58 53 49 > 0.993 || = 0.36 519 475 538 483 516 | 500 < 0.008 50 46 46 66 63 | 50 | 46 47 63 46 49 > 0.992 || = 0.35 500 497 500 462 498 | 500 < 0.009 49 52 44 41 50 | 50 | 48 47 42 45 47 > 0.991 || = 0.34 508 520 501 498 505 | 500 < 0.01 51 66 49 59 44 | 50 | 42 47 48 47 43 > 0.99 || = 0.33 487 495 460 541 477 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 537 479 511 488 522 | 500 < 0.01 499 488 486 537 491 | 497.5 | 492 485 513 451 468 > 0.99 || = 0.31 479 483 495 454 492 | 500 = 0.01 252 249 249 280 235 | 252.5 | 238 287 252 266 251 = 0.99 || = 0.30 482 466 492 465 496 | 500 = 0.02 520 505 542 494 511 | 500 | 540 492 497 500 471 = 0.98 || = 0.29 517 497 551 464 502 | 500 =================================================================| 500 | 508 478 464 479 512 = 0.97 || = 0.28 516 525 458 497 499 | 500 sknuth_MaxOft test: | 500 | 522 517 529 517 525 = 0.96 || = 0.27 519 551 469 546 508 | 500 ----------------------------------------------- | 500 | 483 521 472 488 491 = 0.95 || = 0.26 508 510 542 507 484 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 32 | 500 | 466 516 479 514 526 = 0.94 || = 0.25 499 537 548 503 507 | 500 Test results for Anderson-Darling: | 500 | 511 519 498 519 499 = 0.93 || = 0.24 492 514 475 503 503 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 511 523 518 477 491 = 0.92 || = 0.23 501 516 563 493 533 | 500 =================================================================| 500 | 478 493 473 474 499 = 0.91 || = 0.22 485 491 526 553 515 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 509 522 531 497 483 = 0.90 || = 0.21 538 482 487 499 493 | 500 -----------------------------------------------------------------| 500 | 480 483 504 500 471 = 0.89 || = 0.20 487 507 491 468 510 | 500 SD Bern.: d 0.82281 0.90488 0.60028 | 500 | 485 533 487 483 535 = 0.88 || = 0.19 509 460 489 477 504 | 500 s 0.94653 1.14773 1.11858 | 500 | 532 478 486 514 498 = 0.87 || = 0.18 488 509 481 515 464 | 500 t 1.13793 0.90819 1.00945 | 500 | 513 481 466 556 484 = 0.86 || = 0.17 513 506 460 489 517 | 500 m 1.05695 1.15729 1.17956 | 500 | 489 506 514 484 494 = 0.85 || = 0.16 523 521 494 502 501 | 500 x 0.84943 1.34007 1.04549 | 500 | 505 481 448 503 531 = 0.84 || = 0.15 498 505 478 496 517 | 500 | 500 | 510 494 490 512 512 = 0.83 || = 0.14 474 497 484 524 492 | 500 Changes: d 53 6 2 | 500 | 482 526 506 534 498 = 0.82 || = 0.13 465 511 491 487 544 | 500 s 50 6 4 | 500 | 500 493 468 514 497 = 0.81 || = 0.12 494 531 482 520 476 | 500 t 47 3 4 | 500 | 476 498 498 470 447 = 0.80 || = 0.11 501 503 512 493 517 | 500 m 47 5 4 | 500 | 520 483 483 484 510 = 0.79 || = 0.10 483 521 544 487 486 | 500 x 62 5 2 | 500 | 489 529 516 527 500 = 0.78 || = 0.09 514 497 486 476 503 | 500 -----------------------------------------------------------------| 500 | 499 466 481 505 501 = 0.77 || = 0.08 518 448 466 533 494 | 500 Aver./ d 0.49919 500 > 500: 7 4 6 5 5 4 4 4 5 5 | 500 | 509 503 508 498 524 = 0.76 || = 0.07 505 481 487 488 461 | 500 median s 0.50122 498 ----- 2 8 7 1 5 5 5 5 4 6 | 500 | 491 502 487 495 499 = 0.75 || = 0.06 500 488 496 502 535 | 500 t 0.49843 498 3 2 5 5 8 3 4 4 4 3 | 500 | 488 538 500 461 494 = 0.74 || = 0.05 503 502 523 515 477 | 500 m 0.49924 500 5 4 5 2 6 9 4 2 6 4 | 500 | 487 543 502 482 529 = 0.73 || = 0.04 504 468 456 483 506 | 500 x 0.50007 499 4 6 7 4 4 3 4 5 3 3 | 500 | 516 488 511 481 499 = 0.72 || = 0.03 493 500 502 485 491 | 500 -----------------------------------------------------------------| 500 | 514 474 457 480 526 = 0.71 || = 0.02 520 505 542 494 511 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 494 511 491 487 495 = 0.70 || = 0.01 252 249 249 280 235 | 252.5 d 0 0 1 9 83 7 1 0 0 | 500 | 478 491 483 502 497 = 0.69 || < 0.01 499 488 486 537 491 | 497.5 s 0 0 1 10 74 14 2 0 0 | 500 | 473 495 503 475 562 = 0.68 ||========================================================================= t 0 0 2 15 62 17 5 0 0 | 500 | 444 491 524 497 494 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 12 68 14 4 0 0 | 500 | 515 502 498 489 520 = 0.66 ||========================================================================= x 0 0 1 13 75 11 1 0 0 | 500 | 505 492 449 505 499 = 0.65 || sknuth_MaxOft test: no 98 test no 99 TestU01 250000 runs BigCrush Test smarsa_S sknuth_MaxOft test: test no 99 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 3 2 1 | 0.5 | 1 0 0 0 1 > 0.99999 || = 0.64 507 472 481 501 545 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99998 || = 0.63 500 489 515 486 513 | 500 < 0.00003 0 0 2 1 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 469 478 530 494 488 | 500 < 0.00004 1 0 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 458 465 500 503 529 | 500 < 0.00005 0 0 0 2 1 | 0.5 | 0 0 0 0 1 > 0.99995 || = 0.60 485 472 489 512 492 | 500 < 0.00006 2 1 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99994 || = 0.59 494 474 535 482 521 | 500 < 0.00007 1 2 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 527 447 505 460 546 | 500 < 0.00008 0 0 3 0 0 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 498 491 497 522 478 | 500 < 0.00009 0 2 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 516 503 452 510 508 | 500 < 0.0001 1 0 1 1 0 | 0.5 | 0 0 3 0 1 > 0.9999 || = 0.55 462 509 501 508 472 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 470 509 557 456 489 | 500 < 0.0001 5 7 10 9 3 | 5 | 1 2 4 1 4 > 0.9999 || = 0.53 509 526 527 497 474 | 500 < 0.0002 5 5 6 6 4 | 5 | 6 3 0 6 3 > 0.9998 || = 0.52 538 534 475 473 511 | 500 < 0.0003 7 7 2 5 4 | 5 | 5 7 2 2 3 > 0.9997 || = 0.51 516 471 576 467 507 | 500 < 0.0004 12 5 9 3 4 | 5 | 3 2 6 6 5 > 0.9996 || = 0.50 477 500 504 488 475 | 500 < 0.0005 9 3 4 2 9 | 5 | 3 7 1 2 3 > 0.9995 || = 0.49 500 467 516 505 472 | 500 < 0.0006 2 3 5 4 4 | 5 | 6 3 6 5 5 > 0.9994 || = 0.48 514 488 474 525 493 | 500 < 0.0007 6 2 10 5 8 | 5 | 4 5 7 4 7 > 0.9993 || = 0.47 463 521 525 468 492 | 500 < 0.0008 5 13 6 4 5 | 5 | 4 4 9 6 2 > 0.9992 || = 0.46 487 538 514 514 496 | 500 < 0.0009 7 3 2 3 2 | 5 | 5 6 6 4 4 > 0.9991 || = 0.45 505 519 495 485 482 | 500 < 0.001 5 1 7 2 5 | 5 | 3 5 4 2 6 > 0.999 || = 0.44 493 538 518 500 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 493 509 482 532 500 | 500 < 0.001 63 49 61 43 48 | 50 | 40 44 45 38 42 > 0.999 || = 0.42 525 469 525 500 500 | 500 < 0.002 46 42 56 48 45 | 50 | 54 52 52 54 45 > 0.998 || = 0.41 495 495 508 466 481 | 500 < 0.003 51 51 35 40 55 | 50 | 47 58 45 54 45 > 0.997 || = 0.40 521 534 500 481 521 | 500 < 0.004 48 49 45 40 54 | 50 | 54 48 37 35 47 > 0.996 || = 0.39 535 530 477 508 530 | 500 < 0.005 50 51 62 65 47 | 50 | 60 50 34 46 37 > 0.995 || = 0.38 501 527 487 484 498 | 500 < 0.006 53 45 47 56 57 | 50 | 49 35 54 59 46 > 0.994 || = 0.37 510 534 478 532 479 | 500 < 0.007 58 46 51 59 43 | 50 | 49 43 46 56 48 > 0.993 || = 0.36 506 496 453 489 506 | 500 < 0.008 55 43 56 49 40 | 50 | 39 37 58 54 52 > 0.992 || = 0.35 462 511 503 513 545 | 500 < 0.009 55 61 50 51 51 | 50 | 49 61 45 53 44 > 0.991 || = 0.34 534 504 503 493 495 | 500 < 0.01 48 50 46 51 58 | 50 | 48 64 59 46 60 > 0.99 || = 0.33 480 493 480 499 539 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 500 528 465 510 509 | 500 < 0.01 527 487 509 502 498 | 497.5 | 489 492 475 495 466 > 0.99 || = 0.31 448 495 502 504 482 | 500 = 0.01 246 238 234 245 251 | 252.5 | 258 253 250 249 258 = 0.99 || = 0.30 519 524 475 506 480 | 500 = 0.02 501 510 510 519 519 | 500 | 520 495 532 531 499 = 0.98 || = 0.29 494 460 480 544 488 | 500 =================================================================| 500 | 533 495 518 478 485 = 0.97 || = 0.28 492 493 502 510 505 | 500 sknuth_MaxOft test: | 500 | 529 577 524 454 488 = 0.96 || = 0.27 536 495 489 499 511 | 500 ----------------------------------------------- | 500 | 501 487 490 479 515 = 0.95 || = 0.26 537 470 479 485 488 | 500 N = 20, n = 10000000, r = 0, d = 100000, t = 32 | 500 | 523 467 469 503 513 = 0.94 || = 0.25 538 490 522 485 537 | 500 Test results for Anderson-Darling: | 500 | 449 509 485 522 524 = 0.93 || = 0.24 501 533 478 456 517 | 500 Anderson-Darling statistic = A2 | 500 | 487 482 506 571 530 = 0.92 || = 0.23 494 531 502 513 526 | 500 =================================================================| 500 | 531 498 474 538 503 = 0.91 || = 0.22 510 516 520 520 498 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 464 503 471 533 513 = 0.90 || = 0.21 491 477 495 537 517 | 500 -----------------------------------------------------------------| 500 | 473 517 491 505 482 = 0.89 || = 0.20 504 502 499 470 514 | 500 SD Bern.: d 1.03646 0.79663 0.85948 | 500 | 487 480 515 519 547 = 0.88 || = 0.19 513 508 492 487 473 | 500 s 1.12862 0.74736 1.31822 | 500 | 496 519 510 492 498 = 0.87 || = 0.18 543 469 516 494 459 | 500 t 0.96838 1.10779 1.16762 | 500 | 509 489 500 489 503 = 0.86 || = 0.17 454 513 518 507 468 | 500 m 0.98054 1.09415 1.07290 | 500 | 493 503 503 486 469 = 0.85 || = 0.16 503 488 474 503 463 | 500 x 0.96830 0.82744 0.95125 | 500 | 485 492 467 459 518 = 0.84 || = 0.15 480 530 484 482 508 | 500 | 500 | 476 535 498 515 514 = 0.83 || = 0.14 484 506 529 498 477 | 500 Changes: d 49 5 4 | 500 | 524 480 492 490 477 = 0.82 || = 0.13 489 531 497 515 502 | 500 s 46 6 3 | 500 | 461 483 501 503 494 = 0.81 || = 0.12 485 541 507 509 545 | 500 t 51 5 7 | 500 | 459 536 495 520 512 = 0.80 || = 0.11 515 439 506 492 516 | 500 m 41 3 4 | 500 | 512 533 556 528 516 = 0.79 || = 0.10 473 517 507 548 471 | 500 x 51 5 3 | 500 | 470 554 501 510 457 = 0.78 || = 0.09 499 515 496 518 528 | 500 -----------------------------------------------------------------| 500 | 496 496 531 509 500 = 0.77 || = 0.08 513 487 497 528 489 | 500 Aver./ d 0.49960 500 > 500: 5 4 6 6 4 5 5 6 2 7 | 500 | 526 478 530 504 485 = 0.76 || = 0.07 525 507 501 494 483 | 500 median s 0.49914 498 ----- 6 7 4 7 6 5 0 5 5 3 | 500 | 527 482 489 495 452 = 0.75 || = 0.06 485 469 484 487 473 | 500 t 0.50085 500 4 6 4 3 6 6 5 7 4 4 | 500 | 499 516 460 479 505 = 0.74 || = 0.05 483 517 480 477 507 | 500 m 0.50021 501 5 5 5 6 4 4 6 6 5 5 | 500 | 503 491 517 490 506 = 0.73 || = 0.04 481 504 490 470 465 | 500 x 0.50079 500 4 4 7 5 1 5 7 5 5 6 | 500 | 535 480 523 518 473 = 0.72 || = 0.03 516 502 505 504 494 | 500 -----------------------------------------------------------------| 500 | 509 538 506 476 503 = 0.71 || = 0.02 501 510 510 519 519 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 508 484 505 465 500 = 0.70 || = 0.01 246 238 234 245 251 | 252.5 d 0 0 3 15 63 19 1 0 0 | 500 | 547 481 488 471 515 = 0.69 || < 0.01 527 487 509 502 498 | 497.5 s 0 0 3 15 62 19 1 1 0 | 500 | 469 444 478 530 493 = 0.68 ||========================================================================= t 0 0 2 13 71 12 2 1 0 | 500 | 493 499 489 514 512 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 14 73 11 1 1 0 | 500 | 509 461 512 501 515 = 0.66 ||========================================================================= x 0 0 1 17 69 9 5 0 0 | 500 | 521 466 523 508 526 = 0.65 || sknuth_MaxOft test: no 99 test no 100 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleProd test: test no 100 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 1 2 1 1 0 > 0.99999 || = 0.64 502 485 470 498 483 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99998 || = 0.63 512 506 474 520 502 | 500 < 0.00003 0 1 1 0 0 | 0.5 | 1 0 1 1 0 > 0.99997 || = 0.62 515 516 507 528 489 | 500 < 0.00004 1 1 1 2 0 | 0.5 | 1 0 1 1 0 > 0.99996 || = 0.61 509 489 503 486 490 | 500 < 0.00005 1 2 0 0 1 | 0.5 | 1 1 0 0 0 > 0.99995 || = 0.60 498 506 497 531 477 | 500 < 0.00006 2 0 1 0 0 | 0.5 | 1 0 1 1 1 > 0.99994 || = 0.59 484 499 492 501 496 | 500 < 0.00007 0 1 1 0 0 | 0.5 | 3 0 0 0 1 > 0.99993 || = 0.58 502 473 505 523 515 | 500 < 0.00008 1 0 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 519 475 470 508 496 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 522 469 492 502 531 | 500 < 0.0001 0 0 1 1 1 | 0.5 | 1 0 1 1 1 > 0.9999 || = 0.55 482 508 491 486 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 527 544 451 510 493 | 500 < 0.0001 5 5 5 4 2 | 5 | 9 3 5 6 4 > 0.9999 || = 0.53 486 503 461 546 505 | 500 < 0.0002 5 2 5 4 6 | 5 | 2 4 3 6 2 > 0.9998 || = 0.52 498 484 530 477 471 | 500 < 0.0003 3 11 5 4 1 | 5 | 4 4 8 6 6 > 0.9997 || = 0.51 445 503 505 500 531 | 500 < 0.0004 7 5 7 5 5 | 5 | 5 3 3 2 4 > 0.9996 || = 0.50 511 471 480 498 503 | 500 < 0.0005 1 5 8 8 5 | 5 | 2 1 5 2 2 > 0.9995 || = 0.49 482 494 542 529 508 | 500 < 0.0006 6 4 7 9 4 | 5 | 9 7 7 1 4 > 0.9994 || = 0.48 483 459 492 487 502 | 500 < 0.0007 2 4 7 5 3 | 5 | 2 4 2 5 1 > 0.9993 || = 0.47 526 516 521 490 502 | 500 < 0.0008 2 9 6 6 6 | 5 | 4 7 10 3 6 > 0.9992 || = 0.46 508 511 543 480 513 | 500 < 0.0009 4 9 5 8 3 | 5 | 6 4 2 5 5 > 0.9991 || = 0.45 511 519 504 536 500 | 500 < 0.001 5 5 9 1 2 | 5 | 4 7 6 5 3 > 0.999 || = 0.44 486 509 512 499 482 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 513 493 495 497 483 | 500 < 0.001 40 59 64 54 37 | 50 | 47 44 51 41 37 > 0.999 || = 0.42 462 521 497 462 472 | 500 < 0.002 46 44 48 52 49 | 50 | 50 30 42 44 49 > 0.998 || = 0.41 492 484 430 502 481 | 500 < 0.003 57 50 40 40 41 | 50 | 44 57 58 42 48 > 0.997 || = 0.40 462 496 550 479 458 | 500 < 0.004 58 54 42 55 56 | 50 | 37 50 40 44 64 > 0.996 || = 0.39 494 489 502 484 487 | 500 < 0.005 49 69 49 54 42 | 50 | 46 55 56 48 38 > 0.995 || = 0.38 494 491 490 526 488 | 500 < 0.006 44 48 45 43 61 | 50 | 38 54 50 34 41 > 0.994 || = 0.37 453 509 474 527 529 | 500 < 0.007 56 56 55 51 56 | 50 | 44 54 36 41 54 > 0.993 || = 0.36 500 463 516 522 507 | 500 < 0.008 49 50 48 58 51 | 50 | 54 46 45 51 45 > 0.992 || = 0.35 493 516 511 493 513 | 500 < 0.009 53 52 42 50 47 | 50 | 51 45 56 51 42 > 0.991 || = 0.34 544 497 494 470 487 | 500 < 0.01 60 47 40 49 61 | 50 | 58 57 41 46 56 > 0.99 || = 0.33 498 488 523 514 477 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 451 483 529 487 497 | 500 < 0.01 512 529 473 506 501 | 497.5 | 469 492 475 442 474 > 0.99 || = 0.31 493 520 510 495 473 | 500 = 0.01 258 258 273 233 284 | 252.5 | 237 218 236 288 250 = 0.99 || = 0.30 521 518 495 504 466 | 500 = 0.02 503 526 541 538 503 | 500 | 485 460 521 528 497 = 0.98 || = 0.29 489 509 491 494 508 | 500 =================================================================| 500 | 540 506 489 512 530 = 0.97 || = 0.28 495 476 525 478 486 | 500 svaria_SampleProd test: | 500 | 491 511 452 495 513 = 0.96 || = 0.27 522 498 556 534 518 | 500 ----------------------------------------------- | 500 | 507 546 514 479 495 = 0.95 || = 0.26 484 476 493 454 505 | 500 N = 40, n = 10000000, r = 0, t = 8 | 500 | 488 520 482 477 501 = 0.94 || = 0.25 479 501 499 482 515 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 536 486 502 483 506 = 0.93 || = 0.24 506 497 491 551 505 | 500 | 500 | 482 522 497 487 495 = 0.92 || = 0.23 551 500 481 509 516 | 500 =================================================================| 500 | 510 525 534 512 505 = 0.91 || = 0.22 498 488 521 472 498 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 514 478 492 486 515 = 0.90 || = 0.21 506 559 494 465 522 | 500 -----------------------------------------------------------------| 500 | 541 521 515 507 497 = 0.89 || = 0.20 528 473 466 541 490 | 500 SD Bern.: d 1.09103 0.90819 0.99144 | 500 | 508 522 501 501 486 = 0.88 || = 0.19 582 491 508 468 489 | 500 s 1.01823 1.04646 1.12483 | 500 | 485 514 510 516 505 = 0.87 || = 0.18 477 459 500 533 482 | 500 t 1.10798 1.08034 1.09872 | 500 | 493 480 467 474 552 = 0.86 || = 0.17 485 500 474 480 520 | 500 m 1.07143 0.74333 1.07383 | 500 | 491 474 519 474 494 = 0.85 || = 0.16 471 521 540 472 467 | 500 x 0.80118 1.13104 1.21385 | 500 | 477 466 512 486 516 = 0.84 || = 0.15 502 452 502 511 511 | 500 | 500 | 549 502 491 465 516 = 0.83 || = 0.14 501 488 500 494 499 | 500 Changes: d 45 5 1 | 500 | 510 542 456 523 519 = 0.82 || = 0.13 506 530 520 449 484 | 500 s 49 7 5 | 500 | 499 472 508 552 483 = 0.81 || = 0.12 494 502 464 468 497 | 500 t 54 3 7 | 500 | 489 502 533 505 495 = 0.80 || = 0.11 499 458 464 510 511 | 500 m 49 5 2 | 500 | 547 513 488 555 541 = 0.79 || = 0.10 502 488 542 484 503 | 500 x 43 5 5 | 500 | 497 470 480 520 501 = 0.78 || = 0.09 524 516 508 490 518 | 500 -----------------------------------------------------------------| 500 | 559 519 510 487 492 = 0.77 || = 0.08 499 491 503 492 527 | 500 Aver./ d 0.50140 499 > 500: 4 5 5 2 4 4 6 7 5 4 | 500 | 501 545 501 494 483 = 0.76 || = 0.07 470 510 489 525 484 | 500 median s 0.50068 500 ----- 7 3 3 4 5 5 5 7 5 6 | 500 | 511 488 535 502 492 = 0.75 || = 0.06 486 505 491 497 515 | 500 t 0.49858 500 6 5 3 6 6 3 4 6 6 4 | 500 | 482 494 470 482 500 = 0.74 || = 0.05 481 493 531 485 507 | 500 m 0.50128 498 3 3 4 5 3 7 6 7 5 4 | 500 | 507 535 517 535 487 = 0.73 || = 0.04 495 466 484 494 475 | 500 x 0.50033 500 8 4 7 3 4 4 5 2 6 5 | 500 | 503 534 564 512 455 = 0.72 || = 0.03 449 539 501 490 509 | 500 -----------------------------------------------------------------| 500 | 529 520 476 502 498 = 0.71 || = 0.02 503 526 541 538 503 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 489 492 478 510 495 = 0.70 || = 0.01 258 258 273 233 284 | 252.5 d 0 0 5 8 73 10 4 1 0 | 500 | 475 497 488 508 522 = 0.69 || < 0.01 512 529 473 506 501 | 497.5 s 0 0 2 17 70 9 3 0 0 | 500 | 491 503 507 494 495 = 0.68 ||========================================================================= t 0 1 2 17 63 15 3 0 0 | 500 | 507 494 466 475 514 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 63 16 5 0 0 | 500 | 437 518 500 534 513 = 0.66 ||========================================================================= x 0 0 1 10 82 7 1 0 0 | 500 | 532 513 531 502 520 = 0.65 || svaria_SampleProd test: no 100 test no 101 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleProd test: test no 101 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 496 469 504 484 486 | 500 < 0.00002 0 1 1 1 1 | 0.5 | 1 0 0 0 2 > 0.99998 || = 0.63 497 535 517 526 515 | 500 < 0.00003 0 1 1 0 0 | 0.5 | 1 1 0 1 2 > 0.99997 || = 0.62 492 485 517 516 494 | 500 < 0.00004 0 0 0 0 1 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 500 482 508 521 537 | 500 < 0.00005 1 1 2 0 0 | 0.5 | 0 0 3 3 0 > 0.99995 || = 0.60 497 507 505 526 479 | 500 < 0.00006 0 1 0 1 1 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 487 511 508 490 495 | 500 < 0.00007 0 0 0 1 1 | 0.5 | 1 3 1 0 0 > 0.99993 || = 0.58 533 494 463 518 539 | 500 < 0.00008 1 1 1 1 0 | 0.5 | 0 0 1 1 0 > 0.99992 || = 0.57 505 468 491 498 525 | 500 < 0.00009 0 1 0 0 1 | 0.5 | 0 0 1 0 0 > 0.99991 || = 0.56 549 531 497 497 461 | 500 < 0.0001 0 1 2 0 0 | 0.5 | 1 1 0 1 0 > 0.9999 || = 0.55 492 503 552 509 498 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 490 517 498 488 490 | 500 < 0.0001 2 7 7 4 6 | 5 | 4 5 7 7 4 > 0.9999 || = 0.53 481 478 472 525 463 | 500 < 0.0002 3 6 7 6 5 | 5 | 3 1 2 4 1 > 0.9998 || = 0.52 466 519 520 490 482 | 500 < 0.0003 4 5 4 6 6 | 5 | 5 4 4 4 8 > 0.9997 || = 0.51 522 486 500 512 507 | 500 < 0.0004 5 2 6 6 2 | 5 | 4 4 3 5 3 > 0.9996 || = 0.50 497 510 494 495 542 | 500 < 0.0005 6 6 1 6 7 | 5 | 3 6 3 4 7 > 0.9995 || = 0.49 494 500 546 492 504 | 500 < 0.0006 3 5 6 6 4 | 5 | 4 7 6 3 8 > 0.9994 || = 0.48 487 496 461 518 486 | 500 < 0.0007 7 6 1 2 6 | 5 | 5 5 7 6 5 > 0.9993 || = 0.47 514 503 490 519 469 | 500 < 0.0008 3 9 8 5 4 | 5 | 6 6 5 10 6 > 0.9992 || = 0.46 502 485 481 481 440 | 500 < 0.0009 7 3 3 4 2 | 5 | 5 3 4 2 5 > 0.9991 || = 0.45 491 468 502 469 527 | 500 < 0.001 0 1 4 7 3 | 5 | 8 5 2 4 5 > 0.999 || = 0.44 490 470 512 497 516 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 536 505 506 514 538 | 500 < 0.001 40 50 47 52 45 | 50 | 47 46 43 49 52 > 0.999 || = 0.42 485 494 496 495 478 | 500 < 0.002 43 45 58 45 52 | 50 | 51 60 61 49 50 > 0.998 || = 0.41 460 546 492 456 520 | 500 < 0.003 54 60 55 51 59 | 50 | 63 52 48 50 51 > 0.997 || = 0.40 494 496 519 494 490 | 500 < 0.004 61 48 50 47 41 | 50 | 42 44 50 50 62 > 0.996 || = 0.39 496 528 489 509 461 | 500 < 0.005 49 55 46 42 48 | 50 | 49 52 45 36 59 > 0.995 || = 0.38 499 525 523 518 514 | 500 < 0.006 42 49 55 56 48 | 50 | 50 46 39 45 56 > 0.994 || = 0.37 527 531 466 504 489 | 500 < 0.007 38 55 51 49 50 | 50 | 53 55 53 55 53 > 0.993 || = 0.36 495 502 470 501 496 | 500 < 0.008 59 38 52 46 45 | 50 | 61 39 59 52 48 > 0.992 || = 0.35 502 523 493 517 503 | 500 < 0.009 52 49 42 41 53 | 50 | 70 49 46 49 53 > 0.991 || = 0.34 512 488 525 511 476 | 500 < 0.01 61 41 39 41 49 | 50 | 60 56 52 55 50 > 0.99 || = 0.33 526 497 520 513 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 491 479 470 486 461 | 500 < 0.01 499 490 495 470 490 | 497.5 | 546 499 496 490 534 > 0.99 || = 0.31 488 552 523 488 511 | 500 = 0.01 247 250 234 263 256 | 252.5 | 255 241 247 264 268 = 0.99 || = 0.30 504 505 489 510 505 | 500 = 0.02 457 507 476 513 501 | 500 | 488 500 474 519 537 = 0.98 || = 0.29 471 482 484 496 499 | 500 =================================================================| 500 | 518 484 489 500 495 = 0.97 || = 0.28 530 487 480 445 526 | 500 svaria_SampleProd test: | 500 | 526 501 504 481 481 = 0.96 || = 0.27 530 522 491 504 485 | 500 ----------------------------------------------- | 500 | 531 486 503 506 526 = 0.95 || = 0.26 489 541 498 512 485 | 500 N = 40, n = 10000000, r = 0, t = 8 | 500 | 451 494 533 486 457 = 0.94 || = 0.25 507 458 505 546 530 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 468 536 500 478 518 = 0.93 || = 0.24 525 476 484 509 504 | 500 | 500 | 478 476 520 502 489 = 0.92 || = 0.23 447 450 533 511 502 | 500 =================================================================| 500 | 485 534 510 466 489 = 0.91 || = 0.22 486 494 507 508 481 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 556 481 521 511 535 = 0.90 || = 0.21 504 494 470 518 500 | 500 -----------------------------------------------------------------| 500 | 515 502 494 523 468 = 0.89 || = 0.20 477 495 508 538 529 | 500 SD Bern.: d 1.03566 1.18464 1.32277 | 500 | 519 550 510 495 492 = 0.88 || = 0.19 531 468 495 517 514 | 500 s 1.01831 0.90155 0.84776 | 500 | 501 502 468 509 497 = 0.87 || = 0.18 481 510 511 515 542 | 500 t 0.94934 0.81157 0.92781 | 500 | 500 516 502 495 481 = 0.86 || = 0.17 499 552 509 495 502 | 500 m 0.89832 0.79789 0.74601 | 500 | 530 506 492 477 483 = 0.85 || = 0.16 494 524 490 536 509 | 500 x 0.99805 0.68444 0.75931 | 500 | 436 477 509 500 485 = 0.84 || = 0.15 529 524 512 519 498 | 500 | 500 | 514 524 509 521 481 = 0.83 || = 0.14 513 473 490 521 494 | 500 Changes: d 46 3 3 | 500 | 512 492 537 476 470 = 0.82 || = 0.13 478 488 489 454 527 | 500 s 49 6 7 | 500 | 500 537 571 526 506 = 0.81 || = 0.12 455 500 465 503 536 | 500 t 48 4 5 | 500 | 495 493 502 472 526 = 0.80 || = 0.11 526 533 518 482 498 | 500 m 50 5 3 | 500 | 514 500 514 507 519 = 0.79 || = 0.10 512 482 465 504 484 | 500 x 47 4 5 | 500 | 474 493 495 500 502 = 0.78 || = 0.09 521 485 501 475 501 | 500 -----------------------------------------------------------------| 500 | 481 491 500 475 505 = 0.77 || = 0.08 489 512 528 484 490 | 500 Aver./ d 0.50050 499 > 500: 5 5 5 5 3 4 3 4 7 5 | 500 | 476 450 468 484 506 = 0.76 || = 0.07 491 511 468 473 538 | 500 median s 0.50115 500 ----- 3 5 2 7 3 6 5 4 7 4 | 500 | 511 520 480 531 505 = 0.75 || = 0.06 506 471 482 532 488 | 500 t 0.50268 500 3 4 4 4 5 4 6 6 7 5 | 500 | 495 469 522 511 480 = 0.74 || = 0.05 546 457 483 467 471 | 500 m 0.49870 502 5 7 8 8 3 5 4 3 5 4 | 500 | 500 522 536 494 520 = 0.73 || = 0.04 505 465 513 526 488 | 500 x 0.49926 499 5 6 5 4 5 3 4 8 2 5 | 500 | 515 505 532 495 500 = 0.72 || = 0.03 494 493 482 514 535 | 500 -----------------------------------------------------------------| 500 | 531 522 510 485 527 = 0.71 || = 0.02 457 507 476 513 501 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 499 525 533 468 503 = 0.70 || = 0.01 247 250 234 263 256 | 252.5 d 0 0 5 9 69 14 4 0 0 | 500 | 453 502 499 458 484 = 0.69 || < 0.01 499 490 495 470 490 | 497.5 s 0 0 2 14 66 15 4 0 0 | 500 | 502 492 482 502 471 = 0.68 ||========================================================================= t 0 0 0 16 72 10 2 1 0 | 500 | 518 486 504 488 471 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 14 74 10 1 0 0 | 500 | 506 506 467 492 480 = 0.66 ||========================================================================= x 0 0 1 12 68 20 0 0 0 | 500 | 465 504 482 476 513 = 0.65 || svaria_SampleProd test: no 101 test no 102 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleProd test: test no 102 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 0 0 0 0 4 > 0.99999 || = 0.64 526 501 505 545 531 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 0 0 1 1 1 > 0.99998 || = 0.63 491 513 488 507 519 | 500 < 0.00003 0 1 0 1 1 | 0.5 | 0 1 0 0 0 > 0.99997 || = 0.62 499 517 532 499 466 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 528 501 486 517 486 | 500 < 0.00005 1 2 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 498 450 502 458 458 | 500 < 0.00006 1 1 0 0 0 | 0.5 | 1 1 0 1 0 > 0.99994 || = 0.59 525 523 486 507 479 | 500 < 0.00007 0 1 1 0 0 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 498 480 512 489 508 | 500 < 0.00008 0 0 0 0 2 | 0.5 | 2 0 0 1 0 > 0.99992 || = 0.57 508 476 490 511 506 | 500 < 0.00009 0 1 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99991 || = 0.56 497 479 491 475 524 | 500 < 0.0001 0 0 0 2 2 | 0.5 | 0 0 1 1 0 > 0.9999 || = 0.55 514 534 514 497 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 498 499 506 516 466 | 500 < 0.0001 2 7 1 6 7 | 5 | 4 3 3 4 5 > 0.9999 || = 0.53 526 505 501 497 490 | 500 < 0.0002 5 4 3 3 1 | 5 | 4 2 2 2 2 > 0.9998 || = 0.52 497 464 480 525 462 | 500 < 0.0003 5 5 7 4 4 | 5 | 4 8 3 5 5 > 0.9997 || = 0.51 522 494 493 508 446 | 500 < 0.0004 5 3 6 4 3 | 5 | 3 9 3 7 8 > 0.9996 || = 0.50 484 468 461 527 498 | 500 < 0.0005 2 7 4 2 2 | 5 | 3 6 5 4 5 > 0.9995 || = 0.49 491 514 487 532 513 | 500 < 0.0006 6 5 3 6 7 | 5 | 5 4 4 7 6 > 0.9994 || = 0.48 460 502 516 523 507 | 500 < 0.0007 5 8 1 7 1 | 5 | 7 5 3 7 5 > 0.9993 || = 0.47 556 497 507 505 527 | 500 < 0.0008 5 0 8 2 9 | 5 | 5 3 4 7 4 > 0.9992 || = 0.46 502 492 499 537 497 | 500 < 0.0009 5 3 10 5 3 | 5 | 7 1 4 6 6 > 0.9991 || = 0.45 510 505 469 497 484 | 500 < 0.001 3 4 5 5 5 | 5 | 7 5 7 6 4 > 0.999 || = 0.44 526 464 497 510 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 484 462 489 477 455 | 500 < 0.001 43 46 48 44 42 | 50 | 49 46 38 55 50 > 0.999 || = 0.42 484 471 498 515 483 | 500 < 0.002 30 59 50 49 41 | 50 | 43 38 55 40 45 > 0.998 || = 0.41 526 501 516 521 507 | 500 < 0.003 56 53 56 42 39 | 50 | 58 54 60 46 51 > 0.997 || = 0.40 475 512 493 468 508 | 500 < 0.004 48 48 50 51 51 | 50 | 48 51 52 49 48 > 0.996 || = 0.39 531 510 501 497 523 | 500 < 0.005 48 48 55 59 50 | 50 | 48 48 46 62 60 > 0.995 || = 0.38 478 513 466 530 513 | 500 < 0.006 57 39 55 71 44 | 50 | 51 54 61 52 53 > 0.994 || = 0.37 497 505 492 450 515 | 500 < 0.007 42 49 50 48 52 | 50 | 51 68 50 47 44 > 0.993 || = 0.36 476 490 513 512 508 | 500 < 0.008 43 67 55 55 43 | 50 | 51 57 54 41 63 > 0.992 || = 0.35 541 477 504 477 520 | 500 < 0.009 57 46 61 48 66 | 50 | 57 46 46 38 53 > 0.991 || = 0.34 470 503 525 480 499 | 500 < 0.01 44 54 48 58 54 | 50 | 55 41 53 56 59 > 0.99 || = 0.33 490 455 475 465 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 503 500 520 469 504 | 500 < 0.01 468 509 528 525 482 | 497.5 | 511 503 515 486 526 > 0.99 || = 0.31 532 496 481 482 471 | 500 = 0.01 289 267 250 238 273 | 252.5 | 232 247 257 274 232 = 0.99 || = 0.30 503 471 507 541 473 | 500 = 0.02 505 519 462 514 485 | 500 | 509 546 530 534 499 = 0.98 || = 0.29 515 534 516 493 518 | 500 =================================================================| 500 | 542 508 533 504 479 = 0.97 || = 0.28 488 515 508 501 509 | 500 svaria_SampleProd test: | 500 | 467 508 498 503 495 = 0.96 || = 0.27 517 507 514 508 491 | 500 ----------------------------------------------- | 500 | 449 479 488 488 498 = 0.95 || = 0.26 488 484 555 515 509 | 500 N = 40, n = 10000000, r = 0, t = 8 | 500 | 481 481 500 498 500 = 0.94 || = 0.25 486 508 483 455 509 | 500 Anderson-Darling statistic = A2 | 500 | 533 507 506 456 483 = 0.93 || = 0.24 555 527 495 497 474 | 500 | 500 | 511 479 500 530 508 = 0.92 || = 0.23 527 503 521 484 498 | 500 =================================================================| 500 | 458 488 524 513 469 = 0.91 || = 0.22 524 509 503 505 522 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 492 491 505 460 506 = 0.90 || = 0.21 499 496 484 517 478 | 500 -----------------------------------------------------------------| 500 | 505 490 520 496 523 = 0.89 || = 0.20 512 499 524 479 558 | 500 SD Bern.: d 1.09402 1.21715 0.63117 | 500 | 525 533 481 533 516 = 0.88 || = 0.19 537 502 524 528 540 | 500 s 0.93623 1.05598 1.15555 | 500 | 504 494 475 477 480 = 0.87 || = 0.18 510 475 481 488 481 | 500 t 0.88659 0.69315 0.95020 | 500 | 482 523 535 514 496 = 0.86 || = 0.17 482 521 488 478 509 | 500 m 1.02166 1.20142 1.05882 | 500 | 471 517 497 511 530 = 0.85 || = 0.16 556 485 503 512 526 | 500 x 0.95700 1.12126 0.93212 | 500 | 477 475 489 515 504 = 0.84 || = 0.15 495 496 446 482 529 | 500 | 500 | 537 541 493 505 482 = 0.83 || = 0.14 481 538 475 512 533 | 500 Changes: d 57 6 3 | 500 | 506 504 487 515 495 = 0.82 || = 0.13 471 503 494 473 485 | 500 s 48 5 4 | 500 | 513 508 520 517 487 = 0.81 || = 0.12 459 492 522 503 502 | 500 t 50 6 7 | 500 | 487 565 499 494 491 = 0.80 || = 0.11 469 475 513 482 504 | 500 m 59 5 4 | 500 | 477 530 462 512 494 = 0.79 || = 0.10 480 514 493 517 487 | 500 x 41 5 5 | 500 | 504 497 489 465 493 = 0.78 || = 0.09 507 486 505 505 527 | 500 -----------------------------------------------------------------| 500 | 489 520 528 481 502 = 0.77 || = 0.08 486 472 474 464 454 | 500 Aver./ d 0.49996 498 > 500: 4 3 6 5 5 5 3 4 6 5 | 500 | 535 528 518 515 504 = 0.76 || = 0.07 514 476 501 438 466 | 500 median s 0.50141 502 ----- 5 5 7 4 5 3 6 8 6 5 | 500 | 485 481 506 482 534 = 0.75 || = 0.06 477 512 497 490 513 | 500 t 0.50175 499 3 4 7 6 3 5 5 5 4 6 | 500 | 467 521 495 516 479 = 0.74 || = 0.05 460 485 491 517 504 | 500 m 0.50186 503 5 5 5 3 7 5 7 4 7 6 | 500 | 534 516 539 490 508 = 0.73 || = 0.04 485 486 469 486 550 | 500 x 0.49846 502 6 7 6 7 5 4 4 5 5 2 | 500 | 483 511 484 522 498 = 0.72 || = 0.03 486 516 494 502 512 | 500 -----------------------------------------------------------------| 500 | 536 520 504 469 520 = 0.71 || = 0.02 505 519 462 514 485 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 489 476 524 504 510 = 0.70 || = 0.01 289 267 250 238 273 | 252.5 d 0 0 1 18 59 19 4 0 0 | 500 | 469 503 454 520 486 = 0.69 || < 0.01 468 509 528 525 482 | 497.5 s 0 0 2 15 72 10 2 0 0 | 500 | 502 485 499 503 487 = 0.68 ||========================================================================= t 0 0 2 10 75 13 1 0 0 | 500 | 490 468 489 498 496 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 15 68 13 2 0 0 | 500 | 494 499 536 474 494 = 0.66 ||========================================================================= x 0 0 3 10 72 14 2 0 0 | 500 | 480 503 506 552 509 = 0.65 || svaria_SampleProd test: no 102 test no 103 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleProd test: test no 103 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 0 | 0.5 | 0 1 1 0 0 > 0.99999 || = 0.64 534 497 450 486 488 | 500 < 0.00002 0 1 0 2 0 | 0.5 | 0 1 0 1 0 > 0.99998 || = 0.63 509 468 482 533 500 | 500 < 0.00003 0 1 3 0 1 | 0.5 | 1 0 0 1 0 > 0.99997 || = 0.62 486 549 497 493 502 | 500 < 0.00004 3 1 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 513 560 562 505 503 | 500 < 0.00005 1 1 1 1 1 | 0.5 | 2 0 0 1 1 > 0.99995 || = 0.60 475 531 490 513 491 | 500 < 0.00006 0 1 0 0 0 | 0.5 | 1 0 0 1 0 > 0.99994 || = 0.59 510 512 493 471 542 | 500 < 0.00007 0 0 0 0 1 | 0.5 | 0 0 3 0 0 > 0.99993 || = 0.58 486 514 497 477 502 | 500 < 0.00008 1 0 1 1 0 | 0.5 | 0 0 0 1 2 > 0.99992 || = 0.57 489 549 523 477 548 | 500 < 0.00009 0 1 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 529 492 482 498 494 | 500 < 0.0001 0 1 1 0 1 | 0.5 | 0 2 0 0 1 > 0.9999 || = 0.55 520 509 476 507 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 521 501 489 476 536 | 500 < 0.0001 5 7 7 7 4 | 5 | 5 4 4 5 4 > 0.9999 || = 0.53 548 501 511 536 477 | 500 < 0.0002 1 3 6 6 2 | 5 | 0 4 2 1 3 > 0.9998 || = 0.52 500 447 505 484 500 | 500 < 0.0003 2 3 6 5 8 | 5 | 3 7 3 9 3 > 0.9997 || = 0.51 514 490 460 504 476 | 500 < 0.0004 4 5 6 4 6 | 5 | 6 7 1 6 3 > 0.9996 || = 0.50 495 534 502 469 522 | 500 < 0.0005 5 7 3 7 4 | 5 | 7 5 7 3 6 > 0.9995 || = 0.49 537 525 488 497 474 | 500 < 0.0006 3 3 6 3 5 | 5 | 6 4 4 6 5 > 0.9994 || = 0.48 506 478 516 509 502 | 500 < 0.0007 6 8 5 3 5 | 5 | 7 7 2 7 6 > 0.9993 || = 0.47 499 500 527 438 478 | 500 < 0.0008 9 7 2 7 6 | 5 | 6 11 4 2 5 > 0.9992 || = 0.46 533 540 508 532 516 | 500 < 0.0009 3 1 7 4 3 | 5 | 3 7 3 4 4 > 0.9991 || = 0.45 472 483 571 503 532 | 500 < 0.001 2 5 4 7 0 | 5 | 5 7 2 2 7 > 0.999 || = 0.44 491 515 517 543 476 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 495 484 526 536 499 | 500 < 0.001 40 49 52 53 43 | 50 | 48 63 32 45 46 > 0.999 || = 0.42 497 508 510 483 527 | 500 < 0.002 37 43 56 50 44 | 50 | 50 38 48 45 46 > 0.998 || = 0.41 519 521 472 468 500 | 500 < 0.003 60 50 61 56 50 | 50 | 34 50 49 42 51 > 0.997 || = 0.40 491 512 505 471 485 | 500 < 0.004 36 46 40 53 47 | 50 | 43 38 42 45 48 > 0.996 || = 0.39 509 499 499 488 497 | 500 < 0.005 53 51 51 60 54 | 50 | 70 63 61 50 56 > 0.995 || = 0.38 482 520 491 506 493 | 500 < 0.006 53 40 51 63 57 | 50 | 45 52 54 57 46 > 0.994 || = 0.37 499 492 549 543 481 | 500 < 0.007 58 38 49 60 52 | 50 | 50 54 52 48 51 > 0.993 || = 0.36 468 508 490 499 532 | 500 < 0.008 44 49 38 46 52 | 50 | 45 42 58 44 49 > 0.992 || = 0.35 498 526 532 507 537 | 500 < 0.009 73 60 64 40 50 | 50 | 60 62 54 47 51 > 0.991 || = 0.34 517 511 496 497 485 | 500 < 0.01 57 54 54 52 43 | 50 | 45 50 47 39 46 > 0.99 || = 0.33 498 528 524 492 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 486 479 512 504 492 | 500 < 0.01 511 480 516 533 492 | 497.5 | 490 512 497 462 490 > 0.99 || = 0.31 511 498 461 494 507 | 500 = 0.01 235 258 256 244 242 | 252.5 | 283 269 252 228 240 = 0.99 || = 0.30 524 492 507 536 493 | 500 = 0.02 514 509 493 536 466 | 500 | 534 450 471 521 475 = 0.98 || = 0.29 480 517 491 481 551 | 500 =================================================================| 500 | 465 503 546 510 497 = 0.97 || = 0.28 514 495 476 493 489 | 500 svaria_SampleProd test: | 500 | 499 500 518 520 491 = 0.96 || = 0.27 468 504 516 499 492 | 500 ----------------------------------------------- | 500 | 459 508 502 517 509 = 0.95 || = 0.26 490 478 523 505 503 | 500 N = 20, n = 10000000, r = 0, t = 16 | 500 | 480 540 481 514 504 = 0.94 || = 0.25 516 496 521 515 477 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 506 478 496 547 510 = 0.93 || = 0.24 533 529 483 502 525 | 500 | 500 | 485 467 513 493 505 = 0.92 || = 0.23 521 472 510 541 473 | 500 =================================================================| 500 | 490 504 471 479 490 = 0.91 || = 0.22 499 486 500 481 495 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 500 507 503 516 549 = 0.90 || = 0.21 529 518 495 495 493 | 500 -----------------------------------------------------------------| 500 | 490 499 500 508 507 = 0.89 || = 0.20 481 508 481 472 499 | 500 SD Bern.: d 0.91335 1.58887 1.33031 | 500 | 476 521 503 520 500 = 0.88 || = 0.19 524 511 513 444 512 | 500 s 1.05465 0.92566 1.30755 | 500 | 510 508 494 502 525 = 0.87 || = 0.18 522 486 499 478 509 | 500 t 1.08195 1.11410 1.11679 | 500 | 516 520 501 468 499 = 0.86 || = 0.17 484 522 498 509 458 | 500 m 1.04514 1.04263 0.84658 | 500 | 503 450 518 540 535 = 0.85 || = 0.16 506 476 472 507 532 | 500 x 0.92154 0.65758 0.46497 | 500 | 503 510 487 483 505 = 0.84 || = 0.15 490 477 509 518 504 | 500 | 500 | 461 505 478 501 536 = 0.83 || = 0.14 469 496 497 481 471 | 500 Changes: d 59 5 4 | 500 | 495 529 482 498 460 = 0.82 || = 0.13 497 455 552 485 503 | 500 s 49 3 5 | 500 | 507 508 450 523 475 = 0.81 || = 0.12 510 494 493 478 492 | 500 t 55 4 2 | 500 | 496 509 492 480 501 = 0.80 || = 0.11 452 524 510 557 512 | 500 m 49 4 2 | 500 | 488 465 462 483 467 = 0.79 || = 0.10 488 524 542 507 452 | 500 x 52 2 8 | 500 | 535 449 553 512 518 = 0.78 || = 0.09 526 513 479 498 500 | 500 -----------------------------------------------------------------| 500 | 497 496 476 497 501 = 0.77 || = 0.08 506 479 529 494 493 | 500 Aver./ d 0.49918 499 > 500: 5 4 5 4 4 6 6 3 5 3 | 500 | 456 499 497 485 532 = 0.76 || = 0.07 500 479 493 526 508 | 500 median s 0.50040 502 ----- 4 4 5 5 6 7 3 4 8 6 | 500 | 513 502 499 485 488 = 0.75 || = 0.06 505 489 500 497 503 | 500 t 0.49770 498 4 5 4 5 8 3 3 2 4 4 | 500 | 456 476 549 485 493 = 0.74 || = 0.05 498 488 493 502 515 | 500 m 0.49889 498 6 5 4 5 5 4 5 1 7 6 | 500 | 493 506 492 477 521 = 0.73 || = 0.04 479 465 518 531 492 | 500 x 0.50140 499 3 6 3 3 4 5 4 5 6 4 | 500 | 517 486 444 473 489 = 0.72 || = 0.03 500 511 490 516 483 | 500 -----------------------------------------------------------------| 500 | 495 538 463 488 496 = 0.71 || = 0.02 514 509 493 536 466 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 501 500 462 516 520 = 0.70 || = 0.01 235 258 256 244 242 | 252.5 d 0 0 1 13 73 13 1 0 0 | 500 | 492 506 473 478 488 = 0.69 || < 0.01 511 480 516 533 492 | 497.5 s 0 0 7 8 70 13 3 0 0 | 500 | 491 481 481 486 464 = 0.68 ||========================================================================= t 0 0 3 13 69 9 6 1 0 | 500 | 526 455 512 519 491 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 14 68 15 2 0 0 | 500 | 507 447 489 529 494 = 0.66 ||========================================================================= x 0 0 1 14 71 12 3 0 0 | 500 | 477 485 525 457 510 = 0.65 || svaria_SampleProd test: no 103 test no 104 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleProd test: test no 104 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 2 1 0 | 0.5 | 0 0 1 0 1 > 0.99999 || = 0.64 474 479 539 485 490 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99998 || = 0.63 525 517 471 450 493 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 1 1 0 0 > 0.99997 || = 0.62 533 562 490 482 504 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 0 0 2 1 0 > 0.99996 || = 0.61 523 482 484 506 521 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 0 1 1 0 0 > 0.99995 || = 0.60 492 521 529 470 508 | 500 < 0.00006 0 1 1 0 1 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 504 526 493 500 494 | 500 < 0.00007 1 0 2 0 3 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 537 457 496 544 522 | 500 < 0.00008 1 1 0 0 0 | 0.5 | 0 0 2 1 0 > 0.99992 || = 0.57 477 527 489 475 484 | 500 < 0.00009 0 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 507 496 484 512 484 | 500 < 0.0001 0 0 1 0 0 | 0.5 | 1 1 0 1 1 > 0.9999 || = 0.55 467 489 544 526 486 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 502 486 498 520 501 | 500 < 0.0001 2 2 7 3 6 | 5 | 1 4 7 5 2 > 0.9999 || = 0.53 513 481 497 517 485 | 500 < 0.0002 2 4 3 6 7 | 5 | 2 2 2 1 1 > 0.9998 || = 0.52 485 529 493 527 494 | 500 < 0.0003 2 5 6 4 4 | 5 | 5 5 7 5 6 > 0.9997 || = 0.51 526 494 459 502 508 | 500 < 0.0004 11 4 3 3 3 | 5 | 7 4 7 3 6 > 0.9996 || = 0.50 538 477 465 527 484 | 500 < 0.0005 8 6 5 4 7 | 5 | 5 6 5 3 3 > 0.9995 || = 0.49 498 478 507 511 485 | 500 < 0.0006 5 10 11 5 2 | 5 | 4 6 3 3 7 > 0.9994 || = 0.48 487 534 502 516 507 | 500 < 0.0007 8 4 3 3 3 | 5 | 6 4 5 10 8 > 0.9993 || = 0.47 488 553 496 461 522 | 500 < 0.0008 4 5 6 4 10 | 5 | 6 8 2 6 5 > 0.9992 || = 0.46 520 493 544 534 482 | 500 < 0.0009 7 4 9 4 5 | 5 | 5 8 6 4 5 > 0.9991 || = 0.45 541 489 511 512 496 | 500 < 0.001 7 5 6 6 9 | 5 | 2 5 3 4 3 > 0.999 || = 0.44 496 534 468 492 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 498 463 456 504 538 | 500 < 0.001 56 49 59 42 56 | 50 | 43 52 47 44 46 > 0.999 || = 0.42 490 462 473 489 506 | 500 < 0.002 54 50 58 32 43 | 50 | 56 52 53 49 41 > 0.998 || = 0.41 461 509 499 505 526 | 500 < 0.003 39 58 53 51 45 | 50 | 59 47 42 52 50 > 0.997 || = 0.40 469 488 483 487 471 | 500 < 0.004 44 43 54 43 42 | 50 | 51 49 49 65 43 > 0.996 || = 0.39 517 477 470 477 483 | 500 < 0.005 54 57 52 55 34 | 50 | 52 56 47 49 56 > 0.995 || = 0.38 508 512 526 515 472 | 500 < 0.006 64 49 45 52 35 | 50 | 56 49 44 36 55 > 0.994 || = 0.37 492 515 482 500 549 | 500 < 0.007 52 40 60 45 55 | 50 | 46 53 52 45 51 > 0.993 || = 0.36 499 534 497 496 487 | 500 < 0.008 54 36 60 49 55 | 50 | 44 42 47 57 51 > 0.992 || = 0.35 503 505 477 479 488 | 500 < 0.009 56 56 46 48 68 | 50 | 54 48 39 40 32 > 0.991 || = 0.34 525 520 471 466 495 | 500 < 0.01 48 49 43 51 57 | 50 | 60 44 42 45 65 > 0.99 || = 0.33 495 440 513 490 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 489 483 485 470 470 | 500 < 0.01 521 487 530 468 490 | 497.5 | 521 492 462 482 490 > 0.99 || = 0.31 471 494 499 494 509 | 500 = 0.01 253 267 232 278 255 | 252.5 | 254 286 243 267 233 = 0.99 || = 0.30 507 500 450 478 542 | 500 = 0.02 534 521 500 530 517 | 500 | 510 486 489 516 492 = 0.98 || = 0.29 471 518 477 507 522 | 500 =================================================================| 500 | 486 505 505 510 497 = 0.97 || = 0.28 463 498 501 460 469 | 500 svaria_SampleProd test: | 500 | 490 527 494 518 498 = 0.96 || = 0.27 484 489 524 470 498 | 500 ----------------------------------------------- | 500 | 538 486 502 476 486 = 0.95 || = 0.26 498 452 507 521 539 | 500 N = 20, n = 10000000, r = 0, t = 16 | 500 | 477 494 474 487 462 = 0.94 || = 0.25 540 515 489 513 490 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 534 476 548 538 483 = 0.93 || = 0.24 507 472 536 498 486 | 500 | 500 | 492 456 483 490 476 = 0.92 || = 0.23 518 499 524 499 498 | 500 =================================================================| 500 | 488 501 556 529 473 = 0.91 || = 0.22 520 497 507 491 542 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 499 472 476 474 523 = 0.90 || = 0.21 494 489 518 546 514 | 500 -----------------------------------------------------------------| 500 | 504 494 505 519 510 = 0.89 || = 0.20 492 512 494 534 510 | 500 SD Bern.: d 0.89328 0.98130 0.86644 | 500 | 472 534 513 522 503 = 0.88 || = 0.19 498 482 535 507 505 | 500 s 1.05057 0.99748 0.57993 | 500 | 481 453 521 479 519 = 0.87 || = 0.18 486 490 492 492 457 | 500 t 1.18645 0.96380 0.80786 | 500 | 475 491 528 522 480 = 0.86 || = 0.17 495 495 482 511 483 | 500 m 0.99240 0.99848 1.15122 | 500 | 479 467 467 499 473 = 0.85 || = 0.16 473 532 502 515 482 | 500 x 0.95134 1.46906 1.23186 | 500 | 522 492 502 498 478 = 0.84 || = 0.15 514 515 469 478 506 | 500 | 500 | 471 517 464 488 494 = 0.83 || = 0.14 506 533 475 504 500 | 500 Changes: d 48 3 3 | 500 | 519 504 520 490 479 = 0.82 || = 0.13 478 519 481 446 497 | 500 s 42 6 5 | 500 | 498 511 495 490 481 = 0.81 || = 0.12 478 490 486 513 519 | 500 t 47 3 4 | 500 | 493 527 543 499 519 = 0.80 || = 0.11 526 495 497 495 504 | 500 m 48 5 4 | 500 | 494 508 492 518 525 = 0.79 || = 0.10 512 500 466 545 441 | 500 x 38 2 3 | 500 | 485 495 492 525 512 = 0.78 || = 0.09 510 490 499 522 529 | 500 -----------------------------------------------------------------| 500 | 495 534 527 493 517 = 0.77 || = 0.08 480 520 449 514 511 | 500 Aver./ d 0.49977 498 > 500: 5 4 4 5 2 6 6 1 3 5 | 500 | 500 511 533 507 512 = 0.76 || = 0.07 523 500 484 507 509 | 500 median s 0.49999 497 ----- 4 4 3 5 4 4 3 9 4 4 | 500 | 478 527 463 533 550 = 0.75 || = 0.06 478 459 531 499 534 | 500 t 0.50183 497 5 2 7 2 4 2 6 6 6 4 | 500 | 488 508 524 446 515 = 0.74 || = 0.05 497 523 519 476 535 | 500 m 0.49999 500 6 6 5 1 6 7 2 5 3 6 | 500 | 493 508 547 499 527 = 0.73 || = 0.04 497 488 527 510 488 | 500 x 0.49848 498 7 4 5 4 6 4 5 9 4 0 | 500 | 523 520 529 493 508 = 0.72 || = 0.03 493 498 505 486 478 | 500 -----------------------------------------------------------------| 500 | 486 519 455 505 460 = 0.71 || = 0.02 534 521 500 530 517 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 538 526 581 517 526 = 0.70 || = 0.01 253 267 232 278 255 | 252.5 d 0 0 0 13 68 20 0 0 0 | 500 | 499 495 511 497 497 = 0.69 || < 0.01 521 487 530 468 490 | 497.5 s 0 0 3 13 67 15 3 0 0 | 500 | 488 474 483 483 482 = 0.68 ||========================================================================= t 0 0 3 20 54 20 3 1 0 | 500 | 524 497 536 471 484 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 70 12 2 0 0 | 500 | 484 490 540 500 513 = 0.66 ||========================================================================= x 0 0 1 11 75 12 2 0 0 | 500 | 526 466 519 466 506 = 0.65 || svaria_SampleProd test: no 104 test no 105 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleProd test: test no 105 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 2 0 0 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 495 542 528 478 531 | 500 < 0.00002 1 0 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 516 473 513 496 499 | 500 < 0.00003 1 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 485 474 507 481 497 | 500 < 0.00004 0 1 1 1 0 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 490 504 513 495 510 | 500 < 0.00005 0 0 1 0 1 | 0.5 | 0 0 0 0 1 > 0.99995 || = 0.60 475 542 527 485 515 | 500 < 0.00006 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 488 513 496 521 459 | 500 < 0.00007 0 1 0 0 1 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 539 510 532 501 523 | 500 < 0.00008 0 2 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 528 496 459 491 526 | 500 < 0.00009 0 0 2 2 0 | 0.5 | 0 1 0 2 0 > 0.99991 || = 0.56 511 489 486 531 486 | 500 < 0.0001 1 0 0 0 0 | 0.5 | 1 0 1 1 0 > 0.9999 || = 0.55 493 526 483 490 514 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 436 506 524 480 457 | 500 < 0.0001 4 6 6 5 2 | 5 | 2 2 1 4 3 > 0.9999 || = 0.53 521 496 514 491 507 | 500 < 0.0002 4 3 9 7 2 | 5 | 2 2 2 3 2 > 0.9998 || = 0.52 501 466 479 476 495 | 500 < 0.0003 4 5 3 3 3 | 5 | 6 3 2 4 5 > 0.9997 || = 0.51 494 498 489 470 477 | 500 < 0.0004 2 2 8 7 1 | 5 | 4 1 10 6 4 > 0.9996 || = 0.50 475 500 548 523 474 | 500 < 0.0005 4 9 6 2 5 | 5 | 3 6 1 5 3 > 0.9995 || = 0.49 494 512 484 468 479 | 500 < 0.0006 7 6 4 4 4 | 5 | 5 5 4 2 6 > 0.9994 || = 0.48 514 510 507 492 489 | 500 < 0.0007 6 8 11 15 6 | 5 | 7 4 2 4 2 > 0.9993 || = 0.47 509 501 478 520 472 | 500 < 0.0008 5 5 6 3 6 | 5 | 1 5 4 4 4 > 0.9992 || = 0.46 487 517 493 489 481 | 500 < 0.0009 2 3 9 4 11 | 5 | 3 7 4 8 4 > 0.9991 || = 0.45 481 512 540 493 491 | 500 < 0.001 5 6 8 7 2 | 5 | 10 4 5 7 5 > 0.999 || = 0.44 449 529 507 499 508 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 516 460 529 517 512 | 500 < 0.001 43 53 70 57 42 | 50 | 43 39 35 47 38 > 0.999 || = 0.42 532 531 488 467 523 | 500 < 0.002 48 47 64 40 53 | 50 | 46 45 49 39 46 > 0.998 || = 0.41 507 524 530 540 541 | 500 < 0.003 51 52 55 66 44 | 50 | 56 44 45 34 60 > 0.997 || = 0.40 491 500 482 539 481 | 500 < 0.004 45 43 44 52 49 | 50 | 53 54 46 40 50 > 0.996 || = 0.39 498 475 524 514 487 | 500 < 0.005 39 50 46 45 51 | 50 | 54 60 45 56 54 > 0.995 || = 0.38 481 506 436 468 472 | 500 < 0.006 57 44 48 59 48 | 50 | 46 52 52 44 55 > 0.994 || = 0.37 520 447 494 513 521 | 500 < 0.007 54 53 57 49 51 | 50 | 57 56 47 53 42 > 0.993 || = 0.36 474 523 524 513 535 | 500 < 0.008 54 41 47 43 41 | 50 | 40 45 51 49 62 > 0.992 || = 0.35 497 429 521 503 484 | 500 < 0.009 50 50 51 59 39 | 50 | 53 48 73 47 51 > 0.991 || = 0.34 542 450 467 523 501 | 500 < 0.01 55 56 53 43 39 | 50 | 60 61 50 53 49 > 0.99 || = 0.33 495 484 493 517 433 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 509 457 504 517 492 | 500 < 0.01 496 489 535 513 457 | 497.5 | 508 504 493 462 507 > 0.99 || = 0.31 488 482 535 497 504 | 500 = 0.01 252 244 295 265 241 | 252.5 | 255 273 251 220 230 = 0.99 || = 0.30 511 451 479 505 485 | 500 = 0.02 527 498 483 521 544 | 500 | 511 522 540 497 514 = 0.98 || = 0.29 517 495 501 493 493 | 500 =================================================================| 500 | 502 504 545 556 527 = 0.97 || = 0.28 484 494 482 515 535 | 500 svaria_SampleProd test: | 500 | 530 497 491 476 519 = 0.96 || = 0.27 485 502 453 494 500 | 500 ----------------------------------------------- | 500 | 493 499 493 557 490 = 0.95 || = 0.26 488 496 523 518 490 | 500 N = 20, n = 10000000, r = 0, t = 16 | 500 | 487 510 496 490 511 = 0.94 || = 0.25 454 492 489 531 519 | 500 Anderson-Darling statistic = A2 | 500 | 519 521 523 511 524 = 0.93 || = 0.24 522 494 505 502 485 | 500 | 500 | 521 519 461 459 497 = 0.92 || = 0.23 471 459 528 456 488 | 500 =================================================================| 500 | 473 484 493 491 468 = 0.91 || = 0.22 499 506 502 509 486 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 456 455 521 518 528 = 0.90 || = 0.21 490 505 488 510 500 | 500 -----------------------------------------------------------------| 500 | 521 495 491 480 529 = 0.89 || = 0.20 472 503 470 487 525 | 500 SD Bern.: d 0.94704 0.78268 0.89486 | 500 | 498 482 494 475 470 = 0.88 || = 0.19 500 520 523 489 529 | 500 s 1.06075 0.68297 0.98841 | 500 | 502 523 515 495 512 = 0.87 || = 0.18 486 513 480 493 530 | 500 t 1.03691 1.22126 1.29292 | 500 | 458 507 485 511 521 = 0.86 || = 0.17 490 480 478 499 514 | 500 m 0.92659 1.17956 1.08312 | 500 | 483 481 510 517 492 = 0.85 || = 0.16 482 493 484 512 508 | 500 x 1.02558 0.93748 1.01143 | 500 | 515 477 532 498 469 = 0.84 || = 0.15 500 433 511 517 519 | 500 | 500 | 497 511 518 522 514 = 0.83 || = 0.14 505 492 503 500 474 | 500 Changes: d 43 5 5 | 500 | 523 464 527 492 509 = 0.82 || = 0.13 467 535 478 495 511 | 500 s 39 6 3 | 500 | 529 519 499 491 519 = 0.81 || = 0.12 483 515 500 470 473 | 500 t 53 4 4 | 500 | 494 524 488 503 479 = 0.80 || = 0.11 490 487 501 509 527 | 500 m 49 7 5 | 500 | 539 500 531 494 480 = 0.79 || = 0.10 475 527 521 486 498 | 500 x 49 6 6 | 500 | 512 516 482 491 537 = 0.78 || = 0.09 556 528 514 481 521 | 500 -----------------------------------------------------------------| 500 | 506 534 483 475 446 = 0.77 || = 0.08 508 524 472 516 489 | 500 Aver./ d 0.50136 499 > 500: 6 1 2 4 5 5 5 8 5 7 | 500 | 486 497 516 487 525 = 0.76 || = 0.07 533 511 489 519 498 | 500 median s 0.50178 503 ----- 6 5 4 2 8 5 6 7 4 7 | 500 | 503 476 516 483 506 = 0.75 || = 0.06 513 514 469 531 500 | 500 t 0.50087 496 4 5 5 5 5 4 5 4 6 3 | 500 | 511 514 471 500 489 = 0.74 || = 0.05 479 504 505 509 494 | 500 m 0.49760 499 9 3 6 8 4 3 4 2 4 3 | 500 | 517 512 479 469 474 = 0.73 || = 0.04 497 485 497 532 472 | 500 x 0.50055 500 3 7 3 4 4 5 6 5 7 6 | 500 | 510 545 504 508 501 = 0.72 || = 0.03 508 506 494 502 509 | 500 -----------------------------------------------------------------| 500 | 537 522 470 471 511 = 0.71 || = 0.02 527 498 483 521 544 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 522 511 485 523 536 = 0.70 || = 0.01 252 244 295 265 241 | 252.5 d 0 0 3 10 76 11 1 0 0 | 500 | 488 501 482 499 520 = 0.69 || < 0.01 496 489 535 513 457 | 497.5 s 0 2 4 11 67 16 1 0 0 | 500 | 498 519 465 504 483 = 0.68 ||========================================================================= t 0 0 2 10 67 19 3 0 0 | 500 | 512 475 512 505 456 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 15 74 9 2 0 0 | 500 | 511 535 472 477 513 = 0.66 ||========================================================================= x 0 1 1 16 64 19 0 0 0 | 500 | 502 493 480 516 504 = 0.65 || svaria_SampleProd test: no 105 test no 106 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleProd test: test no 106 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 1 0 | 0.5 | 0 1 1 0 0 > 0.99999 || = 0.64 491 466 476 477 519 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 1 1 1 0 > 0.99998 || = 0.63 501 494 517 500 524 | 500 < 0.00003 1 1 1 0 2 | 0.5 | 0 0 0 0 2 > 0.99997 || = 0.62 501 491 456 502 510 | 500 < 0.00004 1 0 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99996 || = 0.61 499 495 475 495 481 | 500 < 0.00005 0 1 0 1 0 | 0.5 | 1 1 0 0 0 > 0.99995 || = 0.60 540 503 500 500 497 | 500 < 0.00006 0 1 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 520 511 544 483 474 | 500 < 0.00007 2 1 0 0 0 | 0.5 | 2 0 0 3 0 > 0.99993 || = 0.58 563 503 503 488 511 | 500 < 0.00008 0 0 0 2 1 | 0.5 | 0 2 2 2 0 > 0.99992 || = 0.57 477 524 517 479 537 | 500 < 0.00009 1 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 533 514 528 501 495 | 500 < 0.0001 1 0 0 0 2 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 522 474 521 494 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 492 527 522 509 530 | 500 < 0.0001 7 4 2 4 5 | 5 | 3 5 5 6 3 > 0.9999 || = 0.53 493 484 482 496 509 | 500 < 0.0002 5 5 5 5 4 | 5 | 6 4 5 4 1 > 0.9998 || = 0.52 516 496 482 532 475 | 500 < 0.0003 4 6 4 9 3 | 5 | 7 8 7 7 5 > 0.9997 || = 0.51 495 498 500 537 502 | 500 < 0.0004 4 6 6 8 4 | 5 | 5 8 6 2 9 > 0.9996 || = 0.50 543 556 500 483 519 | 500 < 0.0005 7 3 3 4 5 | 5 | 5 3 3 2 6 > 0.9995 || = 0.49 529 495 527 522 506 | 500 < 0.0006 4 4 4 5 6 | 5 | 6 5 8 9 3 > 0.9994 || = 0.48 492 537 492 477 521 | 500 < 0.0007 3 2 3 1 7 | 5 | 4 8 7 6 3 > 0.9993 || = 0.47 479 485 483 493 455 | 500 < 0.0008 3 5 4 8 4 | 5 | 5 3 1 5 2 > 0.9992 || = 0.46 466 493 504 502 512 | 500 < 0.0009 3 6 5 8 2 | 5 | 2 6 6 4 6 > 0.9991 || = 0.45 460 513 563 529 485 | 500 < 0.001 3 7 4 6 5 | 5 | 3 3 4 5 2 > 0.999 || = 0.44 505 504 482 454 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 508 520 491 482 502 | 500 < 0.001 43 48 40 58 45 | 50 | 46 53 52 50 40 > 0.999 || = 0.42 456 483 512 476 473 | 500 < 0.002 46 34 43 36 42 | 50 | 52 54 43 41 38 > 0.998 || = 0.41 493 515 517 521 501 | 500 < 0.003 45 54 50 55 47 | 50 | 41 39 44 42 50 > 0.997 || = 0.40 530 506 494 519 473 | 500 < 0.004 42 70 47 42 46 | 50 | 52 47 47 48 57 > 0.996 || = 0.39 489 489 494 525 453 | 500 < 0.005 61 43 54 47 52 | 50 | 54 59 60 62 53 > 0.995 || = 0.38 489 503 515 506 495 | 500 < 0.006 60 57 43 63 42 | 50 | 47 59 39 37 49 > 0.994 || = 0.37 475 510 514 491 528 | 500 < 0.007 60 49 37 59 37 | 50 | 50 45 38 51 48 > 0.993 || = 0.36 533 495 507 465 516 | 500 < 0.008 47 43 53 52 46 | 50 | 53 36 47 54 48 > 0.992 || = 0.35 495 508 471 510 498 | 500 < 0.009 49 46 53 57 46 | 50 | 54 36 53 44 54 > 0.991 || = 0.34 526 492 525 508 476 | 500 < 0.01 39 56 66 43 44 | 50 | 55 40 62 58 45 > 0.99 || = 0.33 515 526 475 485 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 515 482 506 520 493 | 500 < 0.01 492 500 486 512 447 | 497.5 | 504 468 485 487 482 > 0.99 || = 0.31 471 511 479 526 498 | 500 = 0.01 244 255 257 253 252 | 252.5 | 258 276 259 219 247 = 0.99 || = 0.30 505 499 472 464 479 | 500 = 0.02 501 502 508 510 482 | 500 | 520 493 478 493 498 = 0.98 || = 0.29 482 480 489 498 514 | 500 =================================================================| 500 | 513 477 490 493 500 = 0.97 || = 0.28 501 517 517 492 494 | 500 svaria_SampleProd test: | 500 | 499 528 498 513 500 = 0.96 || = 0.27 505 502 465 497 488 | 500 ----------------------------------------------- | 500 | 470 482 499 483 484 = 0.95 || = 0.26 468 466 519 501 531 | 500 N = 20, n = 10000000, r = 0, t = 24 | 500 | 503 474 539 527 494 = 0.94 || = 0.25 481 504 484 524 515 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 511 499 511 508 472 = 0.93 || = 0.24 515 490 483 503 511 | 500 | 500 | 506 493 483 496 520 = 0.92 || = 0.23 509 534 507 487 510 | 500 =================================================================| 500 | 488 541 488 469 504 = 0.91 || = 0.22 494 499 528 500 493 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 533 467 500 472 523 = 0.90 || = 0.21 526 478 515 475 492 | 500 -----------------------------------------------------------------| 500 | 480 509 470 453 479 = 0.89 || = 0.20 467 467 489 526 533 | 500 SD Bern.: d 0.98690 1.10145 0.60028 | 500 | 506 483 488 497 514 = 0.88 || = 0.19 501 507 500 545 474 | 500 s 0.94327 1.32428 1.29214 | 500 | 497 507 517 504 477 = 0.87 || = 0.18 524 517 522 515 461 | 500 t 0.95001 1.15469 1.11858 | 500 | 466 477 504 496 506 = 0.86 || = 0.17 518 492 459 475 500 | 500 m 1.07327 1.19222 1.07663 | 500 | 450 527 510 527 488 = 0.85 || = 0.16 496 521 504 469 507 | 500 x 1.01089 0.91587 0.83945 | 500 | 499 526 479 465 541 = 0.84 || = 0.15 501 468 520 486 506 | 500 | 500 | 494 464 491 466 517 = 0.83 || = 0.14 504 494 475 470 527 | 500 Changes: d 55 2 5 | 500 | 479 495 473 498 477 = 0.82 || = 0.13 493 493 491 476 464 | 500 s 61 5 3 | 500 | 507 533 521 545 500 = 0.81 || = 0.12 494 539 483 504 484 | 500 t 40 3 4 | 500 | 494 491 524 536 512 = 0.80 || = 0.11 510 516 496 442 491 | 500 m 45 5 5 | 500 | 534 465 503 523 512 = 0.79 || = 0.10 465 466 519 543 509 | 500 x 46 2 4 | 500 | 536 502 449 520 504 = 0.78 || = 0.09 463 523 511 530 489 | 500 -----------------------------------------------------------------| 500 | 486 502 479 577 486 = 0.77 || = 0.08 479 500 511 514 483 | 500 Aver./ d 0.50001 501 > 500: 5 6 5 5 4 6 4 5 3 7 | 500 | 523 491 483 501 483 = 0.76 || = 0.07 549 505 517 477 459 | 500 median s 0.49896 499 ----- 8 5 4 5 6 6 2 4 5 3 | 500 | 466 488 499 526 557 = 0.75 || = 0.06 501 512 507 532 496 | 500 t 0.49834 500 8 4 5 5 5 6 1 5 4 3 | 500 | 515 481 483 499 513 = 0.74 || = 0.05 523 511 488 515 545 | 500 m 0.50024 500 7 4 4 6 5 4 3 9 3 3 | 500 | 494 507 511 530 470 = 0.73 || = 0.04 518 464 521 477 482 | 500 x 0.50186 500 2 4 6 2 5 6 6 7 5 2 | 500 | 508 459 530 504 563 = 0.72 || = 0.03 497 525 569 460 516 | 500 -----------------------------------------------------------------| 500 | 478 557 532 527 544 = 0.71 || = 0.02 501 502 508 510 482 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 486 490 496 500 512 = 0.70 || = 0.01 244 255 257 253 252 | 252.5 d 0 0 1 15 68 15 2 0 0 | 500 | 504 528 497 473 483 = 0.69 || < 0.01 492 500 486 512 447 | 497.5 s 0 0 0 16 68 15 2 0 0 | 500 | 526 494 484 486 461 = 0.68 ||========================================================================= t 0 0 1 12 77 9 1 1 0 | 500 | 468 514 496 520 528 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 18 59 17 2 1 0 | 500 | 467 471 471 509 496 = 0.66 ||========================================================================= x 0 0 3 14 68 13 3 0 0 | 500 | 494 492 494 499 528 = 0.65 || svaria_SampleProd test: no 106 test no 107 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleProd test: test no 107 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 2 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 500 456 469 498 516 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 532 469 504 515 492 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 485 514 515 492 511 | 500 < 0.00004 0 0 0 1 1 | 0.5 | 1 0 0 1 0 > 0.99996 || = 0.61 488 487 505 478 501 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 1 0 0 0 2 > 0.99995 || = 0.60 502 510 522 497 499 | 500 < 0.00006 0 0 1 0 2 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 457 503 495 478 509 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 0 0 2 1 1 > 0.99993 || = 0.58 481 484 502 522 529 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 0 0 0 2 1 > 0.99992 || = 0.57 502 498 545 526 496 | 500 < 0.00009 1 0 1 0 0 | 0.5 | 1 0 2 0 0 > 0.99991 || = 0.56 480 509 514 491 489 | 500 < 0.0001 0 0 0 1 0 | 0.5 | 0 0 0 0 1 > 0.9999 || = 0.55 489 495 476 514 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 506 468 498 504 498 | 500 < 0.0001 1 2 5 4 3 | 5 | 4 0 4 5 5 > 0.9999 || = 0.53 513 513 526 518 534 | 500 < 0.0002 6 4 5 3 7 | 5 | 6 1 0 5 1 > 0.9998 || = 0.52 519 461 452 497 503 | 500 < 0.0003 3 7 5 7 4 | 5 | 5 5 3 4 7 > 0.9997 || = 0.51 494 472 491 511 511 | 500 < 0.0004 5 4 5 5 8 | 5 | 4 2 5 3 7 > 0.9996 || = 0.50 500 563 523 467 496 | 500 < 0.0005 5 7 2 4 8 | 5 | 5 6 6 9 7 > 0.9995 || = 0.49 523 501 478 517 534 | 500 < 0.0006 6 1 10 5 2 | 5 | 4 6 5 3 2 > 0.9994 || = 0.48 499 529 510 533 504 | 500 < 0.0007 7 3 2 7 6 | 5 | 8 9 7 5 3 > 0.9993 || = 0.47 458 530 484 507 506 | 500 < 0.0008 2 6 4 7 5 | 5 | 5 2 7 6 5 > 0.9992 || = 0.46 504 499 512 491 507 | 500 < 0.0009 1 6 8 7 11 | 5 | 5 5 5 2 10 > 0.9991 || = 0.45 502 497 507 450 472 | 500 < 0.001 4 5 7 5 4 | 5 | 2 2 2 4 7 > 0.999 || = 0.44 470 472 490 471 541 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 494 494 505 542 525 | 500 < 0.001 40 45 53 54 58 | 50 | 48 38 44 46 54 > 0.999 || = 0.42 455 495 520 546 491 | 500 < 0.002 56 46 46 48 37 | 50 | 45 55 64 56 37 > 0.998 || = 0.41 457 469 515 476 477 | 500 < 0.003 64 48 51 49 49 | 50 | 65 57 72 36 41 > 0.997 || = 0.40 504 536 474 547 509 | 500 < 0.004 55 47 43 49 41 | 50 | 58 53 59 57 44 > 0.996 || = 0.39 514 484 526 523 515 | 500 < 0.005 46 62 49 54 40 | 50 | 58 48 56 50 47 > 0.995 || = 0.38 526 510 532 510 495 | 500 < 0.006 62 51 67 41 44 | 50 | 45 57 46 43 50 > 0.994 || = 0.37 547 474 510 523 460 | 500 < 0.007 54 41 48 51 56 | 50 | 59 43 48 45 45 > 0.993 || = 0.36 472 468 490 528 516 | 500 < 0.008 42 40 36 57 48 | 50 | 46 50 42 43 63 > 0.992 || = 0.35 516 512 479 464 517 | 500 < 0.009 61 46 41 52 39 | 50 | 61 45 54 58 64 > 0.991 || = 0.34 491 509 516 511 498 | 500 < 0.01 47 45 46 55 63 | 50 | 54 45 53 46 54 > 0.99 || = 0.33 495 526 475 515 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 490 491 493 468 504 | 500 < 0.01 527 471 480 510 475 | 497.5 | 539 491 538 480 499 > 0.99 || = 0.31 459 498 440 515 473 | 500 = 0.01 259 244 268 251 248 | 252.5 | 276 237 229 232 237 = 0.99 || = 0.30 470 499 474 514 525 | 500 = 0.02 511 495 504 517 462 | 500 | 513 528 503 472 471 = 0.98 || = 0.29 520 484 503 501 481 | 500 =================================================================| 500 | 486 483 504 514 466 = 0.97 || = 0.28 482 462 469 485 506 | 500 svaria_SampleProd test: | 500 | 483 518 512 495 540 = 0.96 || = 0.27 496 509 498 464 532 | 500 ----------------------------------------------- | 500 | 512 555 521 504 512 = 0.95 || = 0.26 509 525 522 540 523 | 500 N = 20, n = 10000000, r = 0, t = 24 | 500 | 522 506 457 495 463 = 0.94 || = 0.25 504 487 507 494 480 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 508 487 482 490 488 = 0.93 || = 0.24 507 492 510 497 518 | 500 | 500 | 492 481 483 475 523 = 0.92 || = 0.23 468 531 494 484 511 | 500 =================================================================| 500 | 493 546 505 536 494 = 0.91 || = 0.22 480 510 477 464 506 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 493 523 519 503 495 = 0.90 || = 0.21 513 502 508 530 488 | 500 -----------------------------------------------------------------| 500 | 497 502 525 518 501 = 0.89 || = 0.20 503 515 535 476 485 | 500 SD Bern.: d 0.92301 1.20642 1.13281 | 500 | 484 488 496 520 498 = 0.88 || = 0.19 510 533 503 478 515 | 500 s 0.99959 0.91805 0.87105 | 500 | 512 489 459 530 498 = 0.87 || = 0.18 515 509 493 480 507 | 500 t 0.95583 1.15122 1.37326 | 500 | 490 522 505 541 544 = 0.86 || = 0.17 496 462 513 492 504 | 500 m 1.15393 0.62958 1.00048 | 500 | 483 474 542 517 463 = 0.85 || = 0.16 525 502 475 455 499 | 500 x 0.95763 1.25041 1.19808 | 500 | 511 485 504 520 491 = 0.84 || = 0.15 473 494 480 493 525 | 500 | 500 | 495 516 502 510 509 = 0.83 || = 0.14 459 500 506 495 499 | 500 Changes: d 44 6 5 | 500 | 477 488 540 503 478 = 0.82 || = 0.13 502 514 504 496 502 | 500 s 46 2 4 | 500 | 522 516 511 506 511 = 0.81 || = 0.12 508 492 492 494 458 | 500 t 49 5 3 | 500 | 506 494 482 460 482 = 0.80 || = 0.11 501 519 541 485 484 | 500 m 41 4 6 | 500 | 472 519 466 486 488 = 0.79 || = 0.10 513 494 506 496 494 | 500 x 55 4 2 | 500 | 494 501 507 469 527 = 0.78 || = 0.09 503 470 495 540 500 | 500 -----------------------------------------------------------------| 500 | 471 484 506 506 481 = 0.77 || = 0.08 523 493 512 527 481 | 500 Aver./ d 0.49967 501 > 500: 7 7 6 4 4 5 5 5 3 6 | 500 | 543 494 492 516 514 = 0.76 || = 0.07 496 482 501 449 505 | 500 median s 0.50040 498 ----- 3 5 6 4 4 4 4 6 5 5 | 500 | 524 502 485 491 466 = 0.75 || = 0.06 490 531 507 481 492 | 500 t 0.50009 503 6 6 6 4 6 5 6 3 8 6 | 500 | 473 498 482 447 493 = 0.74 || = 0.05 547 553 492 527 489 | 500 m 0.49991 498 7 0 3 8 6 6 4 3 10 3 | 500 | 494 508 503 476 457 = 0.73 || = 0.04 537 508 509 531 538 | 500 x 0.49900 499 3 5 6 6 7 5 4 4 4 4 | 500 | 517 521 478 412 517 = 0.72 || = 0.03 497 497 493 506 563 | 500 -----------------------------------------------------------------| 500 | 513 501 499 540 548 = 0.71 || = 0.02 511 495 504 517 462 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 510 524 466 493 492 = 0.70 || = 0.01 259 244 268 251 248 | 252.5 d 0 0 1 14 72 12 2 0 0 | 500 | 508 516 534 470 485 = 0.69 || < 0.01 527 471 480 510 475 | 497.5 s 0 0 1 14 71 11 4 0 0 | 500 | 501 522 540 517 516 = 0.68 ||========================================================================= t 0 0 2 14 72 12 1 0 0 | 500 | 498 485 506 482 493 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 4 15 61 18 2 0 0 | 500 | 524 486 474 542 472 = 0.66 ||========================================================================= x 0 0 0 15 70 14 2 0 0 | 500 | 496 435 479 535 476 = 0.65 || svaria_SampleProd test: no 107 test no 108 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleProd test: test no 108 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 1 0 | 0.5 | 2 0 0 0 0 > 0.99999 || = 0.64 486 546 530 496 492 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 0 0 1 1 1 > 0.99998 || = 0.63 529 480 474 509 506 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 494 544 479 508 515 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 501 515 524 508 520 | 500 < 0.00005 0 1 0 0 0 | 0.5 | 1 0 0 1 2 > 0.99995 || = 0.60 512 501 479 506 522 | 500 < 0.00006 0 1 0 0 1 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 520 489 482 513 514 | 500 < 0.00007 2 1 1 0 1 | 0.5 | 0 2 0 1 0 > 0.99993 || = 0.58 456 537 518 504 503 | 500 < 0.00008 0 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 520 509 480 478 488 | 500 < 0.00009 1 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99991 || = 0.56 475 521 494 500 498 | 500 < 0.0001 0 0 1 2 1 | 0.5 | 0 1 1 1 0 > 0.9999 || = 0.55 505 524 469 534 540 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 486 479 471 521 515 | 500 < 0.0001 3 5 2 3 5 | 5 | 5 3 2 5 4 > 0.9999 || = 0.53 536 494 492 512 478 | 500 < 0.0002 8 7 4 4 2 | 5 | 1 0 5 5 6 > 0.9998 || = 0.52 526 479 521 491 504 | 500 < 0.0003 5 5 2 8 4 | 5 | 3 4 5 4 1 > 0.9997 || = 0.51 481 502 509 482 510 | 500 < 0.0004 5 2 2 6 4 | 5 | 5 4 1 6 4 > 0.9996 || = 0.50 530 534 509 498 460 | 500 < 0.0005 2 3 5 11 5 | 5 | 5 5 4 3 6 > 0.9995 || = 0.49 516 488 465 487 519 | 500 < 0.0006 6 4 10 6 6 | 5 | 6 5 5 6 5 > 0.9994 || = 0.48 502 493 501 526 513 | 500 < 0.0007 8 5 4 8 3 | 5 | 5 6 5 8 2 > 0.9993 || = 0.47 485 495 518 494 495 | 500 < 0.0008 1 4 5 9 4 | 5 | 3 4 3 11 4 > 0.9992 || = 0.46 462 503 520 494 489 | 500 < 0.0009 3 8 3 6 4 | 5 | 7 3 6 3 3 > 0.9991 || = 0.45 497 521 493 478 530 | 500 < 0.001 4 8 6 5 6 | 5 | 3 5 4 3 2 > 0.999 || = 0.44 489 471 490 527 527 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 469 489 491 554 494 | 500 < 0.001 45 51 43 66 43 | 50 | 43 39 40 54 37 > 0.999 || = 0.42 506 482 489 510 510 | 500 < 0.002 50 50 43 51 43 | 50 | 53 49 44 48 56 > 0.998 || = 0.41 485 456 510 496 489 | 500 < 0.003 47 39 58 36 37 | 50 | 41 39 43 53 61 > 0.997 || = 0.40 484 485 486 513 506 | 500 < 0.004 37 51 39 47 47 | 50 | 45 59 40 59 55 > 0.996 || = 0.39 499 506 518 510 462 | 500 < 0.005 53 62 43 52 60 | 50 | 46 42 26 55 43 > 0.995 || = 0.38 528 520 500 478 468 | 500 < 0.006 56 49 49 44 37 | 50 | 61 50 48 48 49 > 0.994 || = 0.37 489 517 499 518 527 | 500 < 0.007 44 65 51 48 55 | 50 | 52 59 52 49 65 > 0.993 || = 0.36 478 526 479 492 516 | 500 < 0.008 47 54 62 65 39 | 50 | 58 58 49 48 48 > 0.992 || = 0.35 497 463 542 509 506 | 500 < 0.009 66 41 57 45 43 | 50 | 52 48 52 61 43 > 0.991 || = 0.34 513 483 462 494 507 | 500 < 0.01 44 41 46 66 37 | 50 | 51 48 42 53 48 > 0.99 || = 0.33 504 510 483 475 507 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 464 506 490 499 503 | 500 < 0.01 489 503 491 520 441 | 497.5 | 502 491 436 528 505 > 0.99 || = 0.31 489 509 497 502 523 | 500 = 0.01 293 240 263 254 235 | 252.5 | 249 271 233 248 254 = 0.99 || = 0.30 517 505 508 501 480 | 500 = 0.02 520 506 482 523 489 | 500 | 513 529 522 508 536 = 0.98 || = 0.29 521 522 531 506 487 | 500 =================================================================| 500 | 520 513 520 543 503 = 0.97 || = 0.28 555 538 477 505 548 | 500 svaria_SampleProd test: | 500 | 486 464 484 481 524 = 0.96 || = 0.27 442 478 506 479 507 | 500 ----------------------------------------------- | 500 | 490 483 510 511 494 = 0.95 || = 0.26 487 460 471 500 492 | 500 N = 20, n = 10000000, r = 0, t = 24 | 500 | 518 505 485 496 523 = 0.94 || = 0.25 495 512 524 491 463 | 500 Anderson-Darling statistic = A2 | 500 | 505 498 520 508 502 = 0.93 || = 0.24 509 542 479 511 505 | 500 | 500 | 534 494 492 541 537 = 0.92 || = 0.23 481 508 513 476 483 | 500 =================================================================| 500 | 503 472 518 459 450 = 0.91 || = 0.22 474 534 526 481 504 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 464 493 505 475 539 = 0.90 || = 0.21 487 527 487 533 471 | 500 -----------------------------------------------------------------| 500 | 474 520 539 487 490 = 0.89 || = 0.20 531 509 529 531 501 | 500 SD Bern.: d 1.03100 1.08220 0.86529 | 500 | 491 479 545 513 516 = 0.88 || = 0.19 507 487 498 510 509 | 500 s 0.96974 1.15902 1.04070 | 500 | 527 502 514 473 502 = 0.87 || = 0.18 466 515 500 535 502 | 500 t 0.97471 1.04263 1.37035 | 500 | 492 495 480 525 528 = 0.86 || = 0.17 511 516 525 499 460 | 500 m 0.94127 1.42337 0.74062 | 500 | 477 485 493 485 470 = 0.85 || = 0.16 539 477 488 491 483 | 500 x 0.97810 1.34900 1.16933 | 500 | 493 534 521 498 487 = 0.84 || = 0.15 511 472 491 521 497 | 500 | 500 | 544 526 460 545 465 = 0.83 || = 0.14 471 478 525 504 476 | 500 Changes: d 53 4 3 | 500 | 489 491 473 483 516 = 0.82 || = 0.13 531 531 480 487 506 | 500 s 43 5 4 | 500 | 487 495 480 520 482 = 0.81 || = 0.12 503 502 509 475 502 | 500 t 54 4 4 | 500 | 481 503 548 509 505 = 0.80 || = 0.11 503 501 503 485 533 | 500 m 42 6 4 | 500 | 515 487 505 509 500 = 0.79 || = 0.10 520 479 514 471 508 | 500 x 49 4 4 | 500 | 509 463 505 528 463 = 0.78 || = 0.09 463 503 544 481 476 | 500 -----------------------------------------------------------------| 500 | 479 496 503 481 534 = 0.77 || = 0.08 506 493 503 496 516 | 500 Aver./ d 0.49875 501 > 500: 6 8 4 4 3 6 5 5 2 7 | 500 | 459 465 519 476 505 = 0.76 || = 0.07 497 503 478 457 517 | 500 median s 0.49909 501 ----- 6 5 8 8 2 6 7 2 4 4 | 500 | 472 468 519 450 475 = 0.75 || = 0.06 552 485 491 454 508 | 500 t 0.49893 500 6 5 6 3 4 3 5 7 5 5 | 500 | 505 503 461 484 518 = 0.74 || = 0.05 513 494 508 474 517 | 500 m 0.50128 499 4 4 5 5 5 6 4 4 4 6 | 500 | 492 458 491 492 492 = 0.73 || = 0.04 479 504 526 485 495 | 500 x 0.50194 503 4 6 5 7 6 7 5 5 5 8 | 500 | 510 491 526 533 517 = 0.72 || = 0.03 530 513 533 510 463 | 500 -----------------------------------------------------------------| 500 | 516 450 479 494 497 = 0.71 || = 0.02 520 506 482 523 489 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 515 508 469 499 449 = 0.70 || = 0.01 293 240 263 254 235 | 252.5 d 0 0 1 15 69 13 3 0 0 | 500 | 479 535 501 466 512 = 0.69 || < 0.01 489 503 491 520 441 | 497.5 s 0 0 1 12 71 16 1 0 0 | 500 | 485 528 483 475 479 = 0.68 ||========================================================================= t 0 0 1 12 72 14 2 0 0 | 500 | 507 501 506 497 517 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 12 70 15 2 0 0 | 500 | 474 499 504 493 496 = 0.66 ||========================================================================= x 0 0 3 14 70 13 1 0 0 | 500 | 528 491 484 525 488 = 0.65 || svaria_SampleProd test: no 108 test no 109 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleMean test: test no 109 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 469 500 523 517 499 | 500 < 0.00002 0 0 1 0 0 | 0.5 | 0 1 0 0 0 > 0.99998 || = 0.63 447 518 495 490 494 | 500 < 0.00003 1 1 0 2 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 491 485 519 488 465 | 500 < 0.00004 0 0 0 1 1 | 0.5 | 1 1 0 0 1 > 0.99996 || = 0.61 497 480 493 487 512 | 500 < 0.00005 1 1 1 1 0 | 0.5 | 1 0 0 2 0 > 0.99995 || = 0.60 490 488 498 541 464 | 500 < 0.00006 2 2 0 0 0 | 0.5 | 2 0 0 0 0 > 0.99994 || = 0.59 530 482 520 518 439 | 500 < 0.00007 0 0 1 0 1 | 0.5 | 0 1 1 0 2 > 0.99993 || = 0.58 497 513 485 488 503 | 500 < 0.00008 0 0 0 0 2 | 0.5 | 1 1 0 0 0 > 0.99992 || = 0.57 503 527 517 484 515 | 500 < 0.00009 0 2 1 0 1 | 0.5 | 0 1 1 2 0 > 0.99991 || = 0.56 502 507 547 542 507 | 500 < 0.0001 0 0 2 1 0 | 0.5 | 1 1 1 0 0 > 0.9999 || = 0.55 484 496 473 499 473 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 496 506 495 484 487 | 500 < 0.0001 5 6 7 5 5 | 5 | 6 6 3 4 3 > 0.9999 || = 0.53 531 466 499 505 474 | 500 < 0.0002 4 1 3 6 5 | 5 | 3 3 3 3 2 > 0.9998 || = 0.52 511 516 501 527 503 | 500 < 0.0003 11 5 3 4 5 | 5 | 8 6 8 4 4 > 0.9997 || = 0.51 467 512 495 478 504 | 500 < 0.0004 3 6 4 4 4 | 5 | 4 5 3 4 7 > 0.9996 || = 0.50 504 517 495 464 519 | 500 < 0.0005 5 3 2 4 3 | 5 | 4 5 3 3 2 > 0.9995 || = 0.49 504 454 489 510 493 | 500 < 0.0006 7 3 3 2 7 | 5 | 6 9 8 4 8 > 0.9994 || = 0.48 476 493 469 477 504 | 500 < 0.0007 6 9 8 1 6 | 5 | 5 5 4 6 5 > 0.9993 || = 0.47 465 490 501 499 483 | 500 < 0.0008 4 4 4 4 5 | 5 | 5 2 6 6 2 > 0.9992 || = 0.46 545 498 528 481 510 | 500 < 0.0009 6 3 5 4 4 | 5 | 8 6 6 3 5 > 0.9991 || = 0.45 485 497 481 492 487 | 500 < 0.001 6 5 7 4 1 | 5 | 4 6 3 6 5 > 0.999 || = 0.44 513 502 509 512 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 497 470 498 467 513 | 500 < 0.001 57 45 46 38 45 | 50 | 53 53 47 43 43 > 0.999 || = 0.42 506 519 474 488 512 | 500 < 0.002 46 61 55 46 70 | 50 | 55 55 42 48 50 > 0.998 || = 0.41 458 497 484 505 481 | 500 < 0.003 75 39 52 54 62 | 50 | 51 54 46 47 61 > 0.997 || = 0.40 487 525 488 494 458 | 500 < 0.004 46 55 52 48 50 | 50 | 43 59 46 44 56 > 0.996 || = 0.39 499 494 497 478 507 | 500 < 0.005 39 51 43 43 51 | 50 | 38 52 53 52 49 > 0.995 || = 0.38 518 510 515 562 542 | 500 < 0.006 45 39 57 58 45 | 50 | 41 51 56 65 53 > 0.994 || = 0.37 491 452 492 481 521 | 500 < 0.007 54 48 54 55 55 | 50 | 46 44 50 48 61 > 0.993 || = 0.36 505 516 516 515 536 | 500 < 0.008 45 60 41 59 34 | 50 | 53 43 45 41 44 > 0.992 || = 0.35 554 500 461 510 501 | 500 < 0.009 55 57 57 38 46 | 50 | 55 34 46 62 52 > 0.991 || = 0.34 486 468 482 472 481 | 500 < 0.01 61 50 42 46 55 | 50 | 43 48 57 47 49 > 0.99 || = 0.33 519 523 498 502 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 518 521 520 500 521 | 500 < 0.01 523 505 499 485 513 | 497.5 | 478 493 488 497 518 > 0.99 || = 0.31 480 547 509 477 549 | 500 = 0.01 215 269 261 239 262 | 252.5 | 243 275 249 243 248 = 0.99 || = 0.30 528 511 498 502 503 | 500 = 0.02 475 484 492 466 494 | 500 | 511 544 482 537 502 = 0.98 || = 0.29 473 497 489 482 516 | 500 =================================================================| 500 | 494 457 497 510 500 = 0.97 || = 0.28 490 500 499 491 497 | 500 svaria_SampleMean test: | 500 | 491 497 474 486 523 = 0.96 || = 0.27 520 501 506 516 468 | 500 ----------------------------------------------- | 500 | 531 503 496 517 518 = 0.95 || = 0.26 501 531 470 481 524 | 500 N = 20000000, n = 30, r = 0 | 500 | 533 512 511 476 492 = 0.94 || = 0.25 503 444 534 532 502 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 469 481 511 497 451 = 0.93 || = 0.24 486 469 525 494 494 | 500 | 500 | 502 452 520 509 507 = 0.92 || = 0.23 523 486 461 496 526 | 500 =================================================================| 500 | 475 499 501 544 458 = 0.91 || = 0.22 532 469 490 528 521 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 514 473 466 494 494 = 0.90 || = 0.21 498 506 485 518 496 | 500 -----------------------------------------------------------------| 500 | 498 515 535 528 523 = 0.89 || = 0.20 520 501 538 522 533 | 500 SD Bern.: d 0.98516 1.44224 0.90376 | 500 | 492 477 476 486 511 = 0.88 || = 0.19 500 498 478 511 469 | 500 s 0.99415 1.06542 0.98129 | 500 | 531 488 501 478 476 = 0.87 || = 0.18 501 501 534 500 490 | 500 t 0.89547 0.84539 0.69315 | 500 | 469 524 501 503 528 = 0.86 || = 0.17 517 531 509 513 499 | 500 m 0.93417 1.05787 1.06353 | 500 | 522 481 508 479 494 = 0.85 || = 0.16 515 491 493 504 488 | 500 x 0.98607 1.35492 0.86990 | 500 | 475 500 516 510 510 = 0.84 || = 0.15 487 483 542 525 484 | 500 | 500 | 493 484 493 516 505 = 0.83 || = 0.14 505 471 528 526 528 | 500 Changes: d 61 6 3 | 500 | 512 489 552 511 511 = 0.82 || = 0.13 513 506 515 508 499 | 500 s 51 6 1 | 500 | 450 517 489 514 475 = 0.81 || = 0.12 504 511 495 511 523 | 500 t 51 6 3 | 500 | 489 475 492 502 509 = 0.80 || = 0.11 473 495 479 540 487 | 500 m 48 4 4 | 500 | 512 535 481 541 552 = 0.79 || = 0.10 484 552 477 480 493 | 500 x 52 7 6 | 500 | 494 515 488 516 486 = 0.78 || = 0.09 559 490 520 510 489 | 500 -----------------------------------------------------------------| 500 | 481 492 510 500 486 = 0.77 || = 0.08 493 510 524 486 489 | 500 Aver./ d 0.49917 499 > 500: 4 6 6 6 4 5 3 5 4 4 | 500 | 528 541 470 494 482 = 0.76 || = 0.07 499 502 497 500 507 | 500 median s 0.49963 500 ----- 6 5 4 6 3 6 5 7 3 4 | 500 | 499 506 547 538 458 = 0.75 || = 0.06 472 540 520 467 544 | 500 t 0.49934 497 5 5 4 4 3 4 4 3 6 4 | 500 | 518 497 496 485 534 = 0.74 || = 0.05 489 526 499 510 512 | 500 m 0.50037 499 3 8 5 5 3 5 1 4 6 5 | 500 | 520 527 475 500 500 = 0.73 || = 0.04 515 470 489 507 513 | 500 x 0.49865 500 6 2 6 8 4 5 3 4 6 5 | 500 | 515 518 465 495 501 = 0.72 || = 0.03 512 481 482 484 480 | 500 -----------------------------------------------------------------| 500 | 478 505 511 463 480 = 0.71 || = 0.02 475 484 492 466 494 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 536 521 489 482 497 = 0.70 || = 0.01 215 269 261 239 262 | 252.5 d 0 0 3 13 70 12 3 0 0 | 500 | 492 513 499 490 523 = 0.69 || < 0.01 523 505 499 485 513 | 497.5 s 0 0 4 12 69 14 2 0 0 | 500 | 486 462 483 486 500 = 0.68 ||========================================================================= t 0 0 0 13 74 11 3 0 0 | 500 | 523 497 532 463 451 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 11 76 13 1 0 0 | 500 | 502 513 507 479 530 = 0.66 ||========================================================================= x 0 0 3 11 71 14 2 0 0 | 500 | 494 502 495 463 489 = 0.65 || svaria_SampleMean test: no 109 test no 110 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleMean test: test no 110 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 0 0 0 | 0.5 | 0 1 0 1 0 > 0.99999 || = 0.64 483 490 544 519 486 | 500 < 0.00002 1 0 1 0 0 | 0.5 | 0 0 0 3 1 > 0.99998 || = 0.63 549 494 487 532 494 | 500 < 0.00003 0 1 1 1 0 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 529 490 474 440 529 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 526 503 499 484 475 | 500 < 0.00005 0 0 1 1 0 | 0.5 | 1 0 2 1 0 > 0.99995 || = 0.60 511 460 554 531 431 | 500 < 0.00006 0 1 1 1 0 | 0.5 | 0 1 0 1 0 > 0.99994 || = 0.59 489 506 510 509 497 | 500 < 0.00007 2 0 0 0 2 | 0.5 | 1 0 2 0 1 > 0.99993 || = 0.58 469 526 508 494 472 | 500 < 0.00008 0 1 0 1 1 | 0.5 | 0 0 1 1 0 > 0.99992 || = 0.57 471 510 480 541 538 | 500 < 0.00009 1 1 0 1 2 | 0.5 | 0 0 1 0 1 > 0.99991 || = 0.56 482 532 481 488 477 | 500 < 0.0001 1 2 1 0 0 | 0.5 | 0 2 1 1 0 > 0.9999 || = 0.55 545 501 513 502 520 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 491 527 491 469 484 | 500 < 0.0001 5 8 6 5 6 | 5 | 4 4 7 8 3 > 0.9999 || = 0.53 445 505 487 487 453 | 500 < 0.0002 3 3 6 9 4 | 5 | 2 2 0 1 1 > 0.9998 || = 0.52 511 518 504 512 479 | 500 < 0.0003 8 7 5 3 0 | 5 | 9 2 7 2 6 > 0.9997 || = 0.51 505 511 511 504 512 | 500 < 0.0004 5 5 4 6 5 | 5 | 7 3 5 1 3 > 0.9996 || = 0.50 502 528 520 520 497 | 500 < 0.0005 7 4 8 8 8 | 5 | 9 9 4 9 3 > 0.9995 || = 0.49 465 498 527 476 475 | 500 < 0.0006 1 3 6 6 8 | 5 | 5 6 5 3 9 > 0.9994 || = 0.48 502 480 473 495 524 | 500 < 0.0007 4 3 5 6 8 | 5 | 3 4 3 3 5 > 0.9993 || = 0.47 477 489 509 487 500 | 500 < 0.0008 5 6 0 2 3 | 5 | 6 5 2 5 5 > 0.9992 || = 0.46 544 512 484 483 538 | 500 < 0.0009 3 7 2 3 2 | 5 | 2 5 7 3 1 > 0.9991 || = 0.45 482 492 502 487 523 | 500 < 0.001 4 3 8 5 8 | 5 | 6 4 6 4 3 > 0.999 || = 0.44 460 521 525 456 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 509 500 512 481 499 | 500 < 0.001 45 49 50 53 52 | 50 | 53 44 46 39 39 > 0.999 || = 0.42 482 476 487 516 503 | 500 < 0.002 54 62 55 47 50 | 50 | 56 58 45 51 46 > 0.998 || = 0.41 542 500 475 520 507 | 500 < 0.003 61 34 48 52 54 | 50 | 47 48 48 62 45 > 0.997 || = 0.40 501 484 509 473 547 | 500 < 0.004 56 44 56 47 47 | 50 | 61 56 53 50 69 > 0.996 || = 0.39 505 504 503 509 508 | 500 < 0.005 55 54 53 54 52 | 50 | 55 47 50 42 50 > 0.995 || = 0.38 507 480 499 551 531 | 500 < 0.006 46 59 56 63 66 | 50 | 55 45 41 51 46 > 0.994 || = 0.37 531 508 507 477 455 | 500 < 0.007 51 43 46 44 59 | 50 | 66 56 46 52 50 > 0.993 || = 0.36 503 493 472 501 497 | 500 < 0.008 45 55 46 59 54 | 50 | 43 63 57 56 46 > 0.992 || = 0.35 516 472 448 497 521 | 500 < 0.009 40 60 42 51 41 | 50 | 62 48 65 49 49 > 0.991 || = 0.34 477 514 503 502 508 | 500 < 0.01 34 45 44 55 53 | 50 | 46 48 67 66 56 > 0.99 || = 0.33 537 502 496 476 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 455 474 512 514 511 | 500 < 0.01 487 505 496 525 528 | 497.5 | 544 513 518 518 496 > 0.99 || = 0.31 500 486 469 492 498 | 500 = 0.01 232 239 234 217 248 | 252.5 | 230 245 269 249 256 = 0.99 || = 0.30 511 543 479 508 471 | 500 = 0.02 515 500 494 496 497 | 500 | 522 513 504 489 518 = 0.98 || = 0.29 513 527 487 501 484 | 500 =================================================================| 500 | 512 485 525 506 527 = 0.97 || = 0.28 484 493 524 450 481 | 500 svaria_SampleMean test: | 500 | 528 502 479 519 503 = 0.96 || = 0.27 507 510 473 506 522 | 500 ----------------------------------------------- | 500 | 532 492 516 514 519 = 0.95 || = 0.26 489 488 519 533 484 | 500 N = 20000000, n = 30, r = 0 | 500 | 521 531 488 442 491 = 0.94 || = 0.25 508 510 549 458 499 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 505 503 472 459 535 = 0.93 || = 0.24 515 513 496 530 480 | 500 | 500 | 511 508 501 503 518 = 0.92 || = 0.23 524 503 475 481 523 | 500 =================================================================| 500 | 478 495 499 510 524 = 0.91 || = 0.22 453 515 502 511 467 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 498 502 490 470 482 = 0.90 || = 0.21 473 504 478 485 518 | 500 -----------------------------------------------------------------| 500 | 508 479 515 485 477 = 0.89 || = 0.20 491 523 512 505 514 | 500 SD Bern.: d 1.09257 1.11500 1.17531 | 500 | 493 504 553 517 520 = 0.88 || = 0.19 467 495 525 503 528 | 500 s 0.80105 1.21138 0.88020 | 500 | 503 493 494 525 510 = 0.87 || = 0.18 537 489 490 505 485 | 500 t 0.96335 0.69603 1.19557 | 500 | 548 473 461 522 490 = 0.86 || = 0.17 484 511 495 500 475 | 500 m 1.04327 0.84776 1.12126 | 500 | 496 519 494 505 464 = 0.85 || = 0.16 497 532 513 493 433 | 500 x 1.08035 0.97618 1.08865 | 500 | 496 495 533 475 519 = 0.84 || = 0.15 505 478 514 495 492 | 500 | 500 | 530 476 455 469 512 = 0.83 || = 0.14 482 479 508 463 493 | 500 Changes: d 55 4 5 | 500 | 481 486 479 455 490 = 0.82 || = 0.13 505 492 512 494 544 | 500 s 50 6 6 | 500 | 522 466 466 491 525 = 0.81 || = 0.12 545 512 483 535 468 | 500 t 53 4 3 | 500 | 481 492 519 508 498 = 0.80 || = 0.11 476 531 529 488 477 | 500 m 50 6 5 | 500 | 546 526 506 530 480 = 0.79 || = 0.10 486 469 498 511 532 | 500 x 45 6 3 | 500 | 504 464 449 508 523 = 0.78 || = 0.09 482 483 528 489 489 | 500 -----------------------------------------------------------------| 500 | 484 485 530 481 500 = 0.77 || = 0.08 494 487 541 508 533 | 500 Aver./ d 0.50281 502 > 500: 3 4 5 7 5 4 5 5 5 8 | 500 | 475 476 497 493 509 = 0.76 || = 0.07 506 501 492 510 476 | 500 median s 0.49925 500 ----- 4 4 8 5 2 9 4 3 3 6 | 500 | 524 518 485 537 532 = 0.75 || = 0.06 495 497 497 515 465 | 500 t 0.49960 499 4 6 5 4 6 6 4 5 3 6 | 500 | 518 504 481 505 524 = 0.74 || = 0.05 448 522 504 503 473 | 500 m 0.50035 503 6 4 6 6 2 6 6 8 4 6 | 500 | 481 491 481 537 550 = 0.73 || = 0.04 503 516 485 507 481 | 500 x 0.50254 499 2 3 4 6 6 3 5 6 5 8 | 500 | 481 469 504 510 508 = 0.72 || = 0.03 488 488 501 497 477 | 500 -----------------------------------------------------------------| 500 | 511 495 511 546 473 = 0.71 || = 0.02 515 500 494 496 497 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 461 500 519 533 474 = 0.70 || = 0.01 232 239 234 217 248 | 252.5 d 0 0 4 15 63 13 6 0 0 | 500 | 476 535 494 536 528 = 0.69 || < 0.01 487 505 496 525 528 | 497.5 s 0 0 0 11 77 13 0 0 0 | 500 | 475 486 484 488 508 = 0.68 ||========================================================================= t 0 0 3 11 72 12 3 0 0 | 500 | 528 498 495 509 502 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 5 12 69 13 2 0 0 | 500 | 483 527 505 499 508 = 0.66 ||========================================================================= x 0 2 2 17 58 20 2 0 0 | 500 | 509 513 521 510 485 = 0.65 || svaria_SampleMean test: no 110 test no 111 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleMean test: test no 111 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 2 0 1 0 | 0.5 | 0 1 0 1 1 > 0.99999 || = 0.64 470 528 477 444 500 | 500 < 0.00002 1 0 2 0 1 | 0.5 | 1 0 1 0 0 > 0.99998 || = 0.63 510 490 490 470 515 | 500 < 0.00003 1 0 0 1 0 | 0.5 | 0 0 1 1 0 > 0.99997 || = 0.62 513 502 542 522 470 | 500 < 0.00004 0 1 1 2 3 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 535 472 497 488 499 | 500 < 0.00005 0 1 1 0 0 | 0.5 | 1 0 1 1 3 > 0.99995 || = 0.60 492 536 457 448 520 | 500 < 0.00006 1 1 0 0 1 | 0.5 | 2 1 2 2 1 > 0.99994 || = 0.59 497 456 524 498 490 | 500 < 0.00007 0 2 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99993 || = 0.58 479 511 456 521 490 | 500 < 0.00008 0 2 0 1 0 | 0.5 | 1 0 1 0 1 > 0.99992 || = 0.57 474 491 497 481 493 | 500 < 0.00009 1 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 477 499 473 535 476 | 500 < 0.0001 1 0 1 0 1 | 0.5 | 1 1 2 0 1 > 0.9999 || = 0.55 507 517 482 549 461 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 552 485 520 495 542 | 500 < 0.0001 6 9 5 5 6 | 5 | 6 3 9 6 7 > 0.9999 || = 0.53 481 491 470 496 508 | 500 < 0.0002 6 5 3 5 4 | 5 | 4 1 3 2 2 > 0.9998 || = 0.52 484 507 504 523 499 | 500 < 0.0003 4 6 7 4 8 | 5 | 8 3 8 10 5 > 0.9997 || = 0.51 479 481 492 538 490 | 500 < 0.0004 4 2 2 4 10 | 5 | 2 5 5 4 9 > 0.9996 || = 0.50 528 487 509 497 478 | 500 < 0.0005 7 4 8 6 4 | 5 | 5 8 3 4 3 > 0.9995 || = 0.49 513 525 527 531 541 | 500 < 0.0006 13 5 6 3 5 | 5 | 4 5 7 2 5 > 0.9994 || = 0.48 524 498 481 498 489 | 500 < 0.0007 5 3 5 5 4 | 5 | 2 6 3 4 6 > 0.9993 || = 0.47 492 514 509 486 490 | 500 < 0.0008 10 7 3 4 5 | 5 | 3 3 9 6 4 > 0.9992 || = 0.46 477 482 481 543 479 | 500 < 0.0009 4 6 10 2 6 | 5 | 9 9 3 8 6 > 0.9991 || = 0.45 478 519 462 483 499 | 500 < 0.001 7 6 2 9 7 | 5 | 6 6 7 4 5 > 0.999 || = 0.44 516 489 508 501 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 482 540 511 498 469 | 500 < 0.001 66 53 51 47 59 | 50 | 49 49 57 50 52 > 0.999 || = 0.42 509 517 556 504 489 | 500 < 0.002 38 51 47 49 44 | 50 | 59 53 43 49 44 > 0.998 || = 0.41 524 497 517 528 502 | 500 < 0.003 55 53 66 54 56 | 50 | 51 44 41 45 49 > 0.997 || = 0.40 512 486 492 492 525 | 500 < 0.004 55 59 49 65 48 | 50 | 37 51 44 57 50 > 0.996 || = 0.39 563 504 521 503 536 | 500 < 0.005 64 60 61 55 44 | 50 | 43 53 42 58 48 > 0.995 || = 0.38 478 492 481 500 476 | 500 < 0.006 48 45 48 47 60 | 50 | 53 65 52 60 56 > 0.994 || = 0.37 524 529 508 552 488 | 500 < 0.007 48 51 50 49 58 | 50 | 48 64 57 45 49 > 0.993 || = 0.36 472 519 548 511 498 | 500 < 0.008 63 57 55 42 38 | 50 | 55 39 53 43 46 > 0.992 || = 0.35 492 537 484 506 528 | 500 < 0.009 46 36 63 39 52 | 50 | 37 46 61 42 42 > 0.991 || = 0.34 525 515 501 513 523 | 500 < 0.01 45 55 46 38 54 | 50 | 56 45 53 53 54 > 0.99 || = 0.33 485 496 475 506 468 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 525 477 493 525 468 | 500 < 0.01 528 520 536 485 513 | 497.5 | 488 509 503 502 490 > 0.99 || = 0.31 479 530 488 508 502 | 500 = 0.01 267 219 240 243 235 | 252.5 | 268 237 245 284 266 = 0.99 || = 0.30 494 502 518 483 535 | 500 = 0.02 491 462 456 498 531 | 500 | 541 489 466 521 498 = 0.98 || = 0.29 510 481 495 479 531 | 500 =================================================================| 500 | 479 497 495 509 516 = 0.97 || = 0.28 483 473 527 486 512 | 500 svaria_SampleMean test: | 500 | 513 502 549 469 516 = 0.96 || = 0.27 512 457 477 507 530 | 500 ----------------------------------------------- | 500 | 475 506 508 514 479 = 0.95 || = 0.26 509 515 486 470 495 | 500 N = 20000000, n = 30, r = 0 | 500 | 494 479 488 465 495 = 0.94 || = 0.25 490 516 508 522 469 | 500 Anderson-Darling statistic = A2 | 500 | 521 505 547 475 486 = 0.93 || = 0.24 505 554 505 492 486 | 500 | 500 | 467 479 504 498 491 = 0.92 || = 0.23 539 514 470 494 489 | 500 =================================================================| 500 | 501 475 491 497 480 = 0.91 || = 0.22 501 435 520 487 492 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 487 517 504 493 519 = 0.90 || = 0.21 468 506 524 504 517 | 500 -----------------------------------------------------------------| 500 | 474 483 487 494 503 = 0.89 || = 0.20 581 501 529 503 488 | 500 SD Bern.: d 1.04905 1.31518 1.04358 | 500 | 504 497 502 477 458 = 0.88 || = 0.19 485 484 507 509 499 | 500 s 0.97372 0.99648 1.13104 | 500 | 495 485 477 469 544 = 0.87 || = 0.18 502 495 505 493 496 | 500 t 0.97727 1.09781 0.97104 | 500 | 524 505 483 506 515 = 0.86 || = 0.17 502 502 502 480 501 | 500 m 0.95052 1.10960 0.87906 | 500 | 486 469 508 507 473 = 0.85 || = 0.16 523 523 514 498 468 | 500 x 0.98186 1.02128 0.59694 | 500 | 486 513 489 490 525 = 0.84 || = 0.15 511 449 532 464 470 | 500 | 500 | 503 483 496 505 478 = 0.83 || = 0.14 502 483 468 494 484 | 500 Changes: d 55 5 7 | 500 | 478 500 482 527 508 = 0.82 || = 0.13 471 530 497 492 518 | 500 s 56 4 4 | 500 | 482 509 500 504 485 = 0.81 || = 0.12 475 489 506 504 522 | 500 t 56 7 2 | 500 | 496 514 531 482 478 = 0.80 || = 0.11 490 525 502 532 491 | 500 m 49 2 3 | 500 | 512 502 504 518 490 = 0.79 || = 0.10 492 510 499 479 547 | 500 x 47 6 4 | 500 | 483 512 521 478 504 = 0.78 || = 0.09 477 549 538 505 463 | 500 -----------------------------------------------------------------| 500 | 516 455 495 482 508 = 0.77 || = 0.08 492 521 512 531 544 | 500 Aver./ d 0.49980 496 > 500: 3 5 7 4 6 2 5 5 3 5 | 500 | 499 527 498 502 478 = 0.76 || = 0.07 473 521 482 459 497 | 500 median s 0.49852 501 ----- 6 5 6 7 5 4 4 8 4 4 | 500 | 457 501 472 504 514 = 0.75 || = 0.06 474 501 536 521 506 | 500 t 0.49880 500 5 7 6 5 6 3 4 4 3 5 | 500 | 548 505 517 507 537 = 0.74 || = 0.05 481 499 492 492 489 | 500 m 0.49982 498 4 3 4 8 5 5 3 7 5 5 | 500 | 505 503 474 505 515 = 0.73 || = 0.04 507 486 513 515 486 | 500 x 0.50029 498 4 4 4 5 3 3 5 7 6 3 | 500 | 491 502 483 551 501 = 0.72 || = 0.03 496 530 480 489 469 | 500 -----------------------------------------------------------------| 500 | 551 485 495 509 520 = 0.71 || = 0.02 491 462 456 498 531 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 488 489 504 471 536 = 0.70 || = 0.01 267 219 240 243 235 | 252.5 d 0 0 0 16 67 12 5 1 0 | 500 | 469 506 483 505 518 = 0.69 || < 0.01 528 520 536 485 513 | 497.5 s 0 0 4 8 74 13 2 0 0 | 500 | 497 499 500 494 472 = 0.68 ||========================================================================= t 0 0 0 16 70 11 4 0 0 | 500 | 515 490 468 506 520 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 10 75 11 3 0 0 | 500 | 482 497 502 486 528 = 0.66 ||========================================================================= x 0 0 0 16 68 16 1 0 0 | 500 | 546 503 520 491 499 = 0.65 || svaria_SampleMean test: no 111 test no 112 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleMean test: test no 112 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 3 1 0 0 0 | 0.5 | 1 2 1 1 1 > 0.99999 || = 0.64 518 485 489 507 525 | 500 < 0.00002 0 0 0 1 1 | 0.5 | 2 1 0 1 0 > 0.99998 || = 0.63 522 504 505 495 488 | 500 < 0.00003 1 0 0 3 2 | 0.5 | 0 0 2 1 0 > 0.99997 || = 0.62 549 535 493 502 488 | 500 < 0.00004 1 0 1 2 0 | 0.5 | 2 2 1 0 0 > 0.99996 || = 0.61 471 491 506 502 537 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 2 0 0 0 1 > 0.99995 || = 0.60 506 511 514 488 470 | 500 < 0.00006 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 486 470 512 526 512 | 500 < 0.00007 3 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 522 477 568 515 483 | 500 < 0.00008 0 1 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 518 524 526 501 534 | 500 < 0.00009 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 480 516 514 492 508 | 500 < 0.0001 4 0 1 1 1 | 0.5 | 0 0 0 2 0 > 0.9999 || = 0.55 511 505 511 524 519 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 468 477 498 531 505 | 500 < 0.0001 13 4 2 9 5 | 5 | 7 6 4 5 2 > 0.9999 || = 0.53 494 502 495 485 493 | 500 < 0.0002 6 10 6 4 7 | 5 | 2 3 0 2 2 > 0.9998 || = 0.52 486 546 468 519 484 | 500 < 0.0003 2 7 6 6 10 | 5 | 7 3 5 4 7 > 0.9997 || = 0.51 497 483 498 509 485 | 500 < 0.0004 3 3 4 9 2 | 5 | 4 4 3 3 4 > 0.9996 || = 0.50 494 508 497 473 508 | 500 < 0.0005 4 6 6 7 4 | 5 | 2 8 6 4 8 > 0.9995 || = 0.49 525 503 475 493 505 | 500 < 0.0006 6 3 8 4 4 | 5 | 8 7 7 3 4 > 0.9994 || = 0.48 526 479 493 507 483 | 500 < 0.0007 6 7 6 5 6 | 5 | 5 10 7 4 7 > 0.9993 || = 0.47 517 492 464 493 500 | 500 < 0.0008 4 1 6 3 5 | 5 | 5 2 5 5 5 > 0.9992 || = 0.46 550 452 483 490 477 | 500 < 0.0009 7 7 5 4 2 | 5 | 5 6 7 4 6 > 0.9991 || = 0.45 484 514 502 541 501 | 500 < 0.001 3 5 6 4 4 | 5 | 3 2 3 4 4 > 0.999 || = 0.44 499 468 487 537 482 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 489 473 475 477 454 | 500 < 0.001 54 53 55 55 49 | 50 | 48 51 47 38 49 > 0.999 || = 0.42 494 520 516 516 492 | 500 < 0.002 46 48 38 42 51 | 50 | 47 51 52 43 51 > 0.998 || = 0.41 506 536 507 512 515 | 500 < 0.003 45 51 51 36 46 | 50 | 46 40 51 41 52 > 0.997 || = 0.40 490 520 538 501 509 | 500 < 0.004 51 35 52 56 43 | 50 | 46 47 58 56 40 > 0.996 || = 0.39 479 487 558 500 501 | 500 < 0.005 61 48 39 57 47 | 50 | 58 51 53 51 49 > 0.995 || = 0.38 512 528 513 509 518 | 500 < 0.006 52 49 53 44 57 | 50 | 43 62 49 39 55 > 0.994 || = 0.37 484 487 496 489 512 | 500 < 0.007 48 53 59 43 55 | 50 | 37 41 60 56 55 > 0.993 || = 0.36 503 524 500 499 507 | 500 < 0.008 40 56 40 51 59 | 50 | 55 39 44 50 49 > 0.992 || = 0.35 474 495 470 502 513 | 500 < 0.009 52 46 56 48 54 | 50 | 31 39 54 44 46 > 0.991 || = 0.34 500 496 545 495 470 | 500 < 0.01 51 44 44 56 34 | 50 | 35 51 51 53 54 > 0.99 || = 0.33 513 503 472 510 481 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 517 490 519 530 501 | 500 < 0.01 500 483 487 488 495 | 497.5 | 446 472 519 471 500 > 0.99 || = 0.31 504 519 518 529 497 | 500 = 0.01 261 243 266 245 243 | 252.5 | 267 280 273 240 260 = 0.99 || = 0.30 483 492 515 495 521 | 500 = 0.02 497 502 538 510 543 | 500 | 501 474 472 490 499 = 0.98 || = 0.29 517 512 483 466 504 | 500 =================================================================| 500 | 500 478 486 478 525 = 0.97 || = 0.28 513 503 451 488 499 | 500 svaria_SampleMean test: | 500 | 457 523 521 474 493 = 0.96 || = 0.27 464 482 493 516 501 | 500 ----------------------------------------------- | 500 | 479 500 491 470 524 = 0.95 || = 0.26 493 502 492 514 520 | 500 N = 20000000, n = 30, r = 10 | 500 | 501 510 502 507 499 = 0.94 || = 0.25 507 520 512 484 511 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 465 508 491 485 528 = 0.93 || = 0.24 506 502 508 515 476 | 500 | 500 | 469 491 512 524 476 = 0.92 || = 0.23 508 529 477 493 509 | 500 =================================================================| 500 | 512 464 473 527 472 = 0.91 || = 0.22 518 473 535 478 524 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 487 501 478 481 460 = 0.90 || = 0.21 508 450 518 488 513 | 500 -----------------------------------------------------------------| 500 | 509 476 449 494 516 = 0.89 || = 0.20 503 506 468 525 494 | 500 SD Bern.: d 0.92693 0.76457 1.37034 | 500 | 494 500 485 530 468 = 0.88 || = 0.19 458 540 528 491 517 | 500 s 0.95708 0.82623 1.07756 | 500 | 530 492 505 498 479 = 0.87 || = 0.18 513 507 460 455 500 | 500 t 1.09307 1.05598 0.69460 | 500 | 501 458 513 490 503 = 0.86 || = 0.17 506 514 499 520 498 | 500 m 0.89782 0.99648 1.01341 | 500 | 469 489 484 508 472 = 0.85 || = 0.16 522 507 502 515 511 | 500 x 1.01350 1.00348 0.61674 | 500 | 470 502 486 487 469 = 0.84 || = 0.15 518 503 486 541 496 | 500 | 500 | 509 493 535 517 465 = 0.83 || = 0.14 487 469 513 518 506 | 500 Changes: d 53 4 4 | 500 | 500 541 508 517 521 = 0.82 || = 0.13 528 518 511 505 543 | 500 s 56 5 4 | 500 | 515 515 504 466 459 = 0.81 || = 0.12 499 527 506 469 524 | 500 t 45 7 5 | 500 | 519 497 503 492 503 = 0.80 || = 0.11 503 512 492 489 488 | 500 m 52 6 5 | 500 | 505 493 481 504 505 = 0.79 || = 0.10 510 480 411 540 525 | 500 x 57 4 5 | 500 | 469 482 500 524 513 = 0.78 || = 0.09 493 542 493 489 544 | 500 -----------------------------------------------------------------| 500 | 523 503 519 485 480 = 0.77 || = 0.08 559 514 515 481 452 | 500 Aver./ d 0.49688 502 > 500: 6 7 8 5 5 4 4 6 5 4 | 500 | 502 476 468 468 472 = 0.76 || = 0.07 497 502 514 493 519 | 500 median s 0.49914 502 ----- 5 8 7 4 5 6 7 3 4 4 | 500 | 448 512 513 460 501 = 0.75 || = 0.06 515 512 453 507 505 | 500 t 0.50023 500 6 5 4 6 4 6 4 5 5 5 | 500 | 483 496 536 492 488 = 0.74 || = 0.05 503 478 473 535 505 | 500 m 0.49831 498 4 6 4 5 6 7 6 3 4 3 | 500 | 480 541 490 458 448 = 0.73 || = 0.04 530 470 537 510 463 | 500 x 0.49823 501 5 6 7 7 4 5 5 5 3 5 | 500 | 516 467 486 482 500 = 0.72 || = 0.03 498 485 503 478 462 | 500 -----------------------------------------------------------------| 500 | 507 486 533 532 521 = 0.71 || = 0.02 497 502 538 510 543 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 480 524 531 483 475 = 0.70 || = 0.01 261 243 266 245 243 | 252.5 d 0 0 2 12 78 6 3 0 0 | 500 | 493 504 485 513 544 = 0.69 || < 0.01 500 483 487 488 495 | 497.5 s 0 0 2 15 68 15 1 0 0 | 500 | 500 521 500 523 497 = 0.68 ||========================================================================= t 1 0 3 13 69 12 2 1 0 | 500 | 518 529 488 491 541 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 11 72 17 0 0 0 | 500 | 474 489 489 487 497 = 0.66 ||========================================================================= x 0 0 3 16 67 14 1 0 0 | 500 | 497 514 527 512 559 = 0.65 || svaria_SampleMean test: no 112 test no 113 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleMean test: test no 113 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 1 0 | 0.5 | 1 0 1 0 0 > 0.99999 || = 0.64 515 490 466 505 455 | 500 < 0.00002 0 0 1 1 0 | 0.5 | 2 0 0 2 1 > 0.99998 || = 0.63 519 476 523 439 535 | 500 < 0.00003 0 1 0 1 0 | 0.5 | 2 0 0 1 0 > 0.99997 || = 0.62 531 535 525 464 524 | 500 < 0.00004 0 1 0 1 0 | 0.5 | 0 0 1 2 1 > 0.99996 || = 0.61 511 490 504 530 513 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 515 504 533 488 488 | 500 < 0.00006 0 0 0 1 0 | 0.5 | 0 0 1 0 1 > 0.99994 || = 0.59 497 484 528 485 492 | 500 < 0.00007 1 0 0 0 2 | 0.5 | 1 1 0 1 0 > 0.99993 || = 0.58 514 537 451 489 484 | 500 < 0.00008 3 0 2 0 1 | 0.5 | 1 0 1 0 2 > 0.99992 || = 0.57 496 496 513 518 511 | 500 < 0.00009 0 1 1 1 2 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 490 512 510 552 557 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 2 0 0 1 > 0.9999 || = 0.55 526 498 533 504 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 494 479 495 506 496 | 500 < 0.0001 5 3 5 6 6 | 5 | 7 3 5 6 6 > 0.9999 || = 0.53 509 461 476 532 471 | 500 < 0.0002 6 4 4 6 7 | 5 | 7 3 2 2 0 > 0.9998 || = 0.52 495 517 516 487 509 | 500 < 0.0003 2 1 4 4 10 | 5 | 3 3 6 5 3 > 0.9997 || = 0.51 483 516 522 456 464 | 500 < 0.0004 6 5 2 6 2 | 5 | 4 10 5 6 10 > 0.9996 || = 0.50 510 518 481 505 490 | 500 < 0.0005 4 3 5 4 1 | 5 | 5 4 2 6 6 > 0.9995 || = 0.49 503 491 497 467 541 | 500 < 0.0006 3 7 5 3 3 | 5 | 1 3 5 7 7 > 0.9994 || = 0.48 477 513 494 483 484 | 500 < 0.0007 3 4 7 0 2 | 5 | 4 9 9 2 3 > 0.9993 || = 0.47 477 499 494 504 501 | 500 < 0.0008 9 4 6 10 3 | 5 | 4 6 7 8 3 > 0.9992 || = 0.46 498 472 439 472 533 | 500 < 0.0009 4 7 3 6 6 | 5 | 4 4 5 2 11 > 0.9991 || = 0.45 522 470 469 508 463 | 500 < 0.001 7 2 7 4 7 | 5 | 6 6 7 4 6 > 0.999 || = 0.44 496 538 548 521 514 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 505 524 512 496 516 | 500 < 0.001 49 40 48 49 47 | 50 | 45 51 53 48 55 > 0.999 || = 0.42 506 450 510 486 498 | 500 < 0.002 49 34 34 46 43 | 50 | 46 51 53 50 56 > 0.998 || = 0.41 503 464 496 499 508 | 500 < 0.003 39 56 46 50 48 | 50 | 57 46 58 43 51 > 0.997 || = 0.40 498 496 509 474 492 | 500 < 0.004 34 39 45 47 56 | 50 | 44 60 64 56 50 > 0.996 || = 0.39 503 481 477 528 552 | 500 < 0.005 40 43 53 45 37 | 50 | 58 47 58 51 45 > 0.995 || = 0.38 474 548 509 504 469 | 500 < 0.006 54 54 42 56 46 | 50 | 62 50 48 56 57 > 0.994 || = 0.37 514 521 481 483 479 | 500 < 0.007 54 41 51 45 53 | 50 | 56 48 46 46 38 > 0.993 || = 0.36 532 492 522 468 522 | 500 < 0.008 55 49 49 43 47 | 50 | 59 43 50 39 51 > 0.992 || = 0.35 481 510 494 465 506 | 500 < 0.009 49 40 55 46 43 | 50 | 41 50 43 49 32 > 0.991 || = 0.34 473 548 518 509 470 | 500 < 0.01 49 52 44 57 55 | 50 | 43 54 45 50 54 > 0.99 || = 0.33 485 558 486 553 526 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 473 534 464 544 492 | 500 < 0.01 472 448 467 484 475 | 497.5 | 511 500 518 488 489 > 0.99 || = 0.31 519 518 526 516 486 | 500 = 0.01 268 240 236 265 265 | 252.5 | 270 261 260 262 246 = 0.99 || = 0.30 492 490 495 502 505 | 500 = 0.02 525 508 521 477 492 | 500 | 513 503 511 498 472 = 0.98 || = 0.29 470 515 491 502 473 | 500 =================================================================| 500 | 565 532 492 526 498 = 0.97 || = 0.28 521 470 478 501 495 | 500 svaria_SampleMean test: | 500 | 507 469 507 506 482 = 0.96 || = 0.27 471 469 521 521 491 | 500 ----------------------------------------------- | 500 | 478 498 502 483 511 = 0.95 || = 0.26 431 470 528 534 512 | 500 N = 20000000, n = 30, r = 10 | 500 | 484 490 478 474 465 = 0.94 || = 0.25 493 540 512 498 486 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 495 506 490 520 549 = 0.93 || = 0.24 511 494 500 522 469 | 500 | 500 | 526 539 508 498 515 = 0.92 || = 0.23 481 520 519 495 462 | 500 =================================================================| 500 | 526 497 486 475 512 = 0.91 || = 0.22 476 488 494 437 503 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 539 518 517 551 489 = 0.90 || = 0.21 499 510 496 536 520 | 500 -----------------------------------------------------------------| 500 | 521 487 481 497 528 = 0.89 || = 0.20 516 518 512 501 547 | 500 SD Bern.: d 1.03171 1.03781 1.07848 | 500 | 503 509 510 484 484 = 0.88 || = 0.19 508 470 496 520 525 | 500 s 1.12798 1.23673 0.62640 | 500 | 522 459 504 513 499 = 0.87 || = 0.18 530 501 491 512 530 | 500 t 0.95464 0.93533 0.93426 | 500 | 512 525 500 527 473 = 0.86 || = 0.17 518 471 526 519 479 | 500 m 1.05820 0.67263 0.72699 | 500 | 518 504 473 507 489 = 0.85 || = 0.16 432 541 514 471 497 | 500 x 1.14190 0.86645 1.11499 | 500 | 523 507 489 471 516 = 0.84 || = 0.15 501 510 488 468 501 | 500 | 500 | 516 474 484 471 498 = 0.83 || = 0.14 501 518 534 486 507 | 500 Changes: d 47 2 4 | 500 | 474 503 435 497 567 = 0.82 || = 0.13 487 507 486 482 531 | 500 s 53 5 4 | 500 | 510 516 504 499 479 = 0.81 || = 0.12 499 468 521 475 479 | 500 t 51 6 1 | 500 | 458 525 528 554 481 = 0.80 || = 0.11 488 488 497 506 519 | 500 m 44 3 2 | 500 | 489 491 478 543 593 = 0.79 || = 0.10 489 477 496 485 470 | 500 x 52 5 6 | 500 | 504 572 531 480 484 = 0.78 || = 0.09 491 517 476 495 470 | 500 -----------------------------------------------------------------| 500 | 454 461 531 497 494 = 0.77 || = 0.08 480 522 505 495 482 | 500 Aver./ d 0.50383 503 > 500: 4 5 3 4 5 4 6 5 9 7 | 500 | 522 514 503 507 487 = 0.76 || = 0.07 523 514 481 511 466 | 500 median s 0.50067 500 ----- 5 5 5 7 3 5 2 4 7 6 | 500 | 472 483 458 475 516 = 0.75 || = 0.06 503 483 495 510 478 | 500 t 0.49960 502 5 4 5 4 4 7 8 5 4 6 | 500 | 536 500 486 513 500 = 0.74 || = 0.05 474 490 509 461 504 | 500 m 0.50159 501 3 4 7 7 3 5 7 6 4 4 | 500 | 503 462 497 518 456 = 0.73 || = 0.04 489 469 501 485 508 | 500 x 0.50072 498 4 6 4 5 6 4 6 4 3 4 | 500 | 536 490 464 498 511 = 0.72 || = 0.03 460 505 508 493 531 | 500 -----------------------------------------------------------------| 500 | 460 538 518 533 538 = 0.71 || = 0.02 525 508 521 477 492 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 495 474 507 516 462 = 0.70 || = 0.01 268 240 236 265 265 | 252.5 d 0 2 1 16 66 15 1 0 0 | 500 | 527 516 515 517 493 = 0.69 || < 0.01 472 448 467 484 475 | 497.5 s 0 0 2 21 62 12 3 1 0 | 500 | 496 490 513 506 505 = 0.68 ||========================================================================= t 0 0 3 12 73 12 1 0 0 | 500 | 472 476 514 506 507 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 17 68 10 4 0 0 | 500 | 531 483 476 509 504 = 0.66 ||========================================================================= x 0 0 1 17 66 11 4 1 1 | 500 | 489 457 517 492 482 = 0.65 || svaria_SampleMean test: no 113 test no 114 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleMean test: test no 114 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 0 | 0.5 | 0 0 0 1 1 > 0.99999 || = 0.64 467 488 525 526 500 | 500 < 0.00002 1 0 0 0 0 | 0.5 | 1 1 0 0 1 > 0.99998 || = 0.63 519 532 495 499 493 | 500 < 0.00003 1 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 443 489 493 469 506 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 4 0 0 1 0 > 0.99996 || = 0.61 476 479 505 530 493 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 0 0 1 1 0 > 0.99995 || = 0.60 505 491 496 505 541 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99994 || = 0.59 498 514 496 528 492 | 500 < 0.00007 0 1 0 2 0 | 0.5 | 1 2 0 0 1 > 0.99993 || = 0.58 503 495 495 495 465 | 500 < 0.00008 0 1 0 0 3 | 0.5 | 0 2 0 4 0 > 0.99992 || = 0.57 508 467 506 539 491 | 500 < 0.00009 1 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 505 483 520 496 477 | 500 < 0.0001 1 1 0 0 1 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 507 488 474 491 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 499 502 458 473 505 | 500 < 0.0001 4 3 0 3 5 | 5 | 7 8 1 8 3 > 0.9999 || = 0.53 466 472 494 540 503 | 500 < 0.0002 4 6 6 4 4 | 5 | 5 2 2 1 2 > 0.9998 || = 0.52 514 477 448 501 518 | 500 < 0.0003 7 7 0 5 8 | 5 | 5 3 3 5 3 > 0.9997 || = 0.51 493 466 494 492 509 | 500 < 0.0004 5 3 9 3 4 | 5 | 6 3 4 3 7 > 0.9996 || = 0.50 474 534 521 499 516 | 500 < 0.0005 9 5 4 4 7 | 5 | 4 5 3 8 3 > 0.9995 || = 0.49 493 526 510 511 485 | 500 < 0.0006 2 3 4 9 4 | 5 | 6 5 6 2 6 > 0.9994 || = 0.48 488 516 471 512 518 | 500 < 0.0007 6 4 2 7 6 | 5 | 6 5 4 8 7 > 0.9993 || = 0.47 512 513 524 484 538 | 500 < 0.0008 7 5 3 4 4 | 5 | 5 4 5 5 7 > 0.9992 || = 0.46 482 452 503 505 513 | 500 < 0.0009 5 9 2 6 5 | 5 | 7 4 4 7 7 > 0.9991 || = 0.45 537 534 552 517 494 | 500 < 0.001 10 3 9 5 3 | 5 | 5 3 3 2 6 > 0.999 || = 0.44 500 503 515 504 494 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 472 511 532 479 511 | 500 < 0.001 59 48 39 50 50 | 50 | 56 42 35 49 51 > 0.999 || = 0.42 514 516 498 492 530 | 500 < 0.002 42 47 52 45 37 | 50 | 40 40 55 40 56 > 0.998 || = 0.41 518 484 494 486 486 | 500 < 0.003 29 48 54 49 37 | 50 | 48 47 41 52 52 > 0.997 || = 0.40 486 481 503 513 502 | 500 < 0.004 39 49 36 61 53 | 50 | 38 56 50 36 46 > 0.996 || = 0.39 513 498 508 477 491 | 500 < 0.005 60 45 50 43 52 | 50 | 45 34 52 41 50 > 0.995 || = 0.38 499 487 498 522 477 | 500 < 0.006 37 53 59 52 34 | 50 | 52 51 42 57 49 > 0.994 || = 0.37 533 505 477 523 500 | 500 < 0.007 45 48 44 57 60 | 50 | 51 53 54 56 46 > 0.993 || = 0.36 502 531 450 491 452 | 500 < 0.008 56 46 60 36 72 | 50 | 43 46 44 40 56 > 0.992 || = 0.35 510 505 498 478 471 | 500 < 0.009 48 48 52 35 51 | 50 | 60 51 53 49 46 > 0.991 || = 0.34 514 494 499 518 494 | 500 < 0.01 57 39 55 32 43 | 50 | 56 57 53 47 61 > 0.99 || = 0.33 484 515 486 515 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 504 502 517 484 497 | 500 < 0.01 472 471 501 460 489 | 497.5 | 489 477 479 467 513 > 0.99 || = 0.31 455 513 513 503 469 | 500 = 0.01 257 262 262 252 250 | 252.5 | 233 238 236 239 213 = 0.99 || = 0.30 483 499 519 523 521 | 500 = 0.02 505 471 498 501 495 | 500 | 515 481 495 498 502 = 0.98 || = 0.29 492 505 513 497 501 | 500 =================================================================| 500 | 546 499 479 510 541 = 0.97 || = 0.28 487 502 481 499 536 | 500 svaria_SampleMean test: | 500 | 523 512 513 498 528 = 0.96 || = 0.27 536 501 489 505 521 | 500 ----------------------------------------------- | 500 | 532 472 536 480 490 = 0.95 || = 0.26 500 492 510 456 542 | 500 N = 20000000, n = 30, r = 10 | 500 | 499 481 489 467 504 = 0.94 || = 0.25 500 462 517 515 491 | 500 Anderson-Darling statistic = A2 | 500 | 471 529 502 499 489 = 0.93 || = 0.24 502 521 510 504 470 | 500 | 500 | 518 494 519 503 531 = 0.92 || = 0.23 500 518 494 521 520 | 500 =================================================================| 500 | 523 487 469 465 524 = 0.91 || = 0.22 478 493 502 512 519 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 501 527 548 486 476 = 0.90 || = 0.21 511 558 474 507 464 | 500 -----------------------------------------------------------------| 500 | 513 499 478 552 518 = 0.89 || = 0.20 557 512 477 492 474 | 500 SD Bern.: d 0.91651 1.47721 0.99948 | 500 | 526 502 544 489 494 = 0.88 || = 0.19 519 494 494 492 485 | 500 s 0.95612 0.62799 1.04070 | 500 | 485 473 487 482 490 = 0.87 || = 0.18 509 509 491 491 491 | 500 t 0.99010 1.08035 0.96897 | 500 | 526 516 502 519 519 = 0.86 || = 0.17 511 522 469 493 519 | 500 m 0.95693 1.41066 1.07476 | 500 | 485 486 454 503 469 = 0.85 || = 0.16 492 541 483 473 469 | 500 x 1.00375 1.57622 0.70319 | 500 | 499 538 519 524 500 = 0.84 || = 0.15 500 509 508 521 520 | 500 | 500 | 498 489 488 489 473 = 0.83 || = 0.14 529 500 454 541 528 | 500 Changes: d 50 6 4 | 500 | 508 508 499 561 458 = 0.82 || = 0.13 475 496 541 467 488 | 500 s 50 2 5 | 500 | 508 511 502 479 508 = 0.81 || = 0.12 493 494 514 478 535 | 500 t 45 5 7 | 500 | 490 528 494 494 543 = 0.80 || = 0.11 467 482 485 474 482 | 500 m 50 4 4 | 500 | 528 518 518 502 497 = 0.79 || = 0.10 534 518 501 512 508 | 500 x 49 4 4 | 500 | 494 502 540 500 495 = 0.78 || = 0.09 511 458 510 481 492 | 500 -----------------------------------------------------------------| 500 | 485 497 517 497 486 = 0.77 || = 0.08 493 522 508 475 495 | 500 Aver./ d 0.50004 500 > 500: 5 5 4 6 4 6 4 4 6 6 | 500 | 460 511 502 496 497 = 0.76 || = 0.07 493 518 513 474 517 | 500 median s 0.50016 499 ----- 3 5 7 6 7 2 3 7 6 2 | 500 | 502 457 492 500 523 = 0.75 || = 0.06 511 471 506 499 459 | 500 t 0.50033 498 7 4 5 4 7 2 4 5 5 4 | 500 | 483 497 493 474 454 = 0.74 || = 0.05 495 456 541 509 490 | 500 m 0.50080 499 3 3 6 6 6 5 6 2 5 2 | 500 | 459 510 488 553 502 = 0.73 || = 0.04 497 498 475 488 511 | 500 x 0.50078 497 2 5 6 1 6 6 4 4 3 7 | 500 | 520 533 542 477 497 = 0.72 || = 0.03 518 481 487 527 495 | 500 -----------------------------------------------------------------| 500 | 509 504 495 498 517 = 0.71 || = 0.02 505 471 498 501 495 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 504 499 488 562 509 = 0.70 || = 0.01 257 262 262 252 250 | 252.5 d 0 0 2 14 72 11 2 0 0 | 500 | 477 490 460 507 470 = 0.69 || < 0.01 472 471 501 460 489 | 497.5 s 0 0 1 14 72 13 1 0 0 | 500 | 504 499 556 488 494 = 0.68 ||========================================================================= t 0 0 4 11 74 9 3 0 0 | 500 | 505 541 509 503 477 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 15 72 10 4 0 0 | 500 | 464 469 489 499 539 = 0.66 ||========================================================================= x 0 0 3 16 66 16 0 0 0 | 500 | 498 527 484 504 539 = 0.65 || svaria_SampleMean test: no 114 test no 115 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleCorr test: test no 115 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 2 0 2 | 0.5 | 0 3 1 0 1 > 0.99999 || = 0.64 457 513 497 501 496 | 500 < 0.00002 2 1 2 0 0 | 0.5 | 1 1 0 1 0 > 0.99998 || = 0.63 468 486 450 524 505 | 500 < 0.00003 0 0 1 0 3 | 0.5 | 0 0 1 0 2 > 0.99997 || = 0.62 504 487 482 439 507 | 500 < 0.00004 1 1 1 0 2 | 0.5 | 2 0 0 0 0 > 0.99996 || = 0.61 504 464 541 466 503 | 500 < 0.00005 1 0 1 0 0 | 0.5 | 1 0 2 0 1 > 0.99995 || = 0.60 465 517 504 490 490 | 500 < 0.00006 0 0 1 0 2 | 0.5 | 2 0 1 1 1 > 0.99994 || = 0.59 458 460 513 480 474 | 500 < 0.00007 0 0 0 2 0 | 0.5 | 0 0 0 3 1 > 0.99993 || = 0.58 446 505 488 534 484 | 500 < 0.00008 0 2 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 505 478 485 480 448 | 500 < 0.00009 0 2 1 4 0 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 493 489 494 440 492 | 500 < 0.0001 1 1 1 0 1 | 0.5 | 1 1 1 0 0 > 0.9999 || = 0.55 474 453 414 502 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 504 467 437 490 513 | 500 < 0.0001 7 7 11 6 11 | 5 | 7 5 6 6 6 > 0.9999 || = 0.53 497 513 469 474 517 | 500 < 0.0002 7 2 6 9 11 | 5 | 9 4 6 9 5 > 0.9998 || = 0.52 487 502 497 475 478 | 500 < 0.0003 8 9 7 8 9 | 5 | 7 10 10 2 5 > 0.9997 || = 0.51 430 504 510 473 488 | 500 < 0.0004 13 7 11 9 4 | 5 | 11 4 9 9 11 > 0.9996 || = 0.50 435 462 460 495 520 | 500 < 0.0005 8 7 5 6 4 | 5 | 5 5 5 10 13 > 0.9995 || = 0.49 462 462 466 513 485 | 500 < 0.0006 7 9 8 11 7 | 5 | 10 7 10 3 11 > 0.9994 || = 0.48 470 465 458 479 495 | 500 < 0.0007 11 9 5 9 7 | 5 | 6 7 8 7 8 > 0.9993 || = 0.47 471 485 503 512 477 | 500 < 0.0008 8 7 9 4 9 | 5 | 9 8 6 4 8 > 0.9992 || = 0.46 486 475 460 471 481 | 500 < 0.0009 9 12 4 12 12 | 5 | 4 13 9 7 2 > 0.9991 || = 0.45 508 508 466 499 431 | 500 < 0.001 8 9 7 5 4 | 5 | 11 5 6 9 7 > 0.999 || = 0.44 503 524 499 487 509 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 478 449 503 516 472 | 500 < 0.001 86 78 73 79 78 | 50 | 79 68 75 66 76 > 0.999 || = 0.42 444 482 500 491 465 | 500 < 0.002 78 63 58 71 64 | 50 | 64 55 69 73 64 > 0.998 || = 0.41 469 495 482 473 475 | 500 < 0.003 71 65 67 66 68 | 50 | 46 65 55 53 79 > 0.997 || = 0.40 472 483 473 485 473 | 500 < 0.004 62 59 68 68 62 | 50 | 46 62 62 67 69 > 0.996 || = 0.39 467 485 474 479 495 | 500 < 0.005 75 56 66 66 65 | 50 | 59 73 49 66 57 > 0.995 || = 0.38 485 448 493 489 499 | 500 < 0.006 66 63 60 72 61 | 50 | 61 77 66 56 60 > 0.994 || = 0.37 508 502 515 469 483 | 500 < 0.007 74 77 55 56 61 | 50 | 57 68 55 63 48 > 0.993 || = 0.36 492 482 472 510 477 | 500 < 0.008 61 63 68 58 57 | 50 | 62 64 64 61 56 > 0.992 || = 0.35 482 502 483 472 451 | 500 < 0.009 67 65 56 51 56 | 50 | 51 69 53 47 55 > 0.991 || = 0.34 474 489 457 473 447 | 500 < 0.01 66 64 67 70 50 | 50 | 48 75 66 71 64 > 0.99 || = 0.33 500 471 498 478 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 508 480 489 470 448 | 500 < 0.01 706 653 638 657 622 | 497.5 | 573 676 614 623 628 > 0.99 || = 0.31 510 453 465 484 493 | 500 = 0.01 302 302 291 283 306 | 252.5 | 264 291 296 345 269 = 0.99 || = 0.30 499 475 466 508 532 | 500 = 0.02 605 550 541 523 588 | 500 | 554 592 598 545 611 = 0.98 || = 0.29 481 498 510 485 491 | 500 =================================================================| 500 | 567 543 602 538 526 = 0.97 || = 0.28 493 515 494 458 490 | 500 svaria_SampleCorr test: | 500 | 539 555 556 508 490 = 0.96 || = 0.27 499 444 522 467 486 | 500 ----------------------------------------------- | 500 | 524 548 567 549 566 = 0.95 || = 0.26 474 449 476 457 489 | 500 N = 1, n = 2000000000, r = 0, k = 1 | 500 | 538 524 529 549 538 = 0.94 || = 0.25 494 473 477 474 504 | 500 Normal statistic | 500 | 492 521 549 518 519 = 0.93 || = 0.24 468 505 508 482 447 | 500 | 500 | 531 539 477 565 500 = 0.92 || = 0.23 498 468 463 513 526 | 500 =================================================================| 500 | 529 530 530 495 515 = 0.91 || = 0.22 517 483 518 465 476 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 489 500 511 563 509 = 0.90 || = 0.21 474 497 478 506 543 | 500 -----------------------------------------------------------------| 500 | 508 500 513 467 471 = 0.89 || = 0.20 481 511 474 499 489 | 500 SD Bern.: d 1.65595 3.09605 1.71491 | 500 | 512 512 497 525 497 = 0.88 || = 0.19 544 489 465 485 499 | 500 s 1.67607 2.36041 2.64025 | 500 | 523 488 540 513 467 = 0.87 || = 0.18 477 490 497 484 517 | 500 t 1.68684 2.11576 1.94929 | 500 | 506 497 493 521 535 = 0.86 || = 0.17 474 502 481 478 501 | 500 m 1.69718 2.49242 2.05771 | 500 | 515 504 466 511 452 = 0.85 || = 0.16 475 512 495 510 461 | 500 x 1.62153 2.00099 2.23000 | 500 | 482 515 479 504 488 = 0.84 || = 0.15 542 500 504 498 504 | 500 | 500 | 505 528 469 492 516 = 0.83 || = 0.14 524 521 523 489 500 | 500 Changes: d 38 0 3 | 500 | 477 545 493 512 520 = 0.82 || = 0.13 498 498 487 526 512 | 500 s 40 0 0 | 500 | 466 459 522 467 504 = 0.81 || = 0.12 531 549 523 529 510 | 500 t 38 0 2 | 500 | 479 502 507 489 477 = 0.80 || = 0.11 483 494 497 522 466 | 500 m 34 0 2 | 500 | 518 474 461 451 498 = 0.79 || = 0.10 479 454 526 484 505 | 500 x 42 1 2 | 500 | 518 492 478 435 505 = 0.78 || = 0.09 506 503 520 538 484 | 500 -----------------------------------------------------------------| 500 | 486 459 515 450 475 = 0.77 || = 0.08 501 499 494 532 485 | 500 Aver./ d 0.49808 498 > 500:10 4 1 3 2 2 4 4 6 9 | 500 | 500 482 543 467 483 = 0.76 || = 0.07 574 503 497 540 542 | 500 median s 0.50271 498 ----- 8 4 3 2 2 5 4 1 5 10 | 500 | 488 495 489 483 515 = 0.75 || = 0.06 535 473 570 557 531 | 500 t 0.50185 497 8 4 4 1 2 3 5 3 4 9 | 500 | 502 495 478 524 521 = 0.74 || = 0.05 502 534 540 545 570 | 500 m 0.49977 491 10 4 2 2 3 2 2 1 7 9 | 500 | 467 478 471 486 441 = 0.73 || = 0.04 526 524 505 517 554 | 500 x 0.49928 495 8 6 3 1 1 2 4 4 5 8 | 500 | 517 499 432 473 503 = 0.72 || = 0.03 540 545 518 562 536 | 500 -----------------------------------------------------------------| 500 | 486 493 462 499 465 = 0.71 || = 0.02 605 550 541 523 588 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 463 502 507 455 518 = 0.70 || = 0.01 302 302 291 283 306 | 252.5 d 0 1 3 22 55 13 1 4 2 | 500 | 502 472 448 466 477 = 0.69 || < 0.01 706 653 638 657 622 | 497.5 s 0 0 8 16 58 8 7 1 3 | 500 | 481 479 511 464 444 = 0.68 ||========================================================================= t 0 2 3 24 52 10 4 2 4 | 500 | 503 446 513 489 487 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 6 22 50 12 8 0 3 | 500 | 491 501 512 497 477 = 0.66 ||========================================================================= x 0 1 8 18 56 10 2 3 3 | 500 | 487 511 477 476 476 = 0.65 || svaria_SampleCorr test: no 115 test no 116 TestU01 250000 runs BigCrush Test smarsa_S svaria_SampleCorr test: test no 116 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 2 0 | 0.5 | 1 0 1 0 0 > 0.99999 || = 0.64 512 494 495 495 491 | 500 < 0.00002 1 1 0 0 0 | 0.5 | 1 0 0 0 2 > 0.99998 || = 0.63 488 483 466 462 479 | 500 < 0.00003 1 1 2 1 1 | 0.5 | 0 2 4 0 0 > 0.99997 || = 0.62 497 505 494 509 471 | 500 < 0.00004 1 2 1 1 0 | 0.5 | 0 3 3 2 0 > 0.99996 || = 0.61 443 486 450 497 445 | 500 < 0.00005 1 0 2 3 4 | 0.5 | 1 0 2 1 1 > 0.99995 || = 0.60 475 488 460 484 453 | 500 < 0.00006 0 2 1 0 2 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 511 445 494 457 472 | 500 < 0.00007 1 1 1 0 0 | 0.5 | 1 1 1 2 1 > 0.99993 || = 0.58 495 483 480 492 471 | 500 < 0.00008 0 2 0 1 1 | 0.5 | 1 1 1 0 3 > 0.99992 || = 0.57 500 484 491 479 463 | 500 < 0.00009 0 1 0 0 1 | 0.5 | 0 0 1 0 1 > 0.99991 || = 0.56 482 493 464 469 460 | 500 < 0.0001 1 0 2 0 0 | 0.5 | 0 2 1 0 1 > 0.9999 || = 0.55 505 471 471 478 479 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 453 492 434 491 474 | 500 < 0.0001 7 10 10 8 9 | 5 | 6 9 14 5 9 > 0.9999 || = 0.53 503 474 462 526 482 | 500 < 0.0002 4 9 7 9 6 | 5 | 4 2 7 6 8 > 0.9998 || = 0.52 450 525 437 476 499 | 500 < 0.0003 12 16 7 7 7 | 5 | 10 13 11 7 4 > 0.9997 || = 0.51 492 466 446 461 477 | 500 < 0.0004 7 5 5 6 8 | 5 | 6 6 7 6 5 > 0.9996 || = 0.50 458 494 495 475 461 | 500 < 0.0005 6 8 4 4 7 | 5 | 11 5 5 8 3 > 0.9995 || = 0.49 513 465 465 495 489 | 500 < 0.0006 8 4 7 7 5 | 5 | 5 9 5 10 6 > 0.9994 || = 0.48 460 510 473 462 444 | 500 < 0.0007 7 9 8 3 8 | 5 | 5 8 6 8 10 > 0.9993 || = 0.47 497 452 460 478 480 | 500 < 0.0008 6 9 9 9 6 | 5 | 8 6 11 6 7 > 0.9992 || = 0.46 500 478 455 502 497 | 500 < 0.0009 6 11 5 5 3 | 5 | 7 5 5 7 8 > 0.9991 || = 0.45 471 474 502 474 472 | 500 < 0.001 3 6 9 8 7 | 5 | 11 6 7 4 8 > 0.999 || = 0.44 494 460 492 459 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 494 461 446 482 481 | 500 < 0.001 66 87 71 66 66 | 50 | 73 69 78 67 68 > 0.999 || = 0.42 486 452 468 459 482 | 500 < 0.002 69 70 80 62 61 | 50 | 58 55 72 89 75 > 0.998 || = 0.41 489 514 506 477 502 | 500 < 0.003 68 73 58 67 60 | 50 | 59 57 56 79 59 > 0.997 || = 0.40 485 453 454 535 477 | 500 < 0.004 70 73 59 57 57 | 50 | 77 60 59 67 64 > 0.996 || = 0.39 429 498 551 503 478 | 500 < 0.005 73 77 57 56 65 | 50 | 59 51 71 62 43 > 0.995 || = 0.38 461 472 472 487 474 | 500 < 0.006 66 57 67 53 69 | 50 | 65 70 79 65 76 > 0.994 || = 0.37 470 470 468 476 503 | 500 < 0.007 66 66 68 62 56 | 50 | 71 74 61 58 56 > 0.993 || = 0.36 498 484 511 469 466 | 500 < 0.008 63 51 74 56 55 | 50 | 60 62 74 67 79 > 0.992 || = 0.35 476 495 486 483 490 | 500 < 0.009 67 65 65 53 54 | 50 | 67 62 61 75 73 > 0.991 || = 0.34 477 513 478 475 520 | 500 < 0.01 61 65 42 47 55 | 50 | 59 58 61 58 62 > 0.99 || = 0.33 528 473 496 470 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 482 482 503 457 463 | 500 < 0.01 669 684 641 579 598 | 497.5 | 648 618 672 687 655 > 0.99 || = 0.31 526 509 501 485 491 | 500 = 0.01 312 296 321 305 296 | 252.5 | 308 297 290 316 313 = 0.99 || = 0.30 474 501 511 502 469 | 500 = 0.02 531 602 566 575 619 | 500 | 559 531 525 580 563 = 0.98 || = 0.29 470 486 481 494 497 | 500 =================================================================| 500 | 498 530 583 522 533 = 0.97 || = 0.28 495 453 487 457 464 | 500 svaria_SampleCorr test: | 500 | 505 593 591 553 521 = 0.96 || = 0.27 481 483 500 500 472 | 500 ----------------------------------------------- | 500 | 575 539 532 545 532 = 0.95 || = 0.26 468 435 474 498 489 | 500 N = 1, n = 2000000000, r = 0, k = 2 | 500 | 532 497 539 473 535 = 0.94 || = 0.25 488 496 482 480 500 | 500 Normal statistic | 500 | 481 542 524 541 546 = 0.93 || = 0.24 504 502 490 499 461 | 500 | 500 | 530 515 531 501 547 = 0.92 || = 0.23 456 514 507 472 506 | 500 =================================================================| 500 | 493 470 486 511 495 = 0.91 || = 0.22 484 521 461 476 472 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 467 544 520 532 472 = 0.90 || = 0.21 501 480 502 484 527 | 500 -----------------------------------------------------------------| 500 | 533 493 546 521 531 = 0.89 || = 0.20 485 470 478 505 490 | 500 SD Bern.: d 1.66153 2.43472 2.29024 | 500 | 457 543 511 554 490 = 0.88 || = 0.19 508 486 475 456 524 | 500 s 1.67256 2.93813 1.93176 | 500 | 521 486 493 511 485 = 0.87 || = 0.18 475 513 482 506 505 | 500 t 1.75207 2.45601 2.68685 | 500 | 531 479 504 484 515 = 0.86 || = 0.17 517 461 531 495 497 | 500 m 1.67752 1.40141 2.95138 | 500 | 467 511 477 481 479 = 0.85 || = 0.16 483 515 521 510 537 | 500 x 1.60528 1.55897 2.64744 | 500 | 516 483 522 518 497 = 0.84 || = 0.15 488 485 497 498 497 | 500 | 500 | 506 502 496 486 517 = 0.83 || = 0.14 456 525 484 510 478 | 500 Changes: d 40 0 0 | 500 | 457 487 453 507 485 = 0.82 || = 0.13 535 521 489 496 499 | 500 s 38 0 0 | 500 | 520 454 543 564 504 = 0.81 || = 0.12 524 482 497 516 504 | 500 t 40 1 0 | 500 | 480 493 475 474 530 = 0.80 || = 0.11 503 479 529 480 462 | 500 m 36 1 0 | 500 | 480 490 525 506 515 = 0.79 || = 0.10 516 522 499 487 531 | 500 x 36 0 2 | 500 | 526 458 481 504 475 = 0.78 || = 0.09 518 538 512 549 542 | 500 -----------------------------------------------------------------| 500 | 511 483 513 430 530 = 0.77 || = 0.08 530 534 475 522 504 | 500 Aver./ d 0.49932 497 > 500:10 6 2 2 1 3 3 2 6 7 | 500 | 469 501 505 481 475 = 0.76 || = 0.07 535 520 510 519 473 | 500 median s 0.49904 493 ----- 10 5 3 3 2 1 2 4 4 8 | 500 | 482 502 469 459 511 = 0.75 || = 0.06 564 508 516 497 497 | 500 t 0.50151 495 9 3 2 5 2 0 2 4 6 9 | 500 | 474 476 499 527 487 = 0.74 || = 0.05 542 530 559 517 565 | 500 m 0.50191 495 9 4 1 2 2 1 2 3 7 9 | 500 | 491 461 497 487 502 = 0.73 || = 0.04 528 547 517 571 539 | 500 x 0.50084 491 8 5 2 2 1 0 1 6 4 9 | 500 | 500 513 473 466 541 = 0.72 || = 0.03 505 527 545 549 537 | 500 -----------------------------------------------------------------| 500 | 477 531 522 499 483 = 0.71 || = 0.02 531 602 566 575 619 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 513 500 470 492 490 = 0.70 || = 0.01 312 296 321 305 296 | 252.5 d 0 1 3 22 54 14 2 3 2 | 500 | 458 486 502 489 482 = 0.69 || < 0.01 669 684 641 579 598 | 497.5 s 0 0 7 16 58 13 3 0 4 | 500 | 498 511 489 458 494 = 0.68 ||========================================================================= t 0 0 8 20 53 9 6 1 4 | 500 | 489 486 479 481 468 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 0 26 56 5 6 5 2 | 500 | 497 487 483 519 477 = 0.66 ||========================================================================= x 0 0 3 25 50 14 5 1 3 | 500 | 506 494 515 458 507 = 0.65 || svaria_SampleCorr test: no 116 test no 117 TestU01 250000 runs BigCrush Test smarsa_S svaria_AppearanceSpacings test: test no 117 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 2 0 | 0.5 | 0 1 0 3 1 > 0.99999 || = 0.64 486 516 480 459 530 | 500 < 0.00002 1 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 495 540 492 522 494 | 500 < 0.00003 0 1 1 0 2 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 540 505 482 470 508 | 500 < 0.00004 0 0 1 0 0 | 0.5 | 0 0 1 1 1 > 0.99996 || = 0.61 461 484 475 522 510 | 500 < 0.00005 0 0 1 1 1 | 0.5 | 0 3 0 0 1 > 0.99995 || = 0.60 522 511 453 471 537 | 500 < 0.00006 1 0 0 0 1 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 500 528 477 453 524 | 500 < 0.00007 0 2 1 1 0 | 0.5 | 0 1 3 0 1 > 0.99993 || = 0.58 508 521 492 513 513 | 500 < 0.00008 0 0 0 1 2 | 0.5 | 0 0 1 0 0 > 0.99992 || = 0.57 490 502 488 463 518 | 500 < 0.00009 1 0 0 0 1 | 0.5 | 1 1 0 0 0 > 0.99991 || = 0.56 490 514 498 577 470 | 500 < 0.0001 2 0 0 1 1 | 0.5 | 0 1 0 0 0 > 0.9999 || = 0.55 538 529 490 526 498 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 504 483 515 503 489 | 500 < 0.0001 5 3 4 6 8 | 5 | 2 7 6 5 4 > 0.9999 || = 0.53 501 475 532 488 501 | 500 < 0.0002 5 3 3 5 9 | 5 | 4 4 3 5 3 > 0.9998 || = 0.52 481 516 536 522 526 | 500 < 0.0003 9 8 4 8 5 | 5 | 8 2 7 4 7 > 0.9997 || = 0.51 491 500 530 489 512 | 500 < 0.0004 8 3 3 5 3 | 5 | 6 2 5 1 3 > 0.9996 || = 0.50 525 483 524 524 522 | 500 < 0.0005 4 5 4 7 7 | 5 | 4 4 2 4 4 > 0.9995 || = 0.49 527 505 518 472 487 | 500 < 0.0006 5 4 5 1 6 | 5 | 2 5 3 0 3 > 0.9994 || = 0.48 497 527 503 503 517 | 500 < 0.0007 5 3 5 5 12 | 5 | 5 3 7 4 3 > 0.9993 || = 0.47 513 496 512 518 533 | 500 < 0.0008 7 2 3 4 1 | 5 | 2 4 7 4 4 > 0.9992 || = 0.46 546 514 517 509 510 | 500 < 0.0009 4 7 1 6 2 | 5 | 6 4 4 9 5 > 0.9991 || = 0.45 488 468 497 545 509 | 500 < 0.001 4 7 8 2 3 | 5 | 3 7 6 2 2 > 0.999 || = 0.44 485 520 506 470 471 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 507 517 493 522 477 | 500 < 0.001 56 45 40 49 56 | 50 | 42 42 50 38 38 > 0.999 || = 0.42 512 463 483 469 473 | 500 < 0.002 48 44 36 42 49 | 50 | 55 59 58 67 55 > 0.998 || = 0.41 496 504 508 492 490 | 500 < 0.003 51 51 54 46 51 | 50 | 57 49 52 40 62 > 0.997 || = 0.40 497 494 522 511 469 | 500 < 0.004 61 46 37 51 48 | 50 | 61 59 63 47 39 > 0.996 || = 0.39 488 535 497 477 501 | 500 < 0.005 46 49 55 39 37 | 50 | 46 44 53 42 60 > 0.995 || = 0.38 464 512 482 488 485 | 500 < 0.006 58 54 59 41 50 | 50 | 52 48 48 40 49 > 0.994 || = 0.37 485 503 501 534 507 | 500 < 0.007 56 46 58 39 51 | 50 | 56 53 51 49 50 > 0.993 || = 0.36 490 445 498 523 523 | 500 < 0.008 41 33 59 50 42 | 50 | 53 50 44 50 52 > 0.992 || = 0.35 494 508 476 494 528 | 500 < 0.009 48 52 62 53 53 | 50 | 37 46 53 32 50 > 0.991 || = 0.34 462 466 497 472 495 | 500 < 0.01 63 48 55 61 40 | 50 | 44 68 47 51 63 > 0.99 || = 0.33 491 479 517 515 484 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 521 488 500 531 494 | 500 < 0.01 528 468 515 471 477 | 497.5 | 503 518 519 456 518 > 0.99 || = 0.31 516 481 531 474 522 | 500 = 0.01 219 247 258 215 225 | 252.5 | 236 218 272 242 265 = 0.99 || = 0.30 529 489 524 477 516 | 500 = 0.02 478 507 500 501 510 | 500 | 512 493 518 475 530 = 0.98 || = 0.29 481 495 528 497 488 | 500 =================================================================| 500 | 486 533 496 489 495 = 0.97 || = 0.28 470 500 482 533 496 | 500 svaria_AppearanceSpacings test: | 500 | 540 499 507 455 466 = 0.96 || = 0.27 504 504 495 485 525 | 500 ----------------------------------------------- | 500 | 535 470 490 507 527 = 0.95 || = 0.26 528 479 510 504 484 | 500 N = 1, Q = 10000000, K = 1000000000, r = 0, s = 3, L = 15 | 500 | 481 498 502 504 489 = 0.94 || = 0.25 494 487 479 478 461 | 500 Normal statistic | 500 | 490 481 530 525 510 = 0.93 || = 0.24 503 527 519 491 508 | 500 | 500 | 515 481 496 488 518 = 0.92 || = 0.23 503 505 498 506 467 | 500 =================================================================| 500 | 468 522 470 504 501 = 0.91 || = 0.22 523 536 511 486 531 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 515 488 527 523 432 = 0.90 || = 0.21 544 479 463 510 493 | 500 -----------------------------------------------------------------| 500 | 505 564 500 504 476 = 0.89 || = 0.20 483 512 439 521 489 | 500 SD Bern.: d 1.01844 1.03201 1.02909 | 500 | 514 507 499 541 512 = 0.88 || = 0.19 545 477 512 505 520 | 500 s 1.04852 0.90377 1.11049 | 500 | 465 531 500 544 501 = 0.87 || = 0.18 448 499 490 471 521 | 500 t 0.98767 1.34305 0.78140 | 500 | 463 477 520 499 495 = 0.86 || = 0.17 489 559 473 496 484 | 500 m 1.11166 1.03492 1.43737 | 500 | 527 472 493 472 486 = 0.85 || = 0.16 487 475 439 512 477 | 500 x 0.92673 0.87792 1.19054 | 500 | 500 485 500 503 490 = 0.84 || = 0.15 494 483 521 532 503 | 500 | 500 | 526 489 481 445 524 = 0.83 || = 0.14 529 553 471 529 521 | 500 Changes: d 52 6 4 | 500 | 506 510 560 521 512 = 0.82 || = 0.13 472 508 515 520 479 | 500 s 51 6 7 | 500 | 466 507 451 501 498 = 0.81 || = 0.12 486 477 511 469 526 | 500 t 48 3 6 | 500 | 480 501 497 510 489 = 0.80 || = 0.11 504 519 463 518 488 | 500 m 54 3 3 | 500 | 476 527 530 484 493 = 0.79 || = 0.10 518 458 502 494 503 | 500 x 47 7 7 | 500 | 514 463 532 517 496 = 0.78 || = 0.09 492 463 505 470 497 | 500 -----------------------------------------------------------------| 500 | 499 480 469 504 526 = 0.77 || = 0.08 530 497 511 503 514 | 500 Aver./ d 0.49990 497 > 500: 4 4 6 3 5 5 4 2 6 5 | 500 | 483 503 493 528 511 = 0.76 || = 0.07 517 521 502 480 506 | 500 median s 0.50068 501 ----- 4 4 5 4 6 7 6 7 5 3 | 500 | 469 482 532 538 473 = 0.75 || = 0.06 486 543 503 516 470 | 500 t 0.50151 500 6 5 4 4 7 4 3 5 3 6 | 500 | 474 511 509 497 469 = 0.74 || = 0.05 527 463 500 513 483 | 500 m 0.49955 503 6 6 5 4 6 5 4 7 7 4 | 500 | 535 502 480 474 526 = 0.73 || = 0.04 483 518 477 523 494 | 500 x 0.50054 501 4 6 3 6 4 7 5 4 4 7 | 500 | 494 516 491 506 523 = 0.72 || = 0.03 483 484 500 520 535 | 500 -----------------------------------------------------------------| 500 | 474 502 522 526 485 = 0.71 || = 0.02 478 507 500 501 510 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 496 495 515 492 518 = 0.70 || = 0.01 219 247 258 215 225 | 252.5 d 0 0 2 14 64 19 2 0 0 | 500 | 500 514 495 522 504 = 0.69 || < 0.01 528 468 515 471 477 | 497.5 s 0 0 2 16 68 12 3 0 0 | 500 | 508 494 512 477 478 = 0.68 ||========================================================================= t 0 0 5 10 72 13 1 0 0 | 500 | 493 475 443 465 473 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 21 58 16 1 1 0 | 500 | 531 526 500 484 495 = 0.66 ||========================================================================= x 0 1 0 15 68 17 0 0 0 | 500 | 533 502 511 511 478 = 0.65 || svaria_AppearanceSpacings test: no 117 test no 118 TestU01 250000 runs BigCrush Test smarsa_S svaria_AppearanceSpacings test: test no 118 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 0 4 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 508 503 474 494 527 | 500 < 0.00002 0 1 0 0 1 | 0.5 | 2 0 2 1 1 > 0.99998 || = 0.63 499 525 476 502 532 | 500 < 0.00003 1 0 0 1 1 | 0.5 | 0 2 1 1 0 > 0.99997 || = 0.62 498 492 499 534 530 | 500 < 0.00004 0 0 2 2 0 | 0.5 | 0 1 0 3 0 > 0.99996 || = 0.61 494 524 471 513 501 | 500 < 0.00005 1 0 2 0 1 | 0.5 | 0 1 1 0 0 > 0.99995 || = 0.60 482 487 518 533 495 | 500 < 0.00006 0 0 0 1 0 | 0.5 | 1 0 1 0 0 > 0.99994 || = 0.59 504 479 504 473 502 | 500 < 0.00007 1 1 0 0 0 | 0.5 | 0 1 0 1 0 > 0.99993 || = 0.58 516 527 489 553 516 | 500 < 0.00008 1 0 0 1 0 | 0.5 | 1 1 0 1 0 > 0.99992 || = 0.57 491 498 523 555 533 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 1 0 0 1 > 0.99991 || = 0.56 489 515 506 488 450 | 500 < 0.0001 0 0 0 1 1 | 0.5 | 0 0 2 1 0 > 0.9999 || = 0.55 516 485 496 478 480 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 521 471 498 513 517 | 500 < 0.0001 5 2 4 6 8 | 5 | 4 7 7 9 2 > 0.9999 || = 0.53 493 485 502 450 517 | 500 < 0.0002 3 5 4 6 4 | 5 | 7 4 1 2 3 > 0.9998 || = 0.52 483 523 484 489 509 | 500 < 0.0003 8 5 4 4 6 | 5 | 5 4 4 3 5 > 0.9997 || = 0.51 532 526 517 493 487 | 500 < 0.0004 4 4 2 6 4 | 5 | 9 3 6 4 8 > 0.9996 || = 0.50 448 502 492 490 517 | 500 < 0.0005 6 5 2 5 4 | 5 | 4 5 2 2 4 > 0.9995 || = 0.49 526 522 522 512 516 | 500 < 0.0006 7 6 6 6 7 | 5 | 2 4 3 4 5 > 0.9994 || = 0.48 476 516 530 527 486 | 500 < 0.0007 6 4 5 5 4 | 5 | 4 5 2 3 5 > 0.9993 || = 0.47 492 530 502 461 514 | 500 < 0.0008 8 5 9 8 3 | 5 | 3 8 5 2 5 > 0.9992 || = 0.46 510 513 509 452 486 | 500 < 0.0009 2 4 2 7 4 | 5 | 6 1 2 5 0 > 0.9991 || = 0.45 552 499 506 489 510 | 500 < 0.001 4 5 5 4 5 | 5 | 5 6 4 7 6 > 0.999 || = 0.44 502 501 509 501 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 533 469 495 518 500 | 500 < 0.001 53 45 43 57 49 | 50 | 49 47 36 41 43 > 0.999 || = 0.42 478 468 486 520 521 | 500 < 0.002 50 42 44 50 45 | 50 | 51 48 55 42 47 > 0.998 || = 0.41 484 539 465 530 470 | 500 < 0.003 44 48 70 42 58 | 50 | 53 52 54 52 57 > 0.997 || = 0.40 459 508 558 507 516 | 500 < 0.004 52 52 56 46 61 | 50 | 52 45 46 53 69 > 0.996 || = 0.39 528 487 509 537 524 | 500 < 0.005 35 47 52 54 51 | 50 | 51 52 46 57 62 > 0.995 || = 0.38 538 512 473 489 494 | 500 < 0.006 55 42 50 47 45 | 50 | 51 51 44 57 54 > 0.994 || = 0.37 518 532 458 522 508 | 500 < 0.007 53 50 48 54 56 | 50 | 54 38 42 59 66 > 0.993 || = 0.36 499 458 511 496 496 | 500 < 0.008 48 64 55 49 40 | 50 | 51 41 52 50 53 > 0.992 || = 0.35 537 567 481 492 479 | 500 < 0.009 46 56 44 48 43 | 50 | 51 52 54 63 54 > 0.991 || = 0.34 489 462 497 467 524 | 500 < 0.01 40 46 54 48 59 | 50 | 50 40 58 49 49 > 0.99 || = 0.33 496 500 501 517 507 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 522 493 504 505 477 | 500 < 0.01 476 492 516 495 507 | 497.5 | 513 466 487 523 554 > 0.99 || = 0.31 528 527 511 521 509 | 500 = 0.01 251 222 257 244 245 | 252.5 | 211 264 225 226 259 = 0.99 || = 0.30 506 515 512 557 518 | 500 = 0.02 529 467 513 485 479 | 500 | 507 460 481 492 486 = 0.98 || = 0.29 541 487 486 472 495 | 500 =================================================================| 500 | 462 488 496 501 532 = 0.97 || = 0.28 484 535 469 511 496 | 500 svaria_AppearanceSpacings test: | 500 | 511 542 488 504 512 = 0.96 || = 0.27 531 481 503 504 488 | 500 ----------------------------------------------- | 500 | 497 523 492 476 528 = 0.95 || = 0.26 488 475 490 514 488 | 500 N = 1, Q = 10000000, K = 1000000000, r = 27, s = 3, L = 15 | 500 | 512 445 506 521 482 = 0.94 || = 0.25 502 545 485 493 544 | 500 Normal statistic | 500 | 477 496 519 491 499 = 0.93 || = 0.24 499 489 550 505 462 | 500 | 500 | 462 509 512 477 500 = 0.92 || = 0.23 485 490 522 506 546 | 500 =================================================================| 500 | 474 482 474 534 542 = 0.91 || = 0.22 489 533 516 479 472 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 486 522 503 500 483 = 0.90 || = 0.21 474 516 493 543 502 | 500 -----------------------------------------------------------------| 500 | 455 516 495 480 481 = 0.89 || = 0.20 520 471 505 509 499 | 500 SD Bern.: d 1.06037 0.92566 0.26468 | 500 | 536 501 507 478 513 = 0.88 || = 0.19 493 552 513 486 498 | 500 s 1.20634 0.91478 0.86760 | 500 | 478 481 505 498 504 = 0.87 || = 0.18 512 502 483 464 485 | 500 t 0.84262 1.10145 0.95230 | 500 | 524 533 512 490 520 = 0.86 || = 0.17 480 531 504 500 516 | 500 m 1.04822 0.59862 1.00746 | 500 | 483 449 467 490 511 = 0.85 || = 0.16 502 492 476 496 493 | 500 x 0.98046 1.00348 1.34974 | 500 | 499 472 502 488 519 = 0.84 || = 0.15 506 498 505 513 482 | 500 | 500 | 521 487 519 501 489 = 0.83 || = 0.14 506 512 498 485 474 | 500 Changes: d 53 5 2 | 500 | 521 480 473 512 458 = 0.82 || = 0.13 548 519 506 493 506 | 500 s 56 4 6 | 500 | 512 542 484 458 491 = 0.81 || = 0.12 494 535 489 549 457 | 500 t 49 5 3 | 500 | 482 452 473 522 463 = 0.80 || = 0.11 525 461 471 497 507 | 500 m 49 5 4 | 500 | 500 553 489 496 510 = 0.79 || = 0.10 511 499 503 501 527 | 500 x 52 5 2 | 500 | 496 543 498 502 477 = 0.78 || = 0.09 480 502 487 480 499 | 500 -----------------------------------------------------------------| 500 | 545 508 508 471 494 = 0.77 || = 0.08 513 496 510 447 464 | 500 Aver./ d 0.49776 499 > 500: 4 7 4 7 5 5 1 4 5 4 | 500 | 495 497 545 531 514 = 0.76 || = 0.07 464 442 507 523 483 | 500 median s 0.49917 499 ----- 3 6 4 5 7 4 5 5 5 4 | 500 | 465 479 523 532 515 = 0.75 || = 0.06 482 504 520 497 481 | 500 t 0.49820 502 8 5 5 6 7 6 4 3 6 3 | 500 | 543 501 484 502 503 = 0.74 || = 0.05 490 475 492 535 506 | 500 m 0.49946 497 2 3 7 6 7 4 5 6 2 5 | 500 | 495 509 489 512 471 = 0.73 || = 0.04 511 488 524 485 532 | 500 x 0.50173 500 3 4 3 6 5 6 6 5 5 6 | 500 | 516 486 486 470 528 = 0.72 || = 0.03 532 546 543 487 484 | 500 -----------------------------------------------------------------| 500 | 506 487 490 491 499 = 0.71 || = 0.02 529 467 513 485 479 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 484 514 517 468 463 = 0.70 || = 0.01 251 222 257 244 245 | 252.5 d 0 0 4 11 68 15 3 0 0 | 500 | 497 474 519 501 508 = 0.69 || < 0.01 476 492 516 495 507 | 497.5 s 0 0 4 17 57 18 4 1 0 | 500 | 466 460 498 491 502 = 0.68 ||========================================================================= t 0 0 0 14 79 5 3 0 0 | 500 | 481 517 517 475 484 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 13 68 13 4 0 0 | 500 | 454 465 488 527 485 = 0.66 ||========================================================================= x 0 0 2 12 72 13 2 0 0 | 500 | 469 480 505 493 448 = 0.65 || svaria_AppearanceSpacings test: no 118 test no 119 TestU01 250000 runs BigCrush Test smarsa_S svaria_WeightDistrib test: test no 119 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 1 2 0 | 0.5 | 1 1 0 0 0 > 0.99999 || = 0.64 475 524 515 531 487 | 500 < 0.00002 0 0 1 0 1 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 514 451 469 476 498 | 500 < 0.00003 0 0 1 1 1 | 0.5 | 0 0 1 0 1 > 0.99997 || = 0.62 476 482 502 501 545 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99996 || = 0.61 489 520 461 451 466 | 500 < 0.00005 1 1 1 1 1 | 0.5 | 0 1 0 0 0 > 0.99995 || = 0.60 475 511 481 463 522 | 500 < 0.00006 0 1 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 508 514 505 514 487 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 1 1 0 0 0 > 0.99993 || = 0.58 484 472 534 494 514 | 500 < 0.00008 0 1 1 0 0 | 0.5 | 1 0 2 1 0 > 0.99992 || = 0.57 533 500 492 470 506 | 500 < 0.00009 2 0 1 0 0 | 0.5 | 1 1 0 0 0 > 0.99991 || = 0.56 484 482 500 488 526 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 1 1 0 1 > 0.9999 || = 0.55 474 522 521 507 481 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 481 461 476 478 497 | 500 < 0.0001 3 6 6 6 3 | 5 | 4 5 5 1 4 > 0.9999 || = 0.53 496 497 473 503 504 | 500 < 0.0002 7 4 4 10 6 | 5 | 1 2 0 3 2 > 0.9998 || = 0.52 467 537 482 550 454 | 500 < 0.0003 4 2 3 5 8 | 5 | 5 5 7 4 3 > 0.9997 || = 0.51 473 499 471 475 509 | 500 < 0.0004 2 4 6 5 4 | 5 | 3 5 10 4 7 > 0.9996 || = 0.50 499 482 504 492 516 | 500 < 0.0005 8 5 5 2 4 | 5 | 2 7 2 5 7 > 0.9995 || = 0.49 482 485 488 498 526 | 500 < 0.0006 5 8 6 7 5 | 5 | 3 4 8 5 6 > 0.9994 || = 0.48 501 520 494 473 513 | 500 < 0.0007 4 9 5 6 8 | 5 | 6 5 5 3 8 > 0.9993 || = 0.47 480 500 510 522 470 | 500 < 0.0008 8 5 3 1 4 | 5 | 6 7 6 5 7 > 0.9992 || = 0.46 528 490 483 530 503 | 500 < 0.0009 3 3 5 3 9 | 5 | 6 6 2 2 5 > 0.9991 || = 0.45 510 535 516 474 533 | 500 < 0.001 2 3 3 3 8 | 5 | 4 4 5 10 1 > 0.999 || = 0.44 486 501 474 490 503 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 500 500 518 474 488 | 500 < 0.001 46 49 46 48 59 | 50 | 40 50 50 42 50 > 0.999 || = 0.42 490 507 520 503 499 | 500 < 0.002 50 55 57 52 61 | 50 | 51 56 45 40 50 > 0.998 || = 0.41 464 505 468 496 500 | 500 < 0.003 54 45 54 56 54 | 50 | 49 55 42 53 52 > 0.997 || = 0.40 476 497 523 490 528 | 500 < 0.004 52 39 59 43 52 | 50 | 48 50 46 41 48 > 0.996 || = 0.39 488 481 512 520 493 | 500 < 0.005 56 62 53 50 56 | 50 | 38 52 40 44 41 > 0.995 || = 0.38 509 538 463 539 482 | 500 < 0.006 54 45 36 63 46 | 50 | 59 42 52 53 39 > 0.994 || = 0.37 486 563 513 482 469 | 500 < 0.007 51 44 64 46 52 | 50 | 51 51 52 56 51 > 0.993 || = 0.36 489 482 501 518 473 | 500 < 0.008 48 47 51 50 40 | 50 | 50 46 34 47 63 > 0.992 || = 0.35 497 464 537 546 482 | 500 < 0.009 61 45 52 56 59 | 50 | 66 48 43 57 46 > 0.991 || = 0.34 496 501 500 494 512 | 500 < 0.01 39 47 47 44 65 | 50 | 51 61 46 47 53 > 0.99 || = 0.33 516 487 493 487 535 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 535 481 486 553 519 | 500 < 0.01 511 478 519 508 544 | 497.5 | 503 511 450 480 493 > 0.99 || = 0.31 481 513 514 511 486 | 500 = 0.01 264 265 220 224 272 | 252.5 | 252 247 248 259 239 = 0.99 || = 0.30 482 449 511 513 542 | 500 = 0.02 521 494 475 494 501 | 500 | 464 510 500 491 484 = 0.98 || = 0.29 508 528 475 512 463 | 500 =================================================================| 500 | 479 536 438 490 496 = 0.97 || = 0.28 478 520 520 468 523 | 500 svaria_WeightDistrib test: | 500 | 542 477 484 518 510 = 0.96 || = 0.27 501 483 494 476 496 | 500 ----------------------------------------------- | 500 | 497 509 502 488 533 = 0.95 || = 0.26 498 457 485 498 474 | 500 N = 1, n = 20000000, r = 0, k = 256, Alpha = 0, Beta = 0.25 | 500 | 541 495 503 500 457 = 0.94 || = 0.25 512 529 507 498 530 | 500 | 500 | 552 495 488 533 460 = 0.93 || = 0.24 546 481 476 513 465 | 500 | 500 | 485 515 488 490 497 = 0.92 || = 0.23 508 525 507 507 501 | 500 =================================================================| 500 | 478 500 502 487 446 = 0.91 || = 0.22 486 556 491 486 522 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 505 515 509 524 497 = 0.90 || = 0.21 514 497 513 518 473 | 500 -----------------------------------------------------------------| 500 | 477 499 504 512 509 = 0.89 || = 0.20 488 506 483 504 462 | 500 SD Bern.: d 0.95637 0.81893 1.08589 | 500 | 507 477 579 525 494 = 0.88 || = 0.19 526 518 552 513 490 | 500 s 1.00727 0.91696 0.73656 | 500 | 526 523 472 511 517 = 0.87 || = 0.18 507 470 515 456 527 | 500 t 1.02239 1.07477 1.03394 | 500 | 506 476 524 499 499 = 0.86 || = 0.17 494 498 480 454 490 | 500 m 0.99478 0.83707 0.89710 | 500 | 495 465 479 530 484 = 0.85 || = 0.16 526 507 509 479 486 | 500 x 1.03478 1.17019 0.90043 | 500 | 514 479 523 499 498 = 0.84 || = 0.15 486 518 488 518 498 | 500 | 500 | 531 511 545 482 520 = 0.83 || = 0.14 471 539 487 511 473 | 500 Changes: d 54 4 5 | 500 | 496 506 538 526 508 = 0.82 || = 0.13 480 517 498 529 508 | 500 s 61 4 7 | 500 | 503 515 465 513 511 = 0.81 || = 0.12 475 492 501 502 534 | 500 t 55 4 2 | 500 | 524 461 485 525 514 = 0.80 || = 0.11 517 472 490 481 543 | 500 m 53 6 6 | 500 | 495 541 498 503 491 = 0.79 || = 0.10 512 521 498 492 509 | 500 x 47 4 5 | 500 | 482 473 488 500 494 = 0.78 || = 0.09 523 491 502 480 462 | 500 -----------------------------------------------------------------| 500 | 459 500 510 478 495 = 0.77 || = 0.08 502 505 545 505 463 | 500 Aver./ d 0.49995 498 > 500: 8 5 6 3 3 2 4 5 7 4 | 500 | 513 489 531 477 543 = 0.76 || = 0.07 499 518 498 506 515 | 500 median s 0.49906 500 ----- 4 6 6 4 5 4 4 3 5 5 | 500 | 472 520 509 506 515 = 0.75 || = 0.06 507 496 512 483 469 | 500 t 0.49914 500 7 4 4 6 5 3 3 6 7 3 | 500 | 525 477 511 522 486 = 0.74 || = 0.05 522 495 529 510 506 | 500 m 0.50081 500 5 5 5 7 3 4 5 5 7 3 | 500 | 490 503 541 472 525 = 0.73 || = 0.04 503 498 510 499 497 | 500 x 0.49895 498 6 5 4 4 6 6 3 4 5 2 | 500 | 522 461 496 519 483 = 0.72 || = 0.03 489 505 517 515 535 | 500 -----------------------------------------------------------------| 500 | 523 490 503 461 486 = 0.71 || = 0.02 521 494 475 494 501 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 518 502 485 469 493 = 0.70 || = 0.01 264 265 220 224 272 | 252.5 d 0 0 0 15 70 13 2 1 0 | 500 | 489 491 490 551 491 = 0.69 || < 0.01 511 478 519 508 544 | 497.5 s 0 0 2 14 71 12 2 0 0 | 500 | 572 492 528 480 482 = 0.68 ||========================================================================= t 0 0 3 13 71 10 3 1 0 | 500 | 486 479 491 532 494 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 69 11 4 0 0 | 500 | 472 535 497 504 524 = 0.66 ||========================================================================= x 0 0 2 15 64 18 2 0 0 | 500 | 507 493 490 499 533 = 0.65 || svaria_WeightDistrib test: no 119 test no 120 TestU01 250000 runs BigCrush Test smarsa_S svaria_WeightDistrib test: test no 120 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 1 0 1 | 0.5 | 0 0 1 1 0 > 0.99999 || = 0.64 514 474 478 471 503 | 500 < 0.00002 0 0 2 0 0 | 0.5 | 0 3 1 0 1 > 0.99998 || = 0.63 487 458 481 517 511 | 500 < 0.00003 0 0 2 0 0 | 0.5 | 1 0 1 0 0 > 0.99997 || = 0.62 481 477 479 527 455 | 500 < 0.00004 0 1 0 0 1 | 0.5 | 0 1 0 1 1 > 0.99996 || = 0.61 467 514 516 489 493 | 500 < 0.00005 1 0 0 1 0 | 0.5 | 1 0 0 0 1 > 0.99995 || = 0.60 463 487 480 489 493 | 500 < 0.00006 0 0 1 3 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 511 524 502 490 520 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 1 1 0 1 0 > 0.99993 || = 0.58 519 475 574 474 433 | 500 < 0.00008 1 1 0 0 0 | 0.5 | 0 1 1 1 1 > 0.99992 || = 0.57 492 519 515 490 502 | 500 < 0.00009 1 0 1 1 0 | 0.5 | 2 2 1 1 1 > 0.99991 || = 0.56 491 520 483 485 556 | 500 < 0.0001 0 0 0 0 1 | 0.5 | 0 1 0 0 0 > 0.9999 || = 0.55 516 476 508 478 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 504 481 490 482 493 | 500 < 0.0001 3 3 7 5 3 | 5 | 5 9 5 5 5 > 0.9999 || = 0.53 490 488 526 493 470 | 500 < 0.0002 3 6 4 10 10 | 5 | 2 3 1 1 1 > 0.9998 || = 0.52 502 503 484 525 527 | 500 < 0.0003 4 6 6 5 5 | 5 | 5 5 3 6 6 > 0.9997 || = 0.51 463 512 449 514 488 | 500 < 0.0004 3 2 8 8 5 | 5 | 7 6 6 5 3 > 0.9996 || = 0.50 511 496 450 478 531 | 500 < 0.0005 3 3 9 7 5 | 5 | 4 3 3 7 5 > 0.9995 || = 0.49 512 510 514 510 495 | 500 < 0.0006 8 6 5 8 0 | 5 | 5 12 5 6 3 > 0.9994 || = 0.48 513 523 505 474 500 | 500 < 0.0007 11 9 6 5 3 | 5 | 7 3 8 4 5 > 0.9993 || = 0.47 477 491 481 534 526 | 500 < 0.0008 3 4 5 9 5 | 5 | 3 6 9 5 7 > 0.9992 || = 0.46 484 501 505 493 527 | 500 < 0.0009 6 6 3 2 6 | 5 | 8 4 4 2 6 > 0.9991 || = 0.45 529 465 491 498 515 | 500 < 0.001 8 4 9 5 4 | 5 | 6 3 6 9 8 > 0.999 || = 0.44 501 496 490 506 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 497 513 497 505 469 | 500 < 0.001 52 49 62 64 46 | 50 | 52 54 50 50 49 > 0.999 || = 0.42 540 548 503 514 500 | 500 < 0.002 44 56 62 61 43 | 50 | 56 50 67 55 52 > 0.998 || = 0.41 490 487 525 483 494 | 500 < 0.003 47 56 41 42 51 | 50 | 48 50 50 68 56 > 0.997 || = 0.40 483 476 522 500 500 | 500 < 0.004 38 51 58 39 63 | 50 | 54 51 57 62 49 > 0.996 || = 0.39 466 479 530 521 546 | 500 < 0.005 48 45 44 37 69 | 50 | 46 46 32 34 47 > 0.995 || = 0.38 534 515 529 464 477 | 500 < 0.006 50 32 57 51 50 | 50 | 57 35 49 51 42 > 0.994 || = 0.37 447 491 547 501 505 | 500 < 0.007 50 49 45 57 54 | 50 | 57 57 51 42 56 > 0.993 || = 0.36 488 498 534 513 525 | 500 < 0.008 44 67 52 57 55 | 50 | 49 56 43 47 62 > 0.992 || = 0.35 485 524 508 473 487 | 500 < 0.009 50 47 40 65 51 | 50 | 52 48 67 49 51 > 0.991 || = 0.34 488 472 469 504 515 | 500 < 0.01 44 61 45 44 62 | 50 | 53 51 55 57 55 > 0.99 || = 0.33 489 471 496 473 527 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 475 494 508 474 506 | 500 < 0.01 467 513 506 517 544 | 497.5 | 524 498 521 515 519 > 0.99 || = 0.31 517 492 500 517 495 | 500 = 0.01 254 247 249 267 259 | 252.5 | 246 234 228 268 279 = 0.99 || = 0.30 479 543 498 492 491 | 500 = 0.02 496 489 552 543 458 | 500 | 517 491 497 502 500 = 0.98 || = 0.29 493 484 496 509 520 | 500 =================================================================| 500 | 502 515 497 503 481 = 0.97 || = 0.28 522 492 529 484 502 | 500 svaria_WeightDistrib test: | 500 | 484 505 507 483 470 = 0.96 || = 0.27 489 511 487 542 492 | 500 ----------------------------------------------- | 500 | 479 540 478 509 523 = 0.95 || = 0.26 493 488 505 537 492 | 500 N = 1, n = 20000000, r = 20, k = 256, Alpha = 0, Beta = 0.25 | 500 | 549 531 491 537 502 = 0.94 || = 0.25 498 514 479 487 470 | 500 | 500 | 500 486 494 499 461 = 0.93 || = 0.24 476 435 476 515 497 | 500 | 500 | 535 483 491 497 506 = 0.92 || = 0.23 482 466 506 525 484 | 500 =================================================================| 500 | 495 534 517 461 527 = 0.91 || = 0.22 544 513 486 488 484 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 475 476 524 499 509 = 0.90 || = 0.21 473 499 557 493 465 | 500 -----------------------------------------------------------------| 500 | 494 513 489 498 499 = 0.89 || = 0.20 496 505 506 470 509 | 500 SD Bern.: d 0.99454 0.73384 0.61348 | 500 | 490 528 500 518 490 = 0.88 || = 0.19 496 505 484 524 506 | 500 s 1.02278 1.29910 0.83467 | 500 | 535 483 483 469 481 = 0.87 || = 0.18 506 509 530 476 516 | 500 t 1.01231 1.15988 1.43388 | 500 | 474 467 480 487 503 = 0.86 || = 0.17 456 542 501 507 513 | 500 m 0.94805 1.43668 1.32201 | 500 | 518 516 531 508 502 = 0.85 || = 0.16 532 514 512 465 531 | 500 x 1.01538 1.25122 0.80164 | 500 | 511 512 499 493 502 = 0.84 || = 0.15 530 503 500 498 521 | 500 | 500 | 547 515 468 527 466 = 0.83 || = 0.14 501 525 506 518 476 | 500 Changes: d 51 1 6 | 500 | 480 508 479 519 472 = 0.82 || = 0.13 510 511 492 515 499 | 500 s 52 5 6 | 500 | 460 490 515 501 523 = 0.81 || = 0.12 493 505 475 473 480 | 500 t 50 7 7 | 500 | 487 484 498 517 491 = 0.80 || = 0.11 488 502 494 475 530 | 500 m 48 3 5 | 500 | 510 499 490 472 505 = 0.79 || = 0.10 521 468 493 499 501 | 500 x 48 3 3 | 500 | 511 558 451 500 482 = 0.78 || = 0.09 524 527 489 539 550 | 500 -----------------------------------------------------------------| 500 | 478 462 476 501 519 = 0.77 || = 0.08 494 515 482 531 473 | 500 Aver./ d 0.50178 497 > 500: 4 6 2 2 5 5 6 7 4 5 | 500 | 532 509 508 523 501 = 0.76 || = 0.07 512 527 494 537 497 | 500 median s 0.49905 500 ----- 7 9 4 3 5 5 3 3 6 6 | 500 | 517 478 488 529 504 = 0.75 || = 0.06 469 466 542 501 481 | 500 t 0.49738 497 5 4 5 6 6 5 4 2 3 3 | 500 | 527 469 472 460 492 = 0.74 || = 0.05 488 560 542 488 527 | 500 m 0.49837 499 8 4 5 5 5 2 4 4 5 6 | 500 | 525 481 484 479 456 = 0.73 || = 0.04 498 513 467 491 495 | 500 x 0.49878 500 5 7 3 6 3 4 5 5 5 6 | 500 | 485 502 516 481 501 = 0.72 || = 0.03 517 505 534 543 513 | 500 -----------------------------------------------------------------| 500 | 544 494 486 478 500 = 0.71 || = 0.02 496 489 552 543 458 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 480 486 493 480 512 = 0.70 || = 0.01 254 247 249 267 259 | 252.5 d 0 0 1 14 69 15 2 0 0 | 500 | 540 526 502 515 464 = 0.69 || < 0.01 467 513 506 517 544 | 497.5 s 0 0 1 18 65 14 3 0 0 | 500 | 510 475 484 496 506 = 0.68 ||========================================================================= t 0 0 3 8 73 13 3 1 0 | 500 | 503 482 500 513 541 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 17 68 16 0 0 0 | 500 | 502 498 514 489 489 = 0.66 ||========================================================================= x 0 1 1 15 66 14 4 0 0 | 500 | 511 526 511 466 476 = 0.65 || svaria_WeightDistrib test: no 120 test no 121 TestU01 250000 runs BigCrush Test smarsa_S svaria_WeightDistrib test: test no 121 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 1 | 0.5 | 0 0 0 3 0 > 0.99999 || = 0.64 500 499 521 507 467 | 500 < 0.00002 1 0 0 3 0 | 0.5 | 0 2 0 2 0 > 0.99998 || = 0.63 490 516 483 466 504 | 500 < 0.00003 3 0 0 0 2 | 0.5 | 0 0 1 0 0 > 0.99997 || = 0.62 474 510 502 489 521 | 500 < 0.00004 3 0 2 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 481 500 505 480 509 | 500 < 0.00005 2 0 0 1 0 | 0.5 | 1 1 0 1 1 > 0.99995 || = 0.60 500 465 485 503 486 | 500 < 0.00006 2 1 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99994 || = 0.59 496 524 505 479 481 | 500 < 0.00007 0 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 525 503 450 460 480 | 500 < 0.00008 0 2 0 0 2 | 0.5 | 0 1 1 0 0 > 0.99992 || = 0.57 516 543 493 490 491 | 500 < 0.00009 0 0 0 2 0 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 526 514 499 511 472 | 500 < 0.0001 1 0 1 0 1 | 0.5 | 2 1 0 1 1 > 0.9999 || = 0.55 500 508 479 513 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 502 465 510 507 499 | 500 < 0.0001 12 3 5 7 6 | 5 | 3 6 2 7 3 > 0.9999 || = 0.53 494 480 498 502 498 | 500 < 0.0002 7 4 8 3 2 | 5 | 7 4 3 1 2 > 0.9998 || = 0.52 534 470 505 499 506 | 500 < 0.0003 2 6 5 6 5 | 5 | 6 4 4 5 6 > 0.9997 || = 0.51 510 522 521 499 514 | 500 < 0.0004 3 7 1 3 4 | 5 | 4 7 10 3 6 > 0.9996 || = 0.50 477 472 517 532 490 | 500 < 0.0005 4 8 5 6 6 | 5 | 9 0 3 6 8 > 0.9995 || = 0.49 507 529 509 473 495 | 500 < 0.0006 6 6 2 3 8 | 5 | 6 6 5 6 6 > 0.9994 || = 0.48 489 491 508 513 501 | 500 < 0.0007 8 5 6 5 4 | 5 | 5 6 5 2 3 > 0.9993 || = 0.47 492 491 500 488 491 | 500 < 0.0008 5 5 4 7 6 | 5 | 7 4 6 2 6 > 0.9992 || = 0.46 499 541 461 514 470 | 500 < 0.0009 3 3 6 2 6 | 5 | 3 3 6 2 1 > 0.9991 || = 0.45 504 443 501 525 530 | 500 < 0.001 1 8 2 5 2 | 5 | 7 2 5 6 4 > 0.999 || = 0.44 497 482 539 490 501 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 458 531 537 513 501 | 500 < 0.001 51 55 44 47 49 | 50 | 57 42 49 40 45 > 0.999 || = 0.42 497 515 481 530 510 | 500 < 0.002 53 43 40 53 42 | 50 | 48 64 50 36 42 > 0.998 || = 0.41 505 512 490 544 511 | 500 < 0.003 52 45 49 60 61 | 50 | 56 41 47 38 50 > 0.997 || = 0.40 513 519 469 517 478 | 500 < 0.004 51 43 51 48 51 | 50 | 47 48 54 48 46 > 0.996 || = 0.39 534 529 532 480 484 | 500 < 0.005 62 43 51 50 47 | 50 | 45 61 62 52 41 > 0.995 || = 0.38 489 489 498 518 443 | 500 < 0.006 43 47 48 52 49 | 50 | 52 54 43 60 46 > 0.994 || = 0.37 535 489 511 487 488 | 500 < 0.007 71 50 48 48 43 | 50 | 44 45 41 50 37 > 0.993 || = 0.36 450 505 529 488 487 | 500 < 0.008 51 53 65 53 56 | 50 | 68 44 41 51 53 > 0.992 || = 0.35 446 487 506 444 543 | 500 < 0.009 59 44 45 57 51 | 50 | 57 61 54 48 47 > 0.991 || = 0.34 520 493 505 454 499 | 500 < 0.01 53 59 62 57 55 | 50 | 53 52 40 48 59 > 0.99 || = 0.33 524 529 504 500 467 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 482 462 515 510 501 | 500 < 0.01 546 482 503 525 504 | 497.5 | 527 512 481 471 466 > 0.99 || = 0.31 495 480 497 474 505 | 500 = 0.01 270 291 229 255 269 | 252.5 | 254 251 259 255 217 = 0.99 || = 0.30 512 510 494 508 481 | 500 = 0.02 480 514 461 488 528 | 500 | 492 479 495 488 519 = 0.98 || = 0.29 491 484 523 477 505 | 500 =================================================================| 500 | 508 519 466 515 461 = 0.97 || = 0.28 464 456 493 501 495 | 500 svaria_WeightDistrib test: | 500 | 535 498 501 513 521 = 0.96 || = 0.27 515 495 499 508 515 | 500 ----------------------------------------------- | 500 | 504 485 542 514 520 = 0.95 || = 0.26 523 511 513 512 505 | 500 N = 1, n = 20000000, r = 28, k = 256, Alpha = 0, Beta = 0.25 | 500 | 493 540 534 516 467 = 0.94 || = 0.25 502 473 472 531 449 | 500 | 500 | 499 503 552 491 476 = 0.93 || = 0.24 487 529 476 494 470 | 500 | 500 | 501 512 505 526 518 = 0.92 || = 0.23 484 513 505 461 508 | 500 =================================================================| 500 | 504 490 520 501 495 = 0.91 || = 0.22 506 463 493 500 531 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 450 488 515 525 473 = 0.90 || = 0.21 513 498 466 491 519 | 500 -----------------------------------------------------------------| 500 | 473 448 495 521 485 = 0.89 || = 0.20 493 493 499 526 477 | 500 SD Bern.: d 0.97561 1.21715 1.04454 | 500 | 473 502 482 483 510 = 0.88 || = 0.19 491 483 511 532 504 | 500 s 1.06932 0.81526 1.15642 | 500 | 500 487 473 524 498 = 0.87 || = 0.18 483 506 541 489 542 | 500 t 0.97805 1.04070 0.99748 | 500 | 524 492 480 470 538 = 0.86 || = 0.17 544 481 506 521 525 | 500 m 0.96592 0.68881 1.05598 | 500 | 562 485 516 524 499 = 0.85 || = 0.16 475 509 454 489 471 | 500 x 1.05864 0.78523 0.97001 | 500 | 480 486 473 538 536 = 0.84 || = 0.15 496 521 516 539 462 | 500 | 500 | 498 529 507 492 508 = 0.83 || = 0.14 496 511 524 477 506 | 500 Changes: d 46 2 6 | 500 | 486 549 523 498 534 = 0.82 || = 0.13 468 548 508 489 547 | 500 s 47 4 5 | 500 | 471 551 482 508 487 = 0.81 || = 0.12 476 479 506 482 485 | 500 t 51 5 4 | 500 | 496 514 512 527 519 = 0.80 || = 0.11 499 502 497 466 522 | 500 m 49 5 4 | 500 | 514 471 499 476 495 = 0.79 || = 0.10 550 511 531 510 552 | 500 x 51 3 3 | 500 | 531 452 459 467 507 = 0.78 || = 0.09 510 501 497 521 491 | 500 -----------------------------------------------------------------| 500 | 503 510 503 454 477 = 0.77 || = 0.08 476 471 450 470 475 | 500 Aver./ d 0.50006 499 > 500: 6 2 5 5 4 6 2 5 2 7 | 500 | 516 480 500 516 502 = 0.76 || = 0.07 490 487 526 495 522 | 500 median s 0.49957 501 ----- 7 7 3 4 6 6 4 5 4 5 | 500 | 488 489 503 517 481 = 0.75 || = 0.06 511 530 487 491 479 | 500 t 0.50110 501 2 8 3 7 5 4 5 5 4 7 | 500 | 500 510 493 525 498 = 0.74 || = 0.05 471 501 469 527 498 | 500 m 0.50109 501 4 4 5 3 7 5 5 6 6 7 | 500 | 508 520 506 501 513 = 0.73 || = 0.04 506 512 493 458 539 | 500 x 0.49837 501 6 7 6 3 6 3 6 5 5 4 | 500 | 492 534 489 514 521 = 0.72 || = 0.03 536 507 499 500 527 | 500 -----------------------------------------------------------------| 500 | 490 480 535 479 490 = 0.71 || = 0.02 480 514 461 488 528 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 523 507 528 508 536 = 0.70 || = 0.01 270 291 229 255 269 | 252.5 d 0 0 3 13 67 15 3 0 0 | 500 | 498 461 500 506 545 = 0.69 || < 0.01 546 482 503 525 504 | 497.5 s 0 0 3 11 70 13 4 0 0 | 500 | 510 481 524 482 525 = 0.68 ||========================================================================= t 0 0 4 12 69 15 1 0 0 | 500 | 477 486 494 498 474 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 67 17 0 0 0 | 500 | 496 533 499 503 470 = 0.66 ||========================================================================= x 0 0 3 17 64 14 3 0 0 | 500 | 499 486 449 522 487 = 0.65 || svaria_WeightDistrib test: no 121 test no 122 TestU01 250000 runs BigCrush Test smarsa_S svaria_WeightDistrib test: test no 122 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 1 0 | 0.5 | 2 0 0 0 1 > 0.99999 || = 0.64 478 507 502 542 520 | 500 < 0.00002 1 1 0 1 2 | 0.5 | 2 0 2 3 0 > 0.99998 || = 0.63 498 538 541 529 524 | 500 < 0.00003 0 1 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 490 520 459 505 498 | 500 < 0.00004 1 0 0 0 0 | 0.5 | 1 0 0 0 1 > 0.99996 || = 0.61 512 462 525 464 501 | 500 < 0.00005 1 0 1 0 1 | 0.5 | 1 0 0 1 0 > 0.99995 || = 0.60 503 483 485 508 498 | 500 < 0.00006 0 1 0 0 1 | 0.5 | 1 0 0 1 0 > 0.99994 || = 0.59 520 476 476 501 507 | 500 < 0.00007 0 1 0 1 2 | 0.5 | 0 0 1 0 0 > 0.99993 || = 0.58 431 526 526 532 508 | 500 < 0.00008 1 2 1 0 1 | 0.5 | 1 0 0 1 0 > 0.99992 || = 0.57 519 542 525 500 496 | 500 < 0.00009 0 1 1 0 0 | 0.5 | 1 1 0 2 0 > 0.99991 || = 0.56 489 485 482 505 459 | 500 < 0.0001 0 0 0 1 0 | 0.5 | 0 1 0 1 1 > 0.9999 || = 0.55 483 532 496 477 521 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 520 479 497 505 493 | 500 < 0.0001 5 7 4 5 7 | 5 | 10 2 3 9 3 > 0.9999 || = 0.53 507 522 511 480 505 | 500 < 0.0002 4 6 3 8 7 | 5 | 3 3 2 4 3 > 0.9998 || = 0.52 563 511 527 554 541 | 500 < 0.0003 6 5 7 5 5 | 5 | 9 5 7 6 5 > 0.9997 || = 0.51 463 496 491 511 488 | 500 < 0.0004 5 7 5 7 2 | 5 | 7 8 5 6 3 > 0.9996 || = 0.50 487 468 498 474 496 | 500 < 0.0005 6 5 7 9 5 | 5 | 2 3 6 3 3 > 0.9995 || = 0.49 475 493 472 448 530 | 500 < 0.0006 7 5 8 4 3 | 5 | 4 3 6 6 4 > 0.9994 || = 0.48 467 494 463 499 487 | 500 < 0.0007 8 6 5 3 7 | 5 | 3 4 7 8 8 > 0.9993 || = 0.47 486 528 470 463 479 | 500 < 0.0008 7 2 3 7 2 | 5 | 7 5 5 6 4 > 0.9992 || = 0.46 498 493 490 508 457 | 500 < 0.0009 6 6 5 3 5 | 5 | 5 7 8 3 5 > 0.9991 || = 0.45 474 499 457 496 476 | 500 < 0.001 5 0 3 6 8 | 5 | 3 6 5 6 4 > 0.999 || = 0.44 487 498 502 479 501 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 491 491 457 475 550 | 500 < 0.001 59 49 50 57 51 | 50 | 53 46 54 57 42 > 0.999 || = 0.42 514 509 535 543 508 | 500 < 0.002 50 55 43 45 45 | 50 | 52 63 55 61 54 > 0.998 || = 0.41 491 513 499 480 519 | 500 < 0.003 40 54 56 50 51 | 50 | 61 34 49 50 39 > 0.997 || = 0.40 480 474 470 531 494 | 500 < 0.004 58 53 50 51 56 | 50 | 62 39 51 45 47 > 0.996 || = 0.39 521 484 516 468 533 | 500 < 0.005 55 54 47 57 54 | 50 | 46 44 55 41 61 > 0.995 || = 0.38 504 487 520 520 468 | 500 < 0.006 51 58 59 53 53 | 50 | 58 51 40 44 55 > 0.994 || = 0.37 506 496 477 524 471 | 500 < 0.007 47 60 54 44 36 | 50 | 51 58 48 50 43 > 0.993 || = 0.36 504 507 516 536 447 | 500 < 0.008 36 53 59 52 46 | 50 | 48 35 50 54 46 > 0.992 || = 0.35 503 473 467 476 514 | 500 < 0.009 54 51 51 64 42 | 50 | 38 61 47 36 54 > 0.991 || = 0.34 485 506 515 498 481 | 500 < 0.01 45 57 48 57 56 | 50 | 70 37 48 56 46 > 0.99 || = 0.33 477 490 494 518 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 502 478 508 471 501 | 500 < 0.01 495 544 517 530 490 | 497.5 | 539 468 497 494 487 > 0.99 || = 0.31 515 538 488 486 500 | 500 = 0.01 262 256 251 261 249 | 252.5 | 235 292 254 255 238 = 0.99 || = 0.30 491 488 521 493 487 | 500 = 0.02 529 524 528 455 534 | 500 | 509 481 486 500 479 = 0.98 || = 0.29 508 490 500 506 476 | 500 =================================================================| 500 | 522 482 513 523 500 = 0.97 || = 0.28 549 520 487 486 517 | 500 svaria_WeightDistrib test: | 500 | 482 487 523 512 525 = 0.96 || = 0.27 490 472 478 498 496 | 500 ----------------------------------------------- | 500 | 449 522 491 464 510 = 0.95 || = 0.26 492 529 496 517 492 | 500 N = 1, n = 20000000, r = 0, k = 256, Alpha = 0, Beta = 0.0625 | 500 | 517 483 481 499 463 = 0.94 || = 0.25 518 509 463 447 492 | 500 | 500 | 516 489 511 537 503 = 0.93 || = 0.24 474 537 486 475 490 | 500 | 500 | 541 520 499 455 510 = 0.92 || = 0.23 513 500 507 489 503 | 500 =================================================================| 500 | 480 435 500 513 499 = 0.91 || = 0.22 537 481 552 521 477 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 480 499 496 518 494 = 0.90 || = 0.21 531 510 496 529 457 | 500 -----------------------------------------------------------------| 500 | 500 479 501 501 512 = 0.89 || = 0.20 496 536 494 509 481 | 500 SD Bern.: d 1.01010 1.01736 1.34751 | 500 | 470 466 503 533 512 = 0.88 || = 0.19 509 495 504 502 497 | 500 s 1.02881 0.76195 1.53568 | 500 | 511 523 506 492 500 = 0.87 || = 0.18 466 484 496 491 516 | 500 t 0.96189 0.74468 0.60857 | 500 | 489 522 482 506 518 = 0.86 || = 0.17 525 490 490 519 506 | 500 m 1.05344 0.91477 1.05882 | 500 | 483 520 484 522 503 = 0.85 || = 0.16 537 530 497 517 510 | 500 x 1.03535 0.89486 0.95230 | 500 | 472 484 481 513 492 = 0.84 || = 0.15 537 533 475 477 523 | 500 | 500 | 473 511 488 530 490 = 0.83 || = 0.14 523 482 532 489 505 | 500 Changes: d 47 5 4 | 500 | 512 446 473 515 482 = 0.82 || = 0.13 483 483 511 494 476 | 500 s 51 1 6 | 500 | 510 503 494 472 495 = 0.81 || = 0.12 475 475 494 504 493 | 500 t 43 4 3 | 500 | 495 478 484 497 512 = 0.80 || = 0.11 489 517 488 494 509 | 500 m 51 4 4 | 500 | 510 516 519 513 497 = 0.79 || = 0.10 515 502 466 491 572 | 500 x 50 4 6 | 500 | 483 463 513 531 557 = 0.78 || = 0.09 499 478 504 450 500 | 500 -----------------------------------------------------------------| 500 | 475 494 526 511 511 = 0.77 || = 0.08 510 501 511 464 528 | 500 Aver./ d 0.49751 502 > 500: 7 6 6 7 1 6 6 4 3 6 | 500 | 512 541 522 552 466 = 0.76 || = 0.07 511 488 559 489 471 | 500 median s 0.49834 498 ----- 6 4 6 3 3 5 7 4 5 3 | 500 | 464 497 509 481 505 = 0.75 || = 0.06 530 481 517 479 495 | 500 t 0.49933 499 9 3 2 6 2 4 7 7 3 4 | 500 | 510 501 499 487 506 = 0.74 || = 0.05 516 525 503 481 453 | 500 m 0.50294 500 3 4 5 4 3 7 6 5 8 5 | 500 | 490 523 469 519 463 = 0.73 || = 0.04 482 509 514 502 488 | 500 x 0.50110 498 2 7 2 3 5 5 7 6 4 4 | 500 | 467 470 507 500 554 = 0.72 || = 0.03 516 488 505 497 481 | 500 -----------------------------------------------------------------| 500 | 511 498 525 487 476 = 0.71 || = 0.02 529 524 528 455 534 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 483 494 563 513 497 = 0.70 || = 0.01 262 256 251 261 249 | 252.5 d 0 1 1 15 71 11 2 0 0 | 500 | 505 488 509 490 530 = 0.69 || < 0.01 495 544 517 530 490 | 497.5 s 0 0 2 11 68 18 2 0 0 | 500 | 512 531 523 517 484 = 0.68 ||========================================================================= t 0 0 0 16 70 12 3 0 0 | 500 | 503 509 515 475 534 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 5 14 65 15 2 0 0 | 500 | 502 506 475 481 545 = 0.66 ||========================================================================= x 0 0 2 14 70 10 4 1 0 | 500 | 537 524 480 530 521 = 0.65 || svaria_WeightDistrib test: no 122 test no 123 TestU01 250000 runs BigCrush Test smarsa_S svaria_WeightDistrib test: test no 123 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 0 | 0.5 | 2 1 0 0 0 > 0.99999 || = 0.64 503 495 481 482 504 | 500 < 0.00002 1 0 0 0 2 | 0.5 | 0 1 1 1 0 > 0.99998 || = 0.63 480 556 504 495 497 | 500 < 0.00003 1 1 1 0 0 | 0.5 | 1 0 1 1 0 > 0.99997 || = 0.62 534 527 505 509 453 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 507 469 499 519 512 | 500 < 0.00005 0 0 1 0 1 | 0.5 | 0 1 2 1 0 > 0.99995 || = 0.60 477 503 508 515 485 | 500 < 0.00006 0 0 1 1 2 | 0.5 | 0 0 1 1 1 > 0.99994 || = 0.59 478 513 533 474 463 | 500 < 0.00007 0 1 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 480 504 499 486 482 | 500 < 0.00008 1 1 1 1 0 | 0.5 | 0 1 0 0 2 > 0.99992 || = 0.57 506 512 534 515 481 | 500 < 0.00009 1 0 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99991 || = 0.56 514 484 504 525 473 | 500 < 0.0001 2 0 1 1 1 | 0.5 | 0 0 0 2 1 > 0.9999 || = 0.55 536 493 503 499 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 480 524 456 496 490 | 500 < 0.0001 6 3 6 3 6 | 5 | 4 4 6 7 5 > 0.9999 || = 0.53 480 508 500 518 505 | 500 < 0.0002 7 5 7 8 6 | 5 | 6 2 0 2 1 > 0.9998 || = 0.52 510 530 509 484 488 | 500 < 0.0003 4 5 5 7 5 | 5 | 6 3 5 4 9 > 0.9997 || = 0.51 514 488 503 520 512 | 500 < 0.0004 4 2 7 6 7 | 5 | 7 3 9 1 5 > 0.9996 || = 0.50 526 484 508 486 514 | 500 < 0.0005 6 2 5 4 5 | 5 | 5 4 3 8 5 > 0.9995 || = 0.49 476 514 426 517 482 | 500 < 0.0006 4 4 6 6 2 | 5 | 6 7 1 4 5 > 0.9994 || = 0.48 490 551 456 492 533 | 500 < 0.0007 7 5 6 6 4 | 5 | 7 8 3 3 4 > 0.9993 || = 0.47 519 508 501 526 498 | 500 < 0.0008 7 3 7 3 7 | 5 | 3 6 4 3 6 > 0.9992 || = 0.46 493 512 489 465 494 | 500 < 0.0009 3 4 6 6 4 | 5 | 2 1 6 3 2 > 0.9991 || = 0.45 471 483 548 520 481 | 500 < 0.001 6 8 5 6 7 | 5 | 1 4 4 3 5 > 0.999 || = 0.44 500 532 515 475 536 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 485 537 490 502 535 | 500 < 0.001 54 41 60 55 53 | 50 | 47 42 41 38 47 > 0.999 || = 0.42 463 551 508 481 472 | 500 < 0.002 53 46 49 47 53 | 50 | 44 62 62 49 58 > 0.998 || = 0.41 482 470 501 510 517 | 500 < 0.003 63 46 49 53 58 | 50 | 52 58 55 60 50 > 0.997 || = 0.40 487 529 526 502 514 | 500 < 0.004 46 49 48 58 43 | 50 | 43 45 38 50 45 > 0.996 || = 0.39 490 496 524 517 512 | 500 < 0.005 48 43 37 47 52 | 50 | 44 46 45 54 53 > 0.995 || = 0.38 506 496 479 524 493 | 500 < 0.006 58 45 47 55 57 | 50 | 51 47 52 52 46 > 0.994 || = 0.37 500 497 559 486 503 | 500 < 0.007 45 45 52 50 52 | 50 | 52 45 44 45 45 > 0.993 || = 0.36 503 520 488 547 460 | 500 < 0.008 39 45 44 46 47 | 50 | 53 55 51 58 54 > 0.992 || = 0.35 541 512 455 502 520 | 500 < 0.009 44 49 47 53 59 | 50 | 60 57 51 58 52 > 0.991 || = 0.34 516 477 481 527 551 | 500 < 0.01 51 54 56 55 48 | 50 | 46 42 48 61 49 > 0.99 || = 0.33 501 509 512 464 473 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 506 488 468 497 475 | 500 < 0.01 501 463 489 519 522 | 497.5 | 492 499 487 525 499 > 0.99 || = 0.31 477 498 537 534 454 | 500 = 0.01 236 243 241 272 268 | 252.5 | 252 263 255 236 268 = 0.99 || = 0.30 474 492 509 500 487 | 500 = 0.02 482 503 499 462 512 | 500 | 498 495 512 467 492 = 0.98 || = 0.29 474 487 479 496 502 | 500 =================================================================| 500 | 498 527 485 506 533 = 0.97 || = 0.28 469 488 498 494 500 | 500 svaria_WeightDistrib test: | 500 | 538 462 492 528 472 = 0.96 || = 0.27 533 521 526 513 486 | 500 ----------------------------------------------- | 500 | 509 496 483 525 487 = 0.95 || = 0.26 489 480 506 540 516 | 500 N = 1, n = 20000000, r = 10, k = 256, Alpha = 0, Beta = 0.0625 | 500 | 489 508 505 519 481 = 0.94 || = 0.25 475 483 491 515 445 | 500 | 500 | 548 493 480 505 479 = 0.93 || = 0.24 500 470 509 499 444 | 500 | 500 | 507 489 486 530 506 = 0.92 || = 0.23 512 484 552 456 494 | 500 =================================================================| 500 | 496 535 469 530 512 = 0.91 || = 0.22 459 480 487 499 498 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 506 496 505 503 481 = 0.90 || = 0.21 486 483 483 507 522 | 500 -----------------------------------------------------------------| 500 | 506 473 518 484 506 = 0.89 || = 0.20 494 462 513 488 525 | 500 SD Bern.: d 0.89779 0.96068 0.72698 | 500 | 492 478 477 505 505 = 0.88 || = 0.19 494 488 531 492 536 | 500 s 0.94491 0.71449 0.98536 | 500 | 487 562 522 513 485 = 0.87 || = 0.18 531 472 495 442 530 | 500 t 1.06575 0.85949 0.96483 | 500 | 480 489 503 502 501 = 0.86 || = 0.17 500 514 527 478 473 | 500 m 0.98171 0.61836 1.03877 | 500 | 498 504 511 484 522 = 0.85 || = 0.16 493 495 518 488 524 | 500 x 1.06632 0.75136 0.58165 | 500 | 507 506 506 452 522 = 0.84 || = 0.15 470 488 484 537 494 | 500 | 500 | 492 455 497 511 549 = 0.83 || = 0.14 479 507 487 504 529 | 500 Changes: d 43 4 4 | 500 | 489 533 535 497 480 = 0.82 || = 0.13 511 521 510 512 515 | 500 s 49 1 4 | 500 | 514 510 484 492 495 = 0.81 || = 0.12 521 496 504 512 492 | 500 t 50 4 6 | 500 | 473 518 481 517 488 = 0.80 || = 0.11 530 512 458 451 547 | 500 m 48 6 5 | 500 | 505 479 520 520 481 = 0.79 || = 0.10 512 499 495 499 505 | 500 x 50 5 6 | 500 | 529 487 519 486 513 = 0.78 || = 0.09 510 475 482 497 456 | 500 -----------------------------------------------------------------| 500 | 509 503 515 467 509 = 0.77 || = 0.08 525 475 552 513 519 | 500 Aver./ d 0.50184 500 > 500: 5 5 2 6 1 5 7 7 4 4 | 500 | 486 497 456 472 508 = 0.76 || = 0.07 469 510 536 443 483 | 500 median s 0.50185 496 ----- 3 4 1 3 8 7 4 4 5 5 | 500 | 517 515 520 510 470 = 0.75 || = 0.06 502 526 485 463 535 | 500 t 0.49937 501 3 5 5 5 6 7 2 7 7 3 | 500 | 516 516 528 510 493 = 0.74 || = 0.05 513 498 461 517 538 | 500 m 0.50120 502 5 4 4 6 6 5 5 6 5 8 | 500 | 551 492 489 469 509 = 0.73 || = 0.04 500 480 496 518 466 | 500 x 0.49855 501 7 7 4 4 5 2 5 6 6 5 | 500 | 493 493 528 504 542 = 0.72 || = 0.03 476 485 507 495 521 | 500 -----------------------------------------------------------------| 500 | 532 491 540 507 519 = 0.71 || = 0.02 482 503 499 462 512 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 485 486 479 511 472 = 0.70 || = 0.01 236 243 241 272 268 | 252.5 d 0 0 0 15 71 13 2 0 0 | 500 | 533 495 499 488 476 = 0.69 || < 0.01 501 463 489 519 522 | 497.5 s 0 0 1 11 75 10 4 0 0 | 500 | 501 483 480 495 504 = 0.68 ||========================================================================= t 0 1 1 10 72 13 4 0 0 | 500 | 530 517 469 505 502 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 12 71 13 1 0 0 | 500 | 484 491 484 503 485 = 0.66 ||========================================================================= x 0 0 4 13 68 13 3 0 0 | 500 | 507 514 462 490 519 = 0.65 || svaria_WeightDistrib test: no 123 test no 124 TestU01 250000 runs BigCrush Test smarsa_S svaria_WeightDistrib test: test no 124 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 0 | 0.5 | 2 1 0 0 1 > 0.99999 || = 0.64 522 512 505 509 477 | 500 < 0.00002 1 0 1 0 0 | 0.5 | 1 1 2 0 0 > 0.99998 || = 0.63 511 521 497 503 513 | 500 < 0.00003 2 0 0 2 0 | 0.5 | 0 1 1 0 1 > 0.99997 || = 0.62 536 489 504 495 506 | 500 < 0.00004 0 0 0 1 1 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 476 496 516 521 485 | 500 < 0.00005 0 1 0 1 0 | 0.5 | 1 1 1 0 0 > 0.99995 || = 0.60 437 522 512 504 465 | 500 < 0.00006 0 1 0 2 1 | 0.5 | 0 0 1 1 0 > 0.99994 || = 0.59 497 459 508 480 497 | 500 < 0.00007 1 0 0 0 2 | 0.5 | 0 0 3 1 0 > 0.99993 || = 0.58 458 488 470 456 519 | 500 < 0.00008 1 0 0 1 0 | 0.5 | 0 1 0 0 1 > 0.99992 || = 0.57 480 490 527 503 525 | 500 < 0.00009 0 0 0 2 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 556 486 538 462 507 | 500 < 0.0001 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 516 468 491 488 516 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 502 496 512 504 523 | 500 < 0.0001 6 3 1 10 5 | 5 | 4 5 9 2 3 > 0.9999 || = 0.53 522 486 541 466 464 | 500 < 0.0002 2 4 5 3 5 | 5 | 2 1 5 4 4 > 0.9998 || = 0.52 478 523 477 535 495 | 500 < 0.0003 6 3 3 4 7 | 5 | 4 7 4 4 7 > 0.9997 || = 0.51 503 508 517 503 514 | 500 < 0.0004 5 6 5 3 3 | 5 | 4 2 7 4 6 > 0.9996 || = 0.50 486 525 491 530 461 | 500 < 0.0005 4 5 6 3 5 | 5 | 4 1 6 8 9 > 0.9995 || = 0.49 559 514 495 529 502 | 500 < 0.0006 5 3 7 7 6 | 5 | 6 7 3 7 5 > 0.9994 || = 0.48 507 485 524 491 519 | 500 < 0.0007 7 4 9 6 6 | 5 | 3 3 4 11 9 > 0.9993 || = 0.47 490 506 535 477 499 | 500 < 0.0008 7 9 10 8 2 | 5 | 7 7 1 9 6 > 0.9992 || = 0.46 468 495 499 514 524 | 500 < 0.0009 3 8 7 4 10 | 5 | 6 6 6 9 1 > 0.9991 || = 0.45 507 514 501 472 479 | 500 < 0.001 5 7 2 7 5 | 5 | 2 4 3 5 4 > 0.999 || = 0.44 507 490 514 501 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 490 512 500 540 481 | 500 < 0.001 50 52 55 55 54 | 50 | 42 43 48 63 54 > 0.999 || = 0.42 478 492 490 512 507 | 500 < 0.002 54 47 64 40 42 | 50 | 51 45 37 50 51 > 0.998 || = 0.41 445 498 481 515 533 | 500 < 0.003 53 53 54 48 51 | 50 | 57 55 45 41 43 > 0.997 || = 0.40 494 503 465 483 472 | 500 < 0.004 44 49 43 44 45 | 50 | 48 67 50 47 45 > 0.996 || = 0.39 480 490 492 484 475 | 500 < 0.005 64 41 67 42 52 | 50 | 41 51 51 40 57 > 0.995 || = 0.38 506 458 503 514 511 | 500 < 0.006 47 53 57 46 42 | 50 | 54 58 43 34 46 > 0.994 || = 0.37 444 505 437 510 460 | 500 < 0.007 48 50 54 37 53 | 50 | 57 45 47 63 56 > 0.993 || = 0.36 534 494 508 513 506 | 500 < 0.008 53 56 58 44 49 | 50 | 55 54 50 59 46 > 0.992 || = 0.35 468 481 488 468 474 | 500 < 0.009 53 54 53 43 45 | 50 | 39 40 43 54 52 > 0.991 || = 0.34 504 475 515 485 474 | 500 < 0.01 53 52 48 61 46 | 50 | 43 43 55 56 47 > 0.99 || = 0.33 490 467 484 513 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 479 511 508 499 546 | 500 < 0.01 519 507 553 460 479 | 497.5 | 487 501 469 507 497 > 0.99 || = 0.31 467 496 514 520 468 | 500 = 0.01 269 265 257 234 247 | 252.5 | 254 247 258 245 270 = 0.99 || = 0.30 490 521 498 519 507 | 500 = 0.02 497 475 456 430 508 | 500 | 494 494 502 507 493 = 0.98 || = 0.29 496 507 524 507 500 | 500 =================================================================| 500 | 515 526 492 522 475 = 0.97 || = 0.28 497 472 506 490 519 | 500 svaria_WeightDistrib test: | 500 | 562 493 502 498 533 = 0.96 || = 0.27 507 506 478 532 476 | 500 ----------------------------------------------- | 500 | 462 523 537 536 505 = 0.95 || = 0.26 502 496 530 454 470 | 500 N = 1, n = 20000000, r = 26, k = 256, Alpha = 0, Beta = 0.0625 | 500 | 501 477 527 500 519 = 0.94 || = 0.25 508 523 478 498 532 | 500 | 500 | 528 506 517 514 495 = 0.93 || = 0.24 511 469 538 525 516 | 500 | 500 | 502 496 473 486 505 = 0.92 || = 0.23 451 495 496 494 526 | 500 =================================================================| 500 | 476 530 493 529 523 = 0.91 || = 0.22 500 498 485 514 471 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 527 489 500 469 515 = 0.90 || = 0.21 516 523 505 539 527 | 500 -----------------------------------------------------------------| 500 | 482 470 468 471 499 = 0.89 || = 0.20 501 478 498 480 502 | 500 SD Bern.: d 1.18094 0.77109 0.95859 | 500 | 457 498 514 512 490 = 0.88 || = 0.19 574 467 515 509 522 | 500 s 0.99169 0.58166 1.13457 | 500 | 450 499 520 503 553 = 0.87 || = 0.18 532 488 487 516 516 | 500 t 1.06699 1.19809 0.81403 | 500 | 518 544 482 500 536 = 0.86 || = 0.17 544 487 485 501 487 | 500 m 1.04101 1.11410 1.35492 | 500 | 522 546 540 527 516 = 0.85 || = 0.16 492 487 488 523 486 | 500 x 0.93718 0.67114 0.66515 | 500 | 504 494 466 497 487 = 0.84 || = 0.15 501 487 484 509 527 | 500 | 500 | 515 571 493 506 518 = 0.83 || = 0.14 526 524 469 437 524 | 500 Changes: d 45 5 4 | 500 | 514 487 551 455 491 = 0.82 || = 0.13 491 464 509 470 493 | 500 s 58 6 4 | 500 | 524 480 526 520 472 = 0.81 || = 0.12 459 502 446 503 496 | 500 t 59 3 3 | 500 | 492 502 463 518 490 = 0.80 || = 0.11 516 533 498 544 483 | 500 m 57 2 2 | 500 | 535 490 484 490 508 = 0.79 || = 0.10 510 470 502 487 504 | 500 x 56 7 7 | 500 | 486 498 498 524 489 = 0.78 || = 0.09 495 509 499 501 501 | 500 -----------------------------------------------------------------| 500 | 509 527 524 507 474 = 0.77 || = 0.08 542 495 479 521 487 | 500 Aver./ d 0.49991 501 > 500: 4 7 6 3 4 5 6 5 7 6 | 500 | 504 532 477 517 529 = 0.76 || = 0.07 522 498 502 460 478 | 500 median s 0.50172 496 ----- 6 3 4 3 5 3 4 5 3 5 | 500 | 485 541 571 512 506 = 0.75 || = 0.06 500 548 487 520 511 | 500 t 0.50221 499 3 3 5 5 4 7 6 4 5 6 | 500 | 474 485 496 443 479 = 0.74 || = 0.05 489 508 492 512 490 | 500 m 0.50166 503 5 7 5 6 6 5 6 7 5 6 | 500 | 533 487 542 501 480 = 0.73 || = 0.04 445 484 475 504 488 | 500 x 0.50109 500 3 5 6 5 6 6 4 4 5 6 | 500 | 483 531 470 502 504 = 0.72 || = 0.03 498 517 477 469 491 | 500 -----------------------------------------------------------------| 500 | 523 496 512 493 466 = 0.71 || = 0.02 497 475 456 430 508 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 519 476 485 487 516 = 0.70 || = 0.01 269 265 257 234 247 | 252.5 d 0 0 6 11 67 13 3 1 0 | 500 | 507 490 471 499 482 = 0.69 || < 0.01 519 507 553 460 479 | 497.5 s 0 0 0 16 66 15 3 1 0 | 500 | 502 468 515 523 540 = 0.68 ||========================================================================= t 0 0 2 16 65 15 2 1 0 | 500 | 476 524 505 516 484 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 4 13 69 14 0 0 0 | 500 | 500 469 472 496 490 = 0.66 ||========================================================================= x 0 0 0 17 67 15 2 0 0 | 500 | 481 555 530 507 481 = 0.65 || svaria_WeightDistrib test: no 124 test no 125 TestU01 250000 runs BigCrush Test smarsa_S svaria_SumCollector test: test no 125 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 0 1 | 0.5 | 0 0 1 0 2 > 0.99999 || = 0.64 504 491 491 472 502 | 500 < 0.00002 2 1 0 2 3 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 529 495 482 503 531 | 500 < 0.00003 0 0 0 2 0 | 0.5 | 1 0 1 1 1 > 0.99997 || = 0.62 524 538 464 470 502 | 500 < 0.00004 0 0 0 3 3 | 0.5 | 1 2 2 1 0 > 0.99996 || = 0.61 543 498 496 516 484 | 500 < 0.00005 0 0 0 3 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 494 520 513 503 450 | 500 < 0.00006 2 0 0 1 0 | 0.5 | 1 1 0 0 1 > 0.99994 || = 0.59 520 468 507 462 475 | 500 < 0.00007 0 1 1 1 2 | 0.5 | 0 2 1 0 0 > 0.99993 || = 0.58 492 493 461 521 517 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 3 1 0 1 1 > 0.99992 || = 0.57 519 513 472 494 491 | 500 < 0.00009 1 1 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 514 517 510 502 470 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 0 0 1 3 0 > 0.9999 || = 0.55 546 485 480 507 498 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 509 471 511 512 475 | 500 < 0.0001 6 4 1 13 9 | 5 | 6 6 6 7 6 > 0.9999 || = 0.53 527 497 483 472 496 | 500 < 0.0002 11 5 0 3 6 | 5 | 4 2 1 0 0 > 0.9998 || = 0.52 491 501 516 525 529 | 500 < 0.0003 5 4 9 9 9 | 5 | 4 13 3 7 5 > 0.9997 || = 0.51 496 528 489 486 504 | 500 < 0.0004 8 5 3 3 3 | 5 | 5 1 6 7 8 > 0.9996 || = 0.50 449 529 480 491 502 | 500 < 0.0005 4 6 3 1 6 | 5 | 2 6 5 5 5 > 0.9995 || = 0.49 507 550 449 495 480 | 500 < 0.0006 3 7 6 4 4 | 5 | 4 6 8 2 3 > 0.9994 || = 0.48 520 491 507 526 485 | 500 < 0.0007 9 4 7 1 3 | 5 | 7 5 7 2 5 > 0.9993 || = 0.47 483 459 490 514 528 | 500 < 0.0008 7 4 6 6 5 | 5 | 9 4 3 4 11 > 0.9992 || = 0.46 484 502 530 499 466 | 500 < 0.0009 4 6 5 3 7 | 5 | 8 8 5 2 6 > 0.9991 || = 0.45 474 507 468 502 508 | 500 < 0.001 5 8 4 3 5 | 5 | 6 6 7 10 5 > 0.999 || = 0.44 502 523 472 475 519 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 498 473 514 526 500 | 500 < 0.001 62 53 44 46 57 | 50 | 55 57 51 46 54 > 0.999 || = 0.42 505 497 513 495 449 | 500 < 0.002 42 48 51 52 54 | 50 | 54 50 49 49 52 > 0.998 || = 0.41 482 468 497 503 508 | 500 < 0.003 50 40 55 40 47 | 50 | 40 71 54 45 34 > 0.997 || = 0.40 490 483 447 487 539 | 500 < 0.004 51 47 48 53 53 | 50 | 43 48 42 38 47 > 0.996 || = 0.39 542 470 468 505 504 | 500 < 0.005 46 50 54 42 57 | 50 | 42 48 47 41 57 > 0.995 || = 0.38 459 516 512 451 487 | 500 < 0.006 51 54 44 46 49 | 50 | 49 53 43 48 42 > 0.994 || = 0.37 506 511 490 510 499 | 500 < 0.007 53 58 57 56 47 | 50 | 60 48 51 41 49 > 0.993 || = 0.36 490 476 511 508 501 | 500 < 0.008 57 44 59 46 56 | 50 | 50 41 57 50 52 > 0.992 || = 0.35 479 514 489 549 527 | 500 < 0.009 61 52 49 33 52 | 50 | 50 50 59 61 55 > 0.991 || = 0.34 541 495 496 495 501 | 500 < 0.01 70 45 46 47 51 | 50 | 53 47 58 33 73 > 0.99 || = 0.33 496 511 487 488 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 485 520 479 514 449 | 500 < 0.01 543 491 507 461 523 | 497.5 | 496 513 511 452 515 > 0.99 || = 0.31 512 517 538 507 476 | 500 = 0.01 243 254 273 224 268 | 252.5 | 232 270 279 282 265 = 0.99 || = 0.30 483 519 488 504 530 | 500 = 0.02 508 470 498 472 465 | 500 | 501 488 544 484 462 = 0.98 || = 0.29 477 511 476 460 502 | 500 =================================================================| 500 | 525 517 485 494 487 = 0.97 || = 0.28 504 483 479 477 493 | 500 svaria_SumCollector test: | 500 | 519 483 510 503 559 = 0.96 || = 0.27 476 523 493 508 470 | 500 ----------------------------------------------- | 500 | 523 499 495 511 475 = 0.95 || = 0.26 516 465 509 505 496 | 500 N = 1, n = 500000000, r = 0, g = 10 | 500 | 511 495 503 529 540 = 0.94 || = 0.25 464 489 473 501 482 | 500 | 500 | 492 479 519 501 462 = 0.93 || = 0.24 497 464 495 474 540 | 500 | 500 | 474 514 483 485 441 = 0.92 || = 0.23 497 471 507 483 513 | 500 =================================================================| 500 | 488 486 491 504 497 = 0.91 || = 0.22 505 473 490 478 526 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 477 514 523 505 488 = 0.90 || = 0.21 499 500 505 533 551 | 500 -----------------------------------------------------------------| 500 | 517 517 487 498 515 = 0.89 || = 0.20 526 480 494 518 507 | 500 SD Bern.: d 1.04620 1.26948 0.85364 | 500 | 485 529 550 477 492 = 0.88 || = 0.19 505 469 523 491 483 | 500 s 0.94332 0.73110 1.09690 | 500 | 467 500 507 503 504 = 0.87 || = 0.18 522 506 513 496 516 | 500 t 0.96889 0.72836 0.81893 | 500 | 519 521 498 508 490 = 0.86 || = 0.17 503 514 519 502 466 | 500 m 0.96207 1.05787 1.23511 | 500 | 524 507 481 513 504 = 0.85 || = 0.16 488 510 502 507 511 | 500 x 1.08376 0.60527 1.38415 | 500 | 474 525 500 456 532 = 0.84 || = 0.15 517 505 502 543 505 | 500 | 500 | 486 509 492 516 525 = 0.83 || = 0.14 469 500 508 547 500 | 500 Changes: d 53 4 4 | 500 | 466 506 506 530 480 = 0.82 || = 0.13 470 509 497 496 475 | 500 s 45 5 5 | 500 | 450 495 484 531 492 = 0.81 || = 0.12 486 468 521 527 496 | 500 t 54 6 4 | 500 | 488 508 504 508 487 = 0.80 || = 0.11 557 487 485 513 535 | 500 m 52 6 2 | 500 | 504 538 510 516 510 = 0.79 || = 0.10 486 504 468 497 504 | 500 x 44 4 4 | 500 | 473 479 475 501 506 = 0.78 || = 0.09 528 508 520 527 520 | 500 -----------------------------------------------------------------| 500 | 517 473 493 506 544 = 0.77 || = 0.08 509 549 508 472 502 | 500 Aver./ d 0.49820 498 > 500: 6 5 4 4 4 6 7 4 3 5 | 500 | 496 528 527 511 511 = 0.76 || = 0.07 520 516 477 531 490 | 500 median s 0.50081 500 ----- 7 6 2 7 4 5 2 4 8 4 | 500 | 516 497 534 493 536 = 0.75 || = 0.06 493 500 473 527 489 | 500 t 0.50172 499 5 7 3 3 4 5 3 8 4 6 | 500 | 514 470 511 471 461 = 0.74 || = 0.05 500 526 492 512 462 | 500 m 0.49935 503 5 6 5 7 5 6 4 7 7 6 | 500 | 494 456 543 487 521 = 0.73 || = 0.04 554 509 531 506 486 | 500 x 0.49997 501 5 5 6 5 5 3 5 8 5 4 | 500 | 469 490 501 517 517 = 0.72 || = 0.03 495 508 499 499 522 | 500 -----------------------------------------------------------------| 500 | 496 540 524 503 513 = 0.71 || = 0.02 508 470 498 472 465 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 523 472 533 464 497 = 0.70 || = 0.01 243 254 273 224 268 | 252.5 d 0 0 3 17 64 13 4 0 0 | 500 | 467 497 498 480 531 = 0.69 || < 0.01 543 491 507 461 523 | 497.5 s 0 0 0 19 67 13 2 0 0 | 500 | 470 475 520 517 515 = 0.68 ||========================================================================= t 0 0 2 13 71 13 2 0 0 | 500 | 451 492 500 500 486 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 17 67 13 2 0 0 | 500 | 509 483 477 463 466 = 0.66 ||========================================================================= x 0 0 4 15 64 16 2 0 0 | 500 | 535 527 565 505 494 = 0.65 || svaria_SumCollector test: no 125 test no 126 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 126 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 0 0 | 0.5 | 0 0 0 1 1 > 0.99999 || = 0.64 482 471 511 533 525 | 500 < 0.00002 1 0 1 0 1 | 0.5 | 0 0 2 0 0 > 0.99998 || = 0.63 512 500 537 474 500 | 500 < 0.00003 2 1 1 2 1 | 0.5 | 0 1 1 0 1 > 0.99997 || = 0.62 461 508 538 473 502 | 500 < 0.00004 1 0 3 0 1 | 0.5 | 2 1 0 0 0 > 0.99996 || = 0.61 525 514 506 487 464 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 1 0 0 1 1 > 0.99995 || = 0.60 512 522 516 491 475 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 2 0 > 0.99994 || = 0.59 527 476 469 498 514 | 500 < 0.00007 2 0 0 1 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 541 506 467 455 519 | 500 < 0.00008 1 0 1 0 0 | 0.5 | 0 1 0 1 0 > 0.99992 || = 0.57 492 514 529 511 500 | 500 < 0.00009 0 0 1 0 0 | 0.5 | 1 1 1 0 0 > 0.99991 || = 0.56 493 497 487 500 505 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 1 1 > 0.9999 || = 0.55 562 481 519 476 465 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 486 494 552 480 471 | 500 < 0.0001 8 1 7 3 3 | 5 | 4 4 4 7 4 > 0.9999 || = 0.53 479 535 511 509 498 | 500 < 0.0002 4 1 2 5 3 | 5 | 1 3 2 6 3 > 0.9998 || = 0.52 480 496 509 480 514 | 500 < 0.0003 2 4 8 5 3 | 5 | 4 8 7 7 8 > 0.9997 || = 0.51 497 466 474 521 512 | 500 < 0.0004 5 8 3 9 6 | 5 | 3 8 5 5 6 > 0.9996 || = 0.50 529 508 514 519 505 | 500 < 0.0005 4 9 5 7 5 | 5 | 4 6 9 4 3 > 0.9995 || = 0.49 491 529 501 496 492 | 500 < 0.0006 6 4 3 3 6 | 5 | 5 2 8 7 4 > 0.9994 || = 0.48 468 472 521 489 484 | 500 < 0.0007 8 6 3 7 4 | 5 | 8 3 3 3 4 > 0.9993 || = 0.47 506 522 466 515 499 | 500 < 0.0008 3 3 8 3 8 | 5 | 4 6 4 9 5 > 0.9992 || = 0.46 525 506 508 511 500 | 500 < 0.0009 6 3 5 4 9 | 5 | 4 4 7 5 5 > 0.9991 || = 0.45 509 488 489 496 470 | 500 < 0.001 3 2 4 5 1 | 5 | 2 5 3 6 1 > 0.999 || = 0.44 508 490 491 487 494 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 504 536 564 473 511 | 500 < 0.001 49 41 48 51 48 | 50 | 39 49 52 59 43 > 0.999 || = 0.42 490 527 487 453 498 | 500 < 0.002 49 52 42 44 49 | 50 | 49 44 57 48 51 > 0.998 || = 0.41 524 475 453 497 537 | 500 < 0.003 38 53 62 54 61 | 50 | 47 55 47 41 44 > 0.997 || = 0.40 499 512 484 495 472 | 500 < 0.004 50 51 43 66 44 | 50 | 53 50 42 51 43 > 0.996 || = 0.39 517 547 495 542 537 | 500 < 0.005 41 50 56 45 58 | 50 | 45 51 41 57 48 > 0.995 || = 0.38 514 510 509 496 519 | 500 < 0.006 40 50 54 62 54 | 50 | 64 62 52 55 54 > 0.994 || = 0.37 459 473 474 483 502 | 500 < 0.007 37 45 40 53 52 | 50 | 57 54 46 59 45 > 0.993 || = 0.36 451 509 506 510 500 | 500 < 0.008 42 66 58 49 47 | 50 | 47 42 60 47 54 > 0.992 || = 0.35 481 484 535 509 521 | 500 < 0.009 39 51 45 56 38 | 50 | 51 54 60 50 42 > 0.991 || = 0.34 515 511 505 512 466 | 500 < 0.01 55 44 62 54 56 | 50 | 53 42 43 49 50 > 0.99 || = 0.33 473 447 473 504 482 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 479 498 515 492 502 | 500 < 0.01 440 503 510 534 507 | 497.5 | 505 503 500 516 474 > 0.99 || = 0.31 502 474 486 507 468 | 500 = 0.01 273 258 252 245 278 | 252.5 | 295 260 263 288 283 = 0.99 || = 0.30 499 491 518 497 528 | 500 = 0.02 510 507 529 463 534 | 500 | 488 541 473 518 486 = 0.98 || = 0.29 471 498 498 516 461 | 500 =================================================================| 500 | 478 528 510 510 514 = 0.97 || = 0.28 507 480 499 466 491 | 500 smarsa_MatrixRank test: | 500 | 498 499 476 500 520 = 0.96 || = 0.27 498 488 481 499 501 | 500 ----------------------------------------------- | 500 | 479 494 530 539 513 = 0.95 || = 0.26 492 463 487 525 490 | 500 N = 10, n = 1000000, r = 0, s = 5, L = 30, k = 30 | 500 | 510 525 519 500 482 = 0.94 || = 0.25 486 523 525 496 499 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 470 503 489 502 480 = 0.93 || = 0.24 531 503 506 491 512 | 500 | 500 | 481 513 497 477 488 = 0.92 || = 0.23 497 468 504 490 539 | 500 =================================================================| 500 | 480 481 502 499 505 = 0.91 || = 0.22 509 504 502 500 512 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 490 505 507 512 510 = 0.90 || = 0.21 528 536 526 483 484 | 500 -----------------------------------------------------------------| 500 | 479 500 487 465 454 = 0.89 || = 0.20 532 488 503 500 524 | 500 SD Bern.: d 1.08309 1.18886 0.92673 | 500 | 480 462 460 515 497 = 0.88 || = 0.19 472 488 514 496 524 | 500 s 0.98032 0.90929 0.85715 | 500 | 472 451 547 514 490 = 0.87 || = 0.18 539 472 482 529 489 | 500 t 0.91491 1.13722 0.97618 | 500 | 457 535 487 509 467 = 0.86 || = 0.17 499 485 479 506 472 | 500 m 0.90123 1.03974 0.81525 | 500 | 487 526 530 477 541 = 0.85 || = 0.16 516 493 509 497 522 | 500 x 0.97116 0.93319 0.72146 | 500 | 474 490 481 468 479 = 0.84 || = 0.15 538 488 484 522 500 | 500 | 500 | 500 496 509 488 519 = 0.83 || = 0.14 504 481 501 523 466 | 500 Changes: d 45 1 5 | 500 | 526 499 497 516 482 = 0.82 || = 0.13 497 512 495 482 511 | 500 s 42 4 6 | 500 | 522 509 498 506 510 = 0.81 || = 0.12 498 461 505 520 531 | 500 t 52 7 5 | 500 | 511 529 494 491 488 = 0.80 || = 0.11 484 499 488 492 501 | 500 m 50 6 3 | 500 | 479 468 492 524 541 = 0.79 || = 0.10 486 511 483 525 457 | 500 x 53 5 6 | 500 | 514 478 522 482 488 = 0.78 || = 0.09 510 518 505 509 540 | 500 -----------------------------------------------------------------| 500 | 467 519 464 515 467 = 0.77 || = 0.08 547 520 468 496 519 | 500 Aver./ d 0.49740 499 > 500: 8 4 5 4 6 4 5 6 2 3 | 500 | 527 544 477 506 471 = 0.76 || = 0.07 513 542 490 532 513 | 500 median s 0.50082 503 ----- 9 2 4 4 6 4 5 5 4 7 | 500 | 515 488 479 492 505 = 0.75 || = 0.06 544 503 499 496 493 | 500 t 0.50051 498 3 4 6 6 4 6 6 2 4 6 | 500 | 535 503 498 534 504 = 0.74 || = 0.05 489 499 480 491 473 | 500 m 0.50020 499 3 6 2 6 2 3 4 4 6 6 | 500 | 519 533 496 479 512 = 0.73 || = 0.04 529 512 494 500 484 | 500 x 0.49870 501 7 5 5 6 2 5 5 6 4 5 | 500 | 454 487 496 486 508 = 0.72 || = 0.03 515 504 489 482 514 | 500 -----------------------------------------------------------------| 500 | 482 449 519 469 511 = 0.71 || = 0.02 510 507 529 463 534 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 498 505 520 528 517 = 0.70 || = 0.01 273 258 252 245 278 | 252.5 d 0 0 3 12 66 17 3 0 0 | 500 | 508 516 495 524 488 = 0.69 || < 0.01 440 503 510 534 507 | 497.5 s 0 0 3 13 69 15 1 0 0 | 500 | 497 504 492 534 527 = 0.68 ||========================================================================= t 0 0 1 12 76 9 3 0 0 | 500 | 502 484 515 472 504 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 12 72 14 1 0 0 | 500 | 511 494 486 480 500 = 0.66 ||========================================================================= x 0 0 1 17 68 15 0 0 0 | 500 | 464 483 487 488 483 = 0.65 || smarsa_MatrixRank test: no 126 test no 127 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 127 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 1 | 0.5 | 1 0 1 0 0 > 0.99999 || = 0.64 505 495 516 557 500 | 500 < 0.00002 0 2 0 0 0 | 0.5 | 2 2 1 0 0 > 0.99998 || = 0.63 477 525 463 471 492 | 500 < 0.00003 1 1 0 0 0 | 0.5 | 1 0 3 0 0 > 0.99997 || = 0.62 500 470 480 538 457 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 1 1 0 1 1 > 0.99996 || = 0.61 485 489 521 518 512 | 500 < 0.00005 0 2 0 0 0 | 0.5 | 0 2 0 1 0 > 0.99995 || = 0.60 435 525 495 535 495 | 500 < 0.00006 0 0 1 0 0 | 0.5 | 0 1 1 0 1 > 0.99994 || = 0.59 536 524 519 465 464 | 500 < 0.00007 0 0 1 3 0 | 0.5 | 0 0 1 0 1 > 0.99993 || = 0.58 476 546 513 512 521 | 500 < 0.00008 1 0 0 0 0 | 0.5 | 0 0 0 0 2 > 0.99992 || = 0.57 480 504 510 532 492 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 486 535 484 470 451 | 500 < 0.0001 0 0 0 1 0 | 0.5 | 4 0 2 1 0 > 0.9999 || = 0.55 491 504 506 552 540 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 475 488 527 496 492 | 500 < 0.0001 2 5 2 7 1 | 5 | 9 6 9 3 5 > 0.9999 || = 0.53 491 493 504 460 497 | 500 < 0.0002 4 5 7 6 10 | 5 | 2 5 4 3 5 > 0.9998 || = 0.52 503 527 482 456 499 | 500 < 0.0003 3 8 4 4 3 | 5 | 2 5 5 5 7 > 0.9997 || = 0.51 504 462 497 479 498 | 500 < 0.0004 4 3 5 4 1 | 5 | 6 7 4 5 3 > 0.9996 || = 0.50 469 479 524 530 461 | 500 < 0.0005 6 3 5 10 8 | 5 | 7 6 2 3 3 > 0.9995 || = 0.49 451 508 470 476 491 | 500 < 0.0006 7 13 5 5 6 | 5 | 6 4 5 7 9 > 0.9994 || = 0.48 531 481 463 495 511 | 500 < 0.0007 3 4 2 6 7 | 5 | 2 8 4 3 3 > 0.9993 || = 0.47 490 464 516 495 499 | 500 < 0.0008 3 1 6 5 6 | 5 | 5 5 5 7 3 > 0.9992 || = 0.46 457 473 502 483 502 | 500 < 0.0009 5 8 2 2 5 | 5 | 7 7 4 2 8 > 0.9991 || = 0.45 497 475 551 536 532 | 500 < 0.001 4 6 3 6 6 | 5 | 4 5 2 2 7 > 0.999 || = 0.44 475 498 475 542 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 499 489 533 499 499 | 500 < 0.001 41 56 41 55 53 | 50 | 50 58 44 40 53 > 0.999 || = 0.42 483 502 503 542 453 | 500 < 0.002 58 55 40 50 46 | 50 | 45 45 48 56 48 > 0.998 || = 0.41 509 506 520 473 508 | 500 < 0.003 59 49 41 53 50 | 50 | 55 60 53 56 49 > 0.997 || = 0.40 536 489 517 504 498 | 500 < 0.004 41 41 45 49 60 | 50 | 65 41 43 53 65 > 0.996 || = 0.39 506 464 458 523 508 | 500 < 0.005 58 58 45 48 56 | 50 | 46 59 63 42 54 > 0.995 || = 0.38 481 470 498 526 482 | 500 < 0.006 49 41 62 57 48 | 50 | 55 55 57 47 62 > 0.994 || = 0.37 521 494 508 516 489 | 500 < 0.007 42 42 66 52 61 | 50 | 39 58 48 51 55 > 0.993 || = 0.36 513 503 472 489 512 | 500 < 0.008 54 53 50 57 49 | 50 | 52 45 41 44 51 > 0.992 || = 0.35 503 464 503 471 528 | 500 < 0.009 38 53 40 48 33 | 50 | 63 66 61 43 43 > 0.991 || = 0.34 489 498 488 517 508 | 500 < 0.01 40 43 56 53 51 | 50 | 51 42 38 40 40 > 0.99 || = 0.33 473 468 496 511 478 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 471 505 492 521 468 | 500 < 0.01 480 491 486 522 507 | 497.5 | 521 529 496 472 520 > 0.99 || = 0.31 542 482 489 526 519 | 500 = 0.01 241 263 257 240 237 | 252.5 | 264 255 255 249 269 = 0.99 || = 0.30 481 524 460 471 527 | 500 = 0.02 541 513 485 474 507 | 500 | 526 490 484 464 505 = 0.98 || = 0.29 487 466 460 550 507 | 500 =================================================================| 500 | 560 516 515 535 464 = 0.97 || = 0.28 514 466 525 517 495 | 500 smarsa_MatrixRank test: | 500 | 511 482 493 468 512 = 0.96 || = 0.27 554 475 527 498 503 | 500 ----------------------------------------------- | 500 | 559 488 508 473 544 = 0.95 || = 0.26 487 527 539 489 503 | 500 N = 10, n = 1000000, r = 0, s = 5, L = 30, k = 30 | 500 | 449 495 469 504 464 = 0.94 || = 0.25 502 536 479 542 477 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 499 480 486 470 502 = 0.93 || = 0.24 501 475 531 496 495 | 500 | 500 | 486 516 514 480 517 = 0.92 || = 0.23 546 490 508 495 540 | 500 =================================================================| 500 | 469 503 533 513 470 = 0.91 || = 0.22 493 467 503 461 505 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 498 498 496 472 522 = 0.90 || = 0.21 486 541 479 494 506 | 500 -----------------------------------------------------------------| 500 | 579 492 517 535 520 = 0.89 || = 0.20 487 507 494 491 452 | 500 SD Bern.: d 1.15212 1.18041 1.10598 | 500 | 466 451 533 464 502 = 0.88 || = 0.19 508 502 486 512 510 | 500 s 1.05510 0.91587 1.25361 | 500 | 483 524 484 485 503 = 0.87 || = 0.18 515 488 475 485 500 | 500 t 0.96595 1.30295 1.15469 | 500 | 531 496 497 522 504 = 0.86 || = 0.17 499 507 493 481 500 | 500 m 1.15519 0.55524 0.93854 | 500 | 456 521 493 481 507 = 0.85 || = 0.16 525 553 528 435 502 | 500 x 0.99698 1.07477 1.07197 | 500 | 524 512 501 512 484 = 0.84 || = 0.15 536 524 504 491 448 | 500 | 500 | 495 452 503 528 519 = 0.83 || = 0.14 517 521 515 515 490 | 500 Changes: d 41 6 5 | 500 | 519 528 491 475 531 = 0.82 || = 0.13 484 567 492 535 516 | 500 s 45 5 7 | 500 | 481 516 483 508 496 = 0.81 || = 0.12 472 516 508 445 461 | 500 t 52 3 6 | 500 | 509 522 526 528 513 = 0.80 || = 0.11 481 496 496 528 522 | 500 m 55 6 4 | 500 | 501 538 480 502 515 = 0.79 || = 0.10 498 528 488 493 486 | 500 x 56 6 3 | 500 | 480 506 502 519 538 = 0.78 || = 0.09 515 481 464 492 499 | 500 -----------------------------------------------------------------| 500 | 488 469 509 490 516 = 0.77 || = 0.08 497 495 521 524 543 | 500 Aver./ d 0.50062 498 > 500: 4 5 5 5 3 3 4 5 4 6 | 500 | 494 535 505 518 512 = 0.76 || = 0.07 516 500 501 485 547 | 500 median s 0.49909 498 ----- 4 8 4 3 3 7 3 5 5 5 | 500 | 471 496 466 486 493 = 0.75 || = 0.06 495 494 554 480 475 | 500 t 0.49950 498 6 4 6 2 7 6 4 5 4 5 | 500 | 489 504 485 517 513 = 0.74 || = 0.05 479 492 518 517 512 | 500 m 0.49921 498 5 4 3 7 4 4 5 7 5 3 | 500 | 502 481 482 515 493 = 0.73 || = 0.04 494 530 475 515 511 | 500 x 0.50069 502 6 4 6 6 5 2 3 7 8 7 | 500 | 526 466 526 501 492 = 0.72 || = 0.03 507 518 548 507 497 | 500 -----------------------------------------------------------------| 500 | 534 499 461 472 516 = 0.71 || = 0.02 541 513 485 474 507 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 559 480 498 503 460 = 0.70 || = 0.01 241 263 257 240 237 | 252.5 d 0 0 3 13 66 13 5 1 0 | 500 | 506 527 534 487 527 = 0.69 || < 0.01 480 491 486 522 507 | 497.5 s 0 0 2 17 61 18 2 1 0 | 500 | 489 495 516 460 468 = 0.68 ||========================================================================= t 0 0 0 15 70 13 3 0 0 | 500 | 495 497 497 505 501 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 21 56 19 3 0 0 | 500 | 500 471 470 493 477 = 0.66 ||========================================================================= x 0 0 4 14 70 12 1 0 0 | 500 | 503 518 498 498 471 = 0.65 || smarsa_MatrixRank test: no 127 test no 128 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 128 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 475 483 475 457 494 | 500 < 0.00002 0 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 495 465 500 490 499 | 500 < 0.00003 0 0 0 0 1 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 488 501 464 492 509 | 500 < 0.00004 0 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 511 504 499 487 481 | 500 < 0.00005 0 0 1 0 0 | 0.5 | 0 1 0 0 0 > 0.99995 || = 0.60 488 497 539 546 517 | 500 < 0.00006 3 1 0 1 1 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 479 483 494 521 469 | 500 < 0.00007 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 491 497 481 469 501 | 500 < 0.00008 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 487 495 477 495 469 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 489 522 497 501 492 | 500 < 0.0001 1 0 0 1 0 | 0.5 | 0 1 0 0 0 > 0.9999 || = 0.55 518 499 518 513 537 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 474 490 539 433 496 | 500 < 0.0001 4 4 3 4 5 | 5 | 1 2 1 0 0 > 0.9999 || = 0.53 507 494 498 498 511 | 500 < 0.0002 3 9 6 5 4 | 5 | 1 1 0 1 0 > 0.9998 || = 0.52 549 498 517 516 499 | 500 < 0.0003 2 4 8 2 5 | 5 | 2 2 1 5 7 > 0.9997 || = 0.51 506 488 523 505 484 | 500 < 0.0004 3 6 4 2 5 | 5 | 4 5 2 4 2 > 0.9996 || = 0.50 494 510 531 469 503 | 500 < 0.0005 7 3 9 8 1 | 5 | 5 3 1 5 7 > 0.9995 || = 0.49 518 473 523 497 478 | 500 < 0.0006 6 6 4 4 4 | 5 | 0 3 4 3 2 > 0.9994 || = 0.48 481 539 489 500 497 | 500 < 0.0007 8 5 1 6 3 | 5 | 1 4 3 7 5 > 0.9993 || = 0.47 522 485 504 488 497 | 500 < 0.0008 6 4 7 5 7 | 5 | 6 2 3 4 1 > 0.9992 || = 0.46 518 479 511 513 493 | 500 < 0.0009 8 9 4 4 3 | 5 | 3 2 3 6 2 > 0.9991 || = 0.45 505 487 461 486 488 | 500 < 0.001 10 6 6 2 5 | 5 | 2 6 2 4 1 > 0.999 || = 0.44 476 490 495 496 481 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 517 485 483 503 502 | 500 < 0.001 57 56 52 42 42 | 50 | 25 30 20 39 27 > 0.999 || = 0.42 529 476 490 475 518 | 500 < 0.002 47 49 46 45 40 | 50 | 32 27 40 47 34 > 0.998 || = 0.41 483 489 484 456 494 | 500 < 0.003 45 51 47 56 55 | 50 | 36 50 42 43 43 > 0.997 || = 0.40 496 480 456 526 532 | 500 < 0.004 45 49 46 51 55 | 50 | 49 52 48 53 56 > 0.996 || = 0.39 507 482 486 508 481 | 500 < 0.005 46 59 53 59 59 | 50 | 59 48 43 48 34 > 0.995 || = 0.38 550 487 472 538 523 | 500 < 0.006 56 44 53 52 49 | 50 | 52 50 42 41 43 > 0.994 || = 0.37 483 463 510 507 521 | 500 < 0.007 56 50 63 73 50 | 50 | 49 48 47 36 54 > 0.993 || = 0.36 469 503 479 500 536 | 500 < 0.008 43 47 51 44 44 | 50 | 31 55 59 49 46 > 0.992 || = 0.35 505 485 487 478 482 | 500 < 0.009 53 52 42 63 58 | 50 | 62 65 55 57 61 > 0.991 || = 0.34 479 526 499 485 490 | 500 < 0.01 45 48 48 45 61 | 50 | 41 44 59 47 50 > 0.99 || = 0.33 469 520 516 509 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 495 513 497 499 402 | 500 < 0.01 493 505 501 530 513 | 497.5 | 436 469 455 460 448 > 0.99 || = 0.31 477 521 496 484 524 | 500 = 0.01 225 255 267 255 275 | 252.5 | 248 231 245 244 272 = 0.99 || = 0.30 517 525 484 526 484 | 500 = 0.02 531 498 475 469 507 | 500 | 505 535 534 515 520 = 0.98 || = 0.29 505 502 463 496 550 | 500 =================================================================| 500 | 498 553 495 503 513 = 0.97 || = 0.28 473 479 518 507 492 | 500 smarsa_MatrixRank test: | 500 | 504 497 486 523 520 = 0.96 || = 0.27 551 503 533 480 470 | 500 ----------------------------------------------- | 500 | 534 480 481 501 513 = 0.95 || = 0.26 511 496 500 494 504 | 500 N = 10, n = 1000000, r = 0, s = 5, L = 30, k = 30 | 500 | 506 505 512 520 516 = 0.94 || = 0.25 476 515 514 487 510 | 500 Anderson-Darling statistic = A2 | 500 | 491 515 521 512 495 = 0.93 || = 0.24 532 506 477 508 494 | 500 | 500 | 460 488 499 482 498 = 0.92 || = 0.23 489 458 516 531 509 | 500 =================================================================| 500 | 484 487 502 462 477 = 0.91 || = 0.22 500 528 489 555 535 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 470 494 512 489 486 = 0.90 || = 0.21 503 485 517 496 487 | 500 -----------------------------------------------------------------| 500 | 495 520 516 489 467 = 0.89 || = 0.20 472 467 481 521 475 | 500 SD Bern.: d 1.07434 0.74736 1.90777 | 500 | 500 503 486 497 509 = 0.88 || = 0.19 532 521 501 553 529 | 500 s 0.98515 0.58849 1.56730 | 500 | 495 510 482 500 493 = 0.87 || = 0.18 473 500 524 483 512 | 500 t 0.97049 0.77627 1.66034 | 500 | 490 499 497 472 483 = 0.86 || = 0.17 503 525 469 514 476 | 500 m 0.99714 1.39353 1.02812 | 500 | 500 515 514 529 523 = 0.85 || = 0.16 562 529 503 513 480 | 500 x 1.01494 1.01735 1.63053 | 500 | 521 498 511 513 503 = 0.84 || = 0.15 495 498 518 472 505 | 500 | 500 | 432 475 527 501 513 = 0.83 || = 0.14 487 517 529 470 527 | 500 Changes: d 50 5 4 | 500 | 499 452 518 502 491 = 0.82 || = 0.13 511 503 493 483 514 | 500 s 47 7 4 | 500 | 516 516 485 495 472 = 0.81 || = 0.12 486 487 531 494 498 | 500 t 49 3 1 | 500 | 485 505 469 515 459 = 0.80 || = 0.11 537 492 489 491 504 | 500 m 43 4 4 | 500 | 532 455 488 522 484 = 0.79 || = 0.10 467 515 529 492 503 | 500 x 49 3 6 | 500 | 498 530 525 531 528 = 0.78 || = 0.09 549 464 517 476 520 | 500 -----------------------------------------------------------------| 500 | 482 532 503 492 521 = 0.77 || = 0.08 525 524 503 506 511 | 500 Aver./ d 0.49740 499 > 500: 7 5 5 4 6 4 6 4 2 4 | 500 | 515 523 496 514 503 = 0.76 || = 0.07 516 504 513 501 535 | 500 median s 0.49863 499 ----- 8 6 5 6 1 1 6 5 5 4 | 500 | 501 464 513 538 470 = 0.75 || = 0.06 501 537 488 488 502 | 500 t 0.50026 499 6 7 5 2 3 5 4 5 6 4 | 500 | 529 506 512 513 493 = 0.74 || = 0.05 505 508 468 542 485 | 500 m 0.49952 500 6 3 5 5 3 6 4 7 4 6 | 500 | 460 472 443 482 529 = 0.73 || = 0.04 491 538 462 498 480 | 500 x 0.49816 501 8 7 5 5 3 4 3 5 4 6 | 500 | 497 492 537 491 511 = 0.72 || = 0.03 528 531 509 524 538 | 500 -----------------------------------------------------------------| 500 | 456 476 478 528 487 = 0.71 || = 0.02 531 498 475 469 507 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 497 504 492 511 489 = 0.70 || = 0.01 225 255 267 255 275 | 252.5 d 0 1 1 16 66 12 5 0 0 | 500 | 523 512 511 502 477 = 0.69 || < 0.01 493 505 501 530 513 | 497.5 s 0 0 2 14 68 15 2 0 0 | 500 | 519 556 480 467 469 = 0.68 ||========================================================================= t 0 0 1 14 70 15 1 0 0 | 500 | 530 488 520 458 533 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 0 14 70 13 3 0 0 | 500 | 507 543 547 525 482 = 0.66 ||========================================================================= x 1 0 1 12 69 17 1 0 0 | 500 | 509 476 537 507 523 = 0.65 || smarsa_MatrixRank test: no 128 test no 129 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 129 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 1 | 0.5 | 0 0 1 0 0 > 0.99999 || = 0.64 507 490 506 512 479 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99998 || = 0.63 489 508 505 493 481 | 500 < 0.00003 0 1 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99997 || = 0.62 491 479 515 524 480 | 500 < 0.00004 1 0 0 2 0 | 0.5 | 1 0 0 0 2 > 0.99996 || = 0.61 467 496 510 490 487 | 500 < 0.00005 0 2 0 1 0 | 0.5 | 0 0 0 1 2 > 0.99995 || = 0.60 499 522 479 472 472 | 500 < 0.00006 0 2 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 481 473 525 494 493 | 500 < 0.00007 0 2 0 0 1 | 0.5 | 1 0 0 1 0 > 0.99993 || = 0.58 503 499 515 485 531 | 500 < 0.00008 2 0 0 1 0 | 0.5 | 1 0 1 1 0 > 0.99992 || = 0.57 486 515 533 512 496 | 500 < 0.00009 0 0 0 1 1 | 0.5 | 0 1 1 0 2 > 0.99991 || = 0.56 552 499 475 511 469 | 500 < 0.0001 1 1 0 1 1 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 492 471 463 518 537 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 516 509 496 502 485 | 500 < 0.0001 4 10 0 7 4 | 5 | 5 2 5 3 7 > 0.9999 || = 0.53 521 536 504 482 496 | 500 < 0.0002 4 5 7 4 5 | 5 | 3 2 4 4 5 > 0.9998 || = 0.52 499 436 480 507 463 | 500 < 0.0003 7 8 11 2 6 | 5 | 10 6 5 4 4 > 0.9997 || = 0.51 486 462 505 494 507 | 500 < 0.0004 7 8 4 3 8 | 5 | 4 4 6 4 2 > 0.9996 || = 0.50 498 496 484 478 490 | 500 < 0.0005 4 6 8 6 3 | 5 | 4 9 4 4 3 > 0.9995 || = 0.49 468 478 505 504 532 | 500 < 0.0006 7 2 4 10 6 | 5 | 5 8 5 10 4 > 0.9994 || = 0.48 531 551 483 502 519 | 500 < 0.0007 7 2 3 6 2 | 5 | 2 3 6 7 5 > 0.9993 || = 0.47 487 519 489 462 498 | 500 < 0.0008 3 7 2 3 4 | 5 | 6 3 7 2 5 > 0.9992 || = 0.46 511 463 463 509 488 | 500 < 0.0009 6 2 5 4 4 | 5 | 5 4 5 3 4 > 0.9991 || = 0.45 460 530 514 562 505 | 500 < 0.001 3 4 4 5 2 | 5 | 5 3 5 6 4 > 0.999 || = 0.44 484 511 500 476 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 514 537 510 516 501 | 500 < 0.001 52 54 48 50 44 | 50 | 49 44 52 47 43 > 0.999 || = 0.42 536 463 549 539 543 | 500 < 0.002 47 57 47 54 55 | 50 | 44 49 47 47 48 > 0.998 || = 0.41 540 490 509 479 505 | 500 < 0.003 56 42 48 54 45 | 50 | 37 61 58 53 44 > 0.997 || = 0.40 488 511 465 440 469 | 500 < 0.004 46 53 58 62 51 | 50 | 49 53 52 66 59 > 0.996 || = 0.39 506 467 509 474 556 | 500 < 0.005 57 48 43 50 51 | 50 | 61 53 61 38 57 > 0.995 || = 0.38 498 510 508 502 461 | 500 < 0.006 45 51 43 54 68 | 50 | 58 43 50 44 53 > 0.994 || = 0.37 455 471 522 487 493 | 500 < 0.007 42 50 41 51 54 | 50 | 51 60 37 54 44 > 0.993 || = 0.36 505 494 517 519 494 | 500 < 0.008 57 45 53 60 41 | 50 | 58 53 48 41 63 > 0.992 || = 0.35 463 512 520 499 545 | 500 < 0.009 65 46 52 63 40 | 50 | 56 44 60 48 42 > 0.991 || = 0.34 474 512 495 501 513 | 500 < 0.01 52 54 68 44 49 | 50 | 48 53 51 54 48 > 0.99 || = 0.33 477 453 474 528 473 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 484 522 459 476 511 | 500 < 0.01 519 500 501 542 498 | 497.5 | 511 513 516 492 501 > 0.99 || = 0.31 499 509 515 505 463 | 500 = 0.01 282 261 241 283 280 | 252.5 | 267 273 242 237 273 = 0.99 || = 0.30 504 465 514 533 526 | 500 = 0.02 486 500 495 492 497 | 500 | 501 511 503 519 547 = 0.98 || = 0.29 530 500 483 509 510 | 500 =================================================================| 500 | 547 497 504 483 497 = 0.97 || = 0.28 485 544 483 492 498 | 500 smarsa_MatrixRank test: | 500 | 502 500 492 497 517 = 0.96 || = 0.27 498 498 515 460 527 | 500 ----------------------------------------------- | 500 | 498 509 521 544 506 = 0.95 || = 0.26 515 489 506 488 472 | 500 N = 10, n = 1000000, r = 0, s = 5, L = 30, k = 30 | 500 | 504 481 465 451 488 = 0.94 || = 0.25 482 506 480 495 467 | 500 Test on the sum of all N observations | 500 | 491 503 486 495 481 = 0.93 || = 0.24 510 481 554 507 489 | 500 | 500 | 524 495 482 500 472 = 0.92 || = 0.23 559 494 542 515 481 | 500 =================================================================| 500 | 527 526 480 493 494 = 0.91 || = 0.22 491 509 474 459 471 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 520 526 499 515 537 = 0.90 || = 0.21 502 477 485 461 491 | 500 -----------------------------------------------------------------| 500 | 499 489 490 504 506 = 0.89 || = 0.20 499 472 484 486 470 | 500 SD Bern.: d 0.95061 0.98130 0.99748 | 500 | 525 489 540 485 498 = 0.88 || = 0.19 488 499 480 509 484 | 500 s 0.98435 0.63276 0.87105 | 500 | 502 518 520 473 489 = 0.87 || = 0.18 491 483 515 495 545 | 500 t 0.97908 1.09324 0.97618 | 500 | 493 467 525 473 460 = 0.86 || = 0.17 488 504 509 506 517 | 500 m 1.05915 0.99849 1.07756 | 500 | 504 507 486 507 526 = 0.85 || = 0.16 484 507 516 506 507 | 500 x 1.01372 1.10508 1.00148 | 500 | 508 506 511 529 507 = 0.84 || = 0.15 497 503 476 486 502 | 500 | 500 | 518 544 494 471 487 = 0.83 || = 0.14 499 514 531 532 513 | 500 Changes: d 50 6 2 | 500 | 505 504 515 488 499 = 0.82 || = 0.13 501 488 532 531 506 | 500 s 56 6 5 | 500 | 487 484 499 487 506 = 0.81 || = 0.12 476 518 499 493 494 | 500 t 52 3 4 | 500 | 537 475 505 500 529 = 0.80 || = 0.11 463 531 522 497 506 | 500 m 53 4 5 | 500 | 486 477 487 504 539 = 0.79 || = 0.10 510 488 501 480 488 | 500 x 43 4 4 | 500 | 483 444 449 443 526 = 0.78 || = 0.09 485 548 474 523 552 | 500 -----------------------------------------------------------------| 500 | 514 501 504 522 474 = 0.77 || = 0.08 519 524 499 476 506 | 500 Aver./ d 0.50244 499 > 500: 4 2 5 3 5 4 5 4 7 8 | 500 | 516 510 472 509 513 = 0.76 || = 0.07 504 497 509 494 478 | 500 median s 0.49943 502 ----- 7 6 3 5 6 4 5 4 6 6 | 500 | 488 521 527 531 516 = 0.75 || = 0.06 493 496 495 512 465 | 500 t 0.49880 502 4 7 4 7 5 5 7 4 5 4 | 500 | 482 496 502 489 514 = 0.74 || = 0.05 490 512 496 452 490 | 500 m 0.49939 500 6 5 3 6 6 5 6 7 4 2 | 500 | 462 508 454 514 533 = 0.73 || = 0.04 461 515 522 523 496 | 500 x 0.50080 497 4 7 2 5 6 3 1 7 5 5 | 500 | 496 498 488 526 477 = 0.72 || = 0.03 487 511 522 524 495 | 500 -----------------------------------------------------------------| 500 | 504 485 488 509 482 = 0.71 || = 0.02 486 500 495 492 497 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 551 514 480 531 506 = 0.70 || = 0.01 282 261 241 283 280 | 252.5 d 0 0 1 11 76 9 4 0 0 | 500 | 489 513 507 527 483 = 0.69 || < 0.01 519 500 501 542 498 | 497.5 s 0 0 3 14 72 10 2 0 0 | 500 | 517 472 549 477 493 = 0.68 ||========================================================================= t 0 0 3 11 76 8 3 0 0 | 500 | 508 505 522 514 493 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 13 65 16 3 0 0 | 500 | 504 489 492 497 486 = 0.66 ||========================================================================= x 0 0 0 16 66 14 5 0 0 | 500 | 465 522 448 549 497 = 0.65 || smarsa_MatrixRank test: no 129 test no 130 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 130 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 1 0 0 | 0.5 | 1 1 0 1 3 > 0.99999 || = 0.64 512 522 465 522 510 | 500 < 0.00002 0 1 0 3 0 | 0.5 | 1 1 1 1 0 > 0.99998 || = 0.63 493 484 526 512 530 | 500 < 0.00003 1 0 0 1 0 | 0.5 | 1 1 0 0 0 > 0.99997 || = 0.62 495 489 535 466 519 | 500 < 0.00004 0 3 0 1 0 | 0.5 | 1 2 0 0 2 > 0.99996 || = 0.61 477 486 526 505 509 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 1 0 2 1 > 0.99995 || = 0.60 516 482 525 516 517 | 500 < 0.00006 0 1 1 0 0 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 479 471 474 509 473 | 500 < 0.00007 1 1 1 0 2 | 0.5 | 0 2 0 1 1 > 0.99993 || = 0.58 524 484 448 529 495 | 500 < 0.00008 0 0 1 1 1 | 0.5 | 0 1 1 2 1 > 0.99992 || = 0.57 490 570 475 498 475 | 500 < 0.00009 0 1 0 2 0 | 0.5 | 0 0 2 0 2 > 0.99991 || = 0.56 464 513 509 491 467 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 0 1 > 0.9999 || = 0.55 505 481 505 483 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 461 473 536 511 501 | 500 < 0.0001 4 7 4 8 3 | 5 | 4 9 4 8 11 > 0.9999 || = 0.53 521 502 507 491 508 | 500 < 0.0002 2 5 2 3 2 | 5 | 3 2 4 4 1 > 0.9998 || = 0.52 481 531 519 494 506 | 500 < 0.0003 5 1 2 3 4 | 5 | 3 5 6 5 3 > 0.9997 || = 0.51 506 496 538 503 529 | 500 < 0.0004 7 5 5 3 2 | 5 | 5 4 9 7 6 > 0.9996 || = 0.50 527 521 533 497 468 | 500 < 0.0005 6 2 5 6 15 | 5 | 3 3 7 4 4 > 0.9995 || = 0.49 533 519 521 516 500 | 500 < 0.0006 3 5 8 4 7 | 5 | 6 4 8 5 8 > 0.9994 || = 0.48 518 481 517 533 488 | 500 < 0.0007 7 6 7 4 4 | 5 | 6 8 5 8 5 > 0.9993 || = 0.47 473 534 463 498 517 | 500 < 0.0008 6 5 7 8 4 | 5 | 7 5 5 6 7 > 0.9992 || = 0.46 488 496 516 543 438 | 500 < 0.0009 1 6 2 2 3 | 5 | 3 5 5 2 5 > 0.9991 || = 0.45 476 509 490 506 522 | 500 < 0.001 7 4 5 4 3 | 5 | 7 10 6 6 8 > 0.999 || = 0.44 543 537 489 490 505 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 525 527 534 517 515 | 500 < 0.001 48 46 47 45 47 | 50 | 47 55 59 55 58 > 0.999 || = 0.42 504 512 499 502 551 | 500 < 0.002 44 54 40 35 36 | 50 | 64 56 54 53 51 > 0.998 || = 0.41 524 511 525 473 492 | 500 < 0.003 52 45 53 57 47 | 50 | 53 53 48 57 53 > 0.997 || = 0.40 521 475 466 498 540 | 500 < 0.004 59 58 47 51 49 | 50 | 47 58 48 51 47 > 0.996 || = 0.39 522 480 530 493 543 | 500 < 0.005 39 48 49 73 49 | 50 | 54 56 53 54 40 > 0.995 || = 0.38 512 503 495 462 497 | 500 < 0.006 56 53 43 40 62 | 50 | 59 41 53 50 58 > 0.994 || = 0.37 494 512 519 489 480 | 500 < 0.007 55 51 50 56 50 | 50 | 49 54 43 49 60 > 0.993 || = 0.36 494 507 508 480 467 | 500 < 0.008 51 41 48 53 47 | 50 | 50 62 45 54 53 > 0.992 || = 0.35 510 571 507 525 480 | 500 < 0.009 42 47 51 51 43 | 50 | 50 57 43 45 57 > 0.991 || = 0.34 486 482 470 493 505 | 500 < 0.01 53 45 47 46 54 | 50 | 46 38 50 44 54 > 0.99 || = 0.33 520 482 506 531 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 518 493 512 493 504 | 500 < 0.01 499 488 475 507 484 | 497.5 | 519 530 496 512 531 > 0.99 || = 0.31 512 498 521 509 544 | 500 = 0.01 214 252 246 240 258 | 252.5 | 279 236 266 259 284 = 0.99 || = 0.30 485 490 479 481 493 | 500 = 0.02 524 499 530 541 516 | 500 | 456 504 522 529 523 = 0.98 || = 0.29 508 439 482 484 506 | 500 =================================================================| 500 | 495 507 483 492 492 = 0.97 || = 0.28 488 461 483 527 479 | 500 smarsa_MatrixRank test: | 500 | 484 519 512 521 510 = 0.96 || = 0.27 472 512 484 550 530 | 500 ----------------------------------------------- | 500 | 476 496 478 491 521 = 0.95 || = 0.26 545 487 466 488 470 | 500 N = 10, n = 1000000, r = 25, s = 5, L = 30, k = 30 | 500 | 507 477 542 518 477 = 0.94 || = 0.25 502 504 486 533 500 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 525 494 503 494 484 = 0.93 || = 0.24 508 512 487 557 499 | 500 | 500 | 479 498 478 494 484 = 0.92 || = 0.23 498 505 479 431 508 | 500 =================================================================| 500 | 485 511 513 496 506 = 0.91 || = 0.22 494 476 520 526 523 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 490 531 444 467 471 = 0.90 || = 0.21 490 495 491 545 444 | 500 -----------------------------------------------------------------| 500 | 492 502 486 510 488 = 0.89 || = 0.20 478 492 495 458 466 | 500 SD Bern.: d 0.96488 0.87335 0.82137 | 500 | 487 528 511 503 522 = 0.88 || = 0.19 498 485 490 490 488 | 500 s 1.11435 0.70745 1.09963 | 500 | 498 518 565 523 478 = 0.87 || = 0.18 477 540 498 511 489 | 500 t 1.11425 0.61836 0.70176 | 500 | 490 475 460 510 530 = 0.86 || = 0.17 533 506 534 481 513 | 500 m 1.03169 1.40853 0.59694 | 500 | 470 494 502 506 516 = 0.85 || = 0.16 540 491 481 493 473 | 500 x 1.15364 0.93212 0.91805 | 500 | 522 493 498 473 484 = 0.84 || = 0.15 532 513 522 467 547 | 500 | 500 | 507 493 478 480 521 = 0.83 || = 0.14 505 484 513 500 483 | 500 Changes: d 38 5 4 | 500 | 504 436 485 492 533 = 0.82 || = 0.13 501 481 514 485 501 | 500 s 41 6 3 | 500 | 526 506 483 485 491 = 0.81 || = 0.12 532 514 483 516 484 | 500 t 46 4 3 | 500 | 486 494 480 494 475 = 0.80 || = 0.11 505 449 502 449 494 | 500 m 52 4 3 | 500 | 488 469 514 470 474 = 0.79 || = 0.10 522 469 545 499 543 | 500 x 55 3 2 | 500 | 454 515 516 494 424 = 0.78 || = 0.09 490 467 456 488 463 | 500 -----------------------------------------------------------------| 500 | 522 473 504 465 482 = 0.77 || = 0.08 522 542 453 541 533 | 500 Aver./ d 0.49833 499 > 500: 5 8 4 6 7 5 3 2 4 4 | 500 | 522 557 461 473 502 = 0.76 || = 0.07 514 508 479 530 485 | 500 median s 0.50078 498 ----- 5 4 4 4 7 4 2 6 5 5 | 500 | 461 532 508 486 492 = 0.75 || = 0.06 455 550 523 494 499 | 500 t 0.50071 499 3 6 1 7 5 7 4 7 3 6 | 500 | 499 469 544 486 531 = 0.74 || = 0.05 485 504 526 511 524 | 500 m 0.49963 497 5 2 6 3 6 5 6 1 5 5 | 500 | 495 522 538 519 449 = 0.73 || = 0.04 464 519 458 496 517 | 500 x 0.49991 500 5 4 4 4 6 6 7 3 5 6 | 500 | 486 514 510 483 529 = 0.72 || = 0.03 507 466 497 455 492 | 500 -----------------------------------------------------------------| 500 | 499 506 498 491 475 = 0.71 || = 0.02 524 499 530 541 516 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 487 475 451 516 509 = 0.70 || = 0.01 214 252 246 240 258 | 252.5 d 0 0 3 12 71 14 1 0 0 | 500 | 509 499 489 487 478 = 0.69 || < 0.01 499 488 475 507 484 | 497.5 s 0 0 3 16 67 11 2 2 0 | 500 | 506 499 513 511 515 = 0.68 ||========================================================================= t 0 0 4 12 66 17 2 0 0 | 500 | 487 538 489 497 482 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 2 10 71 14 3 0 0 | 500 | 499 483 497 541 466 = 0.66 ||========================================================================= x 0 1 3 15 61 18 3 0 0 | 500 | 498 473 497 480 549 = 0.65 || smarsa_MatrixRank test: no 130 test no 131 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 131 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 1 0 | 0.5 | 2 0 1 1 0 > 0.99999 || = 0.64 477 518 540 476 475 | 500 < 0.00002 0 0 0 3 1 | 0.5 | 0 0 1 0 2 > 0.99998 || = 0.63 492 483 508 504 511 | 500 < 0.00003 0 2 1 0 0 | 0.5 | 1 1 2 0 0 > 0.99997 || = 0.62 494 482 499 467 485 | 500 < 0.00004 0 0 1 1 0 | 0.5 | 1 1 1 0 0 > 0.99996 || = 0.61 527 494 514 534 505 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 1 1 1 1 0 > 0.99995 || = 0.60 536 470 505 478 472 | 500 < 0.00006 1 0 0 0 0 | 0.5 | 2 1 0 0 1 > 0.99994 || = 0.59 498 493 466 477 515 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 1 3 2 0 0 > 0.99993 || = 0.58 517 524 500 512 483 | 500 < 0.00008 1 0 0 1 1 | 0.5 | 1 1 0 0 1 > 0.99992 || = 0.57 479 487 457 477 449 | 500 < 0.00009 1 1 0 0 2 | 0.5 | 0 0 0 0 2 > 0.99991 || = 0.56 521 513 529 472 475 | 500 < 0.0001 1 0 0 0 1 | 0.5 | 0 4 0 0 0 > 0.9999 || = 0.55 529 501 460 520 470 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 494 506 512 509 493 | 500 < 0.0001 5 4 3 7 5 | 5 | 9 12 8 2 6 > 0.9999 || = 0.53 514 525 539 494 510 | 500 < 0.0002 5 5 2 5 9 | 5 | 0 2 3 1 4 > 0.9998 || = 0.52 504 482 524 497 506 | 500 < 0.0003 10 3 9 6 3 | 5 | 3 4 2 3 6 > 0.9997 || = 0.51 521 556 501 525 492 | 500 < 0.0004 6 9 5 6 5 | 5 | 5 4 6 5 4 > 0.9996 || = 0.50 514 511 522 472 466 | 500 < 0.0005 7 3 6 4 3 | 5 | 5 5 5 6 5 > 0.9995 || = 0.49 489 488 505 502 527 | 500 < 0.0006 2 6 5 6 4 | 5 | 9 4 3 5 7 > 0.9994 || = 0.48 461 520 509 540 508 | 500 < 0.0007 5 5 10 5 3 | 5 | 9 6 2 1 6 > 0.9993 || = 0.47 530 503 500 550 499 | 500 < 0.0008 7 2 3 3 4 | 5 | 2 8 5 5 5 > 0.9992 || = 0.46 496 502 488 507 468 | 500 < 0.0009 8 6 4 5 3 | 5 | 4 3 5 3 3 > 0.9991 || = 0.45 486 500 517 496 536 | 500 < 0.001 8 6 3 9 4 | 5 | 4 6 3 3 8 > 0.999 || = 0.44 449 560 508 524 525 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 501 492 508 478 492 | 500 < 0.001 63 49 50 56 43 | 50 | 50 54 42 34 54 > 0.999 || = 0.42 529 476 494 491 517 | 500 < 0.002 28 38 45 54 43 | 50 | 32 53 48 48 52 > 0.998 || = 0.41 489 480 511 513 490 | 500 < 0.003 48 52 61 49 50 | 50 | 52 48 50 55 49 > 0.997 || = 0.40 484 483 505 521 522 | 500 < 0.004 49 46 60 40 45 | 50 | 55 52 51 63 57 > 0.996 || = 0.39 477 499 468 480 506 | 500 < 0.005 58 51 42 50 45 | 50 | 60 50 54 52 58 > 0.995 || = 0.38 512 506 506 538 503 | 500 < 0.006 43 68 46 49 65 | 50 | 47 59 43 48 49 > 0.994 || = 0.37 515 500 515 513 486 | 500 < 0.007 49 51 46 47 49 | 50 | 47 46 32 51 43 > 0.993 || = 0.36 476 500 493 527 520 | 500 < 0.008 49 57 49 55 61 | 50 | 42 50 59 61 52 > 0.992 || = 0.35 512 516 520 522 555 | 500 < 0.009 42 54 52 53 51 | 50 | 49 40 51 52 49 > 0.991 || = 0.34 535 510 475 484 517 | 500 < 0.01 40 55 50 47 71 | 50 | 51 45 53 54 43 > 0.99 || = 0.33 495 504 489 521 522 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 504 470 519 471 486 | 500 < 0.01 469 521 501 500 523 | 497.5 | 485 497 483 518 506 > 0.99 || = 0.31 461 539 485 524 484 | 500 = 0.01 270 251 234 263 233 | 252.5 | 279 249 270 254 245 = 0.99 || = 0.30 459 497 504 448 515 | 500 = 0.02 487 477 467 482 505 | 500 | 495 522 548 515 516 = 0.98 || = 0.29 495 499 507 493 475 | 500 =================================================================| 500 | 510 462 510 507 459 = 0.97 || = 0.28 525 457 500 465 512 | 500 smarsa_MatrixRank test: | 500 | 474 500 521 478 463 = 0.96 || = 0.27 484 485 502 484 505 | 500 ----------------------------------------------- | 500 | 520 516 513 508 485 = 0.95 || = 0.26 487 519 497 517 490 | 500 N = 10, n = 1000000, r = 25, s = 5, L = 30, k = 30 | 500 | 497 476 483 503 508 = 0.94 || = 0.25 491 513 507 480 466 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 509 509 482 518 518 = 0.93 || = 0.24 506 493 523 499 479 | 500 | 500 | 551 516 520 535 481 = 0.92 || = 0.23 500 492 509 503 511 | 500 =================================================================| 500 | 493 490 491 463 482 = 0.91 || = 0.22 511 488 483 501 503 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 481 496 464 544 545 = 0.90 || = 0.21 521 457 509 506 453 | 500 -----------------------------------------------------------------| 500 | 531 473 509 496 499 = 0.89 || = 0.20 500 483 505 512 544 | 500 SD Bern.: d 0.97883 1.36962 1.03685 | 500 | 519 488 512 467 487 = 0.88 || = 0.19 497 529 478 519 457 | 500 s 0.92737 1.07849 0.71449 | 500 | 498 513 502 452 506 = 0.87 || = 0.18 525 530 495 459 525 | 500 t 0.88241 0.83347 1.04837 | 500 | 460 514 514 489 494 = 0.86 || = 0.17 503 466 510 505 504 | 500 m 1.06838 0.64218 1.09963 | 500 | 515 489 518 571 520 = 0.85 || = 0.16 477 537 453 465 517 | 500 x 1.06454 1.36962 0.69026 | 500 | 493 491 519 474 504 = 0.84 || = 0.15 532 489 454 556 512 | 500 | 500 | 494 481 470 486 480 = 0.83 || = 0.14 491 492 490 507 466 | 500 Changes: d 56 3 3 | 500 | 508 504 509 519 496 = 0.82 || = 0.13 482 471 467 489 504 | 500 s 49 3 5 | 500 | 476 499 524 472 507 = 0.81 || = 0.12 497 539 527 497 481 | 500 t 45 4 3 | 500 | 485 480 512 537 495 = 0.80 || = 0.11 476 515 509 503 520 | 500 m 54 3 3 | 500 | 563 519 478 461 460 = 0.79 || = 0.10 476 520 523 511 519 | 500 x 58 3 5 | 500 | 462 483 480 501 493 = 0.78 || = 0.09 510 542 507 486 502 | 500 -----------------------------------------------------------------| 500 | 558 482 497 499 518 = 0.77 || = 0.08 495 494 542 503 471 | 500 Aver./ d 0.50128 497 > 500: 3 3 4 5 3 7 3 4 4 5 | 500 | 511 512 504 490 530 = 0.76 || = 0.07 524 475 489 512 492 | 500 median s 0.49939 499 ----- 4 6 2 5 4 6 3 6 3 4 | 500 | 466 495 481 491 471 = 0.75 || = 0.06 498 508 481 515 513 | 500 t 0.50087 503 5 4 7 5 7 6 3 3 8 6 | 500 | 502 510 479 509 493 = 0.74 || = 0.05 500 493 494 484 503 | 500 m 0.50039 501 5 6 5 6 7 4 5 3 3 8 | 500 | 498 508 501 473 475 = 0.73 || = 0.04 492 517 518 481 505 | 500 x 0.49980 503 6 7 5 7 6 3 7 3 5 4 | 500 | 500 524 493 476 538 = 0.72 || = 0.03 496 467 511 475 473 | 500 -----------------------------------------------------------------| 500 | 481 526 496 487 491 = 0.71 || = 0.02 487 477 467 482 505 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 494 471 492 522 527 = 0.70 || = 0.01 270 251 234 263 233 | 252.5 d 0 0 1 15 68 14 3 0 0 | 500 | 487 498 483 490 532 = 0.69 || < 0.01 469 521 501 500 523 | 497.5 s 0 0 0 14 73 12 2 0 0 | 500 | 496 506 483 493 521 = 0.68 ||========================================================================= t 0 0 2 10 78 10 1 0 0 | 500 | 478 484 497 497 494 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 18 66 12 2 1 0 | 500 | 514 482 483 534 531 = 0.66 ||========================================================================= x 0 0 2 18 67 11 2 1 0 | 500 | 523 526 492 535 582 = 0.65 || smarsa_MatrixRank test: no 131 test no 132 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 132 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 2 0 1 1 | 0.5 | 0 0 1 0 0 > 0.99999 || = 0.64 498 513 505 518 461 | 500 < 0.00002 1 1 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99998 || = 0.63 498 484 512 452 545 | 500 < 0.00003 2 1 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99997 || = 0.62 503 517 468 508 497 | 500 < 0.00004 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 521 480 519 508 476 | 500 < 0.00005 1 0 0 2 0 | 0.5 | 0 2 1 0 1 > 0.99995 || = 0.60 472 502 516 465 493 | 500 < 0.00006 1 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 503 511 488 491 494 | 500 < 0.00007 0 0 1 1 1 | 0.5 | 1 1 1 0 1 > 0.99993 || = 0.58 491 542 490 481 508 | 500 < 0.00008 0 0 1 1 0 | 0.5 | 1 0 0 0 0 > 0.99992 || = 0.57 446 483 478 539 520 | 500 < 0.00009 1 0 0 0 0 | 0.5 | 1 0 0 2 0 > 0.99991 || = 0.56 500 477 474 512 460 | 500 < 0.0001 1 0 0 0 1 | 0.5 | 0 1 0 0 0 > 0.9999 || = 0.55 502 485 508 515 503 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 522 516 489 510 516 | 500 < 0.0001 8 5 2 8 5 | 5 | 3 5 3 2 3 > 0.9999 || = 0.53 479 493 504 521 517 | 500 < 0.0002 2 5 3 5 3 | 5 | 1 2 0 1 4 > 0.9998 || = 0.52 497 506 506 519 455 | 500 < 0.0003 5 5 2 4 4 | 5 | 1 0 4 1 2 > 0.9997 || = 0.51 503 497 487 498 522 | 500 < 0.0004 5 2 3 3 6 | 5 | 4 3 3 3 3 > 0.9996 || = 0.50 513 471 479 530 498 | 500 < 0.0005 8 7 5 3 1 | 5 | 4 4 5 5 3 > 0.9995 || = 0.49 495 456 475 470 501 | 500 < 0.0006 3 3 5 6 7 | 5 | 6 4 2 3 5 > 0.9994 || = 0.48 530 517 481 510 473 | 500 < 0.0007 5 4 4 3 5 | 5 | 5 4 3 0 7 > 0.9993 || = 0.47 532 566 533 503 514 | 500 < 0.0008 7 5 3 7 6 | 5 | 4 3 3 6 3 > 0.9992 || = 0.46 483 519 460 500 464 | 500 < 0.0009 4 2 5 7 6 | 5 | 2 7 6 3 5 > 0.9991 || = 0.45 535 513 476 521 429 | 500 < 0.001 5 3 5 6 4 | 5 | 4 6 3 5 2 > 0.999 || = 0.44 510 481 557 468 526 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 514 505 474 487 509 | 500 < 0.001 52 41 37 52 47 | 50 | 34 38 32 29 37 > 0.999 || = 0.42 522 519 507 536 491 | 500 < 0.002 58 59 45 46 43 | 50 | 39 42 34 52 46 > 0.998 || = 0.41 529 505 490 504 504 | 500 < 0.003 61 56 52 39 39 | 50 | 49 45 37 47 49 > 0.997 || = 0.40 513 524 502 495 519 | 500 < 0.004 52 61 48 43 58 | 50 | 46 43 48 44 48 > 0.996 || = 0.39 475 509 477 525 493 | 500 < 0.005 40 45 47 47 52 | 50 | 41 54 59 37 49 > 0.995 || = 0.38 498 512 456 508 485 | 500 < 0.006 47 54 56 49 58 | 50 | 46 43 44 54 51 > 0.994 || = 0.37 516 492 527 514 508 | 500 < 0.007 49 51 52 63 43 | 50 | 51 38 51 59 42 > 0.993 || = 0.36 524 469 491 475 533 | 500 < 0.008 37 57 47 63 62 | 50 | 52 47 67 45 59 > 0.992 || = 0.35 484 490 495 480 492 | 500 < 0.009 52 47 46 40 39 | 50 | 48 52 42 42 47 > 0.991 || = 0.34 519 481 470 529 494 | 500 < 0.01 52 35 48 49 55 | 50 | 52 53 54 61 43 > 0.99 || = 0.33 470 552 473 494 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 498 519 500 479 497 | 500 < 0.01 500 506 478 491 496 | 497.5 | 458 455 468 470 471 > 0.99 || = 0.31 546 491 455 507 544 | 500 = 0.01 223 260 231 269 246 | 252.5 | 265 227 258 280 298 = 0.99 || = 0.30 491 508 497 488 493 | 500 = 0.02 485 522 503 511 489 | 500 | 528 552 498 503 488 = 0.98 || = 0.29 501 485 491 470 541 | 500 =================================================================| 500 | 503 506 552 484 549 = 0.97 || = 0.28 512 465 494 475 466 | 500 smarsa_MatrixRank test: | 500 | 499 526 494 537 493 = 0.96 || = 0.27 486 516 526 501 500 | 500 ----------------------------------------------- | 500 | 489 526 495 511 481 = 0.95 || = 0.26 488 471 529 533 484 | 500 N = 10, n = 1000000, r = 25, s = 5, L = 30, k = 30 | 500 | 495 484 505 495 496 = 0.94 || = 0.25 444 535 481 455 500 | 500 Anderson-Darling statistic = A2 | 500 | 493 493 522 537 493 = 0.93 || = 0.24 507 564 497 472 504 | 500 | 500 | 469 505 516 502 505 = 0.92 || = 0.23 509 491 511 533 481 | 500 =================================================================| 500 | 463 547 477 518 502 = 0.91 || = 0.22 502 465 510 500 542 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 476 483 496 482 494 = 0.90 || = 0.21 492 469 470 492 499 | 500 -----------------------------------------------------------------| 500 | 466 514 515 479 510 = 0.89 || = 0.20 535 469 505 506 503 | 500 SD Bern.: d 1.12429 0.98028 1.00448 | 500 | 586 483 506 523 515 = 0.88 || = 0.19 522 499 507 479 507 | 500 s 1.08597 1.13546 1.01341 | 500 | 525 491 498 507 475 = 0.87 || = 0.18 508 503 499 481 519 | 500 t 1.04054 0.74869 1.57557 | 500 | 471 454 529 471 491 = 0.86 || = 0.17 464 511 492 504 490 | 500 m 0.99125 1.13104 1.39065 | 500 | 502 486 471 502 469 = 0.85 || = 0.16 497 487 453 466 495 | 500 x 1.03431 1.14074 0.88925 | 500 | 495 480 534 496 533 = 0.84 || = 0.15 520 484 486 531 480 | 500 | 500 | 461 486 490 546 521 = 0.83 || = 0.14 457 488 511 473 451 | 500 Changes: d 49 2 3 | 500 | 469 472 472 491 468 = 0.82 || = 0.13 486 520 525 511 494 | 500 s 43 4 3 | 500 | 502 469 491 478 502 = 0.81 || = 0.12 512 522 524 484 495 | 500 t 52 4 5 | 500 | 491 447 504 505 469 = 0.80 || = 0.11 519 511 519 492 518 | 500 m 60 3 5 | 500 | 510 528 467 490 501 = 0.79 || = 0.10 499 533 514 490 481 | 500 x 52 5 4 | 500 | 500 521 520 503 526 = 0.78 || = 0.09 516 478 507 504 495 | 500 -----------------------------------------------------------------| 500 | 513 478 470 486 498 = 0.77 || = 0.08 495 491 467 527 508 | 500 Aver./ d 0.49982 500 > 500: 4 5 6 4 8 4 7 4 4 3 | 500 | 486 532 476 509 522 = 0.76 || = 0.07 456 477 530 513 507 | 500 median s 0.49913 500 ----- 6 6 3 5 8 5 5 5 1 6 | 500 | 492 502 515 476 484 = 0.75 || = 0.06 436 505 497 544 545 | 500 t 0.50089 498 6 6 5 1 4 4 7 6 4 5 | 500 | 495 500 534 490 475 = 0.74 || = 0.05 547 509 534 499 519 | 500 m 0.50004 502 7 3 4 5 5 6 5 5 4 7 | 500 | 505 482 495 520 505 = 0.73 || = 0.04 526 467 509 498 532 | 500 x 0.49943 498 6 3 4 3 6 6 3 6 5 4 | 500 | 538 491 518 489 515 = 0.72 || = 0.03 495 527 518 515 522 | 500 -----------------------------------------------------------------| 500 | 479 523 540 537 512 = 0.71 || = 0.02 485 522 503 511 489 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 473 498 515 476 534 = 0.70 || = 0.01 223 260 231 269 246 | 252.5 d 0 0 3 16 66 12 3 1 0 | 500 | 538 510 498 497 479 = 0.69 || < 0.01 500 506 478 491 496 | 497.5 s 0 0 2 15 69 10 5 0 0 | 500 | 550 518 533 502 521 = 0.68 ||========================================================================= t 0 0 2 20 62 14 3 0 0 | 500 | 518 488 539 518 475 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 67 16 1 0 0 | 500 | 503 489 563 472 499 = 0.66 ||========================================================================= x 0 1 2 13 72 9 4 0 0 | 500 | 523 519 489 439 497 = 0.65 || smarsa_MatrixRank test: no 132 test no 133 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 133 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 518 534 473 511 492 | 500 < 0.00002 2 1 0 1 2 | 0.5 | 2 2 0 0 0 > 0.99998 || = 0.63 481 483 477 467 498 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 1 0 0 1 > 0.99997 || = 0.62 525 466 533 504 479 | 500 < 0.00004 1 1 0 0 2 | 0.5 | 0 1 0 0 0 > 0.99996 || = 0.61 489 493 462 518 525 | 500 < 0.00005 1 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99995 || = 0.60 468 485 493 500 519 | 500 < 0.00006 2 2 0 0 0 | 0.5 | 1 0 0 1 0 > 0.99994 || = 0.59 553 453 491 507 537 | 500 < 0.00007 0 1 0 2 0 | 0.5 | 0 0 2 1 0 > 0.99993 || = 0.58 501 516 480 492 514 | 500 < 0.00008 1 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 498 487 540 525 501 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 497 520 493 508 506 | 500 < 0.0001 1 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 511 488 516 490 502 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 489 515 516 501 458 | 500 < 0.0001 8 5 0 4 8 | 5 | 3 5 2 3 2 > 0.9999 || = 0.53 522 506 491 482 510 | 500 < 0.0002 8 6 9 4 2 | 5 | 3 2 1 1 3 > 0.9998 || = 0.52 483 500 484 534 475 | 500 < 0.0003 4 4 6 2 2 | 5 | 7 2 6 3 5 > 0.9997 || = 0.51 498 480 478 484 495 | 500 < 0.0004 5 9 4 5 7 | 5 | 5 4 4 4 4 > 0.9996 || = 0.50 482 556 528 486 495 | 500 < 0.0005 5 9 2 4 11 | 5 | 6 7 3 5 1 > 0.9995 || = 0.49 494 524 492 492 509 | 500 < 0.0006 7 6 2 7 4 | 5 | 4 5 5 5 4 > 0.9994 || = 0.48 510 498 521 480 530 | 500 < 0.0007 3 2 7 9 4 | 5 | 3 3 6 7 2 > 0.9993 || = 0.47 480 512 489 502 493 | 500 < 0.0008 3 10 7 6 7 | 5 | 5 2 5 2 8 > 0.9992 || = 0.46 504 493 516 517 481 | 500 < 0.0009 7 7 6 7 5 | 5 | 10 6 0 5 8 > 0.9991 || = 0.45 530 520 456 479 491 | 500 < 0.001 7 4 4 5 6 | 5 | 2 2 4 7 6 > 0.999 || = 0.44 492 487 488 502 522 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 503 489 472 513 540 | 500 < 0.001 57 62 47 53 56 | 50 | 48 38 36 42 43 > 0.999 || = 0.42 493 492 515 501 501 | 500 < 0.002 48 46 45 51 48 | 50 | 46 52 48 52 50 > 0.998 || = 0.41 477 531 489 489 524 | 500 < 0.003 52 51 60 58 60 | 50 | 46 56 58 42 52 > 0.997 || = 0.40 484 505 516 514 458 | 500 < 0.004 39 48 47 47 46 | 50 | 54 44 48 44 50 > 0.996 || = 0.39 483 486 512 500 446 | 500 < 0.005 58 44 39 55 52 | 50 | 48 52 47 56 50 > 0.995 || = 0.38 452 523 468 533 503 | 500 < 0.006 52 59 50 57 48 | 50 | 57 63 49 50 35 > 0.994 || = 0.37 530 496 504 516 488 | 500 < 0.007 50 53 58 42 50 | 50 | 48 44 52 50 41 > 0.993 || = 0.36 533 491 495 478 526 | 500 < 0.008 52 55 46 52 52 | 50 | 46 47 38 50 50 > 0.992 || = 0.35 490 502 537 463 514 | 500 < 0.009 46 58 64 60 47 | 50 | 39 41 43 58 47 > 0.991 || = 0.34 517 493 512 510 510 | 500 < 0.01 52 55 53 56 39 | 50 | 43 52 50 49 51 > 0.99 || = 0.33 462 522 490 499 511 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 459 490 499 467 493 | 500 < 0.01 506 531 509 531 498 | 497.5 | 475 489 469 493 469 > 0.99 || = 0.31 505 516 515 541 487 | 500 = 0.01 243 260 231 252 269 | 252.5 | 270 246 262 262 266 = 0.99 || = 0.30 477 502 528 489 507 | 500 = 0.02 501 498 503 508 526 | 500 | 476 496 524 543 513 = 0.98 || = 0.29 489 491 497 478 521 | 500 =================================================================| 500 | 484 493 520 515 511 = 0.97 || = 0.28 482 487 511 492 511 | 500 smarsa_MatrixRank test: | 500 | 494 503 514 519 483 = 0.96 || = 0.27 508 498 493 515 485 | 500 ----------------------------------------------- | 500 | 524 517 445 487 487 = 0.95 || = 0.26 502 510 515 506 440 | 500 N = 10, n = 1000000, r = 25, s = 5, L = 30, k = 30 | 500 | 484 491 512 459 495 = 0.94 || = 0.25 510 466 500 502 502 | 500 Test on the sum of all N observations | 500 | 478 493 502 517 529 = 0.93 || = 0.24 507 499 511 487 484 | 500 | 500 | 504 515 521 494 521 = 0.92 || = 0.23 526 530 497 481 504 | 500 =================================================================| 500 | 531 515 473 486 511 = 0.91 || = 0.22 469 503 478 513 494 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 495 468 507 481 499 = 0.90 || = 0.21 487 491 513 523 502 | 500 -----------------------------------------------------------------| 500 | 501 525 484 529 501 = 0.89 || = 0.20 458 469 502 502 500 | 500 SD Bern.: d 1.09869 0.73520 0.76849 | 500 | 590 477 502 572 503 = 0.88 || = 0.19 547 501 475 498 507 | 500 s 0.86959 0.90044 1.02324 | 500 | 473 507 490 458 498 = 0.87 || = 0.18 488 476 518 476 494 | 500 t 0.96576 1.04837 0.97515 | 500 | 487 506 488 524 494 = 0.86 || = 0.17 490 512 489 499 480 | 500 m 0.92048 0.85012 0.73383 | 500 | 484 478 525 523 501 = 0.85 || = 0.16 490 526 470 471 452 | 500 x 0.91422 0.77238 0.85949 | 500 | 534 456 512 507 517 = 0.84 || = 0.15 500 492 504 494 490 | 500 | 500 | 498 503 508 485 500 = 0.83 || = 0.14 492 502 514 503 494 | 500 Changes: d 55 8 4 | 500 | 544 513 483 494 483 = 0.82 || = 0.13 554 469 511 531 493 | 500 s 55 4 5 | 500 | 547 521 502 453 492 = 0.81 || = 0.12 515 486 484 527 476 | 500 t 65 5 4 | 500 | 508 496 491 509 505 = 0.80 || = 0.11 491 509 467 469 513 | 500 m 51 4 6 | 500 | 480 497 523 517 535 = 0.79 || = 0.10 502 492 519 472 475 | 500 x 46 7 3 | 500 | 480 504 475 491 525 = 0.78 || = 0.09 497 481 455 463 516 | 500 -----------------------------------------------------------------| 500 | 504 508 479 501 508 = 0.77 || = 0.08 478 523 479 506 536 | 500 Aver./ d 0.50085 497 > 500: 4 4 5 4 4 4 5 4 5 4 | 500 | 486 507 509 476 496 = 0.76 || = 0.07 506 484 516 499 487 | 500 median s 0.49943 499 ----- 6 5 3 5 5 4 1 8 6 4 | 500 | 469 549 524 499 538 = 0.75 || = 0.06 482 527 519 480 512 | 500 t 0.50031 502 6 5 5 6 4 3 4 5 6 7 | 500 | 509 511 499 500 464 = 0.74 || = 0.05 498 476 536 510 516 | 500 m 0.50089 501 6 3 6 4 6 5 7 4 5 5 | 500 | 540 509 538 499 511 = 0.73 || = 0.04 464 520 480 501 504 | 500 x 0.50047 501 9 2 5 6 6 7 4 6 4 6 | 500 | 480 517 542 505 457 = 0.72 || = 0.03 574 521 509 506 507 | 500 -----------------------------------------------------------------| 500 | 497 520 492 468 495 = 0.71 || = 0.02 501 498 503 508 526 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 496 461 488 503 453 = 0.70 || = 0.01 243 260 231 252 269 | 252.5 d 0 0 1 12 71 11 4 1 1 | 500 | 520 482 547 510 514 = 0.69 || < 0.01 506 531 509 531 498 | 497.5 s 0 0 1 12 76 10 2 0 0 | 500 | 489 492 452 532 492 = 0.68 ||========================================================================= t 0 0 3 13 72 12 1 0 0 | 500 | 521 474 520 504 492 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 12 74 13 0 1 0 | 500 | 521 477 488 498 509 = 0.66 ||========================================================================= x 0 0 4 8 76 13 0 0 0 | 500 | 481 500 516 498 505 = 0.65 || smarsa_MatrixRank test: no 133 test no 134 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 134 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 495 534 539 563 577 | 500 < 0.00002 0 2 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 506 521 495 527 502 | 500 < 0.00003 1 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 537 492 509 536 508 | 500 < 0.00004 1 1 2 0 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 516 490 538 507 562 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 466 510 504 472 528 | 500 < 0.00006 0 2 3 0 1 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 546 526 482 523 478 | 500 < 0.00007 2 0 1 1 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 503 479 482 497 489 | 500 < 0.00008 2 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 504 451 476 489 523 | 500 < 0.00009 0 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 465 477 455 467 529 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 504 523 470 485 486 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 500 475 477 510 511 | 500 < 0.0001 6 8 8 4 5 | 5 | 0 0 0 0 0 > 0.9999 || = 0.53 500 513 526 514 473 | 500 < 0.0002 6 5 8 3 11 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 542 524 487 508 560 | 500 < 0.0003 7 3 5 4 6 | 5 | 5 9 6 9 9 > 0.9997 || = 0.51 522 539 495 533 522 | 500 < 0.0004 8 5 5 6 10 | 5 | 8 4 4 7 7 > 0.9996 || = 0.50 515 538 479 500 494 | 500 < 0.0005 5 2 7 6 4 | 5 | 5 2 9 4 6 > 0.9995 || = 0.49 530 550 492 494 525 | 500 < 0.0006 6 2 7 4 4 | 5 | 10 4 10 13 12 > 0.9994 || = 0.48 524 522 498 455 511 | 500 < 0.0007 4 11 3 5 2 | 5 | 10 6 8 8 5 > 0.9993 || = 0.47 484 495 526 478 489 | 500 < 0.0008 6 5 8 3 5 | 5 | 1 5 4 2 4 > 0.9992 || = 0.46 452 473 477 462 464 | 500 < 0.0009 8 8 5 7 1 | 5 | 3 4 9 3 6 > 0.9991 || = 0.45 520 482 467 505 468 | 500 < 0.001 9 4 4 7 8 | 5 | 10 10 13 11 6 > 0.999 || = 0.44 507 479 496 503 449 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 522 496 499 514 533 | 500 < 0.001 65 53 60 49 56 | 50 | 52 44 63 57 55 > 0.999 || = 0.42 530 482 531 506 542 | 500 < 0.002 56 47 35 51 49 | 50 | 44 57 52 54 55 > 0.998 || = 0.41 507 547 497 539 494 | 500 < 0.003 46 54 53 56 58 | 50 | 53 49 56 42 33 > 0.997 || = 0.40 557 510 547 547 529 | 500 < 0.004 47 49 51 50 48 | 50 | 40 57 36 33 32 > 0.996 || = 0.39 505 492 465 548 521 | 500 < 0.005 58 40 53 59 48 | 50 | 36 39 32 39 39 > 0.995 || = 0.38 449 543 487 529 513 | 500 < 0.006 51 45 44 57 53 | 50 | 57 46 56 50 56 > 0.994 || = 0.37 498 501 483 515 488 | 500 < 0.007 59 60 52 57 69 | 50 | 47 40 55 37 46 > 0.993 || = 0.36 485 490 463 529 443 | 500 < 0.008 46 64 48 48 58 | 50 | 61 52 64 62 60 > 0.992 || = 0.35 468 501 485 451 475 | 500 < 0.009 51 45 48 49 50 | 50 | 58 48 53 59 54 > 0.991 || = 0.34 464 502 477 490 490 | 500 < 0.01 56 60 47 48 54 | 50 | 53 58 75 52 48 > 0.99 || = 0.33 530 515 482 487 480 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 520 533 517 525 533 | 500 < 0.01 535 517 491 524 543 | 497.5 | 501 490 542 485 478 > 0.99 || = 0.31 543 532 516 522 550 | 500 = 0.01 250 238 259 258 253 | 252.5 | 279 283 293 283 280 = 0.99 || = 0.30 513 467 572 494 543 | 500 = 0.02 482 482 501 492 492 | 500 | 448 421 424 457 485 = 0.98 || = 0.29 501 477 471 484 458 | 500 =================================================================| 500 | 521 540 526 531 549 = 0.97 || = 0.28 495 511 482 528 511 | 500 smarsa_MatrixRank test: | 500 | 508 503 525 512 486 = 0.96 || = 0.27 522 526 520 488 488 | 500 ----------------------------------------------- | 500 | 518 489 469 496 457 = 0.95 || = 0.26 451 492 457 470 451 | 500 N = 1, n = 5000, r = 0, s = 4, L = 1000, k = 1000 | 500 | 465 495 452 445 473 = 0.94 || = 0.25 423 485 500 475 485 | 500 | 500 | 423 462 456 452 457 = 0.93 || = 0.24 544 478 488 481 494 | 500 | 500 | 532 524 538 511 521 = 0.92 || = 0.23 540 510 517 529 533 | 500 =================================================================| 500 | 533 511 523 522 511 = 0.91 || = 0.22 534 509 520 471 516 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 536 482 532 523 493 = 0.90 || = 0.21 510 503 543 539 515 | 500 -----------------------------------------------------------------| 500 | 477 505 534 499 499 = 0.89 || = 0.20 489 517 460 548 484 | 500 SD Bern.: d 1.28833 0.98537 1.09324 | 500 | 503 517 468 450 498 = 0.88 || = 0.19 487 498 519 487 503 | 500 s 1.22977 1.07849 0.94279 | 500 | 490 459 478 475 468 = 0.87 || = 0.18 502 503 465 514 474 | 500 t 1.32008 0.89598 1.80089 | 500 | 499 481 494 502 443 = 0.86 || = 0.17 454 499 524 508 491 | 500 m 1.23411 0.67263 1.36961 | 500 | 540 530 598 497 538 = 0.85 || = 0.16 496 556 479 520 528 | 500 x 1.35979 1.05787 1.38343 | 500 | 534 523 554 523 557 = 0.84 || = 0.15 509 510 495 498 510 | 500 | 500 | 552 534 553 518 511 = 0.83 || = 0.14 497 494 513 499 487 | 500 Changes: d 42 4 6 | 500 | 480 502 480 493 526 = 0.82 || = 0.13 491 487 510 480 491 | 500 s 43 6 7 | 500 | 478 463 469 491 470 = 0.81 || = 0.12 517 498 506 487 508 | 500 t 41 5 2 | 500 | 463 477 495 461 461 = 0.80 || = 0.11 518 547 507 493 501 | 500 m 37 4 2 | 500 | 485 481 501 456 473 = 0.79 || = 0.10 478 506 501 511 494 | 500 x 46 6 5 | 500 | 490 483 485 475 447 = 0.78 || = 0.09 475 481 488 479 488 | 500 -----------------------------------------------------------------| 500 | 481 434 493 483 458 = 0.77 || = 0.08 464 521 492 457 474 | 500 Aver./ d 0.50004 502 > 500: 3 4 6 5 8 6 4 3 5 7 | 500 | 524 573 533 557 515 = 0.76 || = 0.07 520 483 527 508 519 | 500 median s 0.49870 498 ----- 3 5 6 7 4 6 2 4 6 5 | 500 | 473 528 494 541 562 = 0.75 || = 0.06 490 504 544 496 516 | 500 t 0.50021 496 6 7 4 3 3 2 5 4 5 6 | 500 | 529 545 507 537 541 = 0.74 || = 0.05 463 488 518 462 488 | 500 m 0.49970 498 3 4 4 6 6 5 6 4 4 5 | 500 | 506 475 527 498 476 = 0.73 || = 0.04 496 474 505 492 455 | 500 x 0.49949 498 5 5 4 5 5 6 7 4 4 4 | 500 | 472 498 500 493 530 = 0.72 || = 0.03 528 480 491 482 508 | 500 -----------------------------------------------------------------| 500 | 494 501 484 535 483 = 0.71 || = 0.02 482 482 501 492 492 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 484 456 477 501 520 = 0.70 || = 0.01 250 238 259 258 253 | 252.5 d 0 2 6 13 57 20 3 0 0 | 500 | 445 474 462 475 486 = 0.69 || < 0.01 535 517 491 524 543 | 497.5 s 0 1 3 14 60 17 5 1 0 | 500 | 497 493 467 492 458 = 0.68 ||========================================================================= t 0 1 3 19 53 18 5 1 1 | 500 | 457 444 451 424 444 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 5 14 56 20 5 0 0 | 500 | 508 461 526 496 505 = 0.66 ||========================================================================= x 0 0 7 17 53 16 7 1 0 | 500 | 485 485 506 527 501 = 0.65 || smarsa_MatrixRank test: no 134 test no 135 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 135 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 2 1 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 552 560 533 511 499 | 500 < 0.00002 1 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 486 493 496 546 492 | 500 < 0.00003 1 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 508 500 528 540 527 | 500 < 0.00004 2 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 538 582 552 522 501 | 500 < 0.00005 1 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 514 465 468 501 517 | 500 < 0.00006 1 2 1 1 1 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 474 531 488 518 478 | 500 < 0.00007 0 1 2 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 478 478 445 489 486 | 500 < 0.00008 2 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 469 456 452 485 491 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 458 501 481 490 455 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 489 543 477 481 520 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 520 486 546 489 512 | 500 < 0.0001 8 6 7 5 5 | 5 | 0 0 0 0 0 > 0.9999 || = 0.53 516 547 501 464 542 | 500 < 0.0002 7 5 2 4 3 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 512 534 522 560 535 | 500 < 0.0003 5 6 3 4 7 | 5 | 9 7 5 4 4 > 0.9997 || = 0.51 518 509 516 535 518 | 500 < 0.0004 12 10 3 3 7 | 5 | 7 6 5 5 6 > 0.9996 || = 0.50 500 514 500 504 494 | 500 < 0.0005 3 4 5 1 4 | 5 | 10 4 8 4 2 > 0.9995 || = 0.49 539 491 501 500 481 | 500 < 0.0006 9 5 2 9 4 | 5 | 8 9 5 11 7 > 0.9994 || = 0.48 515 497 480 484 484 | 500 < 0.0007 5 10 6 6 8 | 5 | 2 12 9 4 7 > 0.9993 || = 0.47 511 479 474 507 472 | 500 < 0.0008 5 4 8 4 6 | 5 | 7 2 4 3 4 > 0.9992 || = 0.46 474 475 513 442 485 | 500 < 0.0009 9 5 7 7 4 | 5 | 6 9 5 9 4 > 0.9991 || = 0.45 492 489 499 447 517 | 500 < 0.001 14 7 5 1 1 | 5 | 13 8 7 13 10 > 0.999 || = 0.44 464 507 470 482 526 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 548 525 513 470 508 | 500 < 0.001 77 62 48 44 49 | 50 | 62 57 48 53 44 > 0.999 || = 0.42 552 488 533 524 531 | 500 < 0.002 58 36 49 51 60 | 50 | 64 57 63 68 55 > 0.998 || = 0.41 536 481 543 508 497 | 500 < 0.003 43 50 55 42 52 | 50 | 46 44 47 47 54 > 0.997 || = 0.40 506 522 514 485 477 | 500 < 0.004 54 47 57 41 50 | 50 | 31 47 43 34 45 > 0.996 || = 0.39 520 516 523 542 478 | 500 < 0.005 60 36 50 49 61 | 50 | 35 35 36 35 32 > 0.995 || = 0.38 512 485 464 510 506 | 500 < 0.006 49 60 52 54 51 | 50 | 50 41 61 46 53 > 0.994 || = 0.37 500 489 513 529 482 | 500 < 0.007 64 45 57 55 51 | 50 | 52 46 47 39 60 > 0.993 || = 0.36 454 499 449 520 479 | 500 < 0.008 51 42 51 50 64 | 50 | 67 42 68 56 55 > 0.992 || = 0.35 455 470 457 466 463 | 500 < 0.009 47 61 44 54 45 | 50 | 72 63 64 54 62 > 0.991 || = 0.34 468 485 496 520 500 | 500 < 0.01 43 56 52 51 49 | 50 | 57 52 43 62 55 > 0.99 || = 0.33 488 469 514 493 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 484 512 488 545 555 | 500 < 0.01 546 495 515 491 532 | 497.5 | 536 484 520 494 515 > 0.99 || = 0.31 505 546 526 511 505 | 500 = 0.01 231 249 229 247 243 | 252.5 | 272 272 274 282 266 = 0.99 || = 0.30 533 495 521 491 499 | 500 = 0.02 493 479 458 546 521 | 500 | 451 444 445 462 415 = 0.98 || = 0.29 516 496 523 508 464 | 500 =================================================================| 500 | 497 519 487 519 524 = 0.97 || = 0.28 507 507 515 515 522 | 500 smarsa_MatrixRank test: | 500 | 494 568 547 515 543 = 0.96 || = 0.27 508 472 493 465 495 | 500 ----------------------------------------------- | 500 | 489 449 527 494 532 = 0.95 || = 0.26 500 497 487 525 473 | 500 N = 1, n = 5000, r = 26, s = 4, L = 1000, k = 1000 | 500 | 453 467 469 444 463 = 0.94 || = 0.25 452 461 420 466 471 | 500 | 500 | 465 478 456 423 480 = 0.93 || = 0.24 487 498 524 512 500 | 500 | 500 | 536 536 539 528 510 = 0.92 || = 0.23 529 502 524 521 485 | 500 =================================================================| 500 | 491 518 512 527 570 = 0.91 || = 0.22 493 509 459 536 533 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 540 525 512 566 537 = 0.90 || = 0.21 505 512 540 521 537 | 500 -----------------------------------------------------------------| 500 | 458 473 456 501 469 = 0.89 || = 0.20 506 487 497 493 529 | 500 SD Bern.: d 1.25585 1.55898 1.88135 | 500 | 479 448 493 533 486 = 0.88 || = 0.19 474 519 529 459 465 | 500 s 1.22139 1.33557 1.18548 | 500 | 446 501 430 427 435 = 0.87 || = 0.18 458 508 486 477 478 | 500 t 1.34738 0.58849 1.50140 | 500 | 487 483 485 480 478 = 0.86 || = 0.17 482 517 502 509 499 | 500 m 1.36619 0.69460 1.52127 | 500 | 564 512 571 547 526 = 0.85 || = 0.16 544 532 487 538 515 | 500 x 1.27265 0.94915 1.20807 | 500 | 507 519 503 574 540 = 0.84 || = 0.15 498 465 533 517 502 | 500 | 500 | 508 530 530 564 472 = 0.83 || = 0.14 526 511 510 512 487 | 500 Changes: d 38 5 2 | 500 | 515 496 496 515 512 = 0.82 || = 0.13 494 467 490 484 524 | 500 s 44 4 2 | 500 | 486 499 506 516 453 = 0.81 || = 0.12 522 492 472 481 473 | 500 t 50 5 6 | 500 | 581 495 521 490 514 = 0.80 || = 0.11 548 472 515 478 507 | 500 m 40 5 2 | 500 | 487 473 453 460 495 = 0.79 || = 0.10 487 492 516 484 512 | 500 x 46 4 3 | 500 | 466 472 456 449 477 = 0.78 || = 0.09 478 491 490 475 520 | 500 -----------------------------------------------------------------| 500 | 486 487 454 474 510 = 0.77 || = 0.08 493 501 507 482 500 | 500 Aver./ d 0.49970 499 > 500: 2 4 6 4 7 5 5 4 5 3 | 500 | 499 510 500 537 546 = 0.76 || = 0.07 500 494 495 493 516 | 500 median s 0.50045 497 ----- 3 5 4 3 3 6 2 4 5 5 | 500 | 511 549 548 538 578 = 0.75 || = 0.06 485 500 511 487 508 | 500 t 0.50031 502 4 6 5 5 6 4 7 5 5 6 | 500 | 533 561 505 493 497 = 0.74 || = 0.05 517 536 500 489 486 | 500 m 0.50106 496 1 4 7 7 3 4 6 3 8 5 | 500 | 476 497 512 482 481 = 0.73 || = 0.04 472 498 515 486 510 | 500 x 0.49945 500 6 5 4 4 4 6 4 6 4 7 | 500 | 518 561 540 516 507 = 0.72 || = 0.03 482 523 477 469 479 | 500 -----------------------------------------------------------------| 500 | 500 499 500 481 527 = 0.71 || = 0.02 493 479 458 546 521 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 489 485 521 501 464 = 0.70 || = 0.01 231 249 229 247 243 | 252.5 d 0 0 6 16 59 13 6 1 0 | 500 | 464 477 470 479 503 = 0.69 || < 0.01 546 495 515 491 532 | 497.5 s 0 0 3 17 62 11 6 2 0 | 500 | 475 461 467 486 450 = 0.68 ||========================================================================= t 0 2 6 17 52 18 5 1 0 | 500 | 493 484 502 470 439 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 2 5 13 59 14 7 1 0 | 500 | 503 470 515 502 470 = 0.66 ||========================================================================= x 0 1 5 14 60 17 2 2 0 | 500 | 524 497 563 454 505 = 0.65 || smarsa_MatrixRank test: no 135 test no 136 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 136 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 3 3 2 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 390 357 403 394 414 | 500 < 0.00002 1 3 2 1 2 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 869 800 849 821 816 | 500 < 0.00003 1 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 0 0 0 0 0 | 500 < 0.00004 0 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 0 0 0 0 0 | 500 < 0.00005 2 1 2 0 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 796 761 728 789 771 | 500 < 0.00006 1 2 1 2 1 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 2025 2016 1970 2043 1964 | 500 < 0.00007 3 2 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 0 0 0 0 0 | 500 < 0.00008 3 0 2 0 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 0 0 0 0 0 | 500 < 0.00009 2 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 0 0 0 0 0 | 500 < 0.0001 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 741 764 740 729 772 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 659 674 694 714 737 | 500 < 0.0001 13 16 11 7 8 | 5 | 0 0 0 0 0 > 0.9999 || = 0.53 356 407 400 365 364 | 500 < 0.0002 2 8 8 3 6 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 334 350 336 326 340 | 500 < 0.0003 9 11 5 10 10 | 5 | 0 0 0 0 0 > 0.9997 || = 0.51 748 752 685 726 700 | 500 < 0.0004 4 8 7 3 8 | 5 | 0 0 0 0 0 > 0.9996 || = 0.50 309 307 293 295 322 | 500 < 0.0005 7 5 6 4 6 | 5 | 0 0 0 0 0 > 0.9995 || = 0.49 644 620 584 579 652 | 500 < 0.0006 0 3 2 1 6 | 5 | 0 0 0 0 0 > 0.9994 || = 0.48 968 980 923 968 956 | 500 < 0.0007 4 10 3 7 3 | 5 | 0 0 0 0 0 > 0.9993 || = 0.47 667 654 651 682 672 | 500 < 0.0008 5 4 3 8 5 | 5 | 0 0 0 0 0 > 0.9992 || = 0.46 0 0 0 0 0 | 500 < 0.0009 5 7 2 5 6 | 5 | 0 0 0 0 0 > 0.9991 || = 0.45 608 652 629 558 591 | 500 < 0.001 6 11 14 9 6 | 5 | 0 0 0 0 0 > 0.999 || = 0.44 879 869 885 872 873 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 0 0 0 0 0 | 500 < 0.001 55 83 61 57 64 | 50 | 0 0 0 0 0 > 0.999 || = 0.42 274 286 312 328 321 | 500 < 0.002 57 48 47 47 34 | 50 | 0 0 0 0 0 > 0.998 || = 0.41 844 734 753 780 807 | 500 < 0.003 65 77 65 68 60 | 50 | 0 0 0 0 0 > 0.997 || = 0.40 843 881 847 926 852 | 500 < 0.004 41 32 34 43 32 | 50 | 0 0 0 0 0 > 0.996 || = 0.39 272 280 266 264 288 | 500 < 0.005 40 55 49 46 44 | 50 | 0 0 0 0 0 > 0.995 || = 0.38 266 273 274 224 275 | 500 < 0.006 55 55 58 59 63 | 50 | 609 646 599 609 650 > 0.994 || = 0.37 489 452 471 423 478 | 500 < 0.007 62 62 70 63 58 | 50 | 0 0 0 0 0 > 0.993 || = 0.36 435 445 507 462 468 | 500 < 0.008 21 24 18 17 24 | 50 | 0 0 0 0 0 > 0.992 || = 0.35 222 236 216 220 212 | 500 < 0.009 56 49 48 34 50 | 50 | 0 0 0 0 0 > 0.991 || = 0.34 684 681 672 676 742 | 500 < 0.01 82 100 87 73 94 | 50 | 0 0 0 0 0 > 0.99 || = 0.33 690 649 698 664 663 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 196 202 205 208 217 | 500 < 0.01 534 585 537 507 523 | 497.5 | 609 646 599 609 650 > 0.99 || = 0.31 797 797 788 804 816 | 500 = 0.01 232 233 217 270 214 | 252.5 | 0 0 0 0 0 = 0.99 || = 0.30 1216 1287 1339 1266 1252 | 500 = 0.02 547 545 550 540 518 | 500 | 0 0 0 0 0 = 0.98 || = 0.29 385 374 397 364 376 | 500 =================================================================| 500 | 658 686 623 694 677 = 0.97 || = 0.28 206 184 200 190 202 | 500 smarsa_MatrixRank test: | 500 | 1910 1916 2001 1874 1945 = 0.96 || = 0.27 189 175 186 192 192 | 500 ----------------------------------------------- | 500 | 0 0 0 0 0 = 0.95 || = 0.26 684 645 713 678 597 | 500 N = 1, n = 80, r = 15, s = 15, L = 5000, k = 5000 | 500 | 0 0 0 0 0 = 0.94 || = 0.25 462 448 459 412 462 | 500 | 500 | 0 0 0 0 0 = 0.93 || = 0.24 483 498 484 497 495 | 500 | 500 | 637 703 639 609 626 = 0.92 || = 0.23 341 328 326 339 311 | 500 =================================================================| 500 | 552 583 564 587 581 = 0.91 || = 0.22 444 429 396 449 417 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 556 571 581 595 583 = 0.90 || = 0.21 585 576 595 587 600 | 500 -----------------------------------------------------------------| 500 | 592 592 591 601 567 = 0.89 || = 0.20 878 893 929 906 906 | 500 SD Bern.: d 17.34374 2.25944 25.89657 | 500 | 0 0 0 0 0 = 0.88 || = 0.19 133 152 133 162 154 | 500 s 17.17558 3.32340 27.49887 | 500 | 1115 1082 1210 1142 1151 = 0.87 || = 0.18 398 365 349 366 355 | 500 t 17.34523 2.63684 25.46468 | 500 | 547 545 547 541 554 = 0.86 || = 0.17 1002 934 1004 1009 970 | 500 m 17.35825 2.26873 25.89657 | 500 | 580 617 578 623 574 = 0.85 || = 0.16 93 93 100 106 106 | 500 x 17.20076 2.74253 27.67247 | 500 | 563 629 582 560 612 = 0.84 || = 0.15 580 582 599 650 559 | 500 | 500 | 530 534 527 543 549 = 0.83 || = 0.14 486 471 511 511 503 | 500 Changes: d 52 4 2 | 500 | 567 613 579 548 547 = 0.82 || = 0.13 496 554 536 509 497 | 500 s 54 6 2 | 500 | 558 559 557 519 557 = 0.81 || = 0.12 441 384 421 377 364 | 500 t 54 6 2 | 500 | 0 0 0 0 0 = 0.80 || = 0.11 568 643 624 655 625 | 500 m 50 6 2 | 500 | 0 0 0 0 0 = 0.79 || = 0.10 473 453 474 457 457 | 500 x 54 6 2 | 500 | 505 540 550 578 546 = 0.78 || = 0.09 444 447 470 469 419 | 500 -----------------------------------------------------------------| 500 | 520 498 530 500 481 = 0.77 || = 0.08 571 623 541 582 596 | 500 Aver./ d 0.49933 496 > 500: 6 3 3 4 7 5 3 4 9 5 | 500 | 476 488 455 493 505 = 0.76 || = 0.07 553 527 572 536 572 | 500 median s 0.50041 498 ----- 6 4 3 4 7 5 3 3 9 5 | 500 | 477 444 495 445 450 = 0.75 || = 0.06 270 269 275 282 257 | 500 t 0.49838 511 6 5 3 5 7 5 3 4 9 5 | 500 | 1442 1362 1429 1478 1449 = 0.74 || = 0.05 674 659 640 683 687 | 500 m 0.49883 509 7 5 3 4 7 5 3 3 9 5 | 500 | 0 0 0 0 0 = 0.73 || = 0.04 546 576 601 543 569 | 500 x 0.50071 497 6 4 3 4 7 5 3 4 9 5 | 500 | 949 964 935 989 949 = 0.72 || = 0.03 321 320 312 298 357 | 500 -----------------------------------------------------------------| 500 | 499 454 421 467 489 = 0.71 || = 0.02 547 545 550 540 518 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 0 0 0 0 0 = 0.70 || = 0.01 232 233 217 270 214 | 252.5 d 37 0 5 5 7 2 8 6 31 | 500 | 434 447 405 386 405 = 0.69 || < 0.01 534 585 537 507 523 | 497.5 s 38 1 8 2 3 3 4 6 36 | 500 | 1546 1457 1407 1418 1436 = 0.68 ||========================================================================= t 39 2 2 4 4 5 5 6 34 | 500 | 0 0 0 0 0 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 39 2 2 4 7 6 3 5 33 | 500 | 0 0 0 0 0 = 0.66 ||========================================================================= x 38 3 2 3 8 1 6 6 34 | 500 | 938 939 926 969 922 = 0.65 || smarsa_MatrixRank test: no 136 test no 137 TestU01 250000 runs BigCrush Test smarsa_S smarsa_MatrixRank test: test no 137 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 402 404 390 389 428 | 500 < 0.00002 1 1 1 1 1 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 831 795 902 837 846 | 500 < 0.00003 0 1 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 0 0 0 0 0 | 500 < 0.00004 2 0 0 1 2 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 0 0 0 0 0 | 500 < 0.00005 0 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 751 756 780 768 766 | 500 < 0.00006 1 0 1 2 1 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 2047 1927 2076 1986 1985 | 500 < 0.00007 0 1 2 0 2 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 0 0 0 0 0 | 500 < 0.00008 2 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 0 0 0 0 0 | 500 < 0.00009 0 1 1 2 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 0 0 0 0 0 | 500 < 0.0001 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 770 706 706 732 773 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 673 706 697 659 693 | 500 < 0.0001 6 6 7 10 7 | 5 | 0 0 0 0 0 > 0.9999 || = 0.53 358 385 378 375 378 | 500 < 0.0002 3 6 3 6 6 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 310 339 311 335 328 | 500 < 0.0003 11 5 8 6 9 | 5 | 0 0 0 0 0 > 0.9997 || = 0.51 700 727 718 683 661 | 500 < 0.0004 2 6 6 4 5 | 5 | 0 0 0 0 0 > 0.9996 || = 0.50 291 302 265 289 290 | 500 < 0.0005 6 4 8 6 5 | 5 | 0 0 0 0 0 > 0.9995 || = 0.49 619 643 636 595 583 | 500 < 0.0006 1 2 0 1 4 | 5 | 0 0 0 0 0 > 0.9994 || = 0.48 916 968 878 930 925 | 500 < 0.0007 7 5 3 3 7 | 5 | 0 0 0 0 0 > 0.9993 || = 0.47 649 681 610 660 684 | 500 < 0.0008 6 7 3 3 6 | 5 | 0 0 0 0 0 > 0.9992 || = 0.46 0 0 0 0 0 | 500 < 0.0009 2 3 3 4 3 | 5 | 0 0 0 0 0 > 0.9991 || = 0.45 595 593 637 623 601 | 500 < 0.001 12 3 4 8 7 | 5 | 0 0 0 0 0 > 0.999 || = 0.44 924 924 942 863 880 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 0 0 0 0 0 | 500 < 0.001 56 47 45 51 59 | 50 | 0 0 0 0 0 > 0.999 || = 0.42 301 316 313 337 317 | 500 < 0.002 46 47 41 40 32 | 50 | 0 0 0 0 0 > 0.998 || = 0.41 748 801 767 795 741 | 500 < 0.003 79 57 64 56 69 | 50 | 0 0 0 0 0 > 0.997 || = 0.40 860 872 923 854 870 | 500 < 0.004 35 38 51 36 32 | 50 | 0 0 0 0 0 > 0.996 || = 0.39 286 251 288 286 282 | 500 < 0.005 44 44 32 41 47 | 50 | 0 0 0 0 0 > 0.995 || = 0.38 257 268 303 264 269 | 500 < 0.006 61 63 59 59 47 | 50 | 656 652 688 618 623 > 0.994 || = 0.37 458 440 489 406 448 | 500 < 0.007 56 72 68 72 67 | 50 | 0 0 0 0 0 > 0.993 || = 0.36 456 447 483 487 466 | 500 < 0.008 25 23 19 22 20 | 50 | 0 0 0 0 0 > 0.992 || = 0.35 239 216 216 195 236 | 500 < 0.009 51 48 33 44 46 | 50 | 0 0 0 0 0 > 0.991 || = 0.34 642 706 657 697 703 | 500 < 0.01 96 91 78 80 110 | 50 | 0 0 0 0 0 > 0.99 || = 0.33 648 621 653 638 646 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 209 185 203 191 217 | 500 < 0.01 549 530 490 501 529 | 497.5 | 656 652 688 618 623 > 0.99 || = 0.31 807 843 790 796 836 | 500 = 0.01 251 244 255 251 213 | 252.5 | 0 0 0 0 0 = 0.99 || = 0.30 1289 1264 1258 1220 1218 | 500 = 0.02 564 561 545 548 569 | 500 | 0 0 0 0 0 = 0.98 || = 0.29 363 398 367 383 372 | 500 =================================================================| 500 | 666 640 599 691 654 = 0.97 || = 0.28 201 174 206 203 177 | 500 smarsa_MatrixRank test: | 500 | 1835 1833 1890 1984 1817 = 0.96 || = 0.27 161 189 197 199 193 | 500 ----------------------------------------------- | 500 | 0 0 0 0 0 = 0.95 || = 0.26 708 679 717 686 713 | 500 N = 1, n = 80, r = 0, s = 30, L = 5000, k = 5000 | 500 | 0 0 0 0 0 = 0.94 || = 0.25 485 431 486 466 504 | 500 | 500 | 0 0 0 0 0 = 0.93 || = 0.24 510 461 501 540 518 | 500 | 500 | 660 652 630 637 607 = 0.92 || = 0.23 308 307 312 326 307 | 500 =================================================================| 500 | 553 586 579 630 609 = 0.91 || = 0.22 474 447 435 432 423 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 596 594 586 593 584 = 0.90 || = 0.21 647 593 611 601 642 | 500 -----------------------------------------------------------------| 500 | 592 600 549 563 537 = 0.89 || = 0.20 946 909 892 990 1008 | 500 SD Bern.: d 17.19465 2.84852 27.93299 | 500 | 0 0 0 0 0 = 0.88 || = 0.19 148 145 133 152 147 | 500 s 17.06558 2.57577 27.75929 | 500 | 1133 1184 1124 1101 1183 = 0.87 || = 0.18 374 338 336 369 333 | 500 t 17.30036 2.47752 29.32486 | 500 | 558 556 545 560 532 = 0.86 || = 0.17 982 956 964 1007 932 | 500 m 17.26897 2.32451 26.28571 | 500 | 599 608 611 587 559 = 0.85 || = 0.16 97 114 112 103 102 | 500 x 17.09042 3.44061 26.50207 | 500 | 607 611 569 605 598 = 0.84 || = 0.15 583 632 607 561 631 | 500 | 500 | 495 530 563 527 494 = 0.83 || = 0.14 504 453 484 501 490 | 500 Changes: d 56 6 2 | 500 | 583 566 506 600 579 = 0.82 || = 0.13 469 550 525 493 487 | 500 s 54 5 2 | 500 | 563 567 560 517 561 = 0.81 || = 0.12 425 435 428 427 402 | 500 t 55 5 2 | 500 | 0 0 0 0 0 = 0.80 || = 0.11 625 582 614 646 633 | 500 m 54 6 2 | 500 | 0 0 0 0 0 = 0.79 || = 0.10 479 444 499 435 484 | 500 x 54 6 2 | 500 | 528 557 546 536 548 = 0.78 || = 0.09 442 430 479 447 454 | 500 -----------------------------------------------------------------| 500 | 490 551 551 567 525 = 0.77 || = 0.08 580 592 539 540 563 | 500 Aver./ d 0.49765 495 > 500: 6 4 4 4 7 5 3 3 8 5 | 500 | 478 490 472 466 460 = 0.76 || = 0.07 526 522 551 610 590 | 500 median s 0.50022 490 ----- 6 4 3 4 7 5 3 4 9 5 | 500 | 483 458 465 491 450 = 0.75 || = 0.06 246 251 272 266 280 | 500 t 0.49881 501 6 4 4 4 7 5 3 4 9 5 | 500 | 1436 1445 1454 1438 1432 = 0.74 || = 0.05 720 682 632 663 689 | 500 m 0.49994 501 6 4 4 4 7 5 3 4 9 5 | 500 | 0 0 0 0 0 = 0.73 || = 0.04 581 620 576 569 598 | 500 x 0.49621 494 6 3 5 4 7 5 3 4 8 5 | 500 | 938 1007 972 985 972 = 0.72 || = 0.03 308 317 309 309 334 | 500 -----------------------------------------------------------------| 500 | 440 451 449 439 470 = 0.71 || = 0.02 564 561 545 548 569 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 0 0 0 0 0 = 0.70 || = 0.01 251 244 255 251 213 | 252.5 d 37 1 3 4 9 2 5 4 36 | 500 | 447 441 411 419 412 = 0.69 || < 0.01 549 530 490 501 529 | 497.5 s 37 2 8 2 3 2 6 3 38 | 500 | 1400 1414 1431 1440 1466 = 0.68 ||========================================================================= t 38 1 2 2 10 2 8 4 34 | 500 | 0 0 0 0 0 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 38 3 3 2 7 4 4 3 37 | 500 | 0 0 0 0 0 = 0.66 ||========================================================================= x 37 3 4 3 6 4 4 4 36 | 500 | 972 935 907 892 941 = 0.65 || smarsa_MatrixRank test: no 137 test no 138 TestU01 250000 runs BigCrush Test smarsa_S smarsa_Savir2 test: test no 138 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 2 0 0 0 | 0.5 | 4 1 1 1 2 > 0.99999 || = 0.64 505 494 514 507 474 | 500 < 0.00002 0 0 0 3 0 | 0.5 | 1 2 0 0 2 > 0.99998 || = 0.63 477 491 464 484 483 | 500 < 0.00003 0 0 2 0 1 | 0.5 | 0 2 0 0 0 > 0.99997 || = 0.62 502 500 485 558 461 | 500 < 0.00004 2 0 0 1 0 | 0.5 | 2 1 3 0 1 > 0.99996 || = 0.61 529 504 484 493 474 | 500 < 0.00005 1 2 1 1 0 | 0.5 | 2 1 1 0 0 > 0.99995 || = 0.60 485 508 531 493 513 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 2 2 0 1 0 > 0.99994 || = 0.59 504 477 510 468 506 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 1 0 2 2 0 > 0.99993 || = 0.58 523 500 472 491 540 | 500 < 0.00008 1 1 0 3 0 | 0.5 | 2 0 1 0 0 > 0.99992 || = 0.57 507 520 510 509 491 | 500 < 0.00009 0 0 1 0 0 | 0.5 | 0 1 2 2 0 > 0.99991 || = 0.56 495 522 468 491 482 | 500 < 0.0001 0 1 0 1 1 | 0.5 | 0 1 3 0 1 > 0.9999 || = 0.55 476 526 489 479 567 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 510 507 473 497 508 | 500 < 0.0001 5 6 5 9 3 | 5 | 14 11 13 6 6 > 0.9999 || = 0.53 492 485 481 487 517 | 500 < 0.0002 6 2 9 3 2 | 5 | 3 4 5 6 2 > 0.9998 || = 0.52 497 500 503 469 486 | 500 < 0.0003 7 3 5 3 2 | 5 | 4 11 11 9 7 > 0.9997 || = 0.51 494 499 496 490 485 | 500 < 0.0004 5 5 8 9 9 | 5 | 8 7 8 6 8 > 0.9996 || = 0.50 485 468 499 482 488 | 500 < 0.0005 4 3 8 8 7 | 5 | 17 5 13 5 4 > 0.9995 || = 0.49 530 460 526 521 526 | 500 < 0.0006 5 6 1 7 10 | 5 | 2 4 5 12 11 > 0.9994 || = 0.48 507 501 503 474 542 | 500 < 0.0007 6 7 4 1 7 | 5 | 7 8 6 4 5 > 0.9993 || = 0.47 455 483 519 509 515 | 500 < 0.0008 4 8 11 5 4 | 5 | 9 9 10 4 9 > 0.9992 || = 0.46 481 502 469 508 529 | 500 < 0.0009 2 4 3 4 4 | 5 | 5 5 5 4 9 > 0.9991 || = 0.45 509 471 533 494 512 | 500 < 0.001 7 5 8 6 8 | 5 | 5 6 4 9 10 > 0.999 || = 0.44 523 550 535 526 522 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 504 517 509 479 514 | 500 < 0.001 51 49 62 55 56 | 50 | 74 70 80 65 71 > 0.999 || = 0.42 500 513 499 519 465 | 500 < 0.002 43 66 50 44 45 | 50 | 56 56 60 63 64 > 0.998 || = 0.41 506 494 485 539 497 | 500 < 0.003 65 53 48 55 45 | 50 | 67 67 59 58 54 > 0.997 || = 0.40 491 466 494 513 510 | 500 < 0.004 54 58 49 54 58 | 50 | 66 56 40 42 49 > 0.996 || = 0.39 500 481 510 494 472 | 500 < 0.005 41 61 67 44 41 | 50 | 49 39 44 66 53 > 0.995 || = 0.38 493 511 464 482 499 | 500 < 0.006 42 59 57 69 57 | 50 | 53 51 64 54 58 > 0.994 || = 0.37 494 479 546 520 485 | 500 < 0.007 59 50 51 37 60 | 50 | 62 50 49 50 64 > 0.993 || = 0.36 490 520 523 455 485 | 500 < 0.008 50 52 52 46 57 | 50 | 49 53 54 48 50 > 0.992 || = 0.35 503 507 469 477 506 | 500 < 0.009 49 52 51 49 49 | 50 | 44 52 48 56 63 > 0.991 || = 0.34 499 527 523 504 521 | 500 < 0.01 60 65 57 54 46 | 50 | 56 47 47 41 50 > 0.99 || = 0.33 532 519 487 500 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 484 531 516 485 494 | 500 < 0.01 514 565 544 507 514 | 497.5 | 576 541 545 543 576 > 0.99 || = 0.31 474 465 525 467 478 | 500 = 0.01 276 276 257 266 253 | 252.5 | 271 232 279 251 229 = 0.99 || = 0.30 488 456 519 478 506 | 500 = 0.02 505 509 527 542 533 | 500 | 491 492 516 510 492 = 0.98 || = 0.29 522 490 490 490 508 | 500 =================================================================| 500 | 502 527 490 500 500 = 0.97 || = 0.28 512 465 482 498 529 | 500 smarsa_Savir2 test: | 500 | 471 493 493 498 494 = 0.96 || = 0.27 502 468 500 491 486 | 500 ----------------------------------------------- | 500 | 447 504 461 488 488 = 0.95 || = 0.26 496 448 507 483 492 | 500 N = 10, n = 10000000, r = 10, m = 1048576, t = 30 | 500 | 467 538 502 493 519 = 0.94 || = 0.25 497 439 531 523 477 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 488 462 451 479 556 = 0.93 || = 0.24 489 533 499 481 507 | 500 | 500 | 496 501 493 466 477 = 0.92 || = 0.23 548 503 502 467 508 | 500 =================================================================| 500 | 479 481 468 493 524 = 0.91 || = 0.22 485 437 483 482 478 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 483 503 460 492 478 = 0.90 || = 0.21 506 499 522 516 496 | 500 -----------------------------------------------------------------| 500 | 464 468 507 471 462 = 0.89 || = 0.20 491 465 477 486 451 | 500 SD Bern.: d 1.06730 1.11230 1.66455 | 500 | 526 486 537 457 457 = 0.88 || = 0.19 546 472 524 488 513 | 500 s 1.19869 1.23754 1.34602 | 500 | 481 499 473 478 505 = 0.87 || = 0.18 474 510 458 517 492 | 500 t 1.06251 1.04167 1.69966 | 500 | 486 491 499 485 482 = 0.86 || = 0.17 505 539 525 504 505 | 500 m 1.01191 1.18464 1.35344 | 500 | 459 490 521 503 490 = 0.85 || = 0.16 497 522 512 497 540 | 500 x 1.16158 0.94492 1.47856 | 500 | 531 479 495 524 500 = 0.84 || = 0.15 510 527 507 504 469 | 500 | 500 | 504 515 531 487 513 = 0.83 || = 0.14 499 510 479 500 468 | 500 Changes: d 52 6 4 | 500 | 497 487 484 474 471 = 0.82 || = 0.13 524 507 512 505 544 | 500 s 42 3 5 | 500 | 458 513 481 502 463 = 0.81 || = 0.12 488 493 500 515 478 | 500 t 52 2 5 | 500 | 475 510 525 544 466 = 0.80 || = 0.11 518 528 498 486 518 | 500 m 44 6 5 | 500 | 492 456 477 507 496 = 0.79 || = 0.10 513 476 481 510 531 | 500 x 46 5 5 | 500 | 471 521 467 530 515 = 0.78 || = 0.09 572 524 486 474 525 | 500 -----------------------------------------------------------------| 500 | 473 484 516 476 519 = 0.77 || = 0.08 529 488 481 517 495 | 500 Aver./ d 0.49595 499 > 500: 9 6 5 2 6 4 6 3 3 3 | 500 | 505 459 472 470 483 = 0.76 || = 0.07 502 512 486 520 549 | 500 median s 0.49713 500 ----- 9 7 2 6 5 5 4 4 3 5 | 500 | 490 491 516 560 509 = 0.75 || = 0.06 469 568 513 521 493 | 500 t 0.49703 500 7 5 4 7 6 4 5 3 4 4 | 500 | 464 499 479 491 456 = 0.74 || = 0.05 524 554 531 533 524 | 500 m 0.49821 497 9 6 2 2 7 1 7 5 3 2 | 500 | 538 497 480 488 516 = 0.73 || = 0.04 521 545 532 572 504 | 500 x 0.49736 499 8 6 4 3 8 6 3 4 2 4 | 500 | 492 503 489 517 479 = 0.72 || = 0.03 532 533 557 507 543 | 500 -----------------------------------------------------------------| 500 | 532 513 484 500 463 = 0.71 || = 0.02 505 509 527 542 533 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 465 490 511 518 502 = 0.70 || = 0.01 276 276 257 266 253 | 252.5 d 0 0 2 16 62 17 2 2 0 | 500 | 526 456 518 516 506 = 0.69 || < 0.01 514 565 544 507 514 | 497.5 s 0 0 3 18 60 15 3 2 0 | 500 | 502 524 451 481 493 = 0.68 ||========================================================================= t 0 0 2 16 62 17 4 0 0 | 500 | 469 514 503 533 457 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 13 74 9 3 1 0 | 500 | 526 523 505 510 536 = 0.66 ||========================================================================= x 0 0 1 19 63 14 2 2 0 | 500 | 493 499 485 521 463 = 0.65 || smarsa_Savir2 test: no 138 test no 139 TestU01 250000 runs BigCrush Test smarsa_S smarsa_Savir2 test: test no 139 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 1 1 | 0.5 | 0 2 1 0 0 > 0.99999 || = 0.64 486 515 493 494 498 | 500 < 0.00002 1 1 0 0 1 | 0.5 | 2 1 1 0 0 > 0.99998 || = 0.63 500 477 513 475 505 | 500 < 0.00003 1 0 0 1 0 | 0.5 | 1 0 2 1 1 > 0.99997 || = 0.62 515 474 484 464 494 | 500 < 0.00004 0 1 0 0 1 | 0.5 | 0 0 0 0 2 > 0.99996 || = 0.61 498 466 503 504 467 | 500 < 0.00005 0 1 1 0 0 | 0.5 | 0 0 0 1 0 > 0.99995 || = 0.60 494 478 480 486 518 | 500 < 0.00006 0 1 0 0 1 | 0.5 | 0 0 2 0 1 > 0.99994 || = 0.59 480 505 485 500 479 | 500 < 0.00007 0 1 1 0 0 | 0.5 | 0 1 1 0 0 > 0.99993 || = 0.58 517 549 520 478 460 | 500 < 0.00008 2 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 535 491 495 492 513 | 500 < 0.00009 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 489 505 515 518 490 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 1 0 0 1 > 0.9999 || = 0.55 498 500 488 514 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 522 462 513 498 484 | 500 < 0.0001 5 6 2 2 5 | 5 | 3 5 7 2 5 > 0.9999 || = 0.53 528 487 525 516 507 | 500 < 0.0002 4 5 8 5 1 | 5 | 2 5 4 1 3 > 0.9998 || = 0.52 533 469 482 538 506 | 500 < 0.0003 4 7 3 5 1 | 5 | 3 5 6 6 6 > 0.9997 || = 0.51 465 479 498 481 513 | 500 < 0.0004 7 7 8 5 7 | 5 | 4 3 4 4 3 > 0.9996 || = 0.50 528 494 525 440 515 | 500 < 0.0005 6 6 5 6 6 | 5 | 3 5 7 3 5 > 0.9995 || = 0.49 547 495 496 522 479 | 500 < 0.0006 2 5 5 3 6 | 5 | 6 7 8 1 4 > 0.9994 || = 0.48 487 522 536 508 482 | 500 < 0.0007 5 4 8 8 7 | 5 | 4 3 6 2 6 > 0.9993 || = 0.47 519 534 460 533 481 | 500 < 0.0008 6 3 9 6 4 | 5 | 7 6 8 2 6 > 0.9992 || = 0.46 516 469 491 457 456 | 500 < 0.0009 4 5 4 3 10 | 5 | 2 5 3 7 5 > 0.9991 || = 0.45 521 480 475 498 522 | 500 < 0.001 0 6 3 3 5 | 5 | 7 2 7 2 6 > 0.999 || = 0.44 484 513 507 532 476 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 494 509 501 512 542 | 500 < 0.001 43 54 55 46 52 | 50 | 41 46 60 30 49 > 0.999 || = 0.42 530 471 467 504 515 | 500 < 0.002 49 43 41 53 43 | 50 | 56 60 31 42 49 > 0.998 || = 0.41 493 493 535 483 519 | 500 < 0.003 52 44 50 52 49 | 50 | 55 46 45 40 47 > 0.997 || = 0.40 496 475 460 504 500 | 500 < 0.004 50 46 57 47 45 | 50 | 55 52 73 41 58 > 0.996 || = 0.39 527 492 510 502 488 | 500 < 0.005 52 53 35 56 43 | 50 | 50 48 67 51 40 > 0.995 || = 0.38 482 502 493 467 509 | 500 < 0.006 53 50 46 38 54 | 50 | 50 49 51 52 53 > 0.994 || = 0.37 446 530 501 508 498 | 500 < 0.007 48 41 45 34 51 | 50 | 50 54 54 43 49 > 0.993 || = 0.36 511 486 457 492 476 | 500 < 0.008 58 46 53 46 56 | 50 | 55 55 49 57 45 > 0.992 || = 0.35 491 482 451 497 497 | 500 < 0.009 41 54 49 69 41 | 50 | 53 49 63 48 38 > 0.991 || = 0.34 498 497 500 476 511 | 500 < 0.01 45 49 47 43 57 | 50 | 56 47 54 62 43 > 0.99 || = 0.33 486 502 473 512 511 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 531 462 528 521 557 | 500 < 0.01 491 480 478 484 491 | 497.5 | 521 506 547 466 471 > 0.99 || = 0.31 487 493 459 505 467 | 500 = 0.01 272 231 251 238 245 | 252.5 | 255 214 255 231 253 = 0.99 || = 0.30 496 523 462 498 468 | 500 = 0.02 478 473 449 448 496 | 500 | 528 502 528 562 495 = 0.98 || = 0.29 480 536 491 495 477 | 500 =================================================================| 500 | 502 530 526 510 474 = 0.97 || = 0.28 490 512 513 522 491 | 500 smarsa_Savir2 test: | 500 | 499 447 537 510 522 = 0.96 || = 0.27 495 530 515 501 498 | 500 ----------------------------------------------- | 500 | 480 467 488 487 519 = 0.95 || = 0.26 472 490 479 494 531 | 500 N = 10, n = 10000000, r = 10, m = 1048576, t = 30 | 500 | 498 516 520 492 486 = 0.94 || = 0.25 505 477 473 508 493 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 534 526 535 505 496 = 0.93 || = 0.24 470 506 507 492 470 | 500 | 500 | 536 535 485 477 487 = 0.92 || = 0.23 502 533 503 495 484 | 500 =================================================================| 500 | 464 479 510 499 488 = 0.91 || = 0.22 482 520 485 532 471 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 470 503 470 504 554 = 0.90 || = 0.21 519 482 469 475 518 | 500 -----------------------------------------------------------------| 500 | 466 494 508 492 509 = 0.89 || = 0.20 468 516 490 501 484 | 500 SD Bern.: d 0.99535 0.69460 0.68881 | 500 | 496 525 508 542 533 = 0.88 || = 0.19 524 471 507 510 532 | 500 s 1.13063 0.69315 0.61997 | 500 | 496 548 492 494 533 = 0.87 || = 0.18 517 501 500 450 533 | 500 t 1.10103 0.93854 1.73694 | 500 | 495 509 518 495 484 = 0.86 || = 0.17 495 512 458 459 482 | 500 m 1.10867 1.34230 1.33931 | 500 | 520 527 486 479 526 = 0.85 || = 0.16 503 509 520 519 480 | 500 x 1.06117 0.78905 0.89821 | 500 | 502 508 499 473 491 = 0.84 || = 0.15 518 525 493 481 509 | 500 | 500 | 538 503 544 537 523 = 0.83 || = 0.14 442 479 523 499 495 | 500 Changes: d 47 6 3 | 500 | 529 509 507 481 531 = 0.82 || = 0.13 523 540 492 496 493 | 500 s 45 5 6 | 500 | 531 561 544 503 512 = 0.81 || = 0.12 507 474 470 476 467 | 500 t 57 5 4 | 500 | 505 503 527 477 488 = 0.80 || = 0.11 486 521 522 482 461 | 500 m 48 6 5 | 500 | 482 516 518 538 517 = 0.79 || = 0.10 495 483 502 476 493 | 500 x 46 4 4 | 500 | 531 558 534 504 532 = 0.78 || = 0.09 498 522 465 499 474 | 500 -----------------------------------------------------------------| 500 | 563 479 512 542 542 = 0.77 || = 0.08 510 478 462 499 447 | 500 Aver./ d 0.50195 498 > 500: 3 6 3 3 5 5 2 5 5 6 | 500 | 484 476 535 524 532 = 0.76 || = 0.07 510 469 505 475 518 | 500 median s 0.50230 502 ----- 3 6 7 4 4 3 5 5 9 6 | 500 | 503 515 473 550 537 = 0.75 || = 0.06 469 446 469 474 492 | 500 t 0.50622 501 2 5 4 3 4 4 5 9 6 8 | 500 | 481 514 517 534 528 = 0.74 || = 0.05 486 502 487 512 450 | 500 m 0.50272 499 3 2 5 5 7 4 5 8 4 4 | 500 | 474 488 506 472 478 = 0.73 || = 0.04 475 513 475 504 464 | 500 x 0.50429 497 2 3 2 4 4 5 6 7 8 3 | 500 | 505 494 526 509 535 = 0.72 || = 0.03 495 481 507 549 513 | 500 -----------------------------------------------------------------| 500 | 495 491 514 566 498 = 0.71 || = 0.02 478 473 449 448 496 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 478 545 476 527 519 = 0.70 || = 0.01 272 231 251 238 245 | 252.5 d 0 0 2 11 68 18 2 0 0 | 500 | 484 513 484 524 480 = 0.69 || < 0.01 491 480 478 484 491 | 497.5 s 0 0 3 19 59 15 5 0 0 | 500 | 489 470 540 473 525 = 0.68 ||========================================================================= t 0 0 2 19 60 18 2 0 0 | 500 | 502 525 563 541 517 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 18 63 13 4 0 0 | 500 | 470 472 499 485 519 = 0.66 ||========================================================================= x 0 0 2 16 65 16 2 0 0 | 500 | 487 539 528 521 516 = 0.65 || smarsa_Savir2 test: no 139 test no 140 TestU01 250000 runs BigCrush Test smarsa_S smarsa_Savir2 test: test no 140 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 509 436 501 489 501 | 500 < 0.00002 1 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 455 521 523 484 487 | 500 < 0.00003 0 0 1 0 0 | 0.5 | 0 0 0 0 2 > 0.99997 || = 0.62 493 501 474 489 489 | 500 < 0.00004 0 2 1 0 1 | 0.5 | 0 1 0 0 0 > 0.99996 || = 0.61 463 516 476 498 509 | 500 < 0.00005 1 2 1 1 0 | 0.5 | 0 0 0 0 1 > 0.99995 || = 0.60 507 501 511 509 503 | 500 < 0.00006 0 0 0 1 0 | 0.5 | 0 2 0 0 0 > 0.99994 || = 0.59 509 470 494 503 499 | 500 < 0.00007 0 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 499 492 500 482 484 | 500 < 0.00008 0 1 1 1 0 | 0.5 | 0 1 0 0 1 > 0.99992 || = 0.57 467 463 474 496 435 | 500 < 0.00009 1 0 0 0 0 | 0.5 | 0 0 0 2 0 > 0.99991 || = 0.56 517 484 508 479 487 | 500 < 0.0001 1 1 0 1 0 | 0.5 | 0 0 3 1 0 > 0.9999 || = 0.55 486 507 472 461 507 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 530 516 486 479 498 | 500 < 0.0001 6 6 6 7 2 | 5 | 0 4 4 3 4 > 0.9999 || = 0.53 468 535 485 489 511 | 500 < 0.0002 7 4 3 4 8 | 5 | 1 1 2 0 0 > 0.9998 || = 0.52 550 476 447 477 498 | 500 < 0.0003 5 9 3 9 6 | 5 | 2 1 2 0 3 > 0.9997 || = 0.51 470 562 518 493 496 | 500 < 0.0004 3 3 4 3 4 | 5 | 2 5 2 3 5 > 0.9996 || = 0.50 522 524 487 476 496 | 500 < 0.0005 2 6 4 4 5 | 5 | 4 3 4 4 0 > 0.9995 || = 0.49 494 460 516 478 482 | 500 < 0.0006 5 4 9 4 3 | 5 | 2 5 3 4 2 > 0.9994 || = 0.48 479 488 476 477 490 | 500 < 0.0007 7 10 7 3 6 | 5 | 2 5 0 5 1 > 0.9993 || = 0.47 547 459 476 497 492 | 500 < 0.0008 8 3 6 5 7 | 5 | 1 2 5 3 2 > 0.9992 || = 0.46 531 507 515 494 495 | 500 < 0.0009 5 6 7 2 4 | 5 | 5 0 3 2 4 > 0.9991 || = 0.45 509 503 474 453 533 | 500 < 0.001 3 8 9 4 5 | 5 | 5 3 5 3 5 > 0.999 || = 0.44 468 532 515 497 480 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 479 499 511 491 484 | 500 < 0.001 51 59 58 45 50 | 50 | 24 29 30 27 26 > 0.999 || = 0.42 534 497 537 487 543 | 500 < 0.002 42 49 44 54 61 | 50 | 34 45 37 49 46 > 0.998 || = 0.41 493 442 499 489 492 | 500 < 0.003 64 49 65 45 54 | 50 | 52 42 54 45 43 > 0.997 || = 0.40 458 442 516 451 473 | 500 < 0.004 61 49 56 41 59 | 50 | 43 51 48 52 56 > 0.996 || = 0.39 498 503 446 556 545 | 500 < 0.005 47 41 55 49 53 | 50 | 46 41 56 54 51 > 0.995 || = 0.38 495 503 450 498 528 | 500 < 0.006 46 54 59 50 43 | 50 | 42 55 57 39 48 > 0.994 || = 0.37 495 531 530 480 520 | 500 < 0.007 39 49 62 49 57 | 50 | 40 45 46 39 59 > 0.993 || = 0.36 493 517 528 492 443 | 500 < 0.008 57 66 50 53 48 | 50 | 38 61 46 51 47 > 0.992 || = 0.35 541 475 503 493 494 | 500 < 0.009 64 62 40 59 52 | 50 | 70 69 50 57 60 > 0.991 || = 0.34 504 546 498 507 445 | 500 < 0.01 46 51 57 50 45 | 50 | 47 53 60 53 55 > 0.99 || = 0.33 475 487 517 493 527 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 516 550 478 496 525 | 500 < 0.01 517 529 546 495 522 | 497.5 | 436 491 484 466 491 > 0.99 || = 0.31 480 501 515 483 482 | 500 = 0.01 265 254 238 240 274 | 252.5 | 227 274 271 263 246 = 0.99 || = 0.30 450 545 467 515 547 | 500 = 0.02 530 513 514 511 530 | 500 | 526 539 561 519 514 = 0.98 || = 0.29 512 509 527 499 482 | 500 =================================================================| 500 | 457 505 511 560 508 = 0.97 || = 0.28 543 477 538 494 481 | 500 smarsa_Savir2 test: | 500 | 473 458 469 506 524 = 0.96 || = 0.27 545 472 510 511 502 | 500 ----------------------------------------------- | 500 | 500 520 497 477 497 = 0.95 || = 0.26 504 502 494 510 533 | 500 N = 10, n = 10000000, r = 10, m = 1048576, t = 30 | 500 | 491 495 514 496 500 = 0.94 || = 0.25 482 484 482 541 466 | 500 Anderson-Darling statistic = A2 | 500 | 508 489 550 538 515 = 0.93 || = 0.24 513 514 513 528 521 | 500 | 500 | 490 529 483 510 512 = 0.92 || = 0.23 503 492 492 501 500 | 500 =================================================================| 500 | 511 524 515 522 472 = 0.91 || = 0.22 507 533 513 483 501 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 510 449 513 484 508 = 0.90 || = 0.21 487 549 444 519 468 | 500 -----------------------------------------------------------------| 500 | 502 517 533 521 478 = 0.89 || = 0.20 511 493 483 516 512 | 500 SD Bern.: d 1.10129 1.25680 1.85456 | 500 | 501 488 468 483 480 = 0.88 || = 0.19 514 490 512 491 482 | 500 s 1.29680 1.08035 1.51930 | 500 | 484 437 491 469 475 = 0.87 || = 0.18 501 501 519 552 523 | 500 t 1.10853 1.23349 1.27027 | 500 | 479 496 473 516 482 = 0.86 || = 0.17 539 581 503 511 519 | 500 m 0.95677 0.69171 1.32428 | 500 | 467 460 507 526 510 = 0.85 || = 0.16 545 545 478 509 502 | 500 x 0.97300 0.84658 1.34006 | 500 | 515 527 476 503 489 = 0.84 || = 0.15 503 526 558 515 498 | 500 | 500 | 475 505 480 511 514 = 0.83 || = 0.14 462 513 488 528 482 | 500 Changes: d 45 5 4 | 500 | 489 478 520 525 513 = 0.82 || = 0.13 489 546 545 526 519 | 500 s 49 4 5 | 500 | 490 501 475 452 471 = 0.81 || = 0.12 502 488 482 520 491 | 500 t 59 4 5 | 500 | 510 469 478 474 496 = 0.80 || = 0.11 477 524 534 496 507 | 500 m 34 4 3 | 500 | 524 491 500 484 488 = 0.79 || = 0.10 478 476 503 510 524 | 500 x 53 6 5 | 500 | 475 510 480 510 537 = 0.78 || = 0.09 506 508 475 505 485 | 500 -----------------------------------------------------------------| 500 | 541 463 493 514 507 = 0.77 || = 0.08 505 480 534 515 531 | 500 Aver./ d 0.49635 502 > 500:10 6 8 3 4 5 5 4 4 3 | 500 | 495 474 499 513 526 = 0.76 || = 0.07 528 504 537 489 490 | 500 median s 0.49551 501 ----- 8 7 5 8 3 5 5 3 4 6 | 500 | 528 516 499 494 459 = 0.75 || = 0.06 513 516 478 525 507 | 500 t 0.49856 500 6 7 5 5 6 3 5 3 4 6 | 500 | 487 447 523 517 507 = 0.74 || = 0.05 508 490 506 509 494 | 500 m 0.49845 498 7 8 7 3 0 2 5 4 6 7 | 500 | 474 507 511 476 511 = 0.73 || = 0.04 512 559 522 506 494 | 500 x 0.49866 499 5 6 5 6 2 3 5 6 4 5 | 500 | 465 468 504 494 515 = 0.72 || = 0.03 539 501 490 515 499 | 500 -----------------------------------------------------------------| 500 | 474 473 475 442 499 = 0.71 || = 0.02 530 513 514 511 530 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 494 497 498 503 468 = 0.70 || = 0.01 265 254 238 240 274 | 252.5 d 0 0 3 18 61 15 4 0 0 | 500 | 536 478 504 525 481 = 0.69 || < 0.01 517 529 546 495 522 | 497.5 s 0 0 6 17 56 13 8 1 0 | 500 | 512 504 454 501 525 = 0.68 ||========================================================================= t 0 0 5 15 64 12 5 0 0 | 500 | 497 502 510 491 519 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 9 76 9 3 0 0 | 500 | 510 500 483 506 484 = 0.66 ||========================================================================= x 0 0 3 8 72 16 2 0 0 | 500 | 523 459 517 508 520 = 0.65 || smarsa_Savir2 test: no 140 test no 141 TestU01 250000 runs BigCrush Test smarsa_S smarsa_Savir2 test: test no 141 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 3 1 2 1 0 | 0.5 | 0 1 1 2 0 > 0.99999 || = 0.64 488 468 466 480 490 | 500 < 0.00002 0 0 0 1 1 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 488 471 474 487 484 | 500 < 0.00003 1 1 1 1 0 | 0.5 | 0 0 0 1 1 > 0.99997 || = 0.62 515 508 489 457 526 | 500 < 0.00004 0 0 1 0 2 | 0.5 | 3 0 0 0 0 > 0.99996 || = 0.61 479 463 495 495 527 | 500 < 0.00005 1 1 2 0 0 | 0.5 | 0 0 0 1 1 > 0.99995 || = 0.60 524 490 522 543 503 | 500 < 0.00006 0 0 1 2 1 | 0.5 | 1 2 0 1 0 > 0.99994 || = 0.59 509 486 519 463 498 | 500 < 0.00007 1 1 0 0 2 | 0.5 | 0 0 0 0 2 > 0.99993 || = 0.58 496 524 526 495 501 | 500 < 0.00008 1 1 1 2 1 | 0.5 | 0 0 2 0 1 > 0.99992 || = 0.57 520 449 528 475 470 | 500 < 0.00009 0 1 0 0 2 | 0.5 | 1 1 1 0 1 > 0.99991 || = 0.56 503 499 528 454 510 | 500 < 0.0001 0 1 1 0 1 | 0.5 | 1 0 0 1 1 > 0.9999 || = 0.55 466 538 549 536 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 515 487 501 456 491 | 500 < 0.0001 7 7 9 7 10 | 5 | 6 4 4 6 8 > 0.9999 || = 0.53 498 513 474 484 497 | 500 < 0.0002 5 9 9 2 2 | 5 | 5 2 4 0 3 > 0.9998 || = 0.52 546 532 485 488 485 | 500 < 0.0003 7 8 10 4 6 | 5 | 2 8 2 4 4 > 0.9997 || = 0.51 493 562 474 477 505 | 500 < 0.0004 6 8 5 7 5 | 5 | 6 5 6 8 6 > 0.9996 || = 0.50 490 452 487 504 487 | 500 < 0.0005 7 6 6 6 5 | 5 | 3 8 7 4 2 > 0.9995 || = 0.49 483 480 523 542 502 | 500 < 0.0006 3 2 6 5 10 | 5 | 7 12 10 5 3 > 0.9994 || = 0.48 465 477 469 497 484 | 500 < 0.0007 4 4 4 5 10 | 5 | 3 3 5 2 4 > 0.9993 || = 0.47 443 494 455 520 502 | 500 < 0.0008 6 6 2 7 8 | 5 | 6 5 3 5 3 > 0.9992 || = 0.46 496 517 482 452 476 | 500 < 0.0009 5 5 9 4 9 | 5 | 10 7 6 3 2 > 0.9991 || = 0.45 502 542 524 506 515 | 500 < 0.001 5 3 5 2 6 | 5 | 6 2 5 6 6 > 0.999 || = 0.44 519 483 539 555 508 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 516 498 482 535 505 | 500 < 0.001 55 58 65 49 71 | 50 | 54 56 52 43 41 > 0.999 || = 0.42 500 520 442 521 501 | 500 < 0.002 57 56 65 57 49 | 50 | 53 51 50 52 59 > 0.998 || = 0.41 469 534 487 505 453 | 500 < 0.003 52 56 56 48 56 | 50 | 57 54 54 50 44 > 0.997 || = 0.40 484 525 484 490 487 | 500 < 0.004 58 47 55 61 49 | 50 | 60 47 68 46 52 > 0.996 || = 0.39 500 468 492 494 484 | 500 < 0.005 56 54 51 45 45 | 50 | 48 58 59 50 48 > 0.995 || = 0.38 473 493 510 486 421 | 500 < 0.006 62 44 69 47 53 | 50 | 65 56 53 55 46 > 0.994 || = 0.37 483 485 478 521 474 | 500 < 0.007 50 52 45 49 58 | 50 | 55 58 68 46 55 > 0.993 || = 0.36 489 532 501 486 489 | 500 < 0.008 67 51 42 51 59 | 50 | 55 52 50 44 52 > 0.992 || = 0.35 492 460 459 475 447 | 500 < 0.009 61 48 61 67 48 | 50 | 47 60 50 46 49 > 0.991 || = 0.34 503 499 513 492 516 | 500 < 0.01 38 59 57 62 45 | 50 | 50 60 59 52 54 > 0.99 || = 0.33 466 495 526 457 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 503 456 491 525 491 | 500 < 0.01 556 525 566 536 533 | 497.5 | 544 552 563 484 500 > 0.99 || = 0.31 516 457 521 494 472 | 500 = 0.01 285 272 250 290 290 | 252.5 | 259 252 268 237 266 = 0.99 || = 0.30 498 510 471 527 489 | 500 = 0.02 503 479 492 505 494 | 500 | 533 496 520 527 520 = 0.98 || = 0.29 505 491 477 492 487 | 500 =================================================================| 500 | 503 522 528 518 505 = 0.97 || = 0.28 537 521 488 519 417 | 500 smarsa_Savir2 test: | 500 | 497 527 523 508 515 = 0.96 || = 0.27 522 488 487 512 521 | 500 ----------------------------------------------- | 500 | 499 525 500 524 522 = 0.95 || = 0.26 510 471 499 454 484 | 500 N = 10, n = 10000000, r = 10, m = 1048576, t = 30 | 500 | 492 531 521 467 514 = 0.94 || = 0.25 521 488 486 523 524 | 500 Test on the sum of all N observations | 500 | 528 510 520 529 515 = 0.93 || = 0.24 458 499 469 470 490 | 500 | 500 | 507 527 537 531 478 = 0.92 || = 0.23 542 493 509 484 537 | 500 =================================================================| 500 | 481 518 499 501 476 = 0.91 || = 0.22 488 490 489 513 513 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 494 499 511 530 471 = 0.90 || = 0.21 454 526 461 494 530 | 500 -----------------------------------------------------------------| 500 | 515 482 516 541 537 = 0.89 || = 0.20 485 480 466 531 509 | 500 SD Bern.: d 1.04739 1.32429 0.96172 | 500 | 497 516 531 475 480 = 0.88 || = 0.19 518 498 503 466 480 | 500 s 1.13991 0.75799 0.92781 | 500 | 458 473 488 497 493 = 0.87 || = 0.18 505 467 477 483 483 | 500 t 1.12131 1.50540 1.29601 | 500 | 490 528 472 527 535 = 0.86 || = 0.17 484 508 474 488 516 | 500 m 1.10032 1.13546 0.57647 | 500 | 513 528 469 501 498 = 0.85 || = 0.16 496 506 476 491 491 | 500 x 1.08908 1.17275 0.73247 | 500 | 532 500 526 545 532 = 0.84 || = 0.15 500 491 502 513 535 | 500 | 500 | 546 493 483 485 511 = 0.83 || = 0.14 509 516 485 494 498 | 500 Changes: d 38 3 3 | 500 | 511 457 532 504 457 = 0.82 || = 0.13 444 529 467 484 536 | 500 s 44 6 2 | 500 | 478 490 513 492 523 = 0.81 || = 0.12 491 513 527 546 507 | 500 t 46 2 4 | 500 | 478 506 498 497 528 = 0.80 || = 0.11 496 461 501 473 482 | 500 m 51 5 5 | 500 | 497 475 503 483 500 = 0.79 || = 0.10 511 532 515 499 541 | 500 x 56 5 7 | 500 | 533 475 525 456 529 = 0.78 || = 0.09 537 515 490 515 471 | 500 -----------------------------------------------------------------| 500 | 501 479 505 465 473 = 0.77 || = 0.08 477 539 554 472 506 | 500 Aver./ d 0.50039 498 > 500: 7 4 6 3 3 6 3 2 5 6 | 500 | 485 518 481 523 527 = 0.76 || = 0.07 466 523 468 518 484 | 500 median s 0.49955 499 ----- 8 6 2 2 5 5 5 2 3 8 | 500 | 500 485 495 479 502 = 0.75 || = 0.06 491 492 532 519 518 | 500 t 0.50257 499 6 5 1 5 3 7 3 5 6 8 | 500 | 491 445 534 502 488 = 0.74 || = 0.05 507 535 525 524 511 | 500 m 0.49953 497 9 2 5 3 7 2 3 3 6 7 | 500 | 492 492 501 483 514 = 0.73 || = 0.04 509 512 506 501 505 | 500 x 0.50061 502 7 5 6 1 6 4 6 6 5 8 | 500 | 486 500 490 507 480 = 0.72 || = 0.03 534 523 516 511 506 | 500 -----------------------------------------------------------------| 500 | 483 487 473 490 504 = 0.71 || = 0.02 503 479 492 505 494 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 497 510 511 495 518 = 0.70 || = 0.01 285 272 250 290 290 | 252.5 d 0 0 3 11 72 9 6 0 0 | 500 | 477 501 492 502 509 = 0.69 || < 0.01 556 525 566 536 533 | 497.5 s 0 0 4 15 57 23 2 0 0 | 500 | 497 501 503 500 466 = 0.68 ||========================================================================= t 0 0 2 20 57 18 3 1 0 | 500 | 550 487 457 506 552 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 15 61 18 4 0 0 | 500 | 517 523 502 489 489 = 0.66 ||========================================================================= x 0 2 2 10 69 16 2 0 0 | 500 | 468 440 487 506 503 = 0.65 || smarsa_Savir2 test: no 141 test no 142 TestU01 250000 runs BigCrush Test smarsa_S smarsa_GCD test: test no 142 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 4 0 | 0.5 | 1 1 0 2 0 > 0.99999 || = 0.64 486 509 501 456 472 | 500 < 0.00002 1 0 0 0 0 | 0.5 | 2 0 1 0 0 > 0.99998 || = 0.63 497 535 473 493 551 | 500 < 0.00003 1 2 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 514 523 481 512 479 | 500 < 0.00004 1 0 3 0 0 | 0.5 | 1 0 1 1 2 > 0.99996 || = 0.61 482 473 475 501 482 | 500 < 0.00005 1 1 1 0 0 | 0.5 | 0 1 0 0 2 > 0.99995 || = 0.60 479 499 553 526 492 | 500 < 0.00006 0 1 0 0 1 | 0.5 | 0 0 0 2 1 > 0.99994 || = 0.59 495 509 506 455 510 | 500 < 0.00007 0 0 1 1 0 | 0.5 | 0 0 1 0 0 > 0.99993 || = 0.58 458 537 498 479 510 | 500 < 0.00008 1 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99992 || = 0.57 511 475 478 493 476 | 500 < 0.00009 2 0 0 1 1 | 0.5 | 2 1 0 2 0 > 0.99991 || = 0.56 527 478 429 517 487 | 500 < 0.0001 1 1 1 2 1 | 0.5 | 0 2 0 0 0 > 0.9999 || = 0.55 523 470 509 492 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 503 500 476 478 502 | 500 < 0.0001 9 6 6 8 3 | 5 | 7 5 3 8 5 > 0.9999 || = 0.53 475 443 519 525 464 | 500 < 0.0002 8 8 4 2 4 | 5 | 4 4 4 2 1 > 0.9998 || = 0.52 501 468 429 514 487 | 500 < 0.0003 7 5 4 7 5 | 5 | 6 5 7 9 4 > 0.9997 || = 0.51 509 467 526 503 493 | 500 < 0.0004 10 3 3 6 10 | 5 | 8 5 4 2 8 > 0.9996 || = 0.50 509 479 501 461 475 | 500 < 0.0005 7 4 9 3 5 | 5 | 6 7 3 6 8 > 0.9995 || = 0.49 508 511 496 500 537 | 500 < 0.0006 7 8 6 4 7 | 5 | 4 6 7 4 5 > 0.9994 || = 0.48 459 499 466 538 476 | 500 < 0.0007 2 5 1 3 1 | 5 | 6 4 4 8 9 > 0.9993 || = 0.47 526 494 509 515 489 | 500 < 0.0008 4 1 5 6 6 | 5 | 9 11 6 4 9 > 0.9992 || = 0.46 516 496 515 505 492 | 500 < 0.0009 6 4 3 4 6 | 5 | 7 6 5 4 6 > 0.9991 || = 0.45 498 508 506 483 494 | 500 < 0.001 1 6 8 5 8 | 5 | 7 5 5 6 3 > 0.999 || = 0.44 506 519 485 488 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 491 513 503 482 526 | 500 < 0.001 61 50 49 48 55 | 50 | 64 58 48 53 58 > 0.999 || = 0.42 490 480 502 523 514 | 500 < 0.002 49 60 48 40 44 | 50 | 45 58 54 49 50 > 0.998 || = 0.41 500 500 486 502 495 | 500 < 0.003 48 52 50 50 56 | 50 | 49 50 55 59 51 > 0.997 || = 0.40 481 459 497 487 523 | 500 < 0.004 47 46 39 50 61 | 50 | 57 47 49 65 54 > 0.996 || = 0.39 537 477 502 498 516 | 500 < 0.005 45 56 51 41 45 | 50 | 60 41 65 40 51 > 0.995 || = 0.38 471 506 485 462 478 | 500 < 0.006 47 56 48 50 41 | 50 | 47 51 46 61 56 > 0.994 || = 0.37 498 509 542 523 473 | 500 < 0.007 52 61 60 42 52 | 50 | 53 47 49 67 46 > 0.993 || = 0.36 501 504 516 469 473 | 500 < 0.008 44 55 55 37 52 | 50 | 43 65 40 49 58 > 0.992 || = 0.35 471 510 494 522 487 | 500 < 0.009 49 43 52 48 56 | 50 | 40 66 47 46 48 > 0.991 || = 0.34 508 518 472 518 489 | 500 < 0.01 47 52 45 59 48 | 50 | 51 33 53 48 51 > 0.99 || = 0.33 498 531 489 489 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 489 535 485 517 531 | 500 < 0.01 489 531 497 465 510 | 497.5 | 509 516 506 537 523 > 0.99 || = 0.31 482 509 501 454 498 | 500 = 0.01 255 256 246 290 246 | 252.5 | 273 249 237 270 270 = 0.99 || = 0.30 469 517 503 442 500 | 500 = 0.02 472 495 554 496 502 | 500 | 503 495 553 540 513 = 0.98 || = 0.29 489 463 503 527 480 | 500 =================================================================| 500 | 511 506 492 520 535 = 0.97 || = 0.28 529 506 509 517 484 | 500 smarsa_GCD test: | 500 | 516 509 498 493 514 = 0.96 || = 0.27 561 489 484 487 486 | 500 ----------------------------------------------- | 500 | 505 521 531 470 524 = 0.95 || = 0.26 518 511 519 488 476 | 500 N = 10, n = 50000000, r = 0, s = 30 | 500 | 469 500 474 499 519 = 0.94 || = 0.25 473 481 506 516 509 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 532 518 484 496 517 = 0.93 || = 0.24 494 478 488 487 533 | 500 | 500 | 478 506 485 485 516 = 0.92 || = 0.23 474 481 511 474 516 | 500 =================================================================| 500 | 492 449 506 475 480 = 0.91 || = 0.22 459 478 483 509 537 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 481 480 493 460 478 = 0.90 || = 0.21 503 507 493 456 507 | 500 -----------------------------------------------------------------| 500 | 530 531 508 511 481 = 0.89 || = 0.20 483 519 517 518 490 | 500 SD Bern.: d 0.95337 0.66214 1.03877 | 500 | 459 479 509 499 537 = 0.88 || = 0.19 490 533 494 546 523 | 500 s 0.99653 0.88474 1.41349 | 500 | 521 481 496 494 490 = 0.87 || = 0.18 545 516 492 506 499 | 500 t 0.98171 0.75535 0.90155 | 500 | 501 487 517 480 482 = 0.86 || = 0.17 510 476 503 514 487 | 500 m 1.15006 1.00349 1.30218 | 500 | 485 474 526 502 500 = 0.85 || = 0.16 527 477 499 443 477 | 500 x 0.90155 0.86297 0.63748 | 500 | 501 496 493 493 478 = 0.84 || = 0.15 478 484 526 510 494 | 500 | 500 | 525 461 522 509 502 = 0.83 || = 0.14 476 510 483 539 479 | 500 Changes: d 47 3 6 | 500 | 542 504 466 514 482 = 0.82 || = 0.13 473 470 522 506 486 | 500 s 44 5 5 | 500 | 523 499 519 519 492 = 0.81 || = 0.12 524 523 484 459 547 | 500 t 59 4 5 | 500 | 500 476 471 526 474 = 0.80 || = 0.11 502 512 513 495 498 | 500 m 47 1 5 | 500 | 477 522 513 527 528 = 0.79 || = 0.10 506 480 475 465 526 | 500 x 38 5 6 | 500 | 509 515 527 479 483 = 0.78 || = 0.09 515 531 545 526 537 | 500 -----------------------------------------------------------------| 500 | 498 532 518 512 516 = 0.77 || = 0.08 497 531 481 522 508 | 500 Aver./ d 0.50071 501 > 500: 5 6 4 3 4 6 6 3 7 7 | 500 | 512 522 478 453 506 = 0.76 || = 0.07 503 500 482 516 501 | 500 median s 0.49815 504 ----- 8 5 4 9 4 2 5 6 2 6 | 500 | 489 499 484 512 501 = 0.75 || = 0.06 521 511 521 537 484 | 500 t 0.49903 499 6 4 6 5 5 5 2 5 6 4 | 500 | 530 478 497 490 511 = 0.74 || = 0.05 483 535 528 530 480 | 500 m 0.49962 502 7 6 5 4 5 5 6 5 5 4 | 500 | 454 526 511 520 456 = 0.73 || = 0.04 497 529 532 473 499 | 500 x 0.50035 499 6 3 5 2 5 3 5 7 2 9 | 500 | 491 459 528 476 509 = 0.72 || = 0.03 543 528 513 549 509 | 500 -----------------------------------------------------------------| 500 | 494 504 496 474 502 = 0.71 || = 0.02 472 495 554 496 502 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 504 492 510 488 505 = 0.70 || = 0.01 255 256 246 290 246 | 252.5 d 0 0 1 15 68 15 2 0 0 | 500 | 519 491 498 489 522 = 0.69 || < 0.01 489 531 497 465 510 | 497.5 s 0 0 2 16 66 17 0 0 0 | 500 | 501 520 485 514 466 = 0.68 ||========================================================================= t 0 2 0 10 76 9 4 0 0 | 500 | 510 476 492 557 502 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 5 15 61 16 4 0 0 | 500 | 507 537 490 506 519 = 0.66 ||========================================================================= x 0 0 0 12 72 15 2 0 0 | 500 | 492 489 476 523 493 = 0.65 || smarsa_GCD test: no 142 test no 143 TestU01 250000 runs BigCrush Test smarsa_S smarsa_GCD test: test no 143 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 3 1 0 | 0.5 | 0 4 0 0 0 > 0.99999 || = 0.64 469 519 499 505 478 | 500 < 0.00002 1 0 0 0 0 | 0.5 | 2 0 0 0 2 > 0.99998 || = 0.63 473 516 512 452 491 | 500 < 0.00003 0 1 1 0 0 | 0.5 | 0 2 2 0 1 > 0.99997 || = 0.62 496 515 503 520 490 | 500 < 0.00004 0 1 0 0 1 | 0.5 | 2 0 1 1 1 > 0.99996 || = 0.61 506 488 515 492 517 | 500 < 0.00005 0 1 1 0 0 | 0.5 | 0 2 1 0 0 > 0.99995 || = 0.60 490 509 469 500 514 | 500 < 0.00006 1 0 1 0 1 | 0.5 | 0 0 0 0 2 > 0.99994 || = 0.59 473 456 474 540 515 | 500 < 0.00007 0 0 3 0 0 | 0.5 | 0 1 1 0 1 > 0.99993 || = 0.58 529 563 520 515 503 | 500 < 0.00008 1 1 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99992 || = 0.57 481 495 518 471 503 | 500 < 0.00009 0 2 0 1 0 | 0.5 | 0 1 1 0 0 > 0.99991 || = 0.56 499 444 499 500 494 | 500 < 0.0001 0 0 0 1 1 | 0.5 | 1 0 1 1 1 > 0.9999 || = 0.55 474 480 508 479 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 496 527 534 544 509 | 500 < 0.0001 4 7 9 3 3 | 5 | 5 10 7 3 8 > 0.9999 || = 0.53 464 477 476 483 435 | 500 < 0.0002 10 3 11 2 3 | 5 | 2 3 4 2 4 > 0.9998 || = 0.52 499 500 505 482 521 | 500 < 0.0003 8 5 10 4 7 | 5 | 8 4 3 1 2 > 0.9997 || = 0.51 512 505 474 517 535 | 500 < 0.0004 12 4 5 4 1 | 5 | 9 5 5 3 5 > 0.9996 || = 0.50 487 431 495 539 473 | 500 < 0.0005 5 10 4 5 2 | 5 | 3 9 1 2 6 > 0.9995 || = 0.49 558 461 523 473 494 | 500 < 0.0006 8 5 5 5 5 | 5 | 6 7 4 12 4 > 0.9994 || = 0.48 498 487 477 474 500 | 500 < 0.0007 7 10 3 3 6 | 5 | 4 5 7 5 9 > 0.9993 || = 0.47 536 483 489 523 535 | 500 < 0.0008 3 3 2 3 6 | 5 | 5 3 12 3 6 > 0.9992 || = 0.46 513 467 495 503 462 | 500 < 0.0009 8 6 14 10 8 | 5 | 5 6 4 8 7 > 0.9991 || = 0.45 510 484 454 507 491 | 500 < 0.001 4 3 8 3 5 | 5 | 6 8 6 4 10 > 0.999 || = 0.44 479 484 518 501 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 490 498 515 488 491 | 500 < 0.001 69 56 71 42 46 | 50 | 53 60 53 43 61 > 0.999 || = 0.42 481 482 468 478 501 | 500 < 0.002 48 46 48 38 43 | 50 | 55 71 46 50 54 > 0.998 || = 0.41 485 522 463 509 522 | 500 < 0.003 54 57 65 65 67 | 50 | 59 63 50 44 50 > 0.997 || = 0.40 527 489 477 521 527 | 500 < 0.004 65 60 43 45 49 | 50 | 45 55 44 58 49 > 0.996 || = 0.39 513 514 520 517 500 | 500 < 0.005 56 49 45 53 48 | 50 | 45 59 56 56 52 > 0.995 || = 0.38 457 455 479 514 470 | 500 < 0.006 40 49 44 49 56 | 50 | 46 52 56 43 49 > 0.994 || = 0.37 465 502 475 503 464 | 500 < 0.007 46 40 52 51 48 | 50 | 46 60 58 41 55 > 0.993 || = 0.36 520 504 516 500 482 | 500 < 0.008 63 37 45 50 46 | 50 | 53 46 55 45 52 > 0.992 || = 0.35 509 510 515 497 531 | 500 < 0.009 48 56 51 45 45 | 50 | 34 59 48 54 62 > 0.991 || = 0.34 525 550 474 482 513 | 500 < 0.01 46 43 61 43 59 | 50 | 51 54 52 53 63 > 0.99 || = 0.33 551 501 526 519 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 535 472 520 468 562 | 500 < 0.01 535 493 525 481 507 | 497.5 | 487 579 518 487 547 > 0.99 || = 0.31 497 477 470 493 459 | 500 = 0.01 245 242 265 242 260 | 252.5 | 257 246 302 252 257 = 0.99 || = 0.30 499 509 496 505 489 | 500 = 0.02 519 526 487 521 536 | 500 | 517 521 512 485 511 = 0.98 || = 0.29 497 518 506 476 481 | 500 =================================================================| 500 | 520 477 530 521 509 = 0.97 || = 0.28 496 499 491 483 492 | 500 smarsa_GCD test: | 500 | 501 499 494 501 515 = 0.96 || = 0.27 504 483 497 469 445 | 500 ----------------------------------------------- | 500 | 556 493 524 486 476 = 0.95 || = 0.26 515 512 488 477 483 | 500 N = 10, n = 50000000, r = 0, s = 30 | 500 | 525 507 523 490 484 = 0.94 || = 0.25 485 512 553 459 480 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 475 511 512 516 491 = 0.93 || = 0.24 476 468 487 515 504 | 500 | 500 | 458 475 528 530 502 = 0.92 || = 0.23 537 501 497 488 502 | 500 =================================================================| 500 | 508 580 470 516 504 = 0.91 || = 0.22 473 502 482 522 502 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 500 453 490 529 503 = 0.90 || = 0.21 497 457 519 471 482 | 500 -----------------------------------------------------------------| 500 | 490 504 519 499 498 = 0.89 || = 0.20 493 522 468 477 484 | 500 SD Bern.: d 1.02802 1.37691 0.96276 | 500 | 506 487 529 520 488 = 0.88 || = 0.19 501 527 494 495 465 | 500 s 1.20300 1.05598 1.43806 | 500 | 493 519 504 508 551 = 0.87 || = 0.18 486 477 491 476 482 | 500 t 0.94604 1.36522 0.67856 | 500 | 497 537 526 534 488 = 0.86 || = 0.17 502 486 496 527 515 | 500 m 0.99265 1.04263 0.85481 | 500 | 513 530 486 496 505 = 0.85 || = 0.16 508 447 511 481 485 | 500 x 1.00927 1.02128 0.98536 | 500 | 485 533 528 511 501 = 0.84 || = 0.15 506 514 488 506 478 | 500 | 500 | 482 526 489 520 508 = 0.83 || = 0.14 544 450 517 509 509 | 500 Changes: d 45 5 4 | 500 | 514 484 481 481 533 = 0.82 || = 0.13 533 502 472 468 502 | 500 s 53 5 2 | 500 | 508 476 513 488 471 = 0.81 || = 0.12 514 512 476 512 528 | 500 t 56 6 4 | 500 | 524 500 496 464 511 = 0.80 || = 0.11 496 524 534 495 492 | 500 m 46 6 3 | 500 | 515 499 513 511 490 = 0.79 || = 0.10 483 495 503 527 492 | 500 x 40 5 4 | 500 | 472 568 472 512 493 = 0.78 || = 0.09 462 488 503 524 454 | 500 -----------------------------------------------------------------| 500 | 507 537 482 482 505 = 0.77 || = 0.08 447 502 481 483 536 | 500 Aver./ d 0.50035 499 > 500: 4 7 3 6 5 2 3 6 4 7 | 500 | 501 490 465 488 511 = 0.76 || = 0.07 455 525 509 498 524 | 500 median s 0.50263 500 ----- 4 5 6 7 1 4 6 5 6 5 | 500 | 534 522 514 499 504 = 0.75 || = 0.06 499 498 507 428 507 | 500 t 0.50176 499 6 4 3 5 3 5 6 3 6 8 | 500 | 482 503 490 479 488 = 0.74 || = 0.05 527 513 485 527 472 | 500 m 0.50173 500 5 5 2 5 6 4 6 4 6 5 | 500 | 493 482 491 530 469 = 0.73 || = 0.04 512 496 522 526 524 | 500 x 0.50088 502 8 4 3 3 5 7 5 6 6 7 | 500 | 472 490 511 517 514 = 0.72 || = 0.03 453 499 490 521 534 | 500 -----------------------------------------------------------------| 500 | 506 524 487 489 509 = 0.71 || = 0.02 519 526 487 521 536 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 478 511 492 481 511 = 0.70 || = 0.01 245 242 265 242 260 | 252.5 d 0 0 3 14 67 14 3 0 0 | 500 | 497 504 507 519 500 = 0.69 || < 0.01 535 493 525 481 507 | 497.5 s 0 1 5 13 66 11 2 3 0 | 500 | 527 486 473 509 476 = 0.68 ||========================================================================= t 0 0 1 18 68 12 1 1 0 | 500 | 497 477 517 507 502 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 1 13 72 13 1 0 0 | 500 | 500 510 490 562 541 = 0.66 ||========================================================================= x 0 0 3 11 72 12 3 0 0 | 500 | 507 494 507 483 504 = 0.65 || smarsa_GCD test: no 143 test no 144 TestU01 250000 runs BigCrush Test smarsa_S smarsa_GCD test: test no 144 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 3 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 515 528 467 522 495 | 500 < 0.00002 0 1 0 1 2 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 541 498 540 474 500 | 500 < 0.00003 1 1 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 492 481 492 495 483 | 500 < 0.00004 1 0 1 1 1 | 0.5 | 0 0 1 0 1 > 0.99996 || = 0.61 467 499 501 497 512 | 500 < 0.00005 0 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 518 481 493 490 486 | 500 < 0.00006 3 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 494 479 509 467 508 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 501 497 500 531 523 | 500 < 0.00008 3 1 0 1 1 | 0.5 | 1 0 0 0 0 > 0.99992 || = 0.57 480 515 479 489 454 | 500 < 0.00009 2 1 0 0 0 | 0.5 | 0 1 0 1 0 > 0.99991 || = 0.56 517 493 513 490 497 | 500 < 0.0001 0 0 0 2 1 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 527 472 518 516 484 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 528 462 456 487 495 | 500 < 0.0001 11 8 4 6 6 | 5 | 2 1 1 2 1 > 0.9999 || = 0.53 481 459 492 486 486 | 500 < 0.0002 8 8 6 3 3 | 5 | 1 0 1 0 0 > 0.9998 || = 0.52 497 470 514 457 499 | 500 < 0.0003 3 6 6 5 3 | 5 | 3 2 5 3 5 > 0.9997 || = 0.51 501 499 460 515 477 | 500 < 0.0004 12 3 3 6 6 | 5 | 2 7 6 2 5 > 0.9996 || = 0.50 487 522 507 476 486 | 500 < 0.0005 7 3 4 5 4 | 5 | 5 3 3 4 3 > 0.9995 || = 0.49 462 487 452 500 510 | 500 < 0.0006 5 3 6 3 2 | 5 | 2 4 2 4 2 > 0.9994 || = 0.48 494 512 537 474 505 | 500 < 0.0007 4 8 5 5 7 | 5 | 8 1 8 2 3 > 0.9993 || = 0.47 494 478 495 489 534 | 500 < 0.0008 4 8 5 8 6 | 5 | 3 3 4 5 1 > 0.9992 || = 0.46 536 506 543 481 498 | 500 < 0.0009 2 6 10 5 5 | 5 | 6 7 4 6 5 > 0.9991 || = 0.45 518 488 539 479 481 | 500 < 0.001 5 5 5 9 7 | 5 | 4 4 3 7 1 > 0.999 || = 0.44 509 500 498 493 515 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 475 481 489 521 507 | 500 < 0.001 61 58 54 55 49 | 50 | 36 32 37 35 26 > 0.999 || = 0.42 444 500 477 463 520 | 500 < 0.002 56 53 50 50 44 | 50 | 38 45 40 38 40 > 0.998 || = 0.41 517 497 476 501 482 | 500 < 0.003 63 57 60 49 62 | 50 | 47 43 42 58 58 > 0.997 || = 0.40 519 516 497 488 509 | 500 < 0.004 68 61 59 49 64 | 50 | 43 55 45 51 60 > 0.996 || = 0.39 513 516 490 529 502 | 500 < 0.005 38 49 51 57 61 | 50 | 44 55 37 48 52 > 0.995 || = 0.38 460 517 480 453 494 | 500 < 0.006 62 59 46 55 42 | 50 | 45 43 43 51 45 > 0.994 || = 0.37 468 536 509 511 469 | 500 < 0.007 61 45 56 62 43 | 50 | 51 55 39 44 48 > 0.993 || = 0.36 511 472 526 517 487 | 500 < 0.008 59 61 52 43 58 | 50 | 52 56 42 42 52 > 0.992 || = 0.35 456 508 511 497 491 | 500 < 0.009 47 57 50 57 58 | 50 | 44 55 59 41 44 > 0.991 || = 0.34 521 495 496 459 493 | 500 < 0.01 49 51 49 37 49 | 50 | 56 57 51 52 46 > 0.99 || = 0.33 512 504 544 476 525 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 480 466 510 478 453 | 500 < 0.01 564 551 527 514 530 | 497.5 | 456 496 435 460 471 > 0.99 || = 0.31 531 491 510 530 520 | 500 = 0.01 251 271 275 274 262 | 252.5 | 264 262 256 273 237 = 0.99 || = 0.30 506 498 510 464 501 | 500 = 0.02 498 519 547 527 559 | 500 | 510 516 533 504 543 = 0.98 || = 0.29 521 500 489 509 499 | 500 =================================================================| 500 | 500 535 497 537 567 = 0.97 || = 0.28 527 459 477 482 499 | 500 smarsa_GCD test: | 500 | 463 452 514 510 463 = 0.96 || = 0.27 506 526 486 513 502 | 500 ----------------------------------------------- | 500 | 489 511 517 486 492 = 0.95 || = 0.26 528 514 480 492 505 | 500 N = 10, n = 50000000, r = 0, s = 30 | 500 | 496 444 517 496 468 = 0.94 || = 0.25 502 512 539 474 525 | 500 Anderson-Darling statistic = A2 | 500 | 545 491 478 541 524 = 0.93 || = 0.24 472 499 527 538 486 | 500 | 500 | 486 459 504 517 486 = 0.92 || = 0.23 506 479 449 512 491 | 500 =================================================================| 500 | 551 489 506 506 523 = 0.91 || = 0.22 512 536 499 540 522 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 464 491 493 434 495 = 0.90 || = 0.21 508 550 498 511 538 | 500 -----------------------------------------------------------------| 500 | 501 506 493 489 494 = 0.89 || = 0.20 530 506 502 509 485 | 500 SD Bern.: d 1.04301 1.51733 1.03588 | 500 | 448 528 467 500 498 = 0.88 || = 0.19 494 498 488 516 537 | 500 s 1.01243 1.02128 1.12483 | 500 | 486 509 477 494 477 = 0.87 || = 0.18 472 491 526 540 512 | 500 t 1.13123 0.71449 1.29909 | 500 | 492 481 469 477 498 = 0.86 || = 0.17 499 507 480 529 495 | 500 m 1.02169 1.01242 1.11768 | 500 | 473 462 479 481 459 = 0.85 || = 0.16 480 533 518 479 468 | 500 x 1.08982 1.21715 1.36375 | 500 | 492 512 455 517 508 = 0.84 || = 0.15 512 512 555 503 508 | 500 | 500 | 512 510 491 489 493 = 0.83 || = 0.14 502 487 470 506 487 | 500 Changes: d 45 3 3 | 500 | 495 519 498 528 458 = 0.82 || = 0.13 492 519 493 527 532 | 500 s 41 4 3 | 500 | 524 522 502 536 477 = 0.81 || = 0.12 465 496 506 527 493 | 500 t 51 5 1 | 500 | 514 466 467 505 513 = 0.80 || = 0.11 502 489 515 529 542 | 500 m 45 5 5 | 500 | 527 492 504 520 501 = 0.79 || = 0.10 527 525 493 494 516 | 500 x 43 4 4 | 500 | 489 505 492 491 500 = 0.78 || = 0.09 480 525 551 508 556 | 500 -----------------------------------------------------------------| 500 | 488 493 499 526 548 = 0.77 || = 0.08 498 556 457 474 514 | 500 Aver./ d 0.49812 501 > 500: 6 4 9 6 5 6 7 3 3 4 | 500 | 477 483 476 495 496 = 0.76 || = 0.07 505 492 529 500 520 | 500 median s 0.49628 499 ----- 7 5 6 5 3 1 4 4 7 4 | 500 | 442 521 437 475 494 = 0.75 || = 0.06 515 491 512 533 524 | 500 t 0.49602 500 9 5 3 7 3 4 6 4 1 7 | 500 | 483 459 512 485 484 = 0.74 || = 0.05 502 497 506 496 483 | 500 m 0.49820 500 6 8 7 4 2 3 2 5 3 7 | 500 | 510 471 527 525 469 = 0.73 || = 0.04 519 528 545 482 500 | 500 x 0.49577 498 8 6 5 4 7 2 3 3 1 4 | 500 | 499 505 505 516 469 = 0.72 || = 0.03 505 510 511 519 534 | 500 -----------------------------------------------------------------| 500 | 494 515 466 500 472 = 0.71 || = 0.02 498 519 547 527 559 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 513 506 520 475 540 = 0.70 || = 0.01 251 271 275 274 262 | 252.5 d 0 0 3 14 69 12 3 0 0 | 500 | 509 523 493 499 462 = 0.69 || < 0.01 564 551 527 514 530 | 497.5 s 0 0 2 13 71 12 3 0 0 | 500 | 497 519 520 474 463 = 0.68 ||========================================================================= t 0 0 5 14 64 14 4 0 0 | 500 | 507 474 491 482 514 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 16 63 20 0 0 0 | 500 | 529 482 513 514 479 = 0.66 ||========================================================================= x 0 0 2 16 64 15 3 1 0 | 500 | 509 490 517 491 460 = 0.65 || smarsa_GCD test: no 144 test no 145 TestU01 250000 runs BigCrush Test smarsa_S smarsa_GCD test: test no 145 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 2 | 0.5 | 1 3 0 1 0 > 0.99999 || = 0.64 479 510 484 491 505 | 500 < 0.00002 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 480 499 489 502 494 | 500 < 0.00003 3 1 0 1 1 | 0.5 | 3 1 0 0 0 > 0.99997 || = 0.62 521 485 448 501 492 | 500 < 0.00004 1 1 0 0 1 | 0.5 | 2 0 1 1 0 > 0.99996 || = 0.61 501 495 512 527 497 | 500 < 0.00005 1 1 2 1 1 | 0.5 | 0 0 0 0 1 > 0.99995 || = 0.60 477 495 502 534 501 | 500 < 0.00006 1 0 1 0 0 | 0.5 | 1 2 0 0 0 > 0.99994 || = 0.59 489 498 530 505 488 | 500 < 0.00007 0 0 0 1 1 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 460 499 499 483 485 | 500 < 0.00008 1 0 1 0 1 | 0.5 | 0 0 1 2 0 > 0.99992 || = 0.57 485 477 491 485 526 | 500 < 0.00009 0 2 0 3 0 | 0.5 | 1 0 2 1 0 > 0.99991 || = 0.56 500 488 468 514 486 | 500 < 0.0001 0 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 522 493 522 452 501 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 521 475 517 501 484 | 500 < 0.0001 8 8 5 6 8 | 5 | 8 6 4 6 1 > 0.9999 || = 0.53 529 471 468 518 492 | 500 < 0.0002 6 9 5 3 4 | 5 | 7 4 1 4 3 > 0.9998 || = 0.52 486 496 487 513 485 | 500 < 0.0003 6 4 3 5 2 | 5 | 5 4 2 10 4 > 0.9997 || = 0.51 482 490 514 491 498 | 500 < 0.0004 5 5 6 3 5 | 5 | 6 6 8 2 7 > 0.9996 || = 0.50 484 488 515 522 481 | 500 < 0.0005 7 3 5 9 3 | 5 | 8 7 5 4 7 > 0.9995 || = 0.49 477 511 473 454 515 | 500 < 0.0006 7 9 8 4 7 | 5 | 2 3 8 6 4 > 0.9994 || = 0.48 517 509 498 480 493 | 500 < 0.0007 4 6 3 4 5 | 5 | 5 2 6 5 8 > 0.9993 || = 0.47 514 471 458 490 460 | 500 < 0.0008 4 2 6 9 3 | 5 | 3 4 7 2 5 > 0.9992 || = 0.46 508 505 512 537 465 | 500 < 0.0009 6 6 3 9 13 | 5 | 4 6 4 8 7 > 0.9991 || = 0.45 495 516 500 536 487 | 500 < 0.001 3 9 6 3 4 | 5 | 7 7 4 2 3 > 0.999 || = 0.44 480 502 502 483 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 491 506 506 487 482 | 500 < 0.001 56 61 50 55 54 | 50 | 55 49 49 49 49 > 0.999 || = 0.42 479 491 496 521 491 | 500 < 0.002 52 64 44 50 36 | 50 | 54 65 63 53 80 > 0.998 || = 0.41 492 517 491 517 475 | 500 < 0.003 59 56 58 52 53 | 50 | 72 61 51 49 45 > 0.997 || = 0.40 531 509 478 503 495 | 500 < 0.004 51 38 52 44 52 | 50 | 63 55 50 66 47 > 0.996 || = 0.39 525 484 460 467 524 | 500 < 0.005 59 41 60 58 51 | 50 | 43 53 58 48 57 > 0.995 || = 0.38 500 467 518 504 489 | 500 < 0.006 41 54 54 50 75 | 50 | 59 50 51 52 48 > 0.994 || = 0.37 484 451 506 458 494 | 500 < 0.007 47 46 44 56 57 | 50 | 43 54 46 39 59 > 0.993 || = 0.36 505 507 501 510 527 | 500 < 0.008 44 55 59 47 59 | 50 | 36 50 61 55 39 > 0.992 || = 0.35 543 518 491 482 517 | 500 < 0.009 64 52 51 55 67 | 50 | 47 54 50 45 56 > 0.991 || = 0.34 497 485 496 501 516 | 500 < 0.01 61 43 55 66 54 | 50 | 51 50 54 60 61 > 0.99 || = 0.33 474 507 490 502 458 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 491 492 488 467 495 | 500 < 0.01 534 510 527 533 558 | 497.5 | 523 541 533 516 541 > 0.99 || = 0.31 491 461 484 472 497 | 500 = 0.01 252 256 257 259 282 | 252.5 | 233 280 251 262 255 = 0.99 || = 0.30 530 492 503 483 511 | 500 = 0.02 506 507 547 506 532 | 500 | 529 507 525 524 507 = 0.98 || = 0.29 496 514 493 485 493 | 500 =================================================================| 500 | 509 549 548 494 505 = 0.97 || = 0.28 509 529 526 510 518 | 500 smarsa_GCD test: | 500 | 508 550 477 516 505 = 0.96 || = 0.27 501 503 454 510 463 | 500 ----------------------------------------------- | 500 | 519 464 520 508 518 = 0.95 || = 0.26 491 484 476 437 478 | 500 N = 10, n = 50000000, r = 0, s = 30 | 500 | 519 498 533 522 498 = 0.94 || = 0.25 469 474 482 507 472 | 500 Test on the sum of all N observations | 500 | 505 496 497 536 500 = 0.93 || = 0.24 513 491 499 495 503 | 500 | 500 | 475 493 487 473 493 = 0.92 || = 0.23 494 506 481 484 507 | 500 =================================================================| 500 | 513 481 478 545 486 = 0.91 || = 0.22 521 489 488 501 514 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 463 513 549 455 503 = 0.90 || = 0.21 485 484 497 500 480 | 500 -----------------------------------------------------------------| 500 | 506 519 486 479 481 = 0.89 || = 0.20 529 503 524 499 501 | 500 SD Bern.: d 0.94087 1.13722 1.46973 | 500 | 497 512 505 485 522 = 0.88 || = 0.19 479 477 503 468 487 | 500 s 0.86894 1.17361 0.90929 | 500 | 496 531 513 529 533 = 0.87 || = 0.18 529 520 497 513 469 | 500 t 0.95162 0.85247 0.88247 | 500 | 499 488 497 486 497 = 0.86 || = 0.17 534 504 521 469 454 | 500 m 1.04183 0.95441 1.04550 | 500 | 513 519 527 487 526 = 0.85 || = 0.16 485 508 497 482 507 | 500 x 0.90898 1.60454 1.64215 | 500 | 522 482 512 525 516 = 0.84 || = 0.15 501 504 493 498 517 | 500 | 500 | 495 495 482 517 533 = 0.83 || = 0.14 464 471 534 512 518 | 500 Changes: d 48 2 4 | 500 | 471 501 503 443 483 = 0.82 || = 0.13 500 476 519 454 495 | 500 s 42 5 6 | 500 | 457 508 486 505 493 = 0.81 || = 0.12 475 517 492 532 530 | 500 t 46 3 7 | 500 | 548 516 488 531 504 = 0.80 || = 0.11 491 498 488 514 521 | 500 m 54 8 9 | 500 | 505 503 507 506 490 = 0.79 || = 0.10 542 522 475 495 523 | 500 x 44 2 7 | 500 | 488 497 509 491 500 = 0.78 || = 0.09 520 509 540 527 513 | 500 -----------------------------------------------------------------| 500 | 477 525 524 521 507 = 0.77 || = 0.08 528 504 544 501 555 | 500 Aver./ d 0.49911 500 > 500: 5 4 5 4 4 3 5 5 3 8 | 500 | 500 513 513 492 480 = 0.76 || = 0.07 484 503 490 491 514 | 500 median s 0.50186 501 ----- 7 6 5 3 8 0 5 5 7 5 | 500 | 519 470 516 533 492 = 0.75 || = 0.06 488 494 467 515 470 | 500 t 0.50046 497 7 4 2 4 3 5 2 6 6 5 | 500 | 460 523 484 510 478 = 0.74 || = 0.05 499 482 510 537 486 | 500 m 0.50125 501 8 4 4 4 5 6 5 7 4 8 | 500 | 491 463 502 521 509 = 0.73 || = 0.04 500 530 475 493 509 | 500 x 0.49949 497 7 6 5 5 1 3 3 3 6 6 | 500 | 523 499 483 491 496 = 0.72 || = 0.03 515 493 535 501 499 | 500 -----------------------------------------------------------------| 500 | 503 500 470 514 488 = 0.71 || = 0.02 506 507 547 506 532 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 457 517 482 505 477 = 0.70 || = 0.01 252 256 257 259 282 | 252.5 d 0 0 0 16 70 14 1 0 0 | 500 | 469 468 500 466 493 = 0.69 || < 0.01 534 510 527 533 558 | 497.5 s 0 0 1 14 76 8 2 0 0 | 500 | 509 532 506 500 527 = 0.68 ||========================================================================= t 0 0 2 11 72 13 3 0 0 | 500 | 490 487 492 464 489 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 6 9 70 15 1 0 0 | 500 | 521 518 491 488 496 = 0.66 ||========================================================================= x 0 0 1 9 77 12 2 0 0 | 500 | 514 520 496 539 520 = 0.65 || smarsa_GCD test: no 145 test no 146 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 146 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 479 533 453 500 539 | 500 < 0.00002 0 0 1 1 0 | 0.5 | 0 1 0 0 0 > 0.99998 || = 0.63 483 533 464 490 496 | 500 < 0.00003 1 0 2 0 1 | 0.5 | 0 1 1 2 0 > 0.99997 || = 0.62 481 517 507 458 489 | 500 < 0.00004 1 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 545 500 451 485 473 | 500 < 0.00005 2 0 0 1 0 | 0.5 | 0 1 1 1 0 > 0.99995 || = 0.60 516 506 503 501 506 | 500 < 0.00006 1 3 2 1 2 | 0.5 | 0 1 1 2 0 > 0.99994 || = 0.59 515 532 490 492 462 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 488 504 543 526 521 | 500 < 0.00008 2 2 1 1 1 | 0.5 | 0 2 0 0 0 > 0.99992 || = 0.57 505 501 476 547 476 | 500 < 0.00009 1 0 0 0 1 | 0.5 | 0 0 0 0 2 > 0.99991 || = 0.56 522 479 489 500 542 | 500 < 0.0001 0 0 1 1 1 | 0.5 | 1 0 2 0 0 > 0.9999 || = 0.55 514 506 541 477 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 522 542 478 488 500 | 500 < 0.0001 8 6 7 6 6 | 5 | 1 7 5 5 2 > 0.9999 || = 0.53 532 511 514 498 479 | 500 < 0.0002 4 7 6 5 5 | 5 | 4 1 1 2 1 > 0.9998 || = 0.52 488 507 493 509 503 | 500 < 0.0003 7 8 10 3 5 | 5 | 5 3 2 3 2 > 0.9997 || = 0.51 490 486 508 515 507 | 500 < 0.0004 7 5 6 0 3 | 5 | 2 11 1 5 6 > 0.9996 || = 0.50 483 518 472 512 478 | 500 < 0.0005 4 8 3 4 4 | 5 | 2 9 2 4 8 > 0.9995 || = 0.49 489 520 531 474 489 | 500 < 0.0006 6 8 3 3 7 | 5 | 8 4 5 2 4 > 0.9994 || = 0.48 479 490 481 537 502 | 500 < 0.0007 3 5 8 7 7 | 5 | 6 5 10 3 3 > 0.9993 || = 0.47 493 514 536 506 485 | 500 < 0.0008 4 7 6 3 4 | 5 | 4 6 9 3 8 > 0.9992 || = 0.46 505 498 483 457 521 | 500 < 0.0009 3 2 3 5 5 | 5 | 4 1 3 6 4 > 0.9991 || = 0.45 509 454 559 455 484 | 500 < 0.001 6 8 4 5 0 | 5 | 3 8 5 6 9 > 0.999 || = 0.44 506 543 509 547 548 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 493 517 486 505 486 | 500 < 0.001 52 64 56 41 46 | 50 | 39 55 43 39 47 > 0.999 || = 0.42 498 508 487 474 463 | 500 < 0.002 44 41 39 42 45 | 50 | 47 53 48 63 62 > 0.998 || = 0.41 491 500 525 479 497 | 500 < 0.003 45 40 42 60 46 | 50 | 48 38 53 45 61 > 0.997 || = 0.40 482 445 502 515 497 | 500 < 0.004 46 50 48 50 43 | 50 | 43 54 59 60 53 > 0.996 || = 0.39 504 487 487 484 530 | 500 < 0.005 44 58 38 47 50 | 50 | 57 40 41 57 48 > 0.995 || = 0.38 477 477 474 552 486 | 500 < 0.006 50 49 53 54 45 | 50 | 43 54 37 43 43 > 0.994 || = 0.37 479 500 504 513 470 | 500 < 0.007 55 56 64 48 48 | 50 | 52 50 50 59 37 > 0.993 || = 0.36 536 520 509 509 505 | 500 < 0.008 67 61 59 55 57 | 50 | 56 46 45 49 49 > 0.992 || = 0.35 517 472 523 500 477 | 500 < 0.009 50 45 53 47 49 | 50 | 57 47 49 56 41 > 0.991 || = 0.34 527 500 450 504 529 | 500 < 0.01 45 49 56 38 54 | 50 | 51 54 54 60 52 > 0.99 || = 0.33 460 499 509 456 508 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 515 457 489 500 501 | 500 < 0.01 498 513 508 482 483 | 497.5 | 493 491 479 531 493 > 0.99 || = 0.31 495 467 492 535 508 | 500 = 0.01 244 270 268 260 273 | 252.5 | 268 243 263 257 243 = 0.99 || = 0.30 509 490 516 484 521 | 500 = 0.02 507 493 510 470 478 | 500 | 523 525 549 495 481 = 0.98 || = 0.29 485 538 494 448 461 | 500 =================================================================| 500 | 472 495 494 529 510 = 0.97 || = 0.28 515 483 484 495 486 | 500 swalk_RandomWalk1 test: | 500 | 463 473 532 520 470 = 0.96 || = 0.27 522 502 516 517 471 | 500 ----------------------------------------------- | 500 | 476 487 492 527 512 = 0.95 || = 0.26 461 498 535 524 460 | 500 N = 1, n = 100000000, r = 0, s = 5, L0 = 50, L1 = 50 | 500 | 510 507 467 511 511 = 0.94 || = 0.25 481 476 474 486 540 | 500 Test on the values of the Statistic H | 500 | 502 466 510 490 512 = 0.93 || = 0.24 517 509 530 454 437 | 500 | 500 | 513 530 511 484 549 = 0.92 || = 0.23 497 479 548 478 526 | 500 =================================================================| 500 | 488 490 480 511 504 = 0.91 || = 0.22 492 468 497 474 532 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 480 492 536 511 519 = 0.90 || = 0.21 516 495 508 527 477 | 500 -----------------------------------------------------------------| 500 | 489 519 504 481 475 = 0.89 || = 0.20 510 505 505 502 492 | 500 SD Bern.: d 0.88459 0.95545 0.86181 | 500 | 457 499 504 511 499 = 0.88 || = 0.19 516 485 484 541 479 | 500 s 0.95674 1.11858 0.83826 | 500 | 516 551 505 508 479 = 0.87 || = 0.18 522 476 485 520 472 | 500 t 1.10501 1.18380 0.93319 | 500 | 529 487 479 513 517 = 0.86 || = 0.17 487 501 490 477 479 | 500 m 1.09474 0.95126 1.20972 | 500 | 481 467 502 504 465 = 0.85 || = 0.16 476 529 483 535 507 | 500 x 1.08952 0.63434 1.08773 | 500 | 513 508 471 509 485 = 0.84 || = 0.15 521 488 465 519 509 | 500 | 500 | 475 495 482 477 462 = 0.83 || = 0.14 512 531 484 552 523 | 500 Changes: d 47 3 3 | 500 | 486 491 537 485 521 = 0.82 || = 0.13 491 472 502 469 495 | 500 s 47 5 6 | 500 | 533 493 479 503 464 = 0.81 || = 0.12 552 487 480 493 502 | 500 t 63 2 3 | 500 | 493 496 475 490 507 = 0.80 || = 0.11 516 496 521 516 503 | 500 m 55 6 7 | 500 | 500 499 534 510 514 = 0.79 || = 0.10 477 496 483 478 483 | 500 x 48 3 3 | 500 | 518 489 501 447 508 = 0.78 || = 0.09 501 507 535 502 511 | 500 -----------------------------------------------------------------| 500 | 501 527 517 476 492 = 0.77 || = 0.08 524 481 554 476 506 | 500 Aver./ d 0.49872 499 > 500: 6 6 5 6 3 7 2 5 4 5 | 500 | 506 503 498 508 513 = 0.76 || = 0.07 490 465 493 503 467 | 500 median s 0.50239 499 ----- 4 3 4 1 5 8 7 7 3 3 | 500 | 490 511 482 495 550 = 0.75 || = 0.06 513 453 483 497 491 | 500 t 0.49840 499 7 2 6 5 6 5 3 5 6 5 | 500 | 544 521 517 465 550 = 0.74 || = 0.05 483 488 547 566 462 | 500 m 0.50027 502 5 6 4 5 5 5 3 5 7 7 | 500 | 492 519 472 526 507 = 0.73 || = 0.04 496 491 534 491 501 | 500 x 0.50251 501 4 5 3 7 3 6 6 9 3 6 | 500 | 499 544 507 508 521 = 0.72 || = 0.03 509 513 499 502 486 | 500 -----------------------------------------------------------------| 500 | 511 512 450 532 519 = 0.71 || = 0.02 507 493 510 470 478 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 518 523 473 483 497 = 0.70 || = 0.01 244 270 268 260 273 | 252.5 d 0 0 0 11 80 8 2 0 0 | 500 | 492 494 468 509 529 = 0.69 || < 0.01 498 513 508 482 483 | 497.5 s 0 0 3 12 71 14 1 0 0 | 500 | 459 507 497 467 544 = 0.68 ||========================================================================= t 0 0 4 13 64 15 5 0 0 | 500 | 479 510 501 517 509 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 16 64 12 5 0 0 | 500 | 489 521 476 503 535 = 0.66 ||========================================================================= x 0 0 1 18 65 12 5 0 0 | 500 | 484 494 523 469 546 = 0.65 || swalk_RandomWalk1 test: no 146 test no 147 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 147 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 1 0 1 1 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 459 552 522 469 464 | 500 < 0.00002 1 0 2 0 0 | 0.5 | 0 0 2 0 0 > 0.99998 || = 0.63 469 488 496 490 475 | 500 < 0.00003 0 2 0 0 0 | 0.5 | 1 0 0 0 1 > 0.99997 || = 0.62 503 495 507 485 504 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99996 || = 0.61 494 520 502 504 544 | 500 < 0.00005 0 1 1 0 0 | 0.5 | 1 0 0 0 0 > 0.99995 || = 0.60 508 517 470 503 478 | 500 < 0.00006 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 463 459 488 522 481 | 500 < 0.00007 1 0 1 1 1 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 508 484 483 514 506 | 500 < 0.00008 0 0 0 2 1 | 0.5 | 0 0 2 1 2 > 0.99992 || = 0.57 497 516 497 467 525 | 500 < 0.00009 1 0 1 1 0 | 0.5 | 0 0 0 2 0 > 0.99991 || = 0.56 486 486 499 467 501 | 500 < 0.0001 1 1 1 0 0 | 0.5 | 3 0 0 0 0 > 0.9999 || = 0.55 454 530 478 484 478 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 510 501 499 489 564 | 500 < 0.0001 6 5 6 7 4 | 5 | 5 2 4 4 3 > 0.9999 || = 0.53 483 485 505 501 488 | 500 < 0.0002 5 5 3 5 6 | 5 | 0 2 2 4 5 > 0.9998 || = 0.52 530 521 502 494 468 | 500 < 0.0003 3 8 9 9 4 | 5 | 0 6 3 6 6 > 0.9997 || = 0.51 534 482 523 505 473 | 500 < 0.0004 5 1 7 3 4 | 5 | 9 3 4 5 10 > 0.9996 || = 0.50 478 492 487 505 495 | 500 < 0.0005 6 3 4 6 3 | 5 | 4 3 10 1 3 > 0.9995 || = 0.49 483 469 482 497 486 | 500 < 0.0006 8 3 5 7 5 | 5 | 5 4 5 5 4 > 0.9994 || = 0.48 515 520 503 479 510 | 500 < 0.0007 8 9 6 13 2 | 5 | 5 2 3 4 2 > 0.9993 || = 0.47 527 462 475 512 483 | 500 < 0.0008 5 5 7 2 5 | 5 | 5 6 7 6 4 > 0.9992 || = 0.46 474 511 496 509 495 | 500 < 0.0009 2 4 5 4 9 | 5 | 6 5 7 8 6 > 0.9991 || = 0.45 488 495 520 486 480 | 500 < 0.001 2 6 5 3 4 | 5 | 4 4 6 7 3 > 0.999 || = 0.44 536 489 522 515 461 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 517 491 523 534 515 | 500 < 0.001 50 49 57 59 46 | 50 | 43 37 51 50 46 > 0.999 || = 0.42 504 525 525 494 488 | 500 < 0.002 49 51 61 43 51 | 50 | 50 45 53 47 49 > 0.998 || = 0.41 510 481 471 495 470 | 500 < 0.003 65 56 51 43 46 | 50 | 46 59 40 38 58 > 0.997 || = 0.40 488 490 527 547 469 | 500 < 0.004 58 53 55 54 49 | 50 | 56 47 46 63 67 > 0.996 || = 0.39 480 471 484 460 501 | 500 < 0.005 51 47 59 36 55 | 50 | 69 55 45 49 40 > 0.995 || = 0.38 486 476 489 488 518 | 500 < 0.006 46 61 53 43 49 | 50 | 66 56 58 60 40 > 0.994 || = 0.37 492 542 512 471 474 | 500 < 0.007 47 36 45 51 49 | 50 | 43 48 48 47 45 > 0.993 || = 0.36 515 522 514 468 507 | 500 < 0.008 39 49 53 41 62 | 50 | 56 54 55 53 44 > 0.992 || = 0.35 480 492 477 490 508 | 500 < 0.009 48 52 41 53 39 | 50 | 51 52 34 56 45 > 0.991 || = 0.34 505 495 521 458 457 | 500 < 0.01 53 60 45 69 40 | 50 | 51 49 63 57 53 > 0.99 || = 0.33 490 511 481 544 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 497 501 550 498 537 | 500 < 0.01 506 514 520 492 486 | 497.5 | 531 502 493 520 487 > 0.99 || = 0.31 471 492 483 477 465 | 500 = 0.01 237 254 257 248 249 | 252.5 | 235 252 265 241 272 = 0.99 || = 0.30 499 500 483 483 488 | 500 = 0.02 490 507 490 484 467 | 500 | 509 489 474 475 493 = 0.98 || = 0.29 490 519 466 505 513 | 500 =================================================================| 500 | 513 501 516 528 522 = 0.97 || = 0.28 520 490 485 527 508 | 500 swalk_RandomWalk1 test: | 500 | 493 510 483 514 496 = 0.96 || = 0.27 501 509 489 485 499 | 500 ----------------------------------------------- | 500 | 491 543 504 518 492 = 0.95 || = 0.26 535 522 502 536 540 | 500 N = 1, n = 100000000, r = 0, s = 5, L0 = 50, L1 = 50 | 500 | 503 489 503 502 543 = 0.94 || = 0.25 467 521 519 518 484 | 500 Test on the values of the Statistic M | 500 | 503 498 463 509 495 = 0.93 || = 0.24 475 495 531 528 540 | 500 | 500 | 500 463 465 537 535 = 0.92 || = 0.23 466 531 496 536 503 | 500 =================================================================| 500 | 511 498 533 510 525 = 0.91 || = 0.22 518 496 489 502 497 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 509 502 509 515 496 = 0.90 || = 0.21 481 460 523 539 468 | 500 -----------------------------------------------------------------| 500 | 513 492 484 511 520 = 0.89 || = 0.20 466 490 477 541 532 | 500 SD Bern.: d 0.93786 0.94915 1.26948 | 500 | 518 531 512 503 523 = 0.88 || = 0.19 540 470 494 527 488 | 500 s 0.97596 0.97823 0.86065 | 500 | 522 517 502 478 482 = 0.87 || = 0.18 495 480 504 477 462 | 500 t 0.90236 0.92349 1.15728 | 500 | 494 468 465 490 523 = 0.86 || = 0.17 492 503 505 491 508 | 500 m 1.00796 1.33633 1.02617 | 500 | 493 478 531 479 481 = 0.85 || = 0.16 492 507 488 513 518 | 500 x 1.09283 0.92349 1.15382 | 500 | 489 464 467 485 523 = 0.84 || = 0.15 521 524 455 563 513 | 500 | 500 | 525 523 500 451 473 = 0.83 || = 0.14 554 472 505 488 464 | 500 Changes: d 52 3 3 | 500 | 499 525 487 515 491 = 0.82 || = 0.13 532 496 520 492 525 | 500 s 44 5 6 | 500 | 525 513 485 539 546 = 0.81 || = 0.12 495 470 529 475 543 | 500 t 53 3 6 | 500 | 504 507 518 508 464 = 0.80 || = 0.11 515 493 528 487 519 | 500 m 37 6 5 | 500 | 472 508 500 484 505 = 0.79 || = 0.10 511 483 497 537 506 | 500 x 50 6 3 | 500 | 506 537 505 508 481 = 0.78 || = 0.09 505 502 454 484 530 | 500 -----------------------------------------------------------------| 500 | 474 553 498 510 478 = 0.77 || = 0.08 508 505 512 524 502 | 500 Aver./ d 0.50047 499 > 500: 4 6 4 2 6 5 5 4 6 6 | 500 | 528 481 547 486 541 = 0.76 || = 0.07 491 503 514 503 503 | 500 median s 0.50085 498 ----- 8 3 5 4 3 5 4 6 6 4 | 500 | 497 494 499 508 512 = 0.75 || = 0.06 496 515 525 502 533 | 500 t 0.49928 502 6 6 4 4 6 3 8 6 4 5 | 500 | 493 495 510 478 523 = 0.74 || = 0.05 491 471 472 512 512 | 500 m 0.49909 499 5 4 9 1 5 5 3 4 5 8 | 500 | 468 507 467 475 461 = 0.73 || = 0.04 498 493 491 504 531 | 500 x 0.50014 497 6 7 6 6 2 4 2 5 5 5 | 500 | 476 531 507 482 490 = 0.72 || = 0.03 503 523 520 472 461 | 500 -----------------------------------------------------------------| 500 | 536 484 516 499 520 = 0.71 || = 0.02 490 507 490 484 467 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 480 479 507 484 484 = 0.70 || = 0.01 237 254 257 248 249 | 252.5 d 0 0 1 15 71 12 2 0 0 | 500 | 518 506 523 514 497 = 0.69 || < 0.01 506 514 520 492 486 | 497.5 s 0 0 1 13 72 12 3 0 0 | 500 | 516 483 512 464 484 = 0.68 ||========================================================================= t 0 0 2 13 71 13 2 0 0 | 500 | 553 491 484 473 490 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 15 67 16 2 0 0 | 500 | 474 450 502 526 479 = 0.66 ||========================================================================= x 0 0 0 18 60 21 2 0 0 | 500 | 505 555 511 485 485 = 0.65 || swalk_RandomWalk1 test: no 147 test no 148 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 148 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 0 1 3 > 0.99999 || = 0.64 478 510 473 519 486 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 1 0 1 1 > 0.99998 || = 0.63 507 494 453 520 488 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 514 517 491 501 480 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 1 1 0 1 > 0.99996 || = 0.61 498 491 505 462 514 | 500 < 0.00005 0 0 0 1 1 | 0.5 | 0 1 0 0 0 > 0.99995 || = 0.60 539 514 497 506 541 | 500 < 0.00006 1 1 2 1 0 | 0.5 | 0 0 1 0 1 > 0.99994 || = 0.59 524 529 522 496 516 | 500 < 0.00007 0 0 2 0 0 | 0.5 | 0 1 0 1 0 > 0.99993 || = 0.58 474 411 509 484 495 | 500 < 0.00008 1 0 0 0 0 | 0.5 | 1 1 0 0 2 > 0.99992 || = 0.57 511 498 505 498 540 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 1 1 0 0 1 > 0.99991 || = 0.56 499 512 467 461 482 | 500 < 0.0001 0 1 0 0 2 | 0.5 | 0 2 2 0 0 > 0.9999 || = 0.55 494 488 492 509 472 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 486 489 519 507 497 | 500 < 0.0001 2 2 4 3 3 | 5 | 2 8 4 3 9 > 0.9999 || = 0.53 477 515 514 502 484 | 500 < 0.0002 7 5 3 2 4 | 5 | 1 4 3 4 5 > 0.9998 || = 0.52 485 492 551 456 499 | 500 < 0.0003 1 5 5 4 1 | 5 | 12 5 3 3 3 > 0.9997 || = 0.51 484 479 510 464 537 | 500 < 0.0004 4 8 8 3 9 | 5 | 4 6 5 3 3 > 0.9996 || = 0.50 502 488 487 554 494 | 500 < 0.0005 3 6 4 8 6 | 5 | 5 2 3 5 3 > 0.9995 || = 0.49 552 473 496 496 497 | 500 < 0.0006 4 8 7 4 6 | 5 | 9 5 5 5 1 > 0.9994 || = 0.48 509 512 537 518 507 | 500 < 0.0007 3 4 5 3 3 | 5 | 4 5 2 7 5 > 0.9993 || = 0.47 473 527 519 487 498 | 500 < 0.0008 3 1 3 4 4 | 5 | 4 3 2 5 7 > 0.9992 || = 0.46 530 508 494 493 533 | 500 < 0.0009 6 8 5 3 3 | 5 | 8 9 2 6 8 > 0.9991 || = 0.45 456 486 517 487 528 | 500 < 0.001 12 6 4 4 6 | 5 | 6 10 6 6 7 > 0.999 || = 0.44 534 509 468 507 539 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 515 494 507 511 485 | 500 < 0.001 45 53 48 38 45 | 50 | 55 57 35 47 51 > 0.999 || = 0.42 508 484 487 523 486 | 500 < 0.002 45 39 48 54 46 | 50 | 39 45 54 44 48 > 0.998 || = 0.41 499 494 522 479 513 | 500 < 0.003 47 51 51 49 37 | 50 | 57 49 43 51 48 > 0.997 || = 0.40 487 493 504 493 506 | 500 < 0.004 50 53 49 47 46 | 50 | 44 51 46 47 44 > 0.996 || = 0.39 514 476 483 501 524 | 500 < 0.005 57 53 52 55 53 | 50 | 54 47 41 58 51 > 0.995 || = 0.38 521 482 549 464 457 | 500 < 0.006 58 46 60 41 52 | 50 | 53 45 43 57 53 > 0.994 || = 0.37 516 502 495 511 492 | 500 < 0.007 46 46 42 49 51 | 50 | 40 49 45 61 58 > 0.993 || = 0.36 489 532 515 479 479 | 500 < 0.008 37 51 51 42 51 | 50 | 48 50 58 45 38 > 0.992 || = 0.35 497 511 488 514 546 | 500 < 0.009 47 41 48 47 61 | 50 | 61 48 43 57 48 > 0.991 || = 0.34 448 481 507 508 490 | 500 < 0.01 49 58 55 47 49 | 50 | 35 35 43 62 39 > 0.99 || = 0.33 462 490 502 486 519 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 499 499 500 477 526 | 500 < 0.01 481 491 504 469 491 | 497.5 | 486 476 451 529 478 > 0.99 || = 0.31 464 493 500 478 460 | 500 = 0.01 249 249 236 233 275 | 252.5 | 270 254 264 280 246 = 0.99 || = 0.30 478 506 502 520 508 | 500 = 0.02 502 513 500 513 494 | 500 | 510 508 513 501 498 = 0.98 || = 0.29 522 480 518 493 501 | 500 =================================================================| 500 | 476 471 499 499 528 = 0.97 || = 0.28 521 475 479 513 486 | 500 swalk_RandomWalk1 test: | 500 | 520 517 485 528 469 = 0.96 || = 0.27 525 510 489 506 499 | 500 ----------------------------------------------- | 500 | 518 482 470 524 503 = 0.95 || = 0.26 520 496 524 481 481 | 500 N = 1, n = 100000000, r = 0, s = 5, L0 = 50, L1 = 50 | 500 | 489 538 518 504 498 = 0.94 || = 0.25 481 495 475 493 450 | 500 Test on the values of the Statistic J | 500 | 532 488 503 486 501 = 0.93 || = 0.24 501 487 546 513 520 | 500 | 500 | 468 512 541 539 512 = 0.92 || = 0.23 533 524 506 516 499 | 500 =================================================================| 500 | 481 509 481 522 473 = 0.91 || = 0.22 490 492 515 490 491 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 480 523 481 517 502 = 0.90 || = 0.21 515 498 524 507 468 | 500 -----------------------------------------------------------------| 500 | 487 507 495 482 487 = 0.89 || = 0.20 522 461 514 506 526 | 500 SD Bern.: d 0.93799 0.85716 1.18886 | 500 | 518 494 424 490 497 = 0.88 || = 0.19 503 494 493 531 505 | 500 s 0.92912 0.80910 0.82502 | 500 | 515 502 495 506 529 = 0.87 || = 0.18 469 523 485 512 515 | 500 t 1.05862 0.64529 1.11679 | 500 | 502 505 491 482 532 = 0.86 || = 0.17 480 523 492 488 525 | 500 m 0.93256 0.84776 1.00747 | 500 | 483 502 476 510 519 = 0.85 || = 0.16 507 502 526 485 509 | 500 x 0.97459 0.85247 0.88133 | 500 | 505 477 453 488 481 = 0.84 || = 0.15 465 484 471 484 515 | 500 | 500 | 500 516 514 516 502 = 0.83 || = 0.14 494 513 441 477 453 | 500 Changes: d 52 2 7 | 500 | 505 495 520 467 503 = 0.82 || = 0.13 541 457 480 516 523 | 500 s 50 6 3 | 500 | 508 492 505 502 461 = 0.81 || = 0.12 498 512 506 493 484 | 500 t 49 7 4 | 500 | 509 496 495 493 522 = 0.80 || = 0.11 485 541 495 505 464 | 500 m 49 4 5 | 500 | 482 534 504 500 505 = 0.79 || = 0.10 534 497 511 485 457 | 500 x 56 2 3 | 500 | 501 566 486 504 509 = 0.78 || = 0.09 481 496 513 461 510 | 500 -----------------------------------------------------------------| 500 | 498 523 500 509 491 = 0.77 || = 0.08 508 467 525 486 521 | 500 Aver./ d 0.50035 501 > 500: 5 4 8 3 6 3 7 4 6 5 | 500 | 468 527 493 516 513 = 0.76 || = 0.07 499 506 469 483 477 | 500 median s 0.50116 499 ----- 5 6 2 4 4 4 6 7 6 6 | 500 | 513 503 524 530 448 = 0.75 || = 0.06 511 481 471 507 500 | 500 t 0.49904 502 6 3 7 5 6 7 6 4 3 5 | 500 | 488 509 521 507 509 = 0.74 || = 0.05 514 530 502 472 493 | 500 m 0.50380 502 2 4 6 5 4 4 8 8 5 8 | 500 | 491 468 455 510 488 = 0.73 || = 0.04 452 507 508 487 516 | 500 x 0.50046 499 4 6 3 5 6 4 4 6 6 4 | 500 | 506 495 486 507 538 = 0.72 || = 0.03 508 502 507 466 490 | 500 -----------------------------------------------------------------| 500 | 487 530 553 554 494 = 0.71 || = 0.02 502 513 500 513 494 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 528 476 539 521 495 = 0.70 || = 0.01 249 249 236 233 275 | 252.5 d 0 0 2 12 74 12 1 0 0 | 500 | 509 511 513 518 509 = 0.69 || < 0.01 481 491 504 469 491 | 497.5 s 1 0 0 11 74 14 1 0 0 | 500 | 529 512 470 506 493 = 0.68 ||========================================================================= t 0 1 5 11 70 10 4 0 0 | 500 | 512 515 524 501 506 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 14 76 8 3 0 0 | 500 | 515 510 529 463 490 = 0.66 ||========================================================================= x 0 0 3 10 71 16 1 0 0 | 500 | 477 472 517 547 515 = 0.65 || swalk_RandomWalk1 test: no 148 test no 149 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 149 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 1 1 0 | 0.5 | 0 0 0 1 1 > 0.99999 || = 0.64 478 528 518 480 463 | 500 < 0.00002 1 1 0 0 0 | 0.5 | 1 1 1 2 3 > 0.99998 || = 0.63 544 487 502 484 507 | 500 < 0.00003 0 2 0 0 1 | 0.5 | 1 0 0 0 2 > 0.99997 || = 0.62 498 499 478 498 521 | 500 < 0.00004 0 1 1 0 0 | 0.5 | 0 2 0 0 1 > 0.99996 || = 0.61 505 497 466 535 494 | 500 < 0.00005 0 0 1 0 0 | 0.5 | 1 0 0 0 0 > 0.99995 || = 0.60 523 482 490 519 479 | 500 < 0.00006 1 1 1 0 0 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 467 480 493 493 492 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 0 1 0 1 0 > 0.99993 || = 0.58 499 514 519 495 509 | 500 < 0.00008 0 2 1 0 0 | 0.5 | 1 2 0 0 0 > 0.99992 || = 0.57 456 548 481 504 496 | 500 < 0.00009 1 0 2 2 1 | 0.5 | 0 0 0 2 2 > 0.99991 || = 0.56 500 511 475 487 485 | 500 < 0.0001 1 0 0 1 0 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 480 507 482 444 520 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 504 455 461 468 482 | 500 < 0.0001 5 8 8 4 2 | 5 | 5 7 2 6 9 > 0.9999 || = 0.53 488 546 501 519 510 | 500 < 0.0002 4 1 5 6 2 | 5 | 3 2 5 1 3 > 0.9998 || = 0.52 496 536 502 475 499 | 500 < 0.0003 3 5 6 6 5 | 5 | 2 7 6 6 3 > 0.9997 || = 0.51 519 449 543 492 505 | 500 < 0.0004 5 7 3 8 6 | 5 | 9 4 4 9 5 > 0.9996 || = 0.50 514 493 551 523 489 | 500 < 0.0005 4 3 6 5 9 | 5 | 5 8 4 6 3 > 0.9995 || = 0.49 529 533 527 481 462 | 500 < 0.0006 10 8 5 3 3 | 5 | 7 6 4 2 9 > 0.9994 || = 0.48 517 526 525 510 519 | 500 < 0.0007 5 1 6 3 8 | 5 | 1 4 5 5 1 > 0.9993 || = 0.47 484 446 503 495 541 | 500 < 0.0008 8 4 7 8 2 | 5 | 7 5 8 7 2 > 0.9992 || = 0.46 450 504 477 535 523 | 500 < 0.0009 1 5 7 7 3 | 5 | 7 6 3 8 5 > 0.9991 || = 0.45 498 555 503 511 479 | 500 < 0.001 2 4 6 6 4 | 5 | 2 4 4 3 4 > 0.999 || = 0.44 486 494 512 491 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 498 528 490 493 530 | 500 < 0.001 47 46 59 56 44 | 50 | 48 53 45 53 44 > 0.999 || = 0.42 493 540 509 487 542 | 500 < 0.002 44 55 49 50 51 | 50 | 37 57 50 57 58 > 0.998 || = 0.41 492 459 494 517 502 | 500 < 0.003 62 42 44 61 48 | 50 | 54 50 41 48 50 > 0.997 || = 0.40 467 488 499 489 487 | 500 < 0.004 51 51 43 41 60 | 50 | 52 49 55 55 55 > 0.996 || = 0.39 478 499 512 518 518 | 500 < 0.005 47 46 47 48 52 | 50 | 43 50 47 56 49 > 0.995 || = 0.38 485 461 486 505 499 | 500 < 0.006 57 52 43 49 56 | 50 | 47 54 46 58 35 > 0.994 || = 0.37 521 481 495 481 451 | 500 < 0.007 44 41 52 46 47 | 50 | 51 55 67 41 41 > 0.993 || = 0.36 460 530 515 480 486 | 500 < 0.008 44 56 66 50 66 | 50 | 49 55 54 52 52 > 0.992 || = 0.35 480 540 529 522 501 | 500 < 0.009 48 49 47 53 49 | 50 | 45 53 54 45 56 > 0.991 || = 0.34 496 464 500 506 481 | 500 < 0.01 59 48 54 60 51 | 50 | 38 52 49 41 46 > 0.99 || = 0.33 507 474 493 509 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 500 490 504 484 536 | 500 < 0.01 503 486 504 514 524 | 497.5 | 464 528 508 506 486 > 0.99 || = 0.31 557 507 522 518 501 | 500 = 0.01 266 241 232 235 267 | 252.5 | 247 251 258 237 255 = 0.99 || = 0.30 483 503 508 539 503 | 500 = 0.02 495 551 499 513 494 | 500 | 514 505 521 465 465 = 0.98 || = 0.29 461 502 494 558 530 | 500 =================================================================| 500 | 474 489 509 484 482 = 0.97 || = 0.28 535 466 475 496 514 | 500 swalk_RandomWalk1 test: | 500 | 481 515 482 498 496 = 0.96 || = 0.27 512 521 493 505 483 | 500 ----------------------------------------------- | 500 | 481 503 513 498 473 = 0.95 || = 0.26 534 494 544 494 503 | 500 N = 1, n = 100000000, r = 0, s = 5, L0 = 50, L1 = 50 | 500 | 509 522 483 480 491 = 0.94 || = 0.25 520 504 480 472 482 | 500 Test on the values of the Statistic R | 500 | 466 468 474 518 492 = 0.93 || = 0.24 461 511 493 519 497 | 500 | 500 | 508 484 497 542 543 = 0.92 || = 0.23 506 484 468 464 511 | 500 =================================================================| 500 | 524 471 493 471 488 = 0.91 || = 0.22 450 487 491 499 478 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 552 528 532 493 478 = 0.90 || = 0.21 513 493 483 489 527 | 500 -----------------------------------------------------------------| 500 | 514 511 484 496 532 = 0.89 || = 0.20 485 530 497 501 514 | 500 SD Bern.: d 1.13536 0.90044 0.91914 | 500 | 482 488 534 524 467 = 0.88 || = 0.19 533 527 478 461 478 | 500 s 1.15648 0.70462 0.52560 | 500 | 558 461 482 516 521 = 0.87 || = 0.18 511 526 489 483 483 | 500 t 0.98601 1.01045 0.97823 | 500 | 490 538 497 492 520 = 0.86 || = 0.17 480 491 481 498 499 | 500 m 1.02604 0.85832 0.86990 | 500 | 496 489 532 498 511 = 0.85 || = 0.16 511 519 516 551 498 | 500 x 0.95880 0.94703 0.98841 | 500 | 549 532 493 504 479 = 0.84 || = 0.15 447 521 483 539 474 | 500 | 500 | 518 466 519 482 501 = 0.83 || = 0.14 456 489 507 534 465 | 500 Changes: d 45 5 4 | 500 | 509 525 515 481 496 = 0.82 || = 0.13 496 527 502 510 517 | 500 s 47 8 2 | 500 | 538 505 528 516 500 = 0.81 || = 0.12 490 487 492 449 533 | 500 t 44 4 4 | 500 | 514 488 447 527 478 = 0.80 || = 0.11 507 442 504 484 509 | 500 m 48 4 5 | 500 | 458 468 496 471 514 = 0.79 || = 0.10 509 464 556 497 484 | 500 x 55 7 6 | 500 | 480 483 551 529 486 = 0.78 || = 0.09 520 459 504 481 504 | 500 -----------------------------------------------------------------| 500 | 562 512 496 497 512 = 0.77 || = 0.08 536 478 488 514 487 | 500 Aver./ d 0.50033 499 > 500: 7 5 6 3 2 3 5 3 7 4 | 500 | 473 521 479 496 525 = 0.76 || = 0.07 529 505 525 510 551 | 500 median s 0.50073 499 ----- 4 5 5 4 6 6 3 6 6 5 | 500 | 475 526 503 484 447 = 0.75 || = 0.06 522 525 519 488 500 | 500 t 0.50048 499 5 5 1 6 6 4 6 4 6 5 | 500 | 500 507 448 514 532 = 0.74 || = 0.05 483 477 501 457 494 | 500 m 0.49973 498 6 4 4 7 4 3 5 4 4 3 | 500 | 475 519 524 533 521 = 0.73 || = 0.04 515 469 479 511 524 | 500 x 0.49801 499 6 3 6 6 7 4 3 6 5 2 | 500 | 492 480 529 471 485 = 0.72 || = 0.03 496 524 478 502 512 | 500 -----------------------------------------------------------------| 500 | 514 511 476 469 514 = 0.71 || = 0.02 495 551 499 513 494 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 514 522 495 490 472 = 0.70 || = 0.01 266 241 232 235 267 | 252.5 d 0 0 3 14 68 11 5 0 0 | 500 | 519 464 439 477 494 = 0.69 || < 0.01 503 486 504 514 524 | 497.5 s 0 0 4 15 58 20 4 0 0 | 500 | 499 486 515 523 492 = 0.68 ||========================================================================= t 0 0 3 9 74 12 3 0 0 | 500 | 531 490 515 530 516 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 13 69 14 3 0 0 | 500 | 491 483 503 523 467 = 0.66 ||========================================================================= x 0 0 2 9 75 14 1 0 0 | 500 | 495 507 510 550 485 = 0.65 || swalk_RandomWalk1 test: no 149 test no 150 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 150 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 1 0 | 0.5 | 0 1 1 1 0 > 0.99999 || = 0.64 500 517 472 511 493 | 500 < 0.00002 0 0 1 1 1 | 0.5 | 0 0 0 2 0 > 0.99998 || = 0.63 481 517 490 527 531 | 500 < 0.00003 1 1 2 0 0 | 0.5 | 1 1 1 0 0 > 0.99997 || = 0.62 517 523 507 495 512 | 500 < 0.00004 1 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 504 523 500 501 506 | 500 < 0.00005 1 0 0 0 1 | 0.5 | 2 0 1 1 1 > 0.99995 || = 0.60 491 511 506 497 498 | 500 < 0.00006 0 2 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 517 534 506 509 501 | 500 < 0.00007 0 1 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 515 471 496 477 510 | 500 < 0.00008 0 0 1 1 0 | 0.5 | 1 0 0 0 0 > 0.99992 || = 0.57 517 499 550 485 500 | 500 < 0.00009 0 0 1 0 0 | 0.5 | 0 0 0 0 1 > 0.99991 || = 0.56 481 516 484 511 544 | 500 < 0.0001 1 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.9999 || = 0.55 499 460 522 522 473 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 537 501 520 534 472 | 500 < 0.0001 5 4 5 3 3 | 5 | 4 3 4 5 3 > 0.9999 || = 0.53 517 516 525 544 482 | 500 < 0.0002 7 5 9 7 7 | 5 | 1 1 0 2 5 > 0.9998 || = 0.52 508 544 486 497 447 | 500 < 0.0003 9 3 2 5 6 | 5 | 2 5 7 5 4 > 0.9997 || = 0.51 476 513 516 531 502 | 500 < 0.0004 0 3 2 6 6 | 5 | 6 5 4 4 5 > 0.9996 || = 0.50 514 503 520 484 503 | 500 < 0.0005 5 9 3 3 5 | 5 | 3 4 1 4 5 > 0.9995 || = 0.49 515 494 553 487 496 | 500 < 0.0006 4 3 2 5 13 | 5 | 5 6 5 5 5 > 0.9994 || = 0.48 505 511 492 506 531 | 500 < 0.0007 6 11 7 2 2 | 5 | 7 2 5 3 6 > 0.9993 || = 0.47 491 488 515 485 461 | 500 < 0.0008 7 2 6 6 3 | 5 | 3 0 6 3 3 > 0.9992 || = 0.46 485 503 538 511 557 | 500 < 0.0009 6 10 2 5 4 | 5 | 5 3 3 3 6 > 0.9991 || = 0.45 503 487 502 472 478 | 500 < 0.001 3 3 3 5 4 | 5 | 1 7 3 2 8 > 0.999 || = 0.44 451 508 514 494 497 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 490 506 515 474 487 | 500 < 0.001 52 53 41 47 53 | 50 | 37 36 38 36 50 > 0.999 || = 0.42 489 513 490 484 496 | 500 < 0.002 47 40 51 35 51 | 50 | 62 43 57 52 44 > 0.998 || = 0.41 513 456 487 513 479 | 500 < 0.003 53 44 51 41 40 | 50 | 47 40 52 53 48 > 0.997 || = 0.40 541 498 496 493 502 | 500 < 0.004 48 62 50 38 54 | 50 | 41 41 62 37 43 > 0.996 || = 0.39 457 506 524 458 514 | 500 < 0.005 51 50 50 40 49 | 50 | 48 51 48 37 59 > 0.995 || = 0.38 539 496 538 466 506 | 500 < 0.006 56 64 64 53 56 | 50 | 50 68 48 46 54 > 0.994 || = 0.37 488 501 510 519 485 | 500 < 0.007 57 47 51 51 54 | 50 | 45 64 47 40 50 > 0.993 || = 0.36 506 463 464 500 541 | 500 < 0.008 42 49 35 46 45 | 50 | 60 52 65 57 45 > 0.992 || = 0.35 469 480 506 502 478 | 500 < 0.009 42 51 44 53 53 | 50 | 43 53 44 49 54 > 0.991 || = 0.34 512 480 487 520 504 | 500 < 0.01 47 48 47 52 61 | 50 | 59 47 47 46 39 > 0.99 || = 0.33 495 491 474 535 498 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 482 497 500 470 510 | 500 < 0.01 495 508 484 456 516 | 497.5 | 492 495 508 453 486 > 0.99 || = 0.31 476 560 478 486 472 | 500 = 0.01 252 239 243 253 254 | 252.5 | 246 283 227 261 280 = 0.99 || = 0.30 505 465 528 453 474 | 500 = 0.02 526 507 543 458 522 | 500 | 487 499 533 501 479 = 0.98 || = 0.29 481 503 507 511 519 | 500 =================================================================| 500 | 496 503 508 484 506 = 0.97 || = 0.28 503 485 516 497 455 | 500 swalk_RandomWalk1 test: | 500 | 548 520 510 439 493 = 0.96 || = 0.27 482 523 508 534 478 | 500 ----------------------------------------------- | 500 | 464 481 478 512 539 = 0.95 || = 0.26 494 512 481 464 483 | 500 N = 1, n = 100000000, r = 0, s = 5, L0 = 50, L1 = 50 | 500 | 530 502 489 499 514 = 0.94 || = 0.25 468 535 497 493 528 | 500 Test on the values of the Statistic C | 500 | 493 472 502 520 526 = 0.93 || = 0.24 488 545 453 494 519 | 500 | 500 | 552 469 504 503 543 = 0.92 || = 0.23 529 469 477 504 483 | 500 =================================================================| 500 | 479 520 493 506 495 = 0.91 || = 0.22 492 489 514 476 485 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 506 507 498 465 515 = 0.90 || = 0.21 501 518 503 503 500 | 500 -----------------------------------------------------------------| 500 | 522 473 543 508 497 = 0.89 || = 0.20 484 508 522 513 485 | 500 SD Bern.: d 0.95644 0.70603 1.15121 | 500 | 508 517 498 502 468 = 0.88 || = 0.19 475 497 484 533 492 | 500 s 0.95360 1.00049 1.39280 | 500 | 530 510 494 468 521 = 0.87 || = 0.18 505 462 471 566 462 | 500 t 0.93512 1.04932 1.12126 | 500 | 529 508 494 507 498 = 0.86 || = 0.17 466 517 480 492 477 | 500 m 1.11472 1.09416 1.20807 | 500 | 484 507 484 477 496 = 0.85 || = 0.16 527 492 512 531 509 | 500 x 1.01693 0.81771 0.83467 | 500 | 482 516 520 560 501 = 0.84 || = 0.15 505 463 467 507 470 | 500 | 500 | 499 508 497 512 478 = 0.83 || = 0.14 503 500 513 474 461 | 500 Changes: d 54 5 5 | 500 | 502 489 510 464 496 = 0.82 || = 0.13 535 458 496 540 486 | 500 s 51 7 2 | 500 | 513 492 510 453 480 = 0.81 || = 0.12 498 500 496 484 488 | 500 t 49 4 4 | 500 | 471 482 533 471 489 = 0.80 || = 0.11 507 528 520 494 525 | 500 m 54 3 4 | 500 | 514 513 491 492 506 = 0.79 || = 0.10 481 483 497 513 484 | 500 x 47 6 4 | 500 | 462 472 510 505 509 = 0.78 || = 0.09 484 483 511 519 460 | 500 -----------------------------------------------------------------| 500 | 480 470 490 515 511 = 0.77 || = 0.08 471 505 490 485 507 | 500 Aver./ d 0.50195 498 > 500: 2 6 3 4 5 6 5 3 7 3 | 500 | 480 514 483 480 516 = 0.76 || = 0.07 487 483 494 480 516 | 500 median s 0.50063 503 ----- 6 2 7 3 5 7 7 4 7 5 | 500 | 545 482 482 533 468 = 0.75 || = 0.06 480 499 527 483 524 | 500 t 0.49996 498 4 3 6 5 6 7 3 2 4 6 | 500 | 495 483 461 519 485 = 0.74 || = 0.05 500 512 475 536 524 | 500 m 0.49959 501 4 6 5 4 3 6 8 6 5 6 | 500 | 498 560 467 515 475 = 0.73 || = 0.04 510 503 477 528 507 | 500 x 0.50199 500 8 2 3 5 3 4 9 6 3 6 | 500 | 545 512 467 545 508 = 0.72 || = 0.03 490 506 522 487 494 | 500 -----------------------------------------------------------------| 500 | 499 471 479 490 513 = 0.71 || = 0.02 526 507 543 458 522 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 496 482 510 498 534 = 0.70 || = 0.01 252 239 243 253 254 | 252.5 d 0 0 1 11 74 11 4 0 0 | 500 | 482 509 475 550 561 = 0.69 || < 0.01 495 508 484 456 516 | 497.5 s 0 0 0 15 75 8 3 0 0 | 500 | 519 495 483 503 532 = 0.68 ||========================================================================= t 0 0 1 14 74 10 2 0 0 | 500 | 540 490 493 510 510 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 16 65 12 4 0 0 | 500 | 511 505 470 505 513 = 0.66 ||========================================================================= x 0 0 2 13 70 14 2 0 0 | 500 | 496 506 515 514 506 = 0.65 || swalk_RandomWalk1 test: no 150 test no 151 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 151 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 0 0 0 | 0.5 | 0 1 1 0 0 > 0.99999 || = 0.64 503 495 504 496 470 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 454 483 514 475 496 | 500 < 0.00003 2 2 1 3 1 | 0.5 | 2 0 0 0 0 > 0.99997 || = 0.62 466 501 480 508 511 | 500 < 0.00004 0 1 1 0 0 | 0.5 | 0 1 0 2 0 > 0.99996 || = 0.61 508 483 540 525 521 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 3 0 > 0.99995 || = 0.60 501 503 479 510 494 | 500 < 0.00006 0 0 2 0 0 | 0.5 | 2 0 0 1 0 > 0.99994 || = 0.59 518 530 491 531 510 | 500 < 0.00007 0 1 1 0 1 | 0.5 | 0 1 0 1 1 > 0.99993 || = 0.58 476 502 447 512 482 | 500 < 0.00008 1 0 0 0 0 | 0.5 | 0 1 1 0 1 > 0.99992 || = 0.57 505 488 470 517 517 | 500 < 0.00009 0 0 0 0 1 | 0.5 | 1 1 0 1 1 > 0.99991 || = 0.56 520 485 507 492 486 | 500 < 0.0001 0 0 0 2 2 | 0.5 | 0 0 1 2 0 > 0.9999 || = 0.55 512 523 516 501 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 538 532 500 499 501 | 500 < 0.0001 5 4 5 6 5 | 5 | 6 5 3 10 3 > 0.9999 || = 0.53 489 527 482 479 520 | 500 < 0.0002 8 7 4 13 5 | 5 | 3 4 0 1 3 > 0.9998 || = 0.52 508 465 502 463 486 | 500 < 0.0003 6 5 7 12 2 | 5 | 4 4 3 8 7 > 0.9997 || = 0.51 491 483 501 474 480 | 500 < 0.0004 2 3 7 7 1 | 5 | 6 4 4 4 4 > 0.9996 || = 0.50 501 500 507 500 541 | 500 < 0.0005 3 11 4 5 2 | 5 | 1 3 3 9 5 > 0.9995 || = 0.49 522 508 478 500 515 | 500 < 0.0006 4 4 7 4 3 | 5 | 10 11 4 4 3 > 0.9994 || = 0.48 490 542 531 531 494 | 500 < 0.0007 1 5 10 0 7 | 5 | 6 3 5 2 4 > 0.9993 || = 0.47 482 510 451 503 495 | 500 < 0.0008 1 3 4 5 6 | 5 | 5 3 2 10 2 > 0.9992 || = 0.46 485 494 516 514 460 | 500 < 0.0009 6 3 7 10 4 | 5 | 3 6 8 4 8 > 0.9991 || = 0.45 424 496 485 503 498 | 500 < 0.001 2 4 4 6 7 | 5 | 5 4 4 8 6 > 0.999 || = 0.44 498 471 471 484 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 500 502 522 530 515 | 500 < 0.001 38 49 59 68 42 | 50 | 49 47 36 60 45 > 0.999 || = 0.42 508 500 465 544 490 | 500 < 0.002 47 50 50 45 44 | 50 | 46 42 42 45 44 > 0.998 || = 0.41 479 524 496 500 504 | 500 < 0.003 44 50 56 54 42 | 50 | 53 53 61 53 52 > 0.997 || = 0.40 495 478 509 511 496 | 500 < 0.004 57 44 54 45 46 | 50 | 50 47 57 61 45 > 0.996 || = 0.39 484 466 483 484 515 | 500 < 0.005 60 54 47 53 37 | 50 | 59 45 49 49 50 > 0.995 || = 0.38 499 488 515 520 492 | 500 < 0.006 65 60 64 46 53 | 50 | 49 59 42 46 60 > 0.994 || = 0.37 501 539 520 508 510 | 500 < 0.007 40 42 55 61 39 | 50 | 47 46 41 58 49 > 0.993 || = 0.36 458 499 511 475 507 | 500 < 0.008 58 54 49 52 49 | 50 | 52 54 54 43 54 > 0.992 || = 0.35 455 514 490 499 507 | 500 < 0.009 61 57 52 43 49 | 50 | 60 52 57 46 66 > 0.991 || = 0.34 470 523 506 493 525 | 500 < 0.01 40 42 50 38 54 | 50 | 42 46 46 45 49 > 0.99 || = 0.33 509 508 532 499 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 518 490 501 494 504 | 500 < 0.01 510 502 536 505 455 | 497.5 | 507 491 485 506 514 > 0.99 || = 0.31 509 500 495 467 528 | 500 = 0.01 249 247 252 252 254 | 252.5 | 267 248 264 257 279 = 0.99 || = 0.30 495 514 509 556 529 | 500 = 0.02 535 488 479 531 522 | 500 | 486 508 479 482 503 = 0.98 || = 0.29 468 433 504 520 450 | 500 =================================================================| 500 | 496 520 508 495 480 = 0.97 || = 0.28 456 488 506 496 492 | 500 swalk_RandomWalk1 test: | 500 | 539 505 497 518 494 = 0.96 || = 0.27 490 482 516 527 514 | 500 ----------------------------------------------- | 500 | 500 507 511 531 541 = 0.95 || = 0.26 500 461 490 500 498 | 500 N = 1, n = 100000000, r = 25, s = 5, L0 = 50, L1 = 50 | 500 | 486 506 509 486 475 = 0.94 || = 0.25 564 496 485 462 543 | 500 Test on the values of the Statistic H | 500 | 498 481 538 499 480 = 0.93 || = 0.24 495 507 487 538 525 | 500 | 500 | 474 525 507 489 489 = 0.92 || = 0.23 480 510 471 521 540 | 500 =================================================================| 500 | 487 499 528 485 495 = 0.91 || = 0.22 485 524 527 470 482 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 521 519 523 459 520 = 0.90 || = 0.21 484 504 525 465 517 | 500 -----------------------------------------------------------------| 500 | 511 480 467 496 531 = 0.89 || = 0.20 502 477 460 505 497 | 500 SD Bern.: d 1.13171 1.37763 0.75534 | 500 | 490 541 514 495 463 = 0.88 || = 0.19 492 479 525 546 517 | 500 s 1.02396 0.83227 0.70603 | 500 | 520 478 502 477 528 = 0.87 || = 0.18 512 468 518 505 495 | 500 t 1.03970 0.85832 1.14686 | 500 | 472 529 548 513 504 = 0.86 || = 0.17 512 520 523 522 497 | 500 m 0.98994 1.21138 0.92349 | 500 | 491 494 531 436 500 = 0.85 || = 0.16 448 478 480 482 536 | 500 x 0.94179 0.99749 0.96379 | 500 | 494 516 528 519 498 = 0.84 || = 0.15 495 521 517 508 461 | 500 | 500 | 564 521 468 486 505 = 0.83 || = 0.14 507 508 500 542 491 | 500 Changes: d 48 4 6 | 500 | 484 510 500 540 505 = 0.82 || = 0.13 481 491 477 472 483 | 500 s 53 4 6 | 500 | 547 471 453 491 520 = 0.81 || = 0.12 475 510 495 502 503 | 500 t 49 7 4 | 500 | 527 484 471 511 478 = 0.80 || = 0.11 494 509 476 509 495 | 500 m 44 7 5 | 500 | 541 499 500 513 510 = 0.79 || = 0.10 512 545 528 501 497 | 500 x 53 3 6 | 500 | 513 499 473 499 509 = 0.78 || = 0.09 528 491 507 517 463 | 500 -----------------------------------------------------------------| 500 | 499 457 489 459 520 = 0.77 || = 0.08 473 557 493 493 479 | 500 Aver./ d 0.50092 499 > 500: 7 4 2 4 2 7 4 7 5 3 | 500 | 505 523 500 466 473 = 0.76 || = 0.07 474 447 512 485 512 | 500 median s 0.49981 500 ----- 5 6 4 5 5 6 3 3 6 6 | 500 | 547 479 515 472 489 = 0.75 || = 0.06 580 515 460 502 505 | 500 t 0.50024 502 5 5 5 7 4 4 6 4 6 7 | 500 | 489 485 525 502 504 = 0.74 || = 0.05 511 553 509 491 462 | 500 m 0.49825 500 4 8 5 3 7 5 7 3 3 4 | 500 | 519 491 483 495 477 = 0.73 || = 0.04 534 493 537 487 482 | 500 x 0.50078 498 4 3 5 8 3 5 4 5 7 4 | 500 | 491 519 524 490 464 = 0.72 || = 0.03 524 509 479 481 495 | 500 -----------------------------------------------------------------| 500 | 519 525 533 454 513 = 0.71 || = 0.02 535 488 479 531 522 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 500 437 518 522 495 = 0.70 || = 0.01 249 247 252 252 254 | 252.5 d 0 1 3 13 70 9 4 1 0 | 500 | 481 506 455 507 493 = 0.69 || < 0.01 510 502 536 505 455 | 497.5 s 0 1 2 8 73 14 3 0 0 | 500 | 477 480 466 503 544 = 0.68 ||========================================================================= t 0 0 5 13 63 19 1 0 0 | 500 | 537 484 527 516 503 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 71 11 2 0 0 | 500 | 476 488 506 522 458 = 0.66 ||========================================================================= x 0 0 1 12 75 13 0 0 0 | 500 | 504 516 455 475 482 = 0.65 || swalk_RandomWalk1 test: no 151 test no 152 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 152 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 534 498 521 491 518 | 500 < 0.00002 1 2 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99998 || = 0.63 476 482 500 508 462 | 500 < 0.00003 1 0 1 0 1 | 0.5 | 1 1 0 0 0 > 0.99997 || = 0.62 508 480 492 488 489 | 500 < 0.00004 0 0 2 1 0 | 0.5 | 0 0 0 1 1 > 0.99996 || = 0.61 533 514 524 510 467 | 500 < 0.00005 0 0 1 0 0 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 498 497 510 510 522 | 500 < 0.00006 0 1 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99994 || = 0.59 532 484 515 481 494 | 500 < 0.00007 0 0 0 1 2 | 0.5 | 1 0 0 1 1 > 0.99993 || = 0.58 491 480 505 542 512 | 500 < 0.00008 1 1 0 0 0 | 0.5 | 2 1 0 0 0 > 0.99992 || = 0.57 526 489 518 502 475 | 500 < 0.00009 0 0 0 0 2 | 0.5 | 1 1 2 0 0 > 0.99991 || = 0.56 501 481 572 475 511 | 500 < 0.0001 1 1 0 0 0 | 0.5 | 2 0 1 5 0 > 0.9999 || = 0.55 501 539 473 504 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 505 470 508 497 520 | 500 < 0.0001 4 5 4 2 6 | 5 | 7 3 6 8 4 > 0.9999 || = 0.53 509 529 510 424 512 | 500 < 0.0002 4 5 4 7 3 | 5 | 3 0 4 4 3 > 0.9998 || = 0.52 523 523 506 513 489 | 500 < 0.0003 2 6 7 5 7 | 5 | 4 3 2 9 7 > 0.9997 || = 0.51 509 517 457 487 515 | 500 < 0.0004 9 5 3 5 6 | 5 | 4 4 7 4 2 > 0.9996 || = 0.50 492 503 499 500 509 | 500 < 0.0005 4 8 6 5 8 | 5 | 3 5 8 7 10 > 0.9995 || = 0.49 508 506 452 510 521 | 500 < 0.0006 9 6 5 5 3 | 5 | 4 4 1 3 7 > 0.9994 || = 0.48 494 451 471 467 506 | 500 < 0.0007 3 5 7 5 4 | 5 | 3 9 10 7 4 > 0.9993 || = 0.47 554 494 544 481 500 | 500 < 0.0008 3 8 3 5 6 | 5 | 4 7 7 7 3 > 0.9992 || = 0.46 519 506 501 528 485 | 500 < 0.0009 4 5 2 12 6 | 5 | 8 3 4 6 5 > 0.9991 || = 0.45 487 523 522 475 495 | 500 < 0.001 6 4 7 6 7 | 5 | 10 6 5 3 2 > 0.999 || = 0.44 504 477 470 469 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 507 535 495 508 492 | 500 < 0.001 48 57 48 57 56 | 50 | 50 44 54 58 47 > 0.999 || = 0.42 507 531 508 494 454 | 500 < 0.002 37 58 51 53 47 | 50 | 57 63 53 41 59 > 0.998 || = 0.41 525 490 473 468 519 | 500 < 0.003 56 62 57 52 51 | 50 | 47 45 43 54 51 > 0.997 || = 0.40 484 517 506 496 522 | 500 < 0.004 44 60 53 58 51 | 50 | 48 54 47 55 44 > 0.996 || = 0.39 503 525 488 505 508 | 500 < 0.005 44 50 47 48 47 | 50 | 53 34 52 64 44 > 0.995 || = 0.38 480 521 495 543 458 | 500 < 0.006 48 55 73 52 42 | 50 | 59 50 44 51 62 > 0.994 || = 0.37 509 512 459 502 497 | 500 < 0.007 46 40 49 34 47 | 50 | 51 42 54 54 51 > 0.993 || = 0.36 508 551 514 515 501 | 500 < 0.008 37 50 48 42 44 | 50 | 51 50 55 39 43 > 0.992 || = 0.35 507 470 523 456 486 | 500 < 0.009 59 52 39 49 40 | 50 | 48 45 49 55 65 > 0.991 || = 0.34 516 482 530 488 505 | 500 < 0.01 54 41 54 65 40 | 50 | 54 53 67 48 45 > 0.99 || = 0.33 506 502 496 507 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 497 451 516 522 495 | 500 < 0.01 473 525 519 510 465 | 497.5 | 518 480 518 519 511 > 0.99 || = 0.31 451 473 470 488 497 | 500 = 0.01 263 276 248 247 247 | 252.5 | 223 251 236 257 260 = 0.99 || = 0.30 549 465 500 488 484 | 500 = 0.02 538 483 482 468 499 | 500 | 507 489 477 464 457 = 0.98 || = 0.29 516 480 512 482 477 | 500 =================================================================| 500 | 469 488 521 482 550 = 0.97 || = 0.28 503 513 514 539 532 | 500 swalk_RandomWalk1 test: | 500 | 442 503 533 454 528 = 0.96 || = 0.27 495 482 499 499 503 | 500 ----------------------------------------------- | 500 | 538 490 499 533 529 = 0.95 || = 0.26 445 504 506 501 510 | 500 N = 1, n = 100000000, r = 25, s = 5, L0 = 50, L1 = 50 | 500 | 492 505 515 506 495 = 0.94 || = 0.25 526 491 502 469 455 | 500 Test on the values of the Statistic M | 500 | 503 518 489 531 480 = 0.93 || = 0.24 486 506 542 520 463 | 500 | 500 | 459 508 511 513 493 = 0.92 || = 0.23 494 530 493 505 465 | 500 =================================================================| 500 | 500 506 486 516 490 = 0.91 || = 0.22 478 479 520 526 455 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 521 476 495 515 489 = 0.90 || = 0.21 493 459 474 494 541 | 500 -----------------------------------------------------------------| 500 | 474 482 458 496 555 = 0.89 || = 0.20 480 518 462 532 496 | 500 SD Bern.: d 1.07476 1.06542 0.59019 | 500 | 498 478 500 528 521 = 0.88 || = 0.19 476 522 480 514 548 | 500 s 1.00340 1.06542 1.09598 | 500 | 468 540 500 483 491 = 0.87 || = 0.18 535 524 484 479 544 | 500 t 0.96208 1.21962 0.95335 | 500 | 478 518 522 498 533 = 0.86 || = 0.17 526 503 485 513 501 | 500 m 1.06197 1.16676 1.04837 | 500 | 484 498 497 517 509 = 0.85 || = 0.16 472 535 477 496 497 | 500 x 1.04120 0.85482 1.10236 | 500 | 492 509 485 486 492 = 0.84 || = 0.15 485 465 480 484 501 | 500 | 500 | 455 493 503 489 490 = 0.83 || = 0.14 511 490 488 529 507 | 500 Changes: d 47 3 5 | 500 | 461 484 473 470 476 = 0.82 || = 0.13 493 497 515 518 485 | 500 s 47 5 5 | 500 | 467 478 532 480 517 = 0.81 || = 0.12 482 508 475 494 455 | 500 t 52 5 6 | 500 | 473 503 488 502 493 = 0.80 || = 0.11 539 529 550 496 556 | 500 m 52 4 5 | 500 | 477 466 505 471 508 = 0.79 || = 0.10 488 494 510 466 497 | 500 x 45 3 6 | 500 | 510 537 472 512 496 = 0.78 || = 0.09 456 462 511 482 505 | 500 -----------------------------------------------------------------| 500 | 488 525 523 545 494 = 0.77 || = 0.08 515 471 491 508 506 | 500 Aver./ d 0.49733 501 > 500: 7 4 3 7 7 8 9 3 1 4 | 500 | 536 467 487 552 535 = 0.76 || = 0.07 549 528 482 537 513 | 500 median s 0.49996 499 ----- 4 6 5 5 6 4 4 6 3 5 | 500 | 489 530 502 527 451 = 0.75 || = 0.06 546 500 509 499 503 | 500 t 0.50060 500 5 3 6 4 5 8 5 5 3 5 | 500 | 487 541 525 470 509 = 0.74 || = 0.05 497 484 501 525 536 | 500 m 0.49887 500 6 4 6 6 3 5 5 5 3 7 | 500 | 504 509 522 474 476 = 0.73 || = 0.04 501 473 502 520 514 | 500 x 0.50062 499 6 6 4 3 4 7 4 3 5 5 | 500 | 487 492 480 498 499 = 0.72 || = 0.03 509 517 499 567 492 | 500 -----------------------------------------------------------------| 500 | 489 489 475 487 497 = 0.71 || = 0.02 538 483 482 468 499 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 523 515 510 488 481 = 0.70 || = 0.01 263 276 248 247 247 | 252.5 d 0 0 4 14 65 14 4 0 0 | 500 | 510 522 531 484 489 = 0.69 || < 0.01 473 525 519 510 465 | 497.5 s 0 0 2 13 66 19 1 0 0 | 500 | 518 494 490 510 511 = 0.68 ||========================================================================= t 0 0 1 17 71 10 1 1 0 | 500 | 521 499 501 503 506 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 1 15 68 13 2 1 0 | 500 | 510 495 493 466 467 = 0.66 ||========================================================================= x 0 0 5 12 71 9 4 0 0 | 500 | 506 506 491 513 533 = 0.65 || swalk_RandomWalk1 test: no 152 test no 153 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 153 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 503 520 507 526 509 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 2 0 0 0 > 0.99998 || = 0.63 500 548 497 509 491 | 500 < 0.00003 0 0 0 2 0 | 0.5 | 1 0 0 0 1 > 0.99997 || = 0.62 485 536 515 525 503 | 500 < 0.00004 1 1 0 0 1 | 0.5 | 1 1 1 1 0 > 0.99996 || = 0.61 508 480 493 499 515 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 0 0 2 0 1 > 0.99995 || = 0.60 506 498 463 547 518 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 1 1 1 1 0 > 0.99994 || = 0.59 548 512 508 461 489 | 500 < 0.00007 1 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 482 503 504 503 465 | 500 < 0.00008 1 0 0 1 2 | 0.5 | 0 0 0 1 0 > 0.99992 || = 0.57 528 483 528 472 516 | 500 < 0.00009 0 0 0 0 1 | 0.5 | 1 1 0 0 2 > 0.99991 || = 0.56 499 470 538 505 493 | 500 < 0.0001 0 0 1 0 1 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 523 513 551 492 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 487 562 461 506 490 | 500 < 0.0001 3 3 1 4 5 | 5 | 5 6 4 4 4 > 0.9999 || = 0.53 512 501 465 526 453 | 500 < 0.0002 6 3 5 5 7 | 5 | 5 5 1 5 4 > 0.9998 || = 0.52 516 466 521 506 461 | 500 < 0.0003 11 6 6 7 3 | 5 | 6 4 6 3 9 > 0.9997 || = 0.51 513 473 473 496 527 | 500 < 0.0004 7 4 5 6 3 | 5 | 5 6 5 1 2 > 0.9996 || = 0.50 498 516 481 492 528 | 500 < 0.0005 1 5 2 5 6 | 5 | 7 4 5 7 5 > 0.9995 || = 0.49 486 493 469 520 531 | 500 < 0.0006 5 5 3 2 5 | 5 | 6 4 11 2 8 > 0.9994 || = 0.48 474 527 500 497 498 | 500 < 0.0007 1 7 3 8 3 | 5 | 8 5 1 4 7 > 0.9993 || = 0.47 501 467 518 532 505 | 500 < 0.0008 3 3 7 3 3 | 5 | 9 7 8 3 6 > 0.9992 || = 0.46 527 491 492 473 486 | 500 < 0.0009 5 10 3 5 4 | 5 | 4 4 7 3 3 > 0.9991 || = 0.45 505 480 504 519 469 | 500 < 0.001 2 8 9 7 6 | 5 | 3 6 12 4 5 > 0.999 || = 0.44 478 504 479 509 508 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 515 499 489 500 485 | 500 < 0.001 44 54 44 52 45 | 50 | 58 51 60 36 53 > 0.999 || = 0.42 528 481 488 496 498 | 500 < 0.002 58 54 43 49 45 | 50 | 42 55 54 49 42 > 0.998 || = 0.41 488 493 497 502 517 | 500 < 0.003 36 46 43 50 43 | 50 | 52 57 45 42 58 > 0.997 || = 0.40 474 506 513 529 462 | 500 < 0.004 53 56 48 47 60 | 50 | 50 54 55 42 38 > 0.996 || = 0.39 499 455 533 498 486 | 500 < 0.005 50 60 41 50 59 | 50 | 41 49 40 57 63 > 0.995 || = 0.38 527 483 468 474 490 | 500 < 0.006 46 47 42 45 52 | 50 | 42 49 57 54 37 > 0.994 || = 0.37 523 500 532 486 494 | 500 < 0.007 53 49 55 56 59 | 50 | 34 47 55 37 57 > 0.993 || = 0.36 497 548 494 514 525 | 500 < 0.008 46 52 42 60 56 | 50 | 56 47 50 47 46 > 0.992 || = 0.35 505 499 503 491 531 | 500 < 0.009 34 54 50 45 47 | 50 | 54 39 51 45 41 > 0.991 || = 0.34 501 520 455 518 511 | 500 < 0.01 46 48 53 53 57 | 50 | 41 47 49 52 45 > 0.99 || = 0.33 477 452 499 500 507 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 472 483 463 470 517 | 500 < 0.01 466 520 461 507 523 | 497.5 | 470 495 516 461 480 > 0.99 || = 0.31 484 514 512 494 501 | 500 = 0.01 248 258 253 231 247 | 252.5 | 243 227 250 252 271 = 0.99 || = 0.30 501 462 487 473 511 | 500 = 0.02 528 476 451 532 483 | 500 | 477 513 486 503 511 = 0.98 || = 0.29 514 520 539 502 502 | 500 =================================================================| 500 | 517 537 517 502 485 = 0.97 || = 0.28 483 488 483 514 494 | 500 swalk_RandomWalk1 test: | 500 | 531 504 504 495 512 = 0.96 || = 0.27 488 537 528 570 496 | 500 ----------------------------------------------- | 500 | 491 511 483 501 469 = 0.95 || = 0.26 502 494 530 483 514 | 500 N = 1, n = 100000000, r = 25, s = 5, L0 = 50, L1 = 50 | 500 | 497 523 500 548 493 = 0.94 || = 0.25 536 518 511 506 474 | 500 Test on the values of the Statistic J | 500 | 505 471 491 498 515 = 0.93 || = 0.24 514 482 468 447 552 | 500 | 500 | 491 496 504 504 523 = 0.92 || = 0.23 495 524 479 495 506 | 500 =================================================================| 500 | 493 500 499 469 465 = 0.91 || = 0.22 479 501 514 449 477 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 500 490 524 524 510 = 0.90 || = 0.21 511 473 504 482 524 | 500 -----------------------------------------------------------------| 500 | 506 509 516 472 531 = 0.89 || = 0.20 530 469 489 500 496 | 500 SD Bern.: d 0.82169 1.11230 1.15469 | 500 | 461 539 484 494 494 = 0.88 || = 0.19 483 508 495 528 506 | 500 s 1.03954 0.66062 0.69460 | 500 | 483 488 476 510 484 = 0.87 || = 0.18 498 476 535 509 524 | 500 t 1.03174 0.87335 0.82744 | 500 | 491 492 475 485 480 = 0.86 || = 0.17 510 481 487 499 489 | 500 m 1.01613 0.64684 1.09323 | 500 | 495 457 478 484 474 = 0.85 || = 0.16 530 488 500 504 491 | 500 x 0.91406 0.95859 1.25760 | 500 | 513 500 484 497 491 = 0.84 || = 0.15 521 519 465 464 517 | 500 | 500 | 518 501 538 484 505 = 0.83 || = 0.14 484 497 527 479 490 | 500 Changes: d 48 6 5 | 500 | 479 478 493 498 510 = 0.82 || = 0.13 478 502 513 507 531 | 500 s 51 5 1 | 500 | 488 497 530 489 507 = 0.81 || = 0.12 509 524 524 521 539 | 500 t 53 3 7 | 500 | 483 500 512 522 490 = 0.80 || = 0.11 484 503 497 489 504 | 500 m 55 4 3 | 500 | 514 518 537 514 462 = 0.79 || = 0.10 513 521 527 506 507 | 500 x 47 3 7 | 500 | 502 485 509 484 512 = 0.78 || = 0.09 499 534 531 519 502 | 500 -----------------------------------------------------------------| 500 | 505 529 532 461 479 = 0.77 || = 0.08 492 531 444 546 515 | 500 Aver./ d 0.49841 500 > 500: 5 5 6 5 5 7 3 7 3 3 | 500 | 501 494 486 535 500 = 0.76 || = 0.07 506 528 463 510 480 | 500 median s 0.50025 500 ----- 6 6 5 3 3 5 6 5 3 5 | 500 | 504 525 491 491 480 = 0.75 || = 0.06 518 452 505 508 480 | 500 t 0.50134 500 5 5 6 4 3 6 5 6 4 4 | 500 | 478 507 499 511 478 = 0.74 || = 0.05 488 482 513 521 477 | 500 m 0.49884 500 7 6 4 2 6 6 5 5 2 5 | 500 | 513 518 489 531 463 = 0.73 || = 0.04 524 482 499 499 509 | 500 x 0.49867 502 4 7 5 7 4 4 8 3 5 5 | 500 | 510 472 501 455 507 = 0.72 || = 0.03 524 521 505 499 486 | 500 -----------------------------------------------------------------| 500 | 456 475 533 474 524 = 0.71 || = 0.02 528 476 451 532 483 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 489 465 530 492 545 = 0.70 || = 0.01 248 258 253 231 247 | 252.5 d 0 0 0 10 76 14 1 0 0 | 500 | 493 536 500 489 503 = 0.69 || < 0.01 466 520 461 507 523 | 497.5 s 0 0 3 15 65 15 3 0 0 | 500 | 481 506 469 537 513 = 0.68 ||========================================================================= t 0 0 3 14 63 20 1 0 0 | 500 | 532 510 524 457 503 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 69 11 3 1 0 | 500 | 497 495 512 478 469 = 0.66 ||========================================================================= x 0 0 1 13 71 14 2 0 0 | 500 | 468 490 488 513 519 = 0.65 || swalk_RandomWalk1 test: no 153 test no 154 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 154 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 495 564 513 503 564 | 500 < 0.00002 1 1 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99998 || = 0.63 494 546 512 509 514 | 500 < 0.00003 0 1 0 0 1 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 542 505 483 497 536 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99996 || = 0.61 453 494 501 515 532 | 500 < 0.00005 0 0 1 0 0 | 0.5 | 0 0 1 1 1 > 0.99995 || = 0.60 510 483 483 482 467 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 502 478 498 495 529 | 500 < 0.00007 0 0 1 1 0 | 0.5 | 0 0 0 0 1 > 0.99993 || = 0.58 523 504 523 517 504 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99992 || = 0.57 493 459 491 524 533 | 500 < 0.00009 0 1 0 0 0 | 0.5 | 3 3 1 2 2 > 0.99991 || = 0.56 525 507 524 522 526 | 500 < 0.0001 0 0 0 0 1 | 0.5 | 0 0 2 0 2 > 0.9999 || = 0.55 495 456 527 476 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 500 506 511 495 490 | 500 < 0.0001 1 4 2 4 2 | 5 | 5 3 5 4 7 > 0.9999 || = 0.53 503 522 456 504 507 | 500 < 0.0002 6 6 5 3 2 | 5 | 3 5 1 2 4 > 0.9998 || = 0.52 526 466 495 488 512 | 500 < 0.0003 8 2 3 8 4 | 5 | 7 5 5 5 5 > 0.9997 || = 0.51 469 489 512 486 505 | 500 < 0.0004 10 6 2 3 6 | 5 | 9 5 6 7 4 > 0.9996 || = 0.50 471 525 498 540 500 | 500 < 0.0005 7 6 4 8 2 | 5 | 5 5 8 1 3 > 0.9995 || = 0.49 522 559 482 452 455 | 500 < 0.0006 6 5 5 7 3 | 5 | 5 8 6 7 7 > 0.9994 || = 0.48 502 495 493 503 543 | 500 < 0.0007 5 2 2 5 3 | 5 | 3 5 1 4 1 > 0.9993 || = 0.47 486 533 498 480 488 | 500 < 0.0008 5 4 7 7 2 | 5 | 6 9 5 2 6 > 0.9992 || = 0.46 507 497 469 491 485 | 500 < 0.0009 3 7 10 8 6 | 5 | 4 2 1 7 5 > 0.9991 || = 0.45 475 525 507 504 539 | 500 < 0.001 2 3 3 6 7 | 5 | 2 6 5 2 8 > 0.999 || = 0.44 475 500 467 503 490 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 515 495 513 485 570 | 500 < 0.001 53 45 43 59 37 | 50 | 49 53 43 41 50 > 0.999 || = 0.42 524 467 506 522 494 | 500 < 0.002 49 56 43 37 43 | 50 | 44 49 66 46 62 > 0.998 || = 0.41 484 515 503 483 489 | 500 < 0.003 48 53 45 45 55 | 50 | 53 56 49 50 49 > 0.997 || = 0.40 486 483 549 485 473 | 500 < 0.004 50 45 58 63 59 | 50 | 49 51 48 58 48 > 0.996 || = 0.39 495 514 512 518 487 | 500 < 0.005 52 45 39 55 51 | 50 | 45 49 49 51 48 > 0.995 || = 0.38 528 472 528 499 456 | 500 < 0.006 56 45 55 45 58 | 50 | 55 42 49 46 37 > 0.994 || = 0.37 520 494 467 537 515 | 500 < 0.007 44 50 53 34 50 | 50 | 53 50 50 56 45 > 0.993 || = 0.36 520 515 549 493 497 | 500 < 0.008 48 44 40 55 45 | 50 | 65 41 52 57 59 > 0.992 || = 0.35 484 522 503 524 502 | 500 < 0.009 53 52 57 56 48 | 50 | 52 57 53 47 44 > 0.991 || = 0.34 490 494 498 487 478 | 500 < 0.01 48 46 46 55 48 | 50 | 60 52 64 53 63 > 0.99 || = 0.33 498 511 506 509 519 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 538 513 519 520 505 | 500 < 0.01 501 481 479 504 494 | 497.5 | 525 500 523 505 505 > 0.99 || = 0.31 486 524 506 494 509 | 500 = 0.01 242 227 259 255 256 | 252.5 | 245 247 240 263 264 = 0.99 || = 0.30 468 481 484 487 499 | 500 = 0.02 483 533 501 492 506 | 500 | 533 498 514 508 497 = 0.98 || = 0.29 467 497 518 466 531 | 500 =================================================================| 500 | 500 506 491 510 533 = 0.97 || = 0.28 509 521 476 524 484 | 500 swalk_RandomWalk1 test: | 500 | 500 487 551 561 473 = 0.96 || = 0.27 493 497 515 491 496 | 500 ----------------------------------------------- | 500 | 523 494 504 520 505 = 0.95 || = 0.26 503 478 491 503 492 | 500 N = 1, n = 100000000, r = 25, s = 5, L0 = 50, L1 = 50 | 500 | 505 493 494 523 493 = 0.94 || = 0.25 489 495 509 503 531 | 500 Test on the values of the Statistic R | 500 | 459 552 494 518 515 = 0.93 || = 0.24 506 530 498 484 520 | 500 | 500 | 471 510 516 521 525 = 0.92 || = 0.23 495 473 488 454 476 | 500 =================================================================| 500 | 489 487 489 530 474 = 0.91 || = 0.22 555 461 520 476 495 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 487 490 501 501 492 = 0.90 || = 0.21 459 487 493 467 522 | 500 -----------------------------------------------------------------| 500 | 477 507 537 484 514 = 0.89 || = 0.20 493 485 459 498 491 | 500 SD Bern.: d 0.96465 0.46281 0.93319 | 500 | 469 527 475 492 511 = 0.88 || = 0.19 513 512 492 529 471 | 500 s 1.10579 0.63434 0.70176 | 500 | 514 486 493 532 508 = 0.87 || = 0.18 481 498 537 531 497 | 500 t 0.93797 1.00747 1.02128 | 500 | 497 472 519 480 490 = 0.86 || = 0.17 508 423 487 494 510 | 500 m 0.94124 1.29370 0.75003 | 500 | 565 491 510 472 444 = 0.85 || = 0.16 510 510 527 517 499 | 500 x 1.02697 0.91914 1.12572 | 500 | 472 545 495 538 516 = 0.84 || = 0.15 525 522 488 517 481 | 500 | 500 | 491 496 486 498 509 = 0.83 || = 0.14 508 526 476 509 512 | 500 Changes: d 52 5 3 | 500 | 539 483 502 487 480 = 0.82 || = 0.13 477 460 503 461 494 | 500 s 55 4 4 | 500 | 522 516 481 513 491 = 0.81 || = 0.12 487 527 512 502 469 | 500 t 55 6 3 | 500 | 486 448 483 504 474 = 0.80 || = 0.11 478 502 485 466 455 | 500 m 52 4 5 | 500 | 531 476 522 477 460 = 0.79 || = 0.10 495 495 494 460 490 | 500 x 53 2 5 | 500 | 505 504 524 524 506 = 0.78 || = 0.09 465 534 502 479 476 | 500 -----------------------------------------------------------------| 500 | 514 518 444 505 503 = 0.77 || = 0.08 488 517 500 516 496 | 500 Aver./ d 0.50169 498 > 500: 2 5 4 4 5 6 4 8 4 4 | 500 | 495 484 499 473 481 = 0.76 || = 0.07 500 535 494 524 519 | 500 median s 0.49923 497 ----- 6 6 2 6 4 4 5 3 4 4 | 500 | 503 520 470 523 499 = 0.75 || = 0.06 489 505 480 480 498 | 500 t 0.50016 500 6 4 4 7 5 5 6 3 5 5 | 500 | 507 490 448 503 501 = 0.74 || = 0.05 481 485 501 479 497 | 500 m 0.50225 502 6 6 3 5 4 4 3 6 4 10 | 500 | 525 447 499 478 474 = 0.73 || = 0.04 493 488 511 515 508 | 500 x 0.50079 499 4 2 4 5 3 8 7 3 5 6 | 500 | 506 490 495 520 491 = 0.72 || = 0.03 531 550 519 518 483 | 500 -----------------------------------------------------------------| 500 | 518 495 514 480 495 = 0.71 || = 0.02 483 533 501 492 506 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 471 496 528 482 529 = 0.70 || = 0.01 242 227 259 255 256 | 252.5 d 0 0 1 15 67 16 2 0 0 | 500 | 509 480 455 497 489 = 0.69 || < 0.01 501 481 479 504 494 | 497.5 s 0 1 2 11 70 11 6 0 0 | 500 | 525 502 501 488 487 = 0.68 ||========================================================================= t 0 0 3 10 74 11 3 0 0 | 500 | 497 500 535 494 526 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 11 73 14 1 0 0 | 500 | 482 506 491 458 522 = 0.66 ||========================================================================= x 0 0 4 12 70 13 1 1 0 | 500 | 515 490 477 495 445 = 0.65 || swalk_RandomWalk1 test: no 154 test no 155 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 155 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 497 471 482 506 505 | 500 < 0.00002 1 2 0 0 0 | 0.5 | 0 0 0 1 2 > 0.99998 || = 0.63 447 504 475 501 540 | 500 < 0.00003 0 1 1 0 0 | 0.5 | 0 0 1 1 0 > 0.99997 || = 0.62 468 451 440 496 535 | 500 < 0.00004 0 0 0 0 4 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 479 557 486 525 496 | 500 < 0.00005 0 1 0 1 2 | 0.5 | 0 1 2 0 3 > 0.99995 || = 0.60 527 508 495 528 490 | 500 < 0.00006 0 2 0 1 0 | 0.5 | 2 1 0 0 0 > 0.99994 || = 0.59 493 498 475 520 522 | 500 < 0.00007 1 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99993 || = 0.58 499 517 519 515 491 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99992 || = 0.57 516 523 500 505 503 | 500 < 0.00009 3 1 1 1 2 | 0.5 | 2 0 0 0 0 > 0.99991 || = 0.56 480 499 500 499 505 | 500 < 0.0001 0 0 0 1 1 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 501 481 470 488 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 502 516 510 490 509 | 500 < 0.0001 5 7 2 5 10 | 5 | 6 3 5 2 5 > 0.9999 || = 0.53 512 503 454 522 491 | 500 < 0.0002 4 5 8 7 5 | 5 | 1 4 3 4 4 > 0.9998 || = 0.52 515 501 489 548 530 | 500 < 0.0003 7 9 6 3 7 | 5 | 9 2 5 7 4 > 0.9997 || = 0.51 478 530 492 488 455 | 500 < 0.0004 8 8 4 6 5 | 5 | 6 4 8 3 4 > 0.9996 || = 0.50 505 479 462 504 529 | 500 < 0.0005 6 5 9 4 5 | 5 | 4 4 6 8 6 > 0.9995 || = 0.49 508 498 465 514 470 | 500 < 0.0006 10 6 2 5 6 | 5 | 5 5 3 4 6 > 0.9994 || = 0.48 517 496 507 495 470 | 500 < 0.0007 3 5 5 4 8 | 5 | 7 7 5 6 8 > 0.9993 || = 0.47 508 510 497 503 540 | 500 < 0.0008 5 3 5 5 6 | 5 | 4 6 2 4 3 > 0.9992 || = 0.46 546 506 482 506 489 | 500 < 0.0009 2 5 7 3 5 | 5 | 2 5 3 0 3 > 0.9991 || = 0.45 502 494 496 555 490 | 500 < 0.001 2 4 5 1 6 | 5 | 6 4 3 4 8 > 0.999 || = 0.44 519 529 495 481 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 491 539 522 515 496 | 500 < 0.001 52 57 53 43 63 | 50 | 50 44 43 42 51 > 0.999 || = 0.42 538 510 482 461 441 | 500 < 0.002 44 34 55 44 39 | 50 | 51 50 44 55 52 > 0.998 || = 0.41 500 500 534 488 528 | 500 < 0.003 48 49 47 49 38 | 50 | 48 52 54 59 45 > 0.997 || = 0.40 500 489 494 469 498 | 500 < 0.004 61 46 46 47 39 | 50 | 56 44 42 48 49 > 0.996 || = 0.39 496 496 517 495 505 | 500 < 0.005 50 46 45 51 44 | 50 | 44 62 58 59 43 > 0.995 || = 0.38 505 492 478 484 520 | 500 < 0.006 49 48 53 54 49 | 50 | 57 46 41 54 38 > 0.994 || = 0.37 483 472 523 535 462 | 500 < 0.007 52 51 48 37 45 | 50 | 43 49 55 63 53 > 0.993 || = 0.36 530 509 525 515 488 | 500 < 0.008 66 59 40 40 51 | 50 | 64 53 43 47 61 > 0.992 || = 0.35 516 491 518 508 511 | 500 < 0.009 44 40 55 46 50 | 50 | 47 49 60 64 63 > 0.991 || = 0.34 487 531 535 511 487 | 500 < 0.01 49 58 46 42 48 | 50 | 40 54 44 48 55 > 0.99 || = 0.33 494 545 515 531 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 500 496 476 488 499 | 500 < 0.01 515 488 488 453 466 | 497.5 | 500 503 484 539 510 > 0.99 || = 0.31 513 483 513 483 516 | 500 = 0.01 238 263 255 243 240 | 252.5 | 263 258 236 238 226 = 0.99 || = 0.30 495 523 494 487 529 | 500 = 0.02 533 465 486 512 507 | 500 | 509 468 504 503 475 = 0.98 || = 0.29 513 467 513 504 449 | 500 =================================================================| 500 | 508 502 465 505 490 = 0.97 || = 0.28 501 458 460 494 536 | 500 swalk_RandomWalk1 test: | 500 | 536 500 502 489 538 = 0.96 || = 0.27 536 504 527 543 476 | 500 ----------------------------------------------- | 500 | 450 516 498 511 510 = 0.95 || = 0.26 504 488 525 510 479 | 500 N = 1, n = 100000000, r = 25, s = 5, L0 = 50, L1 = 50 | 500 | 515 513 509 516 458 = 0.94 || = 0.25 479 506 515 516 456 | 500 Test on the values of the Statistic C | 500 | 505 482 528 508 530 = 0.93 || = 0.24 437 477 519 522 505 | 500 | 500 | 513 512 496 532 491 = 0.92 || = 0.23 465 499 521 455 492 | 500 =================================================================| 500 | 491 551 481 530 521 = 0.91 || = 0.22 469 450 485 476 498 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 492 490 510 465 498 = 0.90 || = 0.21 485 523 495 472 518 | 500 -----------------------------------------------------------------| 500 | 502 489 512 524 481 = 0.89 || = 0.20 483 493 519 500 494 | 500 SD Bern.: d 0.98038 0.96276 0.98027 | 500 | 478 529 522 495 516 = 0.88 || = 0.19 485 466 520 550 513 | 500 s 0.94621 1.08497 0.72561 | 500 | 525 485 539 488 540 = 0.87 || = 0.18 485 521 509 506 534 | 500 t 0.97918 0.69026 1.02030 | 500 | 523 470 522 501 508 = 0.86 || = 0.17 498 484 549 485 506 | 500 m 1.06687 0.96068 1.13985 | 500 | 474 501 499 471 508 = 0.85 || = 0.16 475 474 523 474 470 | 500 x 1.04687 1.11589 1.04741 | 500 | 507 517 533 530 499 = 0.84 || = 0.15 486 525 474 538 479 | 500 | 500 | 495 499 506 476 542 = 0.83 || = 0.14 483 505 478 467 505 | 500 Changes: d 48 5 8 | 500 | 456 540 487 454 464 = 0.82 || = 0.13 513 513 484 463 500 | 500 s 53 4 7 | 500 | 481 524 460 487 509 = 0.81 || = 0.12 519 501 512 467 470 | 500 t 48 5 8 | 500 | 498 502 494 487 506 = 0.80 || = 0.11 497 479 503 466 510 | 500 m 43 2 6 | 500 | 521 484 522 498 493 = 0.79 || = 0.10 510 492 525 484 495 | 500 x 61 3 2 | 500 | 477 499 504 474 546 = 0.78 || = 0.09 531 520 476 488 529 | 500 -----------------------------------------------------------------| 500 | 558 535 554 514 522 = 0.77 || = 0.08 507 508 496 495 501 | 500 Aver./ d 0.50009 501 > 500: 7 3 4 4 7 6 3 5 4 8 | 500 | 451 503 486 515 502 = 0.76 || = 0.07 484 494 472 520 501 | 500 median s 0.50194 501 ----- 4 5 3 4 5 7 5 6 5 7 | 500 | 497 487 476 460 468 = 0.75 || = 0.06 509 503 480 505 509 | 500 t 0.49927 499 3 7 7 7 3 2 2 6 7 4 | 500 | 522 477 509 495 474 = 0.74 || = 0.05 524 483 530 489 474 | 500 m 0.50171 501 5 3 5 5 5 6 5 5 3 8 | 500 | 528 522 501 519 534 = 0.73 || = 0.04 475 484 497 504 490 | 500 x 0.50214 501 5 5 3 5 3 5 7 6 6 5 | 500 | 484 501 508 560 476 = 0.72 || = 0.03 519 483 525 502 483 | 500 -----------------------------------------------------------------| 500 | 522 508 497 526 529 = 0.71 || = 0.02 533 465 486 512 507 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 487 513 530 457 510 = 0.70 || = 0.01 238 263 255 243 240 | 252.5 d 0 0 4 9 75 11 2 0 0 | 500 | 515 504 493 506 524 = 0.69 || < 0.01 515 488 488 453 466 | 497.5 s 0 0 3 11 72 12 3 0 0 | 500 | 516 455 503 495 476 = 0.68 ||========================================================================= t 0 0 2 15 68 14 2 0 0 | 500 | 493 510 491 489 520 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 16 66 12 4 0 0 | 500 | 509 495 468 462 488 = 0.66 ||========================================================================= x 0 0 3 17 63 17 1 0 0 | 500 | 474 493 493 519 510 = 0.65 || swalk_RandomWalk1 test: no 155 test no 156 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 156 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 0 | 0.5 | 2 0 0 0 1 > 0.99999 || = 0.64 489 516 499 476 451 | 500 < 0.00002 1 1 1 1 0 | 0.5 | 0 0 1 0 3 > 0.99998 || = 0.63 511 501 519 473 537 | 500 < 0.00003 0 0 1 1 0 | 0.5 | 0 0 0 2 1 > 0.99997 || = 0.62 515 524 516 530 486 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 2 0 0 2 0 > 0.99996 || = 0.61 504 505 517 492 467 | 500 < 0.00005 0 1 0 0 0 | 0.5 | 0 0 1 1 0 > 0.99995 || = 0.60 503 524 538 518 513 | 500 < 0.00006 0 0 1 0 0 | 0.5 | 0 1 0 1 1 > 0.99994 || = 0.59 489 510 525 470 544 | 500 < 0.00007 0 0 2 1 0 | 0.5 | 1 0 0 0 0 > 0.99993 || = 0.58 491 509 537 502 448 | 500 < 0.00008 0 2 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99992 || = 0.57 501 477 501 474 527 | 500 < 0.00009 1 1 1 0 1 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 483 453 534 535 505 | 500 < 0.0001 0 1 1 0 2 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 473 495 527 527 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 502 496 486 525 487 | 500 < 0.0001 2 6 9 3 4 | 5 | 5 2 3 6 7 > 0.9999 || = 0.53 466 491 508 466 493 | 500 < 0.0002 2 7 5 5 7 | 5 | 6 1 0 6 1 > 0.9998 || = 0.52 484 503 503 506 492 | 500 < 0.0003 8 9 6 5 9 | 5 | 2 6 1 4 4 > 0.9997 || = 0.51 509 488 479 534 540 | 500 < 0.0004 8 8 6 6 4 | 5 | 9 2 4 4 2 > 0.9996 || = 0.50 474 470 456 499 524 | 500 < 0.0005 5 8 5 5 2 | 5 | 9 5 3 3 8 > 0.9995 || = 0.49 503 493 497 492 489 | 500 < 0.0006 5 2 6 9 9 | 5 | 2 4 6 0 4 > 0.9994 || = 0.48 501 528 507 503 512 | 500 < 0.0007 6 5 3 2 6 | 5 | 8 7 5 4 6 > 0.9993 || = 0.47 526 468 513 507 512 | 500 < 0.0008 3 8 9 7 5 | 5 | 3 7 0 5 2 > 0.9992 || = 0.46 529 494 463 528 515 | 500 < 0.0009 6 5 6 6 7 | 5 | 3 4 5 0 4 > 0.9991 || = 0.45 529 476 525 494 508 | 500 < 0.001 5 4 8 5 5 | 5 | 4 3 6 3 6 > 0.999 || = 0.44 518 484 475 487 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 511 533 473 522 496 | 500 < 0.001 50 62 63 53 58 | 50 | 51 41 33 35 44 > 0.999 || = 0.42 486 500 522 471 485 | 500 < 0.002 53 48 49 45 50 | 50 | 54 49 51 44 51 > 0.998 || = 0.41 522 509 482 510 518 | 500 < 0.003 59 52 56 42 44 | 50 | 50 38 62 50 53 > 0.997 || = 0.40 460 520 452 454 516 | 500 < 0.004 53 48 55 61 51 | 50 | 54 55 50 60 55 > 0.996 || = 0.39 512 441 492 485 485 | 500 < 0.005 45 43 50 54 48 | 50 | 54 45 47 54 50 > 0.995 || = 0.38 507 507 526 535 514 | 500 < 0.006 38 43 47 51 50 | 50 | 51 52 55 44 58 > 0.994 || = 0.37 502 480 548 460 534 | 500 < 0.007 45 43 41 45 61 | 50 | 49 45 64 45 53 > 0.993 || = 0.36 464 501 493 520 523 | 500 < 0.008 46 49 45 42 71 | 50 | 69 50 59 47 51 > 0.992 || = 0.35 519 517 512 492 496 | 500 < 0.009 45 49 54 50 39 | 50 | 56 53 46 47 53 > 0.991 || = 0.34 499 526 505 475 511 | 500 < 0.01 46 55 54 53 35 | 50 | 51 53 48 49 66 > 0.99 || = 0.33 494 511 535 501 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 470 512 508 488 481 | 500 < 0.01 480 492 514 496 507 | 497.5 | 539 481 515 475 534 > 0.99 || = 0.31 503 483 469 494 501 | 500 = 0.01 263 267 238 274 234 | 252.5 | 243 246 236 227 252 = 0.99 || = 0.30 520 481 482 536 518 | 500 = 0.02 551 553 533 509 481 | 500 | 496 535 515 508 536 = 0.98 || = 0.29 562 489 531 472 509 | 500 =================================================================| 500 | 528 535 477 497 515 = 0.97 || = 0.28 458 483 489 534 511 | 500 swalk_RandomWalk1 test: | 500 | 486 500 513 491 513 = 0.96 || = 0.27 505 489 490 477 491 | 500 ----------------------------------------------- | 500 | 506 515 531 501 496 = 0.95 || = 0.26 517 464 479 486 529 | 500 N = 1, n = 10000000, r = 0, s = 10, L0 = 1000, L1 = 1000 | 500 | 483 470 499 493 547 = 0.94 || = 0.25 476 508 499 488 560 | 500 Test on the values of the Statistic H | 500 | 478 520 502 491 498 = 0.93 || = 0.24 466 530 496 488 461 | 500 | 500 | 492 486 515 515 496 = 0.92 || = 0.23 494 518 489 479 490 | 500 =================================================================| 500 | 537 531 507 507 510 = 0.91 || = 0.22 452 499 507 520 471 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 501 505 496 468 469 = 0.90 || = 0.21 489 499 514 493 483 | 500 -----------------------------------------------------------------| 500 | 544 512 509 480 503 = 0.89 || = 0.20 460 488 519 497 478 | 500 SD Bern.: d 1.02808 0.83707 0.94809 | 500 | 517 514 487 509 491 = 0.88 || = 0.19 526 501 498 555 491 | 500 s 0.94774 0.81280 0.80413 | 500 | 500 484 509 459 488 = 0.87 || = 0.18 505 500 510 500 474 | 500 t 1.05860 0.86991 1.23754 | 500 | 535 519 499 513 473 = 0.86 || = 0.17 484 506 477 513 485 | 500 m 0.95283 0.81771 0.95650 | 500 | 493 500 522 528 482 = 0.85 || = 0.16 498 500 484 491 501 | 500 x 1.05992 1.42408 0.90598 | 500 | 499 500 481 493 488 = 0.84 || = 0.15 484 520 445 505 516 | 500 | 500 | 515 494 526 476 484 = 0.83 || = 0.14 522 514 508 492 548 | 500 Changes: d 51 2 4 | 500 | 505 530 521 485 476 = 0.82 || = 0.13 482 487 493 520 509 | 500 s 44 4 5 | 500 | 531 480 496 487 503 = 0.81 || = 0.12 499 537 454 483 484 | 500 t 46 4 4 | 500 | 540 537 520 506 546 = 0.80 || = 0.11 511 513 464 494 507 | 500 m 54 4 2 | 500 | 483 501 520 510 465 = 0.79 || = 0.10 473 478 471 519 509 | 500 x 46 5 3 | 500 | 479 503 450 503 506 = 0.78 || = 0.09 473 472 498 517 480 | 500 -----------------------------------------------------------------| 500 | 528 444 497 486 492 = 0.77 || = 0.08 481 478 476 528 494 | 500 Aver./ d 0.50207 501 > 500: 5 4 3 6 8 4 7 5 7 4 | 500 | 473 498 489 499 462 = 0.76 || = 0.07 486 479 472 503 518 | 500 median s 0.50040 500 ----- 5 6 3 6 4 4 8 3 5 5 | 500 | 507 493 474 498 480 = 0.75 || = 0.06 515 504 489 534 496 | 500 t 0.50300 499 2 2 4 6 4 8 5 5 5 7 | 500 | 457 493 520 486 452 = 0.74 || = 0.05 488 528 490 522 491 | 500 m 0.49746 499 9 5 2 4 5 7 4 5 3 4 | 500 | 524 477 584 473 538 = 0.73 || = 0.04 510 460 493 509 480 | 500 x 0.50050 498 2 6 4 7 6 6 3 4 2 6 | 500 | 504 462 524 554 530 = 0.72 || = 0.03 502 517 500 507 474 | 500 -----------------------------------------------------------------| 500 | 460 496 464 509 476 = 0.71 || = 0.02 551 553 533 509 481 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 544 490 512 508 499 = 0.70 || = 0.01 263 267 238 274 234 | 252.5 d 0 0 1 16 68 14 2 0 0 | 500 | 467 507 517 527 469 = 0.69 || < 0.01 480 492 514 496 507 | 497.5 s 0 0 3 10 73 14 1 0 0 | 500 | 497 515 485 490 542 = 0.68 ||========================================================================= t 0 0 4 15 67 13 1 1 0 | 500 | 517 495 474 486 476 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 17 67 14 2 0 0 | 500 | 503 526 488 469 481 = 0.66 ||========================================================================= x 0 0 3 14 66 14 4 0 0 | 500 | 508 507 482 507 526 = 0.65 || swalk_RandomWalk1 test: no 156 test no 157 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 157 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 0 2 0 | 0.5 | 0 2 0 0 0 > 0.99999 || = 0.64 513 487 459 494 483 | 500 < 0.00002 2 1 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99998 || = 0.63 528 506 474 555 484 | 500 < 0.00003 0 0 0 1 1 | 0.5 | 1 0 0 0 2 > 0.99997 || = 0.62 512 505 453 533 521 | 500 < 0.00004 1 0 0 1 1 | 0.5 | 1 1 1 1 0 > 0.99996 || = 0.61 527 480 506 518 469 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 2 0 0 0 0 > 0.99995 || = 0.60 494 521 464 481 508 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 461 466 468 507 477 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 0 1 1 0 2 > 0.99993 || = 0.58 485 482 476 504 480 | 500 < 0.00008 1 0 1 1 1 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 472 518 493 519 483 | 500 < 0.00009 0 1 0 0 2 | 0.5 | 0 0 0 0 1 > 0.99991 || = 0.56 497 511 510 507 509 | 500 < 0.0001 0 1 1 0 1 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 484 505 502 489 447 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 480 450 491 501 470 | 500 < 0.0001 4 5 2 6 7 | 5 | 5 5 4 1 5 > 0.9999 || = 0.53 481 480 504 457 488 | 500 < 0.0002 5 1 8 7 3 | 5 | 2 3 3 2 0 > 0.9998 || = 0.52 556 512 514 502 474 | 500 < 0.0003 6 8 7 7 4 | 5 | 4 7 6 5 6 > 0.9997 || = 0.51 489 503 503 516 482 | 500 < 0.0004 2 8 5 5 5 | 5 | 6 3 3 6 1 > 0.9996 || = 0.50 493 506 524 505 489 | 500 < 0.0005 9 3 4 3 9 | 5 | 3 4 1 8 1 > 0.9995 || = 0.49 525 499 486 470 533 | 500 < 0.0006 7 6 2 9 4 | 5 | 4 7 3 5 5 > 0.9994 || = 0.48 469 522 511 531 496 | 500 < 0.0007 7 8 5 6 4 | 5 | 5 5 5 5 3 > 0.9993 || = 0.47 482 486 488 467 483 | 500 < 0.0008 2 3 4 8 6 | 5 | 3 7 7 9 6 > 0.9992 || = 0.46 481 482 482 483 520 | 500 < 0.0009 3 7 6 6 5 | 5 | 3 9 4 4 9 > 0.9991 || = 0.45 453 520 466 450 492 | 500 < 0.001 3 4 3 5 5 | 5 | 4 5 6 2 5 > 0.999 || = 0.44 481 526 514 507 471 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 517 495 510 504 507 | 500 < 0.001 48 53 46 62 52 | 50 | 39 55 42 47 41 > 0.999 || = 0.42 515 483 553 486 476 | 500 < 0.002 46 41 63 40 48 | 50 | 49 48 52 46 47 > 0.998 || = 0.41 514 482 537 509 515 | 500 < 0.003 56 60 55 53 52 | 50 | 46 69 44 42 48 > 0.997 || = 0.40 482 488 481 515 478 | 500 < 0.004 64 57 41 52 62 | 50 | 54 58 52 42 35 > 0.996 || = 0.39 482 440 498 495 486 | 500 < 0.005 45 44 63 47 47 | 50 | 36 54 54 59 43 > 0.995 || = 0.38 515 529 532 515 531 | 500 < 0.006 48 39 58 56 42 | 50 | 57 50 51 52 52 > 0.994 || = 0.37 528 533 532 489 516 | 500 < 0.007 60 52 51 39 49 | 50 | 48 44 52 51 42 > 0.993 || = 0.36 496 503 485 499 502 | 500 < 0.008 49 42 58 41 46 | 50 | 40 54 48 52 56 > 0.992 || = 0.35 493 519 486 476 494 | 500 < 0.009 45 46 60 48 51 | 50 | 57 48 49 68 41 > 0.991 || = 0.34 554 503 488 491 500 | 500 < 0.01 48 49 53 55 53 | 50 | 57 65 55 51 39 > 0.99 || = 0.33 490 505 495 504 459 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 521 544 529 483 503 | 500 < 0.01 509 483 548 493 502 | 497.5 | 483 545 499 510 444 > 0.99 || = 0.31 501 521 517 480 523 | 500 = 0.01 257 244 245 256 256 | 252.5 | 232 251 252 266 276 = 0.99 || = 0.30 518 548 480 524 475 | 500 = 0.02 503 533 519 539 515 | 500 | 500 517 503 503 503 = 0.98 || = 0.29 502 514 484 515 507 | 500 =================================================================| 500 | 515 505 474 481 501 = 0.97 || = 0.28 539 526 518 490 476 | 500 swalk_RandomWalk1 test: | 500 | 489 492 475 517 481 = 0.96 || = 0.27 507 528 485 465 472 | 500 ----------------------------------------------- | 500 | 504 493 497 553 504 = 0.95 || = 0.26 508 520 514 475 502 | 500 N = 1, n = 10000000, r = 0, s = 10, L0 = 1000, L1 = 1000 | 500 | 474 493 493 490 523 = 0.94 || = 0.25 492 493 509 489 535 | 500 Test on the values of the Statistic M | 500 | 483 513 514 476 525 = 0.93 || = 0.24 492 519 503 512 497 | 500 | 500 | 480 553 498 509 495 = 0.92 || = 0.23 488 483 473 484 525 | 500 =================================================================| 500 | 482 464 501 487 540 = 0.91 || = 0.22 487 492 497 528 493 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 525 466 476 489 533 = 0.90 || = 0.21 503 490 500 487 515 | 500 -----------------------------------------------------------------| 500 | 549 469 519 508 519 = 0.89 || = 0.20 472 499 498 517 479 | 500 SD Bern.: d 1.03338 0.90708 1.09689 | 500 | 501 568 514 515 490 = 0.88 || = 0.19 495 460 510 538 477 | 500 s 1.15037 0.98130 1.22616 | 500 | 515 487 518 473 520 = 0.87 || = 0.18 518 487 467 454 510 | 500 t 1.03291 1.18211 0.56418 | 500 | 513 504 483 512 521 = 0.86 || = 0.17 484 486 476 486 496 | 500 m 0.98309 1.03298 1.06635 | 500 | 481 485 461 523 480 = 0.85 || = 0.16 504 452 506 469 525 | 500 x 0.97834 0.71589 1.16160 | 500 | 456 522 495 500 495 = 0.84 || = 0.15 531 506 477 507 481 | 500 | 500 | 501 469 484 486 509 = 0.83 || = 0.14 460 493 521 482 512 | 500 Changes: d 39 4 5 | 500 | 515 445 515 522 541 = 0.82 || = 0.13 492 506 543 519 530 | 500 s 47 5 6 | 500 | 507 543 480 478 501 = 0.81 || = 0.12 493 489 435 482 495 | 500 t 50 3 5 | 500 | 523 502 474 498 476 = 0.80 || = 0.11 453 502 507 523 527 | 500 m 55 6 1 | 500 | 528 493 525 529 544 = 0.79 || = 0.10 505 490 517 476 464 | 500 x 55 4 4 | 500 | 546 525 494 531 490 = 0.78 || = 0.09 492 494 490 528 538 | 500 -----------------------------------------------------------------| 500 | 495 482 496 490 487 = 0.77 || = 0.08 504 468 488 495 520 | 500 Aver./ d 0.49928 497 > 500: 8 4 5 6 4 1 6 5 8 2 | 500 | 482 454 530 513 486 = 0.76 || = 0.07 537 486 542 498 524 | 500 median s 0.50188 499 ----- 2 3 5 9 3 6 5 6 4 5 | 500 | 519 501 550 520 518 = 0.75 || = 0.06 524 456 515 498 516 | 500 t 0.49856 500 6 6 4 4 5 5 5 6 4 4 | 500 | 469 532 529 529 479 = 0.74 || = 0.05 523 460 509 461 523 | 500 m 0.50142 500 4 4 4 3 5 7 4 7 5 6 | 500 | 517 513 522 468 492 = 0.73 || = 0.04 511 511 510 493 473 | 500 x 0.49979 500 8 5 5 5 4 2 3 4 7 7 | 500 | 462 466 539 518 502 = 0.72 || = 0.03 488 488 496 532 499 | 500 -----------------------------------------------------------------| 500 | 467 529 482 516 542 = 0.71 || = 0.02 503 533 519 539 515 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 491 551 515 459 497 = 0.70 || = 0.01 257 244 245 256 256 | 252.5 d 0 0 2 12 69 13 5 0 0 | 500 | 484 548 520 499 490 = 0.69 || < 0.01 509 483 548 493 502 | 497.5 s 0 0 5 10 68 12 5 1 0 | 500 | 539 488 449 526 499 = 0.68 ||========================================================================= t 0 0 3 15 69 11 3 0 0 | 500 | 487 496 508 497 508 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 14 69 14 2 0 0 | 500 | 474 493 516 479 509 = 0.66 ||========================================================================= x 0 0 2 15 65 19 0 0 0 | 500 | 550 525 487 473 472 = 0.65 || swalk_RandomWalk1 test: no 157 test no 158 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 158 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 2 0 1 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 496 522 480 465 504 | 500 < 0.00002 1 0 1 0 2 | 0.5 | 0 1 1 0 1 > 0.99998 || = 0.63 506 490 574 508 501 | 500 < 0.00003 1 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 496 472 458 508 501 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 1 0 2 0 > 0.99996 || = 0.61 508 510 503 526 512 | 500 < 0.00005 0 2 1 0 0 | 0.5 | 0 0 2 3 1 > 0.99995 || = 0.60 512 485 508 527 484 | 500 < 0.00006 0 1 1 3 0 | 0.5 | 0 1 0 2 1 > 0.99994 || = 0.59 530 469 499 496 475 | 500 < 0.00007 0 2 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 481 517 491 484 478 | 500 < 0.00008 0 0 1 1 0 | 0.5 | 0 0 0 1 0 > 0.99992 || = 0.57 532 475 515 505 543 | 500 < 0.00009 1 0 2 0 0 | 0.5 | 0 2 0 0 0 > 0.99991 || = 0.56 512 487 521 509 522 | 500 < 0.0001 1 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 482 481 467 459 497 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 480 490 512 493 479 | 500 < 0.0001 5 5 9 5 4 | 5 | 0 5 3 9 3 > 0.9999 || = 0.53 480 509 509 491 508 | 500 < 0.0002 2 6 5 3 1 | 5 | 2 1 2 4 3 > 0.9998 || = 0.52 516 515 491 486 486 | 500 < 0.0003 5 8 5 6 4 | 5 | 3 7 4 7 7 > 0.9997 || = 0.51 516 536 534 487 496 | 500 < 0.0004 7 5 3 4 2 | 5 | 6 8 2 7 9 > 0.9996 || = 0.50 502 489 453 489 498 | 500 < 0.0005 7 6 2 7 9 | 5 | 6 3 6 8 5 > 0.9995 || = 0.49 505 514 509 521 477 | 500 < 0.0006 4 3 6 9 6 | 5 | 10 3 8 4 6 > 0.9994 || = 0.48 494 480 519 518 503 | 500 < 0.0007 4 7 6 7 5 | 5 | 7 4 4 4 2 > 0.9993 || = 0.47 529 457 506 491 522 | 500 < 0.0008 1 5 8 4 10 | 5 | 3 6 4 3 3 > 0.9992 || = 0.46 496 465 467 513 501 | 500 < 0.0009 6 6 5 7 3 | 5 | 4 5 4 2 4 > 0.9991 || = 0.45 470 461 483 505 527 | 500 < 0.001 4 10 4 5 3 | 5 | 6 8 6 6 6 > 0.999 || = 0.44 527 461 477 487 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 527 489 539 511 492 | 500 < 0.001 45 61 53 57 47 | 50 | 47 50 43 54 48 > 0.999 || = 0.42 516 503 449 532 499 | 500 < 0.002 52 39 50 57 61 | 50 | 37 48 52 56 56 > 0.998 || = 0.41 489 535 501 525 515 | 500 < 0.003 50 58 55 35 39 | 50 | 48 68 54 51 54 > 0.997 || = 0.40 473 471 489 472 496 | 500 < 0.004 50 56 40 50 50 | 50 | 46 58 57 49 58 > 0.996 || = 0.39 510 526 471 503 492 | 500 < 0.005 53 44 39 58 55 | 50 | 55 44 61 44 53 > 0.995 || = 0.38 505 493 521 499 488 | 500 < 0.006 45 54 48 55 50 | 50 | 50 52 68 56 50 > 0.994 || = 0.37 471 520 475 482 530 | 500 < 0.007 64 49 47 53 52 | 50 | 42 49 50 59 50 > 0.993 || = 0.36 498 526 515 507 527 | 500 < 0.008 41 50 54 57 53 | 50 | 51 40 59 58 63 > 0.992 || = 0.35 522 494 471 518 506 | 500 < 0.009 41 47 52 52 41 | 50 | 61 56 60 45 55 > 0.991 || = 0.34 480 500 479 516 555 | 500 < 0.01 44 44 64 54 40 | 50 | 40 51 59 49 36 > 0.99 || = 0.33 498 503 506 531 501 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 534 485 471 487 501 | 500 < 0.01 485 502 502 528 488 | 497.5 | 477 516 563 521 523 > 0.99 || = 0.31 486 513 475 463 481 | 500 = 0.01 258 242 243 252 248 | 252.5 | 268 270 263 248 234 = 0.99 || = 0.30 510 497 492 509 514 | 500 = 0.02 511 535 503 464 472 | 500 | 495 468 498 515 477 = 0.98 || = 0.29 497 487 527 476 491 | 500 =================================================================| 500 | 516 515 467 481 484 = 0.97 || = 0.28 487 498 511 476 514 | 500 swalk_RandomWalk1 test: | 500 | 504 504 523 489 512 = 0.96 || = 0.27 466 471 488 492 528 | 500 ----------------------------------------------- | 500 | 553 501 517 488 524 = 0.95 || = 0.26 505 520 511 478 531 | 500 N = 1, n = 10000000, r = 0, s = 10, L0 = 1000, L1 = 1000 | 500 | 522 503 497 530 472 = 0.94 || = 0.25 514 527 479 511 478 | 500 Test on the values of the Statistic J | 500 | 529 500 510 493 452 = 0.93 || = 0.24 525 493 492 490 484 | 500 | 500 | 437 509 516 502 480 = 0.92 || = 0.23 485 503 477 542 502 | 500 =================================================================| 500 | 463 494 524 502 498 = 0.91 || = 0.22 503 496 490 536 491 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 463 522 488 478 481 = 0.90 || = 0.21 497 483 483 505 510 | 500 -----------------------------------------------------------------| 500 | 492 479 499 547 499 = 0.89 || = 0.20 503 502 447 532 457 | 500 SD Bern.: d 1.00561 0.95650 1.00945 | 500 | 483 514 525 493 498 = 0.88 || = 0.19 493 534 512 505 503 | 500 s 1.03332 0.93854 1.06823 | 500 | 475 528 522 497 503 = 0.87 || = 0.18 521 520 530 495 508 | 500 t 1.10310 0.98435 1.28515 | 500 | 484 493 515 504 509 = 0.86 || = 0.17 492 500 493 502 521 | 500 m 0.91785 0.99043 0.77109 | 500 | 529 453 449 473 473 = 0.85 || = 0.16 481 561 470 476 512 | 500 x 0.99130 0.97001 1.01932 | 500 | 508 486 487 523 501 = 0.84 || = 0.15 517 480 460 465 502 | 500 | 500 | 495 487 484 482 524 = 0.83 || = 0.14 459 493 488 490 502 | 500 Changes: d 52 6 4 | 500 | 493 479 510 498 494 = 0.82 || = 0.13 480 473 524 503 527 | 500 s 52 5 5 | 500 | 523 496 482 455 511 = 0.81 || = 0.12 551 481 473 486 442 | 500 t 54 4 3 | 500 | 520 516 532 474 456 = 0.80 || = 0.11 503 474 526 525 553 | 500 m 50 2 3 | 500 | 484 489 513 476 510 = 0.79 || = 0.10 517 558 509 504 471 | 500 x 41 6 4 | 500 | 488 537 546 512 513 = 0.78 || = 0.09 493 521 525 467 472 | 500 -----------------------------------------------------------------| 500 | 531 474 498 493 467 = 0.77 || = 0.08 452 535 480 522 496 | 500 Aver./ d 0.50082 502 > 500: 3 5 5 5 5 6 6 6 3 6 | 500 | 513 465 510 490 484 = 0.76 || = 0.07 488 502 517 503 503 | 500 median s 0.49904 498 ----- 6 4 4 5 3 4 5 6 3 7 | 500 | 508 524 513 469 497 = 0.75 || = 0.06 532 466 492 509 488 | 500 t 0.50260 501 7 5 3 3 5 6 4 7 4 7 | 500 | 491 502 549 496 516 = 0.74 || = 0.05 497 531 506 517 485 | 500 m 0.49864 502 7 5 5 6 7 3 7 3 3 5 | 500 | 477 531 536 509 506 = 0.73 || = 0.04 434 493 509 535 482 | 500 x 0.49996 501 1 8 5 7 5 3 9 5 5 3 | 500 | 523 532 484 507 511 = 0.72 || = 0.03 499 494 518 533 497 | 500 -----------------------------------------------------------------| 500 | 504 484 483 487 474 = 0.71 || = 0.02 511 535 503 464 472 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 491 488 477 520 548 = 0.70 || = 0.01 258 242 243 252 248 | 252.5 d 0 0 3 10 71 15 2 0 0 | 500 | 527 461 468 502 552 = 0.69 || < 0.01 485 502 502 528 488 | 497.5 s 0 0 1 16 65 17 2 0 0 | 500 | 508 512 516 482 527 = 0.68 ||========================================================================= t 0 0 4 16 64 13 3 1 0 | 500 | 457 491 493 477 546 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 15 68 16 1 0 0 | 500 | 532 531 499 532 479 = 0.66 ||========================================================================= x 0 0 2 13 70 11 5 0 0 | 500 | 503 531 529 513 508 = 0.65 || swalk_RandomWalk1 test: no 158 test no 159 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 159 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 0 0 0 | 0.5 | 0 1 0 2 0 > 0.99999 || = 0.64 491 483 505 458 500 | 500 < 0.00002 1 1 2 0 1 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 511 488 483 506 521 | 500 < 0.00003 1 0 0 1 0 | 0.5 | 1 0 0 0 1 > 0.99997 || = 0.62 528 536 483 508 507 | 500 < 0.00004 0 0 1 3 1 | 0.5 | 0 0 0 1 0 > 0.99996 || = 0.61 509 541 502 479 488 | 500 < 0.00005 0 1 1 2 1 | 0.5 | 0 0 1 2 1 > 0.99995 || = 0.60 461 537 479 490 520 | 500 < 0.00006 1 0 2 0 1 | 0.5 | 0 1 2 0 1 > 0.99994 || = 0.59 488 488 551 521 504 | 500 < 0.00007 0 1 1 1 0 | 0.5 | 0 0 1 1 1 > 0.99993 || = 0.58 504 469 509 505 507 | 500 < 0.00008 0 2 0 0 1 | 0.5 | 0 1 2 1 0 > 0.99992 || = 0.57 463 494 529 478 472 | 500 < 0.00009 2 0 0 2 0 | 0.5 | 1 2 0 1 0 > 0.99991 || = 0.56 491 484 501 456 513 | 500 < 0.0001 0 0 3 0 1 | 0.5 | 1 0 5 0 1 > 0.9999 || = 0.55 456 492 481 499 542 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 542 498 510 521 452 | 500 < 0.0001 5 7 10 9 6 | 5 | 4 5 11 8 5 > 0.9999 || = 0.53 484 486 502 513 502 | 500 < 0.0002 7 2 1 4 1 | 5 | 1 4 1 5 1 > 0.9998 || = 0.52 498 509 453 485 473 | 500 < 0.0003 4 4 7 8 9 | 5 | 5 4 5 4 4 > 0.9997 || = 0.51 517 485 533 492 524 | 500 < 0.0004 6 6 8 5 6 | 5 | 2 5 4 5 8 > 0.9996 || = 0.50 510 515 503 505 505 | 500 < 0.0005 4 1 4 5 4 | 5 | 5 9 4 4 3 > 0.9995 || = 0.49 535 530 519 487 488 | 500 < 0.0006 7 4 4 8 4 | 5 | 4 5 9 3 3 > 0.9994 || = 0.48 481 454 497 490 502 | 500 < 0.0007 2 6 9 6 6 | 5 | 7 5 6 5 3 > 0.9993 || = 0.47 512 480 546 541 556 | 500 < 0.0008 7 2 3 9 6 | 5 | 4 9 3 8 4 > 0.9992 || = 0.46 490 496 478 472 522 | 500 < 0.0009 1 4 10 8 3 | 5 | 6 5 4 6 4 > 0.9991 || = 0.45 515 504 507 454 527 | 500 < 0.001 5 11 6 4 1 | 5 | 6 1 5 1 6 > 0.999 || = 0.44 492 534 520 481 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 483 507 488 427 493 | 500 < 0.001 48 47 62 66 46 | 50 | 44 52 52 49 41 > 0.999 || = 0.42 465 509 503 518 527 | 500 < 0.002 48 48 53 39 47 | 50 | 54 49 47 77 50 > 0.998 || = 0.41 484 543 489 499 451 | 500 < 0.003 41 54 52 53 53 | 50 | 56 53 67 60 52 > 0.997 || = 0.40 501 541 485 514 502 | 500 < 0.004 49 46 56 52 57 | 50 | 47 58 54 57 43 > 0.996 || = 0.39 477 495 491 502 497 | 500 < 0.005 53 55 55 60 52 | 50 | 40 60 50 47 53 > 0.995 || = 0.38 484 517 486 535 452 | 500 < 0.006 53 63 48 50 54 | 50 | 51 38 45 52 52 > 0.994 || = 0.37 500 518 512 491 536 | 500 < 0.007 54 59 47 54 47 | 50 | 43 52 41 40 47 > 0.993 || = 0.36 513 507 510 467 497 | 500 < 0.008 51 56 53 51 51 | 50 | 50 44 58 61 45 > 0.992 || = 0.35 495 509 488 489 540 | 500 < 0.009 41 57 60 49 46 | 50 | 35 50 56 45 60 > 0.991 || = 0.34 549 509 469 493 512 | 500 < 0.01 54 46 39 53 31 | 50 | 48 36 49 51 46 > 0.99 || = 0.33 516 476 530 524 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 465 503 463 527 513 | 500 < 0.01 492 531 525 527 484 | 497.5 | 468 492 519 539 489 > 0.99 || = 0.31 489 527 493 474 453 | 500 = 0.01 256 272 247 259 240 | 252.5 | 256 269 260 262 269 = 0.99 || = 0.30 515 457 500 491 493 | 500 = 0.02 514 485 479 501 502 | 500 | 523 504 493 474 488 = 0.98 || = 0.29 488 489 492 489 501 | 500 =================================================================| 500 | 512 498 471 502 462 = 0.97 || = 0.28 512 494 502 517 510 | 500 swalk_RandomWalk1 test: | 500 | 518 493 489 519 496 = 0.96 || = 0.27 494 494 443 493 478 | 500 ----------------------------------------------- | 500 | 466 501 515 488 488 = 0.95 || = 0.26 553 494 487 534 467 | 500 N = 1, n = 10000000, r = 0, s = 10, L0 = 1000, L1 = 1000 | 500 | 529 508 527 475 514 = 0.94 || = 0.25 520 474 486 509 515 | 500 Test on the values of the Statistic R | 500 | 530 492 538 520 500 = 0.93 || = 0.24 488 496 492 482 496 | 500 | 500 | 541 478 510 500 522 = 0.92 || = 0.23 480 475 462 500 478 | 500 =================================================================| 500 | 463 494 494 455 490 = 0.91 || = 0.22 511 475 501 530 487 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 491 489 540 526 554 = 0.90 || = 0.21 479 502 496 481 496 | 500 -----------------------------------------------------------------| 500 | 495 486 516 484 503 = 0.89 || = 0.20 477 497 483 497 513 | 500 SD Bern.: d 1.00711 0.66666 0.97618 | 500 | 512 494 522 470 520 = 0.88 || = 0.19 492 532 499 477 491 | 500 s 0.96469 0.91805 1.05692 | 500 | 509 490 461 497 515 = 0.87 || = 0.18 512 494 519 496 489 | 500 t 0.98752 0.96068 1.02519 | 500 | 509 472 477 504 481 = 0.86 || = 0.17 528 517 454 462 522 | 500 m 1.01723 1.01735 1.51005 | 500 | 530 472 485 531 523 = 0.85 || = 0.16 519 471 486 503 486 | 500 x 1.04070 0.99043 0.77109 | 500 | 487 518 498 519 511 = 0.84 || = 0.15 495 542 536 469 471 | 500 | 500 | 482 576 487 512 478 = 0.83 || = 0.14 475 473 514 543 464 | 500 Changes: d 48 3 4 | 500 | 492 498 526 486 523 = 0.82 || = 0.13 500 509 476 509 482 | 500 s 43 4 5 | 500 | 547 481 494 515 491 = 0.81 || = 0.12 491 480 468 525 484 | 500 t 48 3 5 | 500 | 508 527 488 512 486 = 0.80 || = 0.11 500 516 468 478 485 | 500 m 48 6 7 | 500 | 500 481 511 479 535 = 0.79 || = 0.10 477 506 524 516 465 | 500 x 60 4 6 | 500 | 488 526 477 514 497 = 0.78 || = 0.09 481 501 529 532 496 | 500 -----------------------------------------------------------------| 500 | 501 500 518 520 526 = 0.77 || = 0.08 506 518 515 505 540 | 500 Aver./ d 0.50112 500 > 500: 6 3 4 4 4 3 7 6 5 7 | 500 | 503 479 520 476 466 = 0.76 || = 0.07 505 519 509 550 489 | 500 median s 0.49944 497 ----- 6 6 1 7 7 2 4 4 2 4 | 500 | 502 510 476 503 500 = 0.75 || = 0.06 547 478 493 519 535 | 500 t 0.50209 500 5 4 2 3 5 7 6 6 4 6 | 500 | 448 475 493 523 519 = 0.74 || = 0.05 521 469 512 490 473 | 500 m 0.49877 502 9 5 4 4 3 4 7 5 6 5 | 500 | 518 479 501 475 511 = 0.73 || = 0.04 459 484 485 519 499 | 500 x 0.50290 499 3 1 4 4 6 7 6 4 7 3 | 500 | 488 477 548 496 467 = 0.72 || = 0.03 456 514 500 507 453 | 500 -----------------------------------------------------------------| 500 | 528 502 517 487 497 = 0.71 || = 0.02 514 485 479 501 502 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 528 522 532 501 537 = 0.70 || = 0.01 256 272 247 259 240 | 252.5 d 0 0 1 15 70 11 4 0 0 | 500 | 503 499 498 508 526 = 0.69 || < 0.01 492 531 525 527 484 | 497.5 s 0 0 1 13 71 15 0 1 0 | 500 | 496 485 518 504 495 = 0.68 ||========================================================================= t 0 0 3 12 71 12 3 0 0 | 500 | 505 491 474 523 527 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 2 14 68 15 1 0 0 | 500 | 516 498 521 470 500 = 0.66 ||========================================================================= x 0 0 5 10 67 17 2 0 0 | 500 | 466 522 506 520 523 = 0.65 || swalk_RandomWalk1 test: no 159 test no 160 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 160 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 0 | 0.5 | 1 0 1 0 1 > 0.99999 || = 0.64 453 512 489 478 507 | 500 < 0.00002 0 1 1 2 0 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 526 464 507 483 473 | 500 < 0.00003 0 0 1 0 0 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 459 517 481 503 497 | 500 < 0.00004 1 0 1 0 0 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 522 470 498 509 515 | 500 < 0.00005 2 0 1 1 0 | 0.5 | 0 0 3 1 1 > 0.99995 || = 0.60 523 501 501 505 488 | 500 < 0.00006 0 1 0 1 0 | 0.5 | 1 2 0 2 0 > 0.99994 || = 0.59 501 487 446 478 445 | 500 < 0.00007 1 0 1 0 0 | 0.5 | 0 0 1 0 3 > 0.99993 || = 0.58 463 518 473 492 465 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99992 || = 0.57 470 476 471 491 482 | 500 < 0.00009 0 1 0 1 0 | 0.5 | 0 0 0 2 1 > 0.99991 || = 0.56 479 505 517 515 524 | 500 < 0.0001 1 0 1 1 0 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 501 493 495 535 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 530 529 506 493 498 | 500 < 0.0001 5 5 6 6 0 | 5 | 3 2 8 6 6 > 0.9999 || = 0.53 481 475 460 506 474 | 500 < 0.0002 4 2 2 2 8 | 5 | 0 3 4 5 2 > 0.9998 || = 0.52 521 511 487 526 488 | 500 < 0.0003 6 3 4 5 5 | 5 | 5 7 4 8 4 > 0.9997 || = 0.51 489 503 494 483 512 | 500 < 0.0004 5 6 8 5 2 | 5 | 7 3 2 4 3 > 0.9996 || = 0.50 507 501 519 474 492 | 500 < 0.0005 8 5 6 8 2 | 5 | 5 6 8 7 4 > 0.9995 || = 0.49 473 461 525 497 486 | 500 < 0.0006 8 7 7 5 4 | 5 | 3 6 4 8 5 > 0.9994 || = 0.48 509 509 509 471 477 | 500 < 0.0007 4 6 3 6 1 | 5 | 8 4 3 4 5 > 0.9993 || = 0.47 494 485 513 516 507 | 500 < 0.0008 9 7 3 4 5 | 5 | 2 6 8 4 3 > 0.9992 || = 0.46 509 492 466 485 481 | 500 < 0.0009 5 5 5 4 4 | 5 | 4 7 4 8 1 > 0.9991 || = 0.45 524 492 489 517 495 | 500 < 0.001 3 6 5 5 8 | 5 | 6 7 6 11 6 > 0.999 || = 0.44 476 470 494 495 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 491 517 488 500 540 | 500 < 0.001 57 52 49 50 39 | 50 | 43 51 51 65 39 > 0.999 || = 0.42 542 474 498 496 523 | 500 < 0.002 45 43 45 38 46 | 50 | 48 50 54 44 52 > 0.998 || = 0.41 513 529 494 488 483 | 500 < 0.003 60 41 53 50 45 | 50 | 54 59 58 39 43 > 0.997 || = 0.40 526 481 501 502 517 | 500 < 0.004 40 56 63 56 52 | 50 | 49 39 57 40 44 > 0.996 || = 0.39 475 497 486 537 523 | 500 < 0.005 63 48 55 49 56 | 50 | 64 64 48 55 50 > 0.995 || = 0.38 488 505 498 483 493 | 500 < 0.006 45 57 57 60 51 | 50 | 54 55 59 49 55 > 0.994 || = 0.37 483 490 519 498 501 | 500 < 0.007 57 62 54 59 48 | 50 | 55 59 56 42 50 > 0.993 || = 0.36 486 530 488 496 514 | 500 < 0.008 59 59 54 51 29 | 50 | 45 48 54 39 67 > 0.992 || = 0.35 507 458 522 447 497 | 500 < 0.009 64 58 59 59 54 | 50 | 67 35 57 60 55 > 0.991 || = 0.34 521 517 488 509 481 | 500 < 0.01 58 57 47 57 52 | 50 | 50 64 58 42 54 > 0.99 || = 0.33 517 525 501 526 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 496 532 515 491 502 | 500 < 0.01 548 533 536 529 472 | 497.5 | 529 524 552 475 509 > 0.99 || = 0.31 467 546 497 483 504 | 500 = 0.01 237 249 285 257 257 | 252.5 | 263 234 276 244 233 = 0.99 || = 0.30 475 503 474 486 471 | 500 = 0.02 502 503 470 510 495 | 500 | 532 534 486 500 517 = 0.98 || = 0.29 512 532 540 480 525 | 500 =================================================================| 500 | 477 512 486 508 489 = 0.97 || = 0.28 518 507 520 467 482 | 500 swalk_RandomWalk1 test: | 500 | 517 531 521 536 530 = 0.96 || = 0.27 518 523 494 511 500 | 500 ----------------------------------------------- | 500 | 514 487 466 492 483 = 0.95 || = 0.26 494 450 509 469 521 | 500 N = 1, n = 10000000, r = 0, s = 10, L0 = 1000, L1 = 1000 | 500 | 497 495 506 467 511 = 0.94 || = 0.25 551 503 516 499 517 | 500 Test on the values of the Statistic C | 500 | 448 503 496 493 495 = 0.93 || = 0.24 464 481 474 484 533 | 500 | 500 | 486 487 512 513 486 = 0.92 || = 0.23 497 504 515 530 512 | 500 =================================================================| 500 | 496 489 521 491 480 = 0.91 || = 0.22 483 477 469 466 515 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 505 499 508 552 479 = 0.90 || = 0.21 462 477 499 500 497 | 500 -----------------------------------------------------------------| 500 | 496 493 492 526 497 = 0.89 || = 0.20 471 504 514 504 460 | 500 SD Bern.: d 1.02413 1.31061 1.11499 | 500 | 527 454 508 518 489 = 0.88 || = 0.19 514 486 462 570 514 | 500 s 1.02467 1.05976 1.36449 | 500 | 482 509 525 508 483 = 0.87 || = 0.18 500 501 500 511 507 | 500 t 0.98085 0.89486 0.87220 | 500 | 475 476 517 455 507 = 0.86 || = 0.17 538 484 495 517 514 | 500 m 1.05906 0.99346 1.30984 | 500 | 502 489 509 521 485 = 0.85 || = 0.16 529 489 512 460 497 | 500 x 0.92930 1.15642 1.06354 | 500 | 469 490 465 523 529 = 0.84 || = 0.15 489 515 502 436 503 | 500 | 500 | 477 514 500 487 505 = 0.83 || = 0.14 493 473 482 501 558 | 500 Changes: d 50 6 6 | 500 | 486 505 489 520 500 = 0.82 || = 0.13 469 525 473 503 491 | 500 s 64 4 6 | 500 | 472 483 477 501 529 = 0.81 || = 0.12 498 507 543 500 515 | 500 t 54 2 2 | 500 | 481 466 470 493 519 = 0.80 || = 0.11 495 497 499 489 515 | 500 m 43 3 5 | 500 | 517 468 508 515 520 = 0.79 || = 0.10 515 514 488 478 471 | 500 x 53 3 5 | 500 | 493 502 538 508 478 = 0.78 || = 0.09 493 495 488 543 507 | 500 -----------------------------------------------------------------| 500 | 489 492 515 517 500 = 0.77 || = 0.08 512 504 461 505 473 | 500 Aver./ d 0.49848 498 > 500: 7 4 4 3 6 5 6 4 3 5 | 500 | 497 501 521 525 546 = 0.76 || = 0.07 488 485 522 450 463 | 500 median s 0.49944 501 ----- 5 5 6 7 3 6 5 6 3 5 | 500 | 525 515 507 515 520 = 0.75 || = 0.06 515 561 476 475 550 | 500 t 0.50050 500 5 3 6 4 4 3 5 7 5 6 | 500 | 470 550 488 470 509 = 0.74 || = 0.05 529 510 503 556 470 | 500 m 0.50058 500 8 5 3 3 3 5 6 6 8 3 | 500 | 489 529 516 514 497 = 0.73 || = 0.04 538 483 492 510 493 | 500 x 0.50009 497 3 7 6 5 4 2 5 6 4 4 | 500 | 520 454 538 469 515 = 0.72 || = 0.03 510 477 561 527 490 | 500 -----------------------------------------------------------------| 500 | 510 550 491 477 471 = 0.71 || = 0.02 502 503 470 510 495 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 525 508 508 485 494 = 0.70 || = 0.01 237 249 285 257 257 | 252.5 d 0 0 2 18 63 15 3 0 0 | 500 | 500 496 487 519 522 = 0.69 || < 0.01 548 533 536 529 472 | 497.5 s 0 0 3 16 64 13 5 0 0 | 500 | 488 548 474 480 492 = 0.68 ||========================================================================= t 0 0 1 17 72 8 3 0 0 | 500 | 521 487 502 532 487 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 12 69 13 2 1 0 | 500 | 501 487 510 516 540 = 0.66 ||========================================================================= x 0 0 1 13 74 10 3 0 0 | 500 | 545 515 506 504 507 = 0.65 || swalk_RandomWalk1 test: no 160 test no 161 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 161 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 2 | 0.5 | 0 2 0 0 0 > 0.99999 || = 0.64 509 460 474 506 517 | 500 < 0.00002 1 0 1 2 0 | 0.5 | 0 1 0 0 1 > 0.99998 || = 0.63 527 497 511 510 477 | 500 < 0.00003 1 0 0 0 1 | 0.5 | 1 1 1 0 1 > 0.99997 || = 0.62 520 495 495 553 488 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 496 498 526 540 481 | 500 < 0.00005 0 2 0 1 1 | 0.5 | 1 0 0 0 0 > 0.99995 || = 0.60 509 484 532 492 505 | 500 < 0.00006 1 1 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 494 535 521 496 553 | 500 < 0.00007 0 1 0 1 0 | 0.5 | 0 1 1 1 0 > 0.99993 || = 0.58 491 509 498 474 497 | 500 < 0.00008 1 0 0 1 1 | 0.5 | 0 0 1 1 1 > 0.99992 || = 0.57 517 461 478 489 477 | 500 < 0.00009 0 1 0 0 0 | 0.5 | 2 0 0 0 0 > 0.99991 || = 0.56 472 484 522 524 500 | 500 < 0.0001 0 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 487 506 469 493 480 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 494 471 491 493 501 | 500 < 0.0001 4 6 2 7 5 | 5 | 4 5 5 2 3 > 0.9999 || = 0.53 476 488 500 509 477 | 500 < 0.0002 4 4 7 3 8 | 5 | 2 6 4 1 3 > 0.9998 || = 0.52 512 505 464 526 552 | 500 < 0.0003 6 4 6 8 5 | 5 | 7 6 1 5 8 > 0.9997 || = 0.51 504 530 501 484 552 | 500 < 0.0004 4 5 8 3 7 | 5 | 6 4 4 5 5 > 0.9996 || = 0.50 471 497 492 513 497 | 500 < 0.0005 7 11 5 4 6 | 5 | 3 6 8 9 1 > 0.9995 || = 0.49 525 489 478 507 506 | 500 < 0.0006 5 2 3 5 5 | 5 | 6 9 4 6 7 > 0.9994 || = 0.48 505 493 493 503 470 | 500 < 0.0007 7 5 6 5 5 | 5 | 5 1 2 6 9 > 0.9993 || = 0.47 547 486 491 476 513 | 500 < 0.0008 5 8 6 5 6 | 5 | 7 6 7 4 7 > 0.9992 || = 0.46 487 486 461 480 491 | 500 < 0.0009 4 6 3 4 3 | 5 | 3 6 4 4 4 > 0.9991 || = 0.45 481 500 466 489 516 | 500 < 0.001 2 4 3 1 6 | 5 | 4 3 4 3 6 > 0.999 || = 0.44 492 492 494 540 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 502 483 505 505 508 | 500 < 0.001 48 55 49 45 56 | 50 | 47 52 43 45 53 > 0.999 || = 0.42 533 531 539 473 505 | 500 < 0.002 53 44 52 54 45 | 50 | 60 56 34 54 40 > 0.998 || = 0.41 491 483 520 442 462 | 500 < 0.003 56 56 47 54 53 | 50 | 46 48 44 54 60 > 0.997 || = 0.40 514 516 457 508 514 | 500 < 0.004 55 57 53 61 45 | 50 | 44 50 58 62 58 > 0.996 || = 0.39 536 502 512 512 531 | 500 < 0.005 51 47 43 61 50 | 50 | 58 40 50 50 41 > 0.995 || = 0.38 508 495 502 540 458 | 500 < 0.006 55 39 41 49 59 | 50 | 50 52 42 58 45 > 0.994 || = 0.37 474 511 486 496 492 | 500 < 0.007 57 54 52 61 38 | 50 | 52 52 67 54 46 > 0.993 || = 0.36 501 515 504 530 507 | 500 < 0.008 54 55 58 55 40 | 50 | 63 36 38 50 57 > 0.992 || = 0.35 451 509 471 485 520 | 500 < 0.009 70 43 57 42 67 | 50 | 47 44 41 48 54 > 0.991 || = 0.34 503 465 533 477 479 | 500 < 0.01 43 50 51 59 48 | 50 | 67 71 44 47 56 > 0.99 || = 0.33 534 483 469 530 540 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 527 476 461 533 491 | 500 < 0.01 542 500 503 541 501 | 497.5 | 534 501 461 522 510 > 0.99 || = 0.31 499 463 495 508 482 | 500 = 0.01 239 274 265 269 261 | 252.5 | 233 268 233 254 284 = 0.99 || = 0.30 483 479 485 496 492 | 500 = 0.02 519 503 491 487 508 | 500 | 513 460 532 498 481 = 0.98 || = 0.29 510 527 506 495 491 | 500 =================================================================| 500 | 479 499 536 488 514 = 0.97 || = 0.28 476 518 495 511 507 | 500 swalk_RandomWalk1 test: | 500 | 464 490 514 490 499 = 0.96 || = 0.27 523 540 540 487 472 | 500 ----------------------------------------------- | 500 | 531 515 509 501 495 = 0.95 || = 0.26 488 467 512 500 482 | 500 N = 1, n = 10000000, r = 20, s = 10, L0 = 1000, L1 = 1000 | 500 | 495 480 510 478 501 = 0.94 || = 0.25 505 482 468 554 494 | 500 Test on the values of the Statistic H | 500 | 473 498 507 486 524 = 0.93 || = 0.24 509 515 503 476 472 | 500 | 500 | 501 512 484 491 490 = 0.92 || = 0.23 474 493 528 494 537 | 500 =================================================================| 500 | 473 506 519 473 490 = 0.91 || = 0.22 469 497 509 481 512 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 475 501 553 526 480 = 0.90 || = 0.21 474 480 445 520 476 | 500 -----------------------------------------------------------------| 500 | 497 531 530 534 513 = 0.89 || = 0.20 504 501 508 462 486 | 500 SD Bern.: d 1.03616 1.10870 1.18041 | 500 | 476 454 498 466 522 = 0.88 || = 0.19 489 482 523 516 493 | 500 s 0.93140 0.85599 1.28515 | 500 | 512 471 537 462 492 = 0.87 || = 0.18 575 516 502 522 470 | 500 t 0.99554 0.73656 1.42829 | 500 | 544 516 485 507 479 = 0.86 || = 0.17 495 493 520 497 563 | 500 m 1.02241 1.08773 0.76718 | 500 | 537 553 500 494 504 = 0.85 || = 0.16 519 543 525 500 485 | 500 x 1.07452 1.19474 0.99647 | 500 | 533 471 483 508 525 = 0.84 || = 0.15 506 500 513 534 488 | 500 | 500 | 508 531 500 491 527 = 0.83 || = 0.14 510 531 503 482 535 | 500 Changes: d 56 2 7 | 500 | 478 479 524 437 484 = 0.82 || = 0.13 509 502 499 484 519 | 500 s 50 5 4 | 500 | 466 529 502 516 484 = 0.81 || = 0.12 463 491 514 487 509 | 500 t 53 5 4 | 500 | 514 503 473 496 502 = 0.80 || = 0.11 493 505 486 494 484 | 500 m 52 5 4 | 500 | 492 482 475 478 545 = 0.79 || = 0.10 489 479 516 495 511 | 500 x 48 7 4 | 500 | 509 525 525 505 479 = 0.78 || = 0.09 453 513 490 497 468 | 500 -----------------------------------------------------------------| 500 | 506 492 454 491 433 = 0.77 || = 0.08 482 502 476 519 520 | 500 Aver./ d 0.49970 499 > 500: 4 5 5 6 6 4 5 6 5 4 | 500 | 489 488 489 519 451 = 0.76 || = 0.07 493 500 523 488 504 | 500 median s 0.49970 500 ----- 7 5 5 4 2 5 3 6 6 5 | 500 | 482 509 514 484 493 = 0.75 || = 0.06 510 518 498 517 490 | 500 t 0.50030 502 5 8 7 4 3 4 5 5 5 7 | 500 | 501 505 502 502 523 = 0.74 || = 0.05 487 494 513 547 473 | 500 m 0.49846 496 5 3 3 6 5 3 5 4 5 3 | 500 | 465 557 502 494 512 = 0.73 || = 0.04 486 495 484 483 503 | 500 x 0.49979 499 7 5 3 4 7 5 3 5 5 5 | 500 | 502 517 464 481 507 = 0.72 || = 0.03 533 514 524 458 533 | 500 -----------------------------------------------------------------| 500 | 522 488 506 542 479 = 0.71 || = 0.02 519 503 491 487 508 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 489 487 487 499 516 = 0.70 || = 0.01 239 274 265 269 261 | 252.5 d 0 0 2 18 64 14 2 1 0 | 500 | 469 529 504 519 487 = 0.69 || < 0.01 542 500 503 541 501 | 497.5 s 0 0 1 10 75 13 2 0 0 | 500 | 522 491 492 492 461 = 0.68 ||========================================================================= t 0 0 2 17 64 17 1 0 0 | 500 | 489 497 477 492 497 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 11 70 15 3 0 0 | 500 | 536 511 509 479 475 = 0.66 ||========================================================================= x 0 1 1 14 69 10 6 0 0 | 500 | 495 502 532 476 546 = 0.65 || swalk_RandomWalk1 test: no 161 test no 162 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 162 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99999 || = 0.64 500 490 510 515 480 | 500 < 0.00002 0 0 1 1 0 | 0.5 | 0 1 0 1 0 > 0.99998 || = 0.63 511 462 498 513 508 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 0 1 1 0 1 > 0.99997 || = 0.62 496 520 490 509 444 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 0 1 1 0 0 > 0.99996 || = 0.61 532 492 513 460 508 | 500 < 0.00005 0 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 490 513 478 470 495 | 500 < 0.00006 0 1 1 0 0 | 0.5 | 1 0 0 0 1 > 0.99994 || = 0.59 506 471 494 483 536 | 500 < 0.00007 1 1 0 1 0 | 0.5 | 0 1 1 0 0 > 0.99993 || = 0.58 567 487 503 527 501 | 500 < 0.00008 0 0 1 2 0 | 0.5 | 1 0 0 0 2 > 0.99992 || = 0.57 466 534 479 480 483 | 500 < 0.00009 1 1 0 2 0 | 0.5 | 1 1 0 2 0 > 0.99991 || = 0.56 530 486 478 470 490 | 500 < 0.0001 0 0 1 0 0 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 485 551 474 526 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 486 495 488 468 469 | 500 < 0.0001 2 4 5 8 0 | 5 | 4 6 4 3 4 > 0.9999 || = 0.53 505 498 487 470 503 | 500 < 0.0002 2 4 4 2 5 | 5 | 4 3 3 2 5 > 0.9998 || = 0.52 493 478 473 513 503 | 500 < 0.0003 8 5 7 4 2 | 5 | 3 6 6 5 4 > 0.9997 || = 0.51 496 482 503 501 513 | 500 < 0.0004 5 5 6 1 7 | 5 | 6 6 6 6 9 > 0.9996 || = 0.50 532 493 467 513 508 | 500 < 0.0005 3 5 8 6 4 | 5 | 10 4 2 8 4 > 0.9995 || = 0.49 497 498 496 466 453 | 500 < 0.0006 6 5 4 4 1 | 5 | 6 6 7 11 3 > 0.9994 || = 0.48 492 500 519 527 523 | 500 < 0.0007 5 4 6 4 5 | 5 | 6 1 4 2 5 > 0.9993 || = 0.47 534 505 476 495 517 | 500 < 0.0008 3 6 9 5 0 | 5 | 7 5 1 5 7 > 0.9992 || = 0.46 506 493 489 504 510 | 500 < 0.0009 3 3 5 6 2 | 5 | 7 3 6 4 3 > 0.9991 || = 0.45 529 510 523 475 490 | 500 < 0.001 4 4 6 7 3 | 5 | 12 5 5 8 5 > 0.999 || = 0.44 513 486 479 522 541 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 513 480 465 517 513 | 500 < 0.001 41 45 60 47 29 | 50 | 65 45 44 54 49 > 0.999 || = 0.42 485 494 476 467 499 | 500 < 0.002 44 47 62 61 44 | 50 | 56 58 39 49 48 > 0.998 || = 0.41 456 506 512 501 502 | 500 < 0.003 52 52 56 41 54 | 50 | 51 69 46 43 50 > 0.997 || = 0.40 515 468 525 484 517 | 500 < 0.004 55 53 52 60 42 | 50 | 53 45 46 59 41 > 0.996 || = 0.39 481 479 503 488 485 | 500 < 0.005 49 58 71 53 46 | 50 | 40 51 48 48 51 > 0.995 || = 0.38 517 488 518 501 486 | 500 < 0.006 45 46 50 50 69 | 50 | 52 57 57 55 38 > 0.994 || = 0.37 520 515 502 508 514 | 500 < 0.007 49 56 59 46 62 | 50 | 52 45 46 42 47 > 0.993 || = 0.36 505 525 532 539 508 | 500 < 0.008 64 53 46 57 46 | 50 | 46 54 46 42 54 > 0.992 || = 0.35 477 493 500 498 487 | 500 < 0.009 51 49 58 46 52 | 50 | 53 54 45 54 46 > 0.991 || = 0.34 538 497 482 530 489 | 500 < 0.01 52 43 58 45 42 | 50 | 51 48 50 52 47 > 0.99 || = 0.33 485 484 515 541 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 503 472 502 470 477 | 500 < 0.01 502 502 572 506 486 | 497.5 | 519 526 467 498 471 > 0.99 || = 0.31 530 482 536 470 530 | 500 = 0.01 246 232 274 241 275 | 252.5 | 254 276 262 258 249 = 0.99 || = 0.30 481 447 522 482 496 | 500 = 0.02 488 518 474 474 490 | 500 | 473 511 516 493 488 = 0.98 || = 0.29 475 504 525 510 473 | 500 =================================================================| 500 | 449 495 516 467 478 = 0.97 || = 0.28 459 525 529 501 499 | 500 swalk_RandomWalk1 test: | 500 | 518 521 513 481 494 = 0.96 || = 0.27 506 498 519 534 499 | 500 ----------------------------------------------- | 500 | 490 462 525 522 469 = 0.95 || = 0.26 513 537 481 487 497 | 500 N = 1, n = 10000000, r = 20, s = 0, L0 = 1000, L1 = 1000 | 500 | 506 522 500 517 490 = 0.94 || = 0.25 504 511 462 510 515 | 500 Test on the values of the Statistic M | 500 | 501 495 490 515 521 = 0.93 || = 0.24 540 514 541 445 494 | 500 | 500 | 515 483 490 537 510 = 0.92 || = 0.23 488 520 490 566 552 | 500 =================================================================| 500 | 503 533 489 478 531 = 0.91 || = 0.22 497 454 505 499 500 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 531 519 525 522 505 = 0.90 || = 0.21 503 492 495 510 538 | 500 -----------------------------------------------------------------| 500 | 489 502 500 516 491 = 0.89 || = 0.20 480 492 471 510 547 | 500 SD Bern.: d 1.06081 0.86529 0.90044 | 500 | 479 492 472 500 479 = 0.88 || = 0.19 505 508 507 483 496 | 500 s 0.89688 0.66665 1.08312 | 500 | 476 511 498 486 471 = 0.87 || = 0.18 477 532 464 496 502 | 500 t 1.05591 1.37909 0.77367 | 500 | 491 531 516 486 536 = 0.86 || = 0.17 490 480 501 481 515 | 500 m 1.03904 0.92349 0.80537 | 500 | 512 487 548 504 539 = 0.85 || = 0.16 529 528 511 466 506 | 500 x 0.99913 1.52522 0.75003 | 500 | 495 516 566 512 537 = 0.84 || = 0.15 466 518 497 552 502 | 500 | 500 | 543 503 493 489 516 = 0.83 || = 0.14 476 522 499 494 489 | 500 Changes: d 54 3 4 | 500 | 540 478 533 492 475 = 0.82 || = 0.13 443 491 534 496 453 | 500 s 50 4 6 | 500 | 504 510 491 457 538 = 0.81 || = 0.12 523 489 472 520 517 | 500 t 45 4 2 | 500 | 484 516 519 509 522 = 0.80 || = 0.11 496 488 475 452 470 | 500 m 51 6 6 | 500 | 523 527 534 516 477 = 0.79 || = 0.10 486 494 511 490 517 | 500 x 52 6 4 | 500 | 506 491 441 498 492 = 0.78 || = 0.09 513 468 489 508 526 | 500 -----------------------------------------------------------------| 500 | 521 494 453 485 509 = 0.77 || = 0.08 451 494 474 467 482 | 500 Aver./ d 0.50165 502 > 500: 5 3 5 6 6 4 6 4 5 7 | 500 | 526 531 526 533 548 = 0.76 || = 0.07 457 479 488 497 457 | 500 median s 0.50249 498 ----- 3 5 6 2 3 3 5 6 7 6 | 500 | 458 518 478 512 490 = 0.75 || = 0.06 514 503 508 503 503 | 500 t 0.50057 499 3 5 5 8 4 2 6 4 5 5 | 500 | 491 496 478 496 481 = 0.74 || = 0.05 482 497 490 522 482 | 500 m 0.50103 501 5 2 7 5 5 4 8 5 4 6 | 500 | 498 502 491 496 513 = 0.73 || = 0.04 515 481 483 501 503 | 500 x 0.49977 499 4 6 4 4 7 5 4 4 6 3 | 500 | 473 518 477 487 499 = 0.72 || = 0.03 518 474 490 482 485 | 500 -----------------------------------------------------------------| 500 | 490 495 507 515 464 = 0.71 || = 0.02 488 518 474 474 490 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 491 526 513 487 479 = 0.70 || = 0.01 246 232 274 241 275 | 252.5 d 0 0 4 13 66 17 0 1 0 | 500 | 522 508 509 502 521 = 0.69 || < 0.01 502 502 572 506 486 | 497.5 s 0 0 2 9 76 13 1 0 0 | 500 | 529 504 525 510 492 = 0.68 ||========================================================================= t 0 0 2 16 64 16 2 1 0 | 500 | 504 476 526 553 473 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 70 11 3 0 0 | 500 | 450 499 486 532 496 = 0.66 ||========================================================================= x 0 0 3 12 71 12 3 0 0 | 500 | 532 507 489 533 503 = 0.65 || swalk_RandomWalk1 test: no 162 test no 163 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 163 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 507 492 514 472 515 | 500 < 0.00002 2 0 0 0 1 | 0.5 | 2 0 0 1 1 > 0.99998 || = 0.63 478 443 542 477 489 | 500 < 0.00003 1 1 1 0 1 | 0.5 | 1 0 0 0 1 > 0.99997 || = 0.62 473 484 472 498 507 | 500 < 0.00004 1 2 1 0 1 | 0.5 | 0 0 0 2 0 > 0.99996 || = 0.61 536 470 514 487 489 | 500 < 0.00005 0 0 1 0 0 | 0.5 | 0 1 0 0 0 > 0.99995 || = 0.60 488 471 501 572 482 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99994 || = 0.59 467 528 522 528 502 | 500 < 0.00007 1 1 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 525 497 533 497 533 | 500 < 0.00008 0 1 0 1 1 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 517 503 511 486 505 | 500 < 0.00009 0 1 0 0 0 | 0.5 | 0 1 1 3 0 > 0.99991 || = 0.56 534 513 475 514 493 | 500 < 0.0001 1 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 487 551 495 490 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 501 518 535 500 509 | 500 < 0.0001 8 6 4 1 5 | 5 | 3 6 1 6 2 > 0.9999 || = 0.53 523 491 502 505 486 | 500 < 0.0002 6 4 3 7 7 | 5 | 5 1 4 4 2 > 0.9998 || = 0.52 492 505 511 488 512 | 500 < 0.0003 3 3 8 6 1 | 5 | 1 2 9 5 10 > 0.9997 || = 0.51 529 509 568 489 514 | 500 < 0.0004 6 4 2 3 7 | 5 | 6 3 6 2 8 > 0.9996 || = 0.50 479 504 508 496 469 | 500 < 0.0005 7 5 1 4 7 | 5 | 4 5 3 3 4 > 0.9995 || = 0.49 502 507 489 504 531 | 500 < 0.0006 8 7 4 10 2 | 5 | 3 4 3 8 3 > 0.9994 || = 0.48 508 529 490 480 482 | 500 < 0.0007 4 4 4 6 1 | 5 | 2 7 4 3 4 > 0.9993 || = 0.47 510 492 520 534 494 | 500 < 0.0008 4 2 5 3 1 | 5 | 1 6 8 6 5 > 0.9992 || = 0.46 520 476 534 524 485 | 500 < 0.0009 9 7 5 3 6 | 5 | 4 2 8 3 3 > 0.9991 || = 0.45 485 449 511 537 500 | 500 < 0.001 3 3 4 4 4 | 5 | 7 5 4 2 3 > 0.999 || = 0.44 483 512 514 529 505 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 488 499 484 523 511 | 500 < 0.001 58 45 40 47 41 | 50 | 36 41 50 42 44 > 0.999 || = 0.42 498 485 517 470 487 | 500 < 0.002 66 37 49 46 54 | 50 | 57 44 55 56 50 > 0.998 || = 0.41 476 516 511 492 469 | 500 < 0.003 33 46 51 53 51 | 50 | 48 47 40 64 54 > 0.997 || = 0.40 447 510 497 513 487 | 500 < 0.004 44 44 51 50 47 | 50 | 41 41 57 42 50 > 0.996 || = 0.39 472 491 496 466 486 | 500 < 0.005 52 52 35 52 51 | 50 | 44 62 39 44 46 > 0.995 || = 0.38 495 482 490 489 510 | 500 < 0.006 38 59 48 55 49 | 50 | 52 48 44 44 42 > 0.994 || = 0.37 477 507 518 456 520 | 500 < 0.007 50 47 59 57 52 | 50 | 54 44 48 52 52 > 0.993 || = 0.36 524 503 524 539 532 | 500 < 0.008 51 59 62 46 57 | 50 | 53 36 62 53 58 > 0.992 || = 0.35 499 457 497 473 502 | 500 < 0.009 58 54 46 42 54 | 50 | 42 46 59 53 49 > 0.991 || = 0.34 498 540 508 464 529 | 500 < 0.01 40 54 54 51 45 | 50 | 47 47 50 65 51 > 0.99 || = 0.33 541 522 492 530 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 487 472 504 475 482 | 500 < 0.01 490 497 495 499 501 | 497.5 | 474 456 504 515 496 > 0.99 || = 0.31 514 482 495 478 533 | 500 = 0.01 268 255 255 266 252 | 252.5 | 274 233 243 243 248 = 0.99 || = 0.30 504 507 522 511 471 | 500 = 0.02 494 469 523 481 462 | 500 | 472 515 449 524 484 = 0.98 || = 0.29 487 521 469 495 511 | 500 =================================================================| 500 | 509 522 471 457 503 = 0.97 || = 0.28 462 492 486 515 526 | 500 swalk_RandomWalk1 test: | 500 | 486 508 509 501 505 = 0.96 || = 0.27 516 488 495 532 483 | 500 ----------------------------------------------- | 500 | 525 538 467 495 537 = 0.95 || = 0.26 511 486 483 501 463 | 500 N = 1, n = 10000000, r = 20, s = 10, L0 = 1000, L1 = 1000 | 500 | 499 492 504 486 502 = 0.94 || = 0.25 489 459 506 485 509 | 500 Test on the values of the Statistic J | 500 | 521 474 499 520 523 = 0.93 || = 0.24 496 504 473 485 536 | 500 | 500 | 526 509 524 471 477 = 0.92 || = 0.23 526 504 521 526 487 | 500 =================================================================| 500 | 481 520 484 479 507 = 0.91 || = 0.22 500 512 515 499 484 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 512 520 500 497 514 = 0.90 || = 0.21 517 481 481 458 573 | 500 -----------------------------------------------------------------| 500 | 472 476 512 526 513 = 0.89 || = 0.20 493 509 529 507 535 | 500 SD Bern.: d 0.89957 1.38488 0.96794 | 500 | 510 504 525 542 458 = 0.88 || = 0.19 514 485 473 525 511 | 500 s 1.12103 0.95231 1.10688 | 500 | 485 496 532 484 500 = 0.87 || = 0.18 489 522 481 519 489 | 500 t 1.03733 1.08589 1.05882 | 500 | 484 516 499 529 465 = 0.86 || = 0.17 493 511 463 516 470 | 500 m 1.05619 0.62159 1.16590 | 500 | 526 472 474 502 486 = 0.85 || = 0.16 495 473 471 511 537 | 500 x 0.96455 0.63749 0.63591 | 500 | 488 508 488 496 480 = 0.84 || = 0.15 519 527 528 508 461 | 500 | 500 | 490 523 498 483 463 = 0.83 || = 0.14 518 563 519 496 485 | 500 Changes: d 56 5 4 | 500 | 496 488 527 472 481 = 0.82 || = 0.13 480 500 468 447 509 | 500 s 52 3 2 | 500 | 511 577 503 485 488 = 0.81 || = 0.12 520 492 488 496 481 | 500 t 49 5 6 | 500 | 519 542 500 520 514 = 0.80 || = 0.11 508 468 453 513 523 | 500 m 48 5 3 | 500 | 507 483 464 476 525 = 0.79 || = 0.10 474 497 541 491 493 | 500 x 47 6 5 | 500 | 524 521 524 463 471 = 0.78 || = 0.09 482 479 460 497 516 | 500 -----------------------------------------------------------------| 500 | 517 461 513 542 536 = 0.77 || = 0.08 476 514 512 520 531 | 500 Aver./ d 0.50148 499 > 500: 3 5 4 4 4 6 4 8 4 5 | 500 | 536 541 490 509 477 = 0.76 || = 0.07 475 491 504 488 473 | 500 median s 0.50160 503 ----- 4 4 5 5 5 7 4 4 6 6 | 500 | 507 468 502 505 496 = 0.75 || = 0.06 517 489 474 496 517 | 500 t 0.49996 500 5 3 4 5 6 8 6 3 5 4 | 500 | 483 535 486 518 503 = 0.74 || = 0.05 486 452 482 484 530 | 500 m 0.49981 497 4 6 5 3 7 4 1 7 4 4 | 500 | 540 475 481 525 478 = 0.73 || = 0.04 505 503 476 550 506 | 500 x 0.49870 500 6 4 6 6 3 7 5 4 2 6 | 500 | 512 491 463 505 496 = 0.72 || = 0.03 461 513 556 491 490 | 500 -----------------------------------------------------------------| 500 | 490 464 472 499 490 = 0.71 || = 0.02 494 469 523 481 462 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 499 519 465 539 497 = 0.70 || = 0.01 268 255 255 266 252 | 252.5 d 0 0 1 14 70 16 0 0 0 | 500 | 500 495 475 497 479 = 0.69 || < 0.01 490 497 495 499 501 | 497.5 s 0 0 3 18 65 12 2 1 0 | 500 | 479 490 520 497 510 = 0.68 ||========================================================================= t 0 0 2 19 63 15 1 1 0 | 500 | 522 532 493 493 528 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 64 18 1 1 0 | 500 | 475 523 533 450 504 = 0.66 ||========================================================================= x 0 0 0 14 69 17 0 1 0 | 500 | 524 540 511 472 494 = 0.65 || swalk_RandomWalk1 test: no 163 test no 164 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 164 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 2 0 0 1 0 > 0.99999 || = 0.64 488 481 478 501 520 | 500 < 0.00002 1 1 0 0 0 | 0.5 | 0 0 1 0 2 > 0.99998 || = 0.63 459 478 462 525 538 | 500 < 0.00003 0 2 0 0 1 | 0.5 | 0 0 1 0 1 > 0.99997 || = 0.62 520 534 543 520 498 | 500 < 0.00004 1 0 2 2 0 | 0.5 | 0 0 0 2 0 > 0.99996 || = 0.61 493 490 537 475 484 | 500 < 0.00005 0 0 0 2 0 | 0.5 | 0 0 0 0 1 > 0.99995 || = 0.60 501 520 542 495 470 | 500 < 0.00006 0 2 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 509 483 481 473 463 | 500 < 0.00007 1 0 0 0 1 | 0.5 | 1 2 0 0 0 > 0.99993 || = 0.58 506 492 496 517 487 | 500 < 0.00008 0 1 1 1 0 | 0.5 | 1 1 1 0 0 > 0.99992 || = 0.57 480 528 538 472 518 | 500 < 0.00009 0 0 0 1 1 | 0.5 | 0 0 0 3 1 > 0.99991 || = 0.56 503 469 499 521 521 | 500 < 0.0001 3 0 0 1 0 | 0.5 | 0 0 2 1 0 > 0.9999 || = 0.55 472 507 489 516 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 477 533 505 515 483 | 500 < 0.0001 6 6 3 7 3 | 5 | 5 3 5 7 5 > 0.9999 || = 0.53 465 475 538 474 521 | 500 < 0.0002 9 2 7 6 2 | 5 | 1 3 2 3 1 > 0.9998 || = 0.52 510 538 475 493 501 | 500 < 0.0003 5 5 7 3 6 | 5 | 3 6 5 5 3 > 0.9997 || = 0.51 504 499 498 474 490 | 500 < 0.0004 6 5 6 5 8 | 5 | 8 3 4 6 5 > 0.9996 || = 0.50 501 456 435 494 495 | 500 < 0.0005 7 6 2 3 12 | 5 | 8 7 6 3 3 > 0.9995 || = 0.49 496 488 530 493 531 | 500 < 0.0006 8 7 2 3 2 | 5 | 5 9 5 5 7 > 0.9994 || = 0.48 512 481 527 493 460 | 500 < 0.0007 5 6 6 5 6 | 5 | 4 5 2 5 7 > 0.9993 || = 0.47 491 492 513 440 522 | 500 < 0.0008 4 10 8 2 10 | 5 | 4 8 3 9 3 > 0.9992 || = 0.46 479 482 571 506 499 | 500 < 0.0009 8 7 9 10 2 | 5 | 5 4 5 4 4 > 0.9991 || = 0.45 540 486 509 530 491 | 500 < 0.001 5 6 6 4 3 | 5 | 7 3 3 7 4 > 0.999 || = 0.44 481 487 480 484 458 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 487 525 523 516 527 | 500 < 0.001 63 60 56 48 54 | 50 | 50 51 40 54 42 > 0.999 || = 0.42 497 479 526 548 491 | 500 < 0.002 56 45 49 47 42 | 50 | 56 47 49 64 51 > 0.998 || = 0.41 469 455 501 505 501 | 500 < 0.003 47 41 61 59 32 | 50 | 37 49 48 48 38 > 0.997 || = 0.40 498 513 499 506 510 | 500 < 0.004 45 48 55 59 54 | 50 | 49 58 45 52 46 > 0.996 || = 0.39 488 536 463 534 482 | 500 < 0.005 51 61 67 55 52 | 50 | 42 54 44 59 49 > 0.995 || = 0.38 483 514 476 495 536 | 500 < 0.006 51 46 50 41 45 | 50 | 36 42 52 44 45 > 0.994 || = 0.37 475 469 487 532 512 | 500 < 0.007 63 43 40 51 65 | 50 | 44 45 45 40 48 > 0.993 || = 0.36 502 491 502 495 502 | 500 < 0.008 46 39 53 54 58 | 50 | 53 50 59 53 50 > 0.992 || = 0.35 485 513 521 523 512 | 500 < 0.009 42 46 52 68 42 | 50 | 45 49 41 54 51 > 0.991 || = 0.34 496 512 500 507 470 | 500 < 0.01 54 64 51 74 52 | 50 | 54 48 49 62 56 > 0.99 || = 0.33 500 464 517 508 484 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 490 534 494 429 492 | 500 < 0.01 518 493 534 556 496 | 497.5 | 466 493 472 530 476 > 0.99 || = 0.31 490 537 477 506 521 | 500 = 0.01 270 256 240 247 274 | 252.5 | 255 282 254 224 276 = 0.99 || = 0.30 507 523 483 509 522 | 500 = 0.02 524 482 498 536 475 | 500 | 528 497 536 488 493 = 0.98 || = 0.29 534 487 508 542 518 | 500 =================================================================| 500 | 539 503 485 519 463 = 0.97 || = 0.28 522 507 514 529 537 | 500 swalk_RandomWalk1 test: | 500 | 475 493 480 478 509 = 0.96 || = 0.27 503 521 522 420 480 | 500 ----------------------------------------------- | 500 | 451 491 464 501 520 = 0.95 || = 0.26 499 506 486 478 521 | 500 N = 1, n = 10000000, r = 20, s = 10, L0 = 1000, L1 = 1000 | 500 | 522 494 503 480 524 = 0.94 || = 0.25 504 505 523 546 484 | 500 Test on the values of the Statistic R | 500 | 490 494 495 491 436 = 0.93 || = 0.24 496 525 475 507 526 | 500 | 500 | 491 493 467 475 489 = 0.92 || = 0.23 498 478 486 515 458 | 500 =================================================================| 500 | 502 492 497 548 528 = 0.91 || = 0.22 548 514 493 522 497 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 553 540 494 439 489 = 0.90 || = 0.21 491 453 517 492 489 | 500 -----------------------------------------------------------------| 500 | 492 512 500 508 493 = 0.89 || = 0.20 485 508 528 507 498 | 500 SD Bern.: d 0.95733 1.00648 1.05122 | 500 | 502 486 505 509 509 = 0.88 || = 0.19 474 515 489 484 501 | 500 s 1.01248 1.20807 0.60856 | 500 | 542 523 451 486 532 = 0.87 || = 0.18 498 472 531 507 483 | 500 t 1.05356 1.08312 0.84658 | 500 | 505 492 442 528 473 = 0.86 || = 0.17 530 496 482 510 486 | 500 m 1.21634 1.54867 1.10144 | 500 | 489 504 490 491 507 = 0.85 || = 0.16 502 466 493 512 487 | 500 x 1.00375 1.27027 0.76457 | 500 | 515 492 494 533 494 = 0.84 || = 0.15 497 520 517 527 513 | 500 | 500 | 491 470 476 513 525 = 0.83 || = 0.14 485 487 485 517 517 | 500 Changes: d 45 4 5 | 500 | 508 503 495 459 491 = 0.82 || = 0.13 487 500 495 506 487 | 500 s 50 4 3 | 500 | 526 499 518 474 522 = 0.81 || = 0.12 508 498 491 529 492 | 500 t 43 4 4 | 500 | 477 478 492 499 524 = 0.80 || = 0.11 506 546 491 531 467 | 500 m 50 3 4 | 500 | 477 479 513 465 466 = 0.79 || = 0.10 512 558 483 490 524 | 500 x 52 6 3 | 500 | 499 481 521 502 516 = 0.78 || = 0.09 479 482 539 504 490 | 500 -----------------------------------------------------------------| 500 | 497 523 502 531 516 = 0.77 || = 0.08 437 479 501 432 484 | 500 Aver./ d 0.50040 499 > 500: 6 5 5 2 2 6 6 2 7 5 | 500 | 498 506 528 471 527 = 0.76 || = 0.07 482 494 504 539 506 | 500 median s 0.49930 496 ----- 3 4 7 7 2 5 3 5 5 2 | 500 | 497 520 453 511 476 = 0.75 || = 0.06 508 499 510 483 489 | 500 t 0.49732 498 8 2 6 3 8 4 3 6 2 3 | 500 | 481 488 508 456 505 = 0.74 || = 0.05 506 503 505 491 483 | 500 m 0.49663 504 6 8 7 7 6 4 6 3 5 4 | 500 | 520 522 496 469 556 = 0.73 || = 0.04 531 564 525 518 519 | 500 x 0.50089 498 3 4 4 6 5 4 4 7 5 5 | 500 | 493 507 489 468 550 = 0.72 || = 0.03 499 485 518 511 489 | 500 -----------------------------------------------------------------| 500 | 541 472 530 486 494 = 0.71 || = 0.02 524 482 498 536 475 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 542 498 496 501 490 = 0.70 || = 0.01 270 256 240 247 274 | 252.5 d 0 0 2 12 71 14 2 0 0 | 500 | 511 484 479 499 466 = 0.69 || < 0.01 518 493 534 556 496 | 497.5 s 0 0 2 9 72 15 3 0 0 | 500 | 519 488 487 504 491 = 0.68 ||========================================================================= t 0 0 4 10 68 18 0 1 0 | 500 | 467 482 517 504 485 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 3 2 15 61 16 4 0 0 | 500 | 526 519 490 457 501 = 0.66 ||========================================================================= x 0 0 1 13 70 15 2 0 0 | 500 | 526 537 483 491 506 = 0.65 || swalk_RandomWalk1 test: no 164 test no 165 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 165 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 2 0 2 | 0.5 | 2 1 0 0 0 > 0.99999 || = 0.64 512 520 499 522 481 | 500 < 0.00002 2 0 1 0 1 | 0.5 | 3 1 0 0 2 > 0.99998 || = 0.63 519 512 479 475 493 | 500 < 0.00003 2 2 1 1 1 | 0.5 | 0 1 0 0 0 > 0.99997 || = 0.62 498 467 509 500 511 | 500 < 0.00004 0 0 0 2 0 | 0.5 | 0 0 2 2 0 > 0.99996 || = 0.61 528 493 507 507 484 | 500 < 0.00005 1 0 2 0 1 | 0.5 | 0 0 1 0 1 > 0.99995 || = 0.60 467 478 504 485 507 | 500 < 0.00006 0 0 0 1 0 | 0.5 | 1 0 1 0 0 > 0.99994 || = 0.59 475 509 530 470 497 | 500 < 0.00007 1 1 2 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 513 492 492 479 491 | 500 < 0.00008 0 0 0 0 2 | 0.5 | 0 0 1 1 1 > 0.99992 || = 0.57 522 485 486 500 496 | 500 < 0.00009 0 1 2 0 2 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 510 511 485 505 485 | 500 < 0.0001 1 1 0 3 0 | 0.5 | 1 0 1 2 0 > 0.9999 || = 0.55 501 505 552 544 497 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 502 526 513 513 489 | 500 < 0.0001 8 6 10 7 10 | 5 | 7 4 6 5 4 > 0.9999 || = 0.53 515 535 524 519 501 | 500 < 0.0002 6 2 5 8 4 | 5 | 0 3 5 5 1 > 0.9998 || = 0.52 477 505 487 530 440 | 500 < 0.0003 2 5 5 3 8 | 5 | 3 1 1 7 6 > 0.9997 || = 0.51 477 493 516 483 504 | 500 < 0.0004 3 5 6 3 6 | 5 | 1 7 1 5 5 > 0.9996 || = 0.50 477 501 477 527 546 | 500 < 0.0005 4 6 5 6 5 | 5 | 7 5 3 7 4 > 0.9995 || = 0.49 474 511 487 447 489 | 500 < 0.0006 4 5 5 3 8 | 5 | 10 5 5 2 4 > 0.9994 || = 0.48 517 480 530 481 537 | 500 < 0.0007 5 3 2 6 4 | 5 | 3 7 4 3 5 > 0.9993 || = 0.47 499 509 512 537 513 | 500 < 0.0008 3 2 3 5 4 | 5 | 5 0 5 6 7 > 0.9992 || = 0.46 509 469 513 544 533 | 500 < 0.0009 7 1 4 5 7 | 5 | 6 2 7 9 2 > 0.9991 || = 0.45 508 490 462 486 463 | 500 < 0.001 3 10 4 3 6 | 5 | 6 5 2 8 6 > 0.999 || = 0.44 508 458 503 521 461 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 508 519 485 481 485 | 500 < 0.001 45 45 49 49 62 | 50 | 48 39 39 57 44 > 0.999 || = 0.42 556 494 517 498 518 | 500 < 0.002 52 44 47 43 45 | 50 | 46 45 38 45 54 > 0.998 || = 0.41 492 460 499 510 506 | 500 < 0.003 46 37 59 44 52 | 50 | 54 40 55 29 53 > 0.997 || = 0.40 506 530 504 493 503 | 500 < 0.004 49 50 47 42 59 | 50 | 46 42 45 45 38 > 0.996 || = 0.39 497 524 508 497 482 | 500 < 0.005 48 59 55 57 67 | 50 | 41 61 43 56 45 > 0.995 || = 0.38 477 452 496 487 470 | 500 < 0.006 43 44 58 52 56 | 50 | 47 51 45 51 52 > 0.994 || = 0.37 503 520 488 479 506 | 500 < 0.007 59 49 58 58 65 | 50 | 55 50 60 55 45 > 0.993 || = 0.36 500 489 487 506 512 | 500 < 0.008 52 59 55 52 51 | 50 | 44 56 40 53 60 > 0.992 || = 0.35 503 491 484 475 516 | 500 < 0.009 44 48 52 42 60 | 50 | 46 57 44 45 50 > 0.991 || = 0.34 514 520 460 520 471 | 500 < 0.01 47 61 44 58 46 | 50 | 53 45 44 49 47 > 0.99 || = 0.33 487 569 515 508 511 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 522 471 511 523 480 | 500 < 0.01 485 496 524 497 563 | 497.5 | 480 486 453 485 488 > 0.99 || = 0.31 522 508 492 467 463 | 500 = 0.01 258 242 230 261 279 | 252.5 | 240 249 287 216 228 = 0.99 || = 0.30 514 455 487 452 482 | 500 = 0.02 497 539 458 533 488 | 500 | 484 535 473 473 482 = 0.98 || = 0.29 507 490 459 515 523 | 500 =================================================================| 500 | 531 489 485 510 506 = 0.97 || = 0.28 500 493 464 525 471 | 500 swalk_RandomWalk1 test: | 500 | 493 506 522 505 475 = 0.96 || = 0.27 510 526 515 480 533 | 500 ----------------------------------------------- | 500 | 504 492 502 477 519 = 0.95 || = 0.26 460 521 505 445 506 | 500 N = 1, n = 10000000, r = 20, s = 10, L0 = 1000, L1 = 1000 | 500 | 520 520 469 475 496 = 0.94 || = 0.25 435 486 443 493 509 | 500 Test on the values of the Statistic C | 500 | 519 535 491 533 467 = 0.93 || = 0.24 530 500 548 482 531 | 500 | 500 | 506 516 515 521 475 = 0.92 || = 0.23 467 462 523 477 514 | 500 =================================================================| 500 | 515 489 541 522 521 = 0.91 || = 0.22 490 530 498 500 504 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 512 462 507 451 489 = 0.90 || = 0.21 479 506 536 556 518 | 500 -----------------------------------------------------------------| 500 | 509 479 500 528 517 = 0.89 || = 0.20 521 508 504 551 492 | 500 SD Bern.: d 0.88671 0.67708 0.67560 | 500 | 509 527 530 485 534 = 0.88 || = 0.19 507 488 511 487 474 | 500 s 1.06032 1.05313 1.04166 | 500 | 509 482 474 504 529 = 0.87 || = 0.18 525 503 503 527 506 | 500 t 1.06123 0.79789 1.15035 | 500 | 533 477 490 521 469 = 0.86 || = 0.17 519 512 508 525 479 | 500 m 1.12986 0.89375 1.12927 | 500 | 460 467 525 482 528 = 0.85 || = 0.16 475 509 483 492 524 | 500 x 1.05070 1.35787 0.85832 | 500 | 499 509 525 491 483 = 0.84 || = 0.15 498 503 495 510 531 | 500 | 500 | 486 546 541 467 459 = 0.83 || = 0.14 508 511 497 458 524 | 500 Changes: d 46 4 5 | 500 | 506 476 508 513 486 = 0.82 || = 0.13 498 482 510 498 534 | 500 s 48 5 4 | 500 | 527 445 489 498 496 = 0.81 || = 0.12 465 476 494 493 479 | 500 t 51 4 4 | 500 | 502 477 472 503 537 = 0.80 || = 0.11 505 471 511 496 497 | 500 m 50 3 3 | 500 | 500 521 473 482 544 = 0.79 || = 0.10 501 534 472 506 507 | 500 x 49 3 6 | 500 | 494 492 506 546 487 = 0.78 || = 0.09 493 537 500 541 498 | 500 -----------------------------------------------------------------| 500 | 488 496 532 518 515 = 0.77 || = 0.08 515 513 499 535 481 | 500 Aver./ d 0.50028 503 > 500: 5 6 4 6 7 6 5 4 7 6 | 500 | 505 534 489 470 487 = 0.76 || = 0.07 522 483 491 506 520 | 500 median s 0.49934 500 ----- 5 6 5 5 4 6 6 4 3 5 | 500 | 501 510 463 525 504 = 0.75 || = 0.06 471 479 488 516 501 | 500 t 0.50141 500 2 5 6 3 6 6 6 4 6 5 | 500 | 436 504 511 539 473 = 0.74 || = 0.05 516 460 501 491 516 | 500 m 0.49802 500 7 4 4 4 4 5 5 5 4 5 | 500 | 503 480 492 477 500 = 0.73 || = 0.04 519 540 492 491 528 | 500 x 0.49691 500 7 6 8 4 6 3 2 5 4 3 | 500 | 487 486 582 488 470 = 0.72 || = 0.03 496 520 498 519 535 | 500 -----------------------------------------------------------------| 500 | 495 494 497 446 521 = 0.71 || = 0.02 497 539 458 533 488 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 473 529 504 504 500 = 0.70 || = 0.01 258 242 230 261 279 | 252.5 d 0 0 2 14 78 6 1 0 0 | 500 | 494 500 467 488 506 = 0.69 || < 0.01 485 496 524 497 563 | 497.5 s 0 0 3 14 67 15 1 1 0 | 500 | 504 501 519 501 467 = 0.68 ||========================================================================= t 0 0 2 16 66 13 3 1 0 | 500 | 491 482 468 524 495 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 6 13 62 17 3 0 0 | 500 | 487 520 515 462 469 = 0.66 ||========================================================================= x 0 0 1 17 64 17 2 0 0 | 500 | 517 516 523 493 490 = 0.65 || swalk_RandomWalk1 test: no 165 test no 166 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 166 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 2 1 1 | 0.5 | 1 0 0 1 1 > 0.99999 || = 0.64 506 513 478 521 537 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 0 0 2 0 1 > 0.99998 || = 0.63 457 498 519 461 481 | 500 < 0.00003 0 2 1 0 0 | 0.5 | 1 1 1 0 0 > 0.99997 || = 0.62 472 494 494 499 508 | 500 < 0.00004 0 0 1 1 1 | 0.5 | 1 0 1 1 0 > 0.99996 || = 0.61 518 483 492 468 489 | 500 < 0.00005 2 0 2 0 0 | 0.5 | 1 1 0 0 2 > 0.99995 || = 0.60 505 475 523 458 500 | 500 < 0.00006 0 1 1 0 0 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 490 471 468 508 460 | 500 < 0.00007 0 1 0 1 0 | 0.5 | 2 1 0 1 0 > 0.99993 || = 0.58 481 541 497 455 499 | 500 < 0.00008 1 0 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 519 531 505 462 503 | 500 < 0.00009 0 0 2 0 0 | 0.5 | 0 1 0 0 1 > 0.99991 || = 0.56 516 458 489 473 469 | 500 < 0.0001 1 1 1 1 0 | 0.5 | 0 4 0 2 0 > 0.9999 || = 0.55 478 514 488 503 477 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 509 470 475 480 490 | 500 < 0.0001 4 5 10 4 4 | 5 | 7 9 4 5 5 > 0.9999 || = 0.53 506 514 497 496 513 | 500 < 0.0002 4 6 5 10 5 | 5 | 3 3 2 2 1 > 0.9998 || = 0.52 536 506 502 508 565 | 500 < 0.0003 9 5 10 8 6 | 5 | 6 8 3 1 5 > 0.9997 || = 0.51 477 512 483 507 475 | 500 < 0.0004 5 4 6 4 6 | 5 | 4 2 6 2 10 > 0.9996 || = 0.50 497 516 557 499 485 | 500 < 0.0005 3 5 3 2 6 | 5 | 8 5 9 1 8 > 0.9995 || = 0.49 519 508 517 509 523 | 500 < 0.0006 7 3 4 7 5 | 5 | 7 2 5 7 6 > 0.9994 || = 0.48 497 517 525 489 493 | 500 < 0.0007 4 11 4 5 8 | 5 | 7 3 2 8 3 > 0.9993 || = 0.47 492 512 517 497 504 | 500 < 0.0008 5 6 3 6 7 | 5 | 8 4 5 4 6 > 0.9992 || = 0.46 529 477 480 500 491 | 500 < 0.0009 7 5 7 7 5 | 5 | 6 8 5 3 6 > 0.9991 || = 0.45 501 515 565 541 499 | 500 < 0.001 4 8 9 6 6 | 5 | 6 4 5 5 1 > 0.999 || = 0.44 476 462 478 521 475 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 527 494 472 476 531 | 500 < 0.001 52 58 61 59 58 | 50 | 62 48 46 38 51 > 0.999 || = 0.42 475 471 494 499 484 | 500 < 0.002 60 43 46 44 41 | 50 | 53 56 60 50 41 > 0.998 || = 0.41 448 517 529 508 498 | 500 < 0.003 58 55 50 57 53 | 50 | 64 50 59 54 59 > 0.997 || = 0.40 486 462 491 515 487 | 500 < 0.004 66 51 51 65 51 | 50 | 51 60 53 50 57 > 0.996 || = 0.39 492 476 512 495 490 | 500 < 0.005 42 52 41 54 57 | 50 | 49 59 53 41 58 > 0.995 || = 0.38 498 450 526 518 504 | 500 < 0.006 60 63 50 46 53 | 50 | 61 41 41 49 51 > 0.994 || = 0.37 543 469 541 482 481 | 500 < 0.007 57 42 55 51 57 | 50 | 47 51 34 42 58 > 0.993 || = 0.36 496 496 505 514 507 | 500 < 0.008 52 44 53 45 55 | 50 | 49 59 53 46 53 > 0.992 || = 0.35 466 476 470 497 541 | 500 < 0.009 51 51 46 60 51 | 50 | 46 44 52 48 56 > 0.991 || = 0.34 504 483 445 499 503 | 500 < 0.01 58 51 58 47 46 | 50 | 43 46 66 45 49 > 0.99 || = 0.33 481 503 536 494 474 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 501 493 479 514 466 | 500 < 0.01 556 510 511 528 522 | 497.5 | 525 514 517 463 533 > 0.99 || = 0.31 528 499 488 475 489 | 500 = 0.01 234 247 245 257 223 | 252.5 | 277 252 253 259 271 = 0.99 || = 0.30 484 472 513 491 470 | 500 = 0.02 481 522 472 519 468 | 500 | 491 542 496 550 487 = 0.98 || = 0.29 477 490 542 496 506 | 500 =================================================================| 500 | 494 509 525 516 531 = 0.97 || = 0.28 538 471 492 554 518 | 500 swalk_RandomWalk1 test: | 500 | 525 526 513 489 515 = 0.96 || = 0.27 479 485 532 504 482 | 500 ----------------------------------------------- | 500 | 552 491 527 515 477 = 0.95 || = 0.26 510 534 466 526 482 | 500 N = 1, n = 1000000, r = 0, s = 15, L0 = 10000, L1 = 10000 | 500 | 500 522 511 509 505 = 0.94 || = 0.25 479 476 479 505 523 | 500 Test on the values of the Statistic H | 500 | 479 498 557 550 513 = 0.93 || = 0.24 509 487 501 524 475 | 500 | 500 | 495 518 541 510 506 = 0.92 || = 0.23 479 501 460 498 494 | 500 =================================================================| 500 | 504 507 521 479 507 = 0.91 || = 0.22 505 482 508 493 489 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 510 466 476 497 485 = 0.90 || = 0.21 464 520 510 487 486 | 500 -----------------------------------------------------------------| 500 | 505 498 510 508 513 = 0.89 || = 0.20 485 518 477 484 500 | 500 SD Bern.: d 1.01999 1.18886 1.04646 | 500 | 475 504 471 475 505 = 0.88 || = 0.19 509 489 503 544 493 | 500 s 1.04065 0.91039 0.93426 | 500 | 519 518 523 494 541 = 0.87 || = 0.18 499 510 467 503 514 | 500 t 1.10355 0.81649 1.28203 | 500 | 467 522 494 499 476 = 0.86 || = 0.17 549 498 499 482 507 | 500 m 0.98105 1.05693 0.83826 | 500 | 480 482 463 506 473 = 0.85 || = 0.16 513 504 504 514 572 | 500 x 1.01927 0.78012 0.88019 | 500 | 510 478 488 523 538 = 0.84 || = 0.15 471 541 471 533 475 | 500 | 500 | 515 527 487 500 500 = 0.83 || = 0.14 489 524 477 513 484 | 500 Changes: d 56 2 3 | 500 | 477 523 512 499 489 = 0.82 || = 0.13 523 488 479 474 497 | 500 s 48 4 6 | 500 | 518 528 519 512 508 = 0.81 || = 0.12 499 464 493 492 508 | 500 t 51 6 3 | 500 | 515 542 477 526 484 = 0.80 || = 0.11 459 547 514 508 472 | 500 m 47 7 2 | 500 | 501 530 490 522 500 = 0.79 || = 0.10 497 538 543 470 504 | 500 x 50 3 3 | 500 | 467 519 494 491 509 = 0.78 || = 0.09 505 474 531 475 501 | 500 -----------------------------------------------------------------| 500 | 492 500 486 471 497 = 0.77 || = 0.08 511 507 498 514 529 | 500 Aver./ d 0.50014 499 > 500: 6 4 4 4 4 6 5 5 6 5 | 500 | 526 524 479 487 492 = 0.76 || = 0.07 521 499 464 499 502 | 500 median s 0.50112 501 ----- 6 6 4 1 5 6 3 6 6 7 | 500 | 467 458 506 517 516 = 0.75 || = 0.06 496 480 477 571 493 | 500 t 0.50233 497 3 4 5 6 5 3 5 2 4 9 | 500 | 519 480 513 480 476 = 0.74 || = 0.05 474 516 489 499 459 | 500 m 0.49855 499 5 6 5 3 5 4 2 3 4 7 | 500 | 485 505 499 486 479 = 0.73 || = 0.04 537 508 471 492 542 | 500 x 0.50224 499 5 5 3 4 3 3 6 4 5 8 | 500 | 498 505 489 483 539 = 0.72 || = 0.03 539 519 508 500 461 | 500 -----------------------------------------------------------------| 500 | 517 496 494 483 535 = 0.71 || = 0.02 481 522 472 519 468 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 532 456 507 445 498 = 0.70 || = 0.01 234 247 245 257 223 | 252.5 d 0 0 1 17 66 14 3 0 0 | 500 | 501 448 557 491 503 = 0.69 || < 0.01 556 510 511 528 522 | 497.5 s 0 0 2 20 63 15 1 0 0 | 500 | 490 495 456 488 519 = 0.68 ||========================================================================= t 0 0 1 20 61 15 4 0 0 | 500 | 478 528 514 504 498 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 13 74 8 3 1 0 | 500 | 492 517 532 485 528 = 0.66 ||========================================================================= x 0 0 0 19 64 16 1 1 0 | 500 | 505 475 470 498 512 = 0.65 || swalk_RandomWalk1 test: no 166 test no 167 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 167 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 1 1 0 | 0.5 | 1 0 0 0 0 > 0.99999 || = 0.64 484 518 481 491 472 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 0 0 1 0 1 > 0.99998 || = 0.63 521 529 470 509 464 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 3 0 0 0 2 > 0.99997 || = 0.62 496 486 516 482 467 | 500 < 0.00004 0 0 1 0 0 | 0.5 | 0 2 0 0 1 > 0.99996 || = 0.61 516 496 506 472 517 | 500 < 0.00005 0 0 1 1 1 | 0.5 | 1 0 0 1 1 > 0.99995 || = 0.60 472 497 462 485 521 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 1 1 1 0 0 > 0.99994 || = 0.59 488 481 498 480 483 | 500 < 0.00007 0 0 0 2 0 | 0.5 | 0 1 0 1 0 > 0.99993 || = 0.58 499 515 503 516 472 | 500 < 0.00008 1 1 0 0 1 | 0.5 | 1 0 0 1 0 > 0.99992 || = 0.57 450 513 508 502 475 | 500 < 0.00009 0 0 2 1 1 | 0.5 | 1 0 0 0 0 > 0.99991 || = 0.56 503 506 479 517 475 | 500 < 0.0001 0 0 4 0 1 | 0.5 | 1 0 1 0 2 > 0.9999 || = 0.55 535 470 481 498 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 499 491 504 481 488 | 500 < 0.0001 2 2 9 6 4 | 5 | 9 4 3 3 7 > 0.9999 || = 0.53 551 510 494 488 501 | 500 < 0.0002 3 9 5 6 3 | 5 | 5 2 3 3 4 > 0.9998 || = 0.52 497 484 511 523 538 | 500 < 0.0003 4 2 1 3 6 | 5 | 6 6 9 2 10 > 0.9997 || = 0.51 517 480 512 515 475 | 500 < 0.0004 8 3 3 3 2 | 5 | 5 7 4 8 13 > 0.9996 || = 0.50 484 493 468 438 543 | 500 < 0.0005 10 7 5 6 2 | 5 | 5 3 1 3 5 > 0.9995 || = 0.49 464 476 477 505 513 | 500 < 0.0006 6 1 5 5 10 | 5 | 8 6 3 4 8 > 0.9994 || = 0.48 489 495 505 541 501 | 500 < 0.0007 7 4 3 5 6 | 5 | 6 5 1 2 6 > 0.9993 || = 0.47 508 488 512 527 515 | 500 < 0.0008 2 2 11 2 4 | 5 | 4 7 6 1 7 > 0.9992 || = 0.46 497 495 483 510 498 | 500 < 0.0009 7 4 2 7 6 | 5 | 4 5 4 3 4 > 0.9991 || = 0.45 494 513 501 495 512 | 500 < 0.001 8 7 8 8 7 | 5 | 6 8 2 5 4 > 0.999 || = 0.44 491 490 480 496 476 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 466 506 479 495 505 | 500 < 0.001 57 41 52 51 50 | 50 | 58 53 36 34 68 > 0.999 || = 0.42 499 462 506 514 527 | 500 < 0.002 56 47 51 47 56 | 50 | 61 44 49 67 48 > 0.998 || = 0.41 524 519 491 491 499 | 500 < 0.003 43 57 47 54 69 | 50 | 48 53 41 49 50 > 0.997 || = 0.40 478 509 525 508 521 | 500 < 0.004 49 59 43 57 44 | 50 | 45 56 52 59 64 > 0.996 || = 0.39 533 517 477 530 434 | 500 < 0.005 47 61 55 56 60 | 50 | 49 32 44 41 61 > 0.995 || = 0.38 486 487 485 505 481 | 500 < 0.006 53 47 59 42 52 | 50 | 56 33 48 45 48 > 0.994 || = 0.37 506 491 482 481 523 | 500 < 0.007 43 42 44 60 45 | 50 | 52 53 50 50 51 > 0.993 || = 0.36 441 512 458 508 476 | 500 < 0.008 54 56 46 57 65 | 50 | 51 46 44 53 55 > 0.992 || = 0.35 461 493 536 492 522 | 500 < 0.009 39 55 59 59 50 | 50 | 53 37 51 51 44 > 0.991 || = 0.34 472 482 503 499 485 | 500 < 0.01 38 52 59 51 51 | 50 | 43 48 62 62 52 > 0.99 || = 0.33 480 498 516 475 501 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 514 535 499 498 469 | 500 < 0.01 479 517 515 534 542 | 497.5 | 516 455 477 511 541 > 0.99 || = 0.31 522 489 500 503 486 | 500 = 0.01 244 259 253 261 271 | 252.5 | 267 276 277 276 245 = 0.99 || = 0.30 510 485 482 472 448 | 500 = 0.02 517 490 518 464 515 | 500 | 503 544 504 546 481 = 0.98 || = 0.29 505 474 506 475 484 | 500 =================================================================| 500 | 495 525 518 467 478 = 0.97 || = 0.28 492 490 499 495 517 | 500 swalk_RandomWalk1 test: | 500 | 521 490 497 514 494 = 0.96 || = 0.27 483 522 515 482 506 | 500 ----------------------------------------------- | 500 | 524 524 505 515 520 = 0.95 || = 0.26 488 508 505 492 491 | 500 N = 1, n = 1000000, r = 0, s = 15, L0 = 10000, L1 = 10000 | 500 | 524 521 504 531 497 = 0.94 || = 0.25 501 473 547 514 472 | 500 Test on the values of the Statistic M | 500 | 510 482 508 497 507 = 0.93 || = 0.24 488 520 507 521 476 | 500 | 500 | 504 483 514 520 462 = 0.92 || = 0.23 522 495 526 517 520 | 500 =================================================================| 500 | 501 491 497 514 481 = 0.91 || = 0.22 453 518 488 485 456 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 517 475 525 459 557 = 0.90 || = 0.21 466 493 523 469 515 | 500 -----------------------------------------------------------------| 500 | 528 492 513 520 484 = 0.89 || = 0.20 445 491 490 456 509 | 500 SD Bern.: d 1.03091 0.98334 0.79284 | 500 | 509 515 483 494 524 = 0.88 || = 0.19 536 485 483 513 522 | 500 s 0.85399 0.97925 1.34304 | 500 | 468 478 469 468 507 = 0.87 || = 0.18 507 528 514 499 457 | 500 t 0.92732 0.87564 1.00348 | 500 | 509 539 539 468 503 = 0.86 || = 0.17 537 489 512 484 512 | 500 m 1.03828 0.90155 1.33257 | 500 | 482 526 467 506 491 = 0.85 || = 0.16 500 511 519 513 536 | 500 x 1.08873 1.25600 1.19641 | 500 | 517 485 521 515 499 = 0.84 || = 0.15 513 520 473 465 473 | 500 | 500 | 487 505 513 518 518 = 0.83 || = 0.14 502 518 493 524 525 | 500 Changes: d 53 5 3 | 500 | 478 491 497 503 497 = 0.82 || = 0.13 487 503 463 522 534 | 500 s 53 3 5 | 500 | 512 514 506 541 526 = 0.81 || = 0.12 487 482 489 510 456 | 500 t 53 4 3 | 500 | 531 516 474 518 495 = 0.80 || = 0.11 514 494 440 473 468 | 500 m 48 4 5 | 500 | 511 486 461 506 521 = 0.79 || = 0.10 498 499 521 529 491 | 500 x 60 7 6 | 500 | 497 460 518 506 518 = 0.78 || = 0.09 482 458 512 486 545 | 500 -----------------------------------------------------------------| 500 | 551 508 485 483 488 = 0.77 || = 0.08 478 516 514 471 487 | 500 Aver./ d 0.50219 501 > 500: 4 6 3 5 2 4 7 6 6 9 | 500 | 483 510 514 532 520 = 0.76 || = 0.07 513 478 491 526 508 | 500 median s 0.50024 498 ----- 6 5 4 3 4 4 6 5 5 5 | 500 | 469 489 526 454 486 = 0.75 || = 0.06 483 516 523 456 504 | 500 t 0.50014 504 8 4 7 3 5 5 6 5 6 7 | 500 | 512 529 510 511 527 = 0.74 || = 0.05 533 521 505 498 518 | 500 m 0.50168 503 4 6 3 4 6 5 4 6 6 8 | 500 | 505 463 497 471 530 = 0.73 || = 0.04 491 512 534 525 476 | 500 x 0.50040 501 8 5 5 3 7 4 3 6 6 3 | 500 | 477 514 476 470 492 = 0.72 || = 0.03 533 500 468 499 507 | 500 -----------------------------------------------------------------| 500 | 532 475 515 503 522 = 0.71 || = 0.02 517 490 518 464 515 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 505 506 509 556 485 = 0.70 || = 0.01 244 259 253 261 271 | 252.5 d 0 0 4 10 72 13 2 0 0 | 500 | 502 522 497 525 498 = 0.69 || < 0.01 479 517 515 534 542 | 497.5 s 0 0 0 11 80 10 0 0 0 | 500 | 458 509 521 488 515 = 0.68 ||========================================================================= t 0 0 1 15 72 12 1 0 0 | 500 | 544 495 529 500 492 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 18 64 15 2 0 0 | 500 | 518 518 530 471 478 = 0.66 ||========================================================================= x 0 0 2 19 63 14 3 0 0 | 500 | 509 498 468 523 517 = 0.65 || swalk_RandomWalk1 test: no 167 test no 168 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 168 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 1 1 0 | 0.5 | 1 1 1 1 2 > 0.99999 || = 0.64 524 481 546 490 527 | 500 < 0.00002 0 0 1 1 0 | 0.5 | 2 2 1 0 0 > 0.99998 || = 0.63 484 496 515 497 474 | 500 < 0.00003 0 0 1 0 1 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 496 454 480 486 491 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99996 || = 0.61 465 478 512 527 502 | 500 < 0.00005 0 0 1 0 1 | 0.5 | 0 0 0 1 1 > 0.99995 || = 0.60 517 490 501 483 484 | 500 < 0.00006 1 1 1 1 2 | 0.5 | 1 0 0 1 0 > 0.99994 || = 0.59 524 509 496 480 517 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 1 0 1 0 0 > 0.99993 || = 0.58 511 506 494 494 492 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 481 511 488 532 461 | 500 < 0.00009 0 1 1 1 0 | 0.5 | 0 0 2 0 4 > 0.99991 || = 0.56 509 497 519 478 502 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 471 494 505 494 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 490 495 474 486 496 | 500 < 0.0001 1 4 6 6 4 | 5 | 6 4 5 5 7 > 0.9999 || = 0.53 498 513 502 491 490 | 500 < 0.0002 7 4 4 4 5 | 5 | 0 1 1 3 5 > 0.9998 || = 0.52 490 498 522 535 522 | 500 < 0.0003 6 6 4 5 6 | 5 | 4 6 5 5 8 > 0.9997 || = 0.51 486 518 501 534 491 | 500 < 0.0004 2 3 11 5 4 | 5 | 5 7 6 1 4 > 0.9996 || = 0.50 536 497 486 510 494 | 500 < 0.0005 3 5 7 3 2 | 5 | 5 3 4 3 9 > 0.9995 || = 0.49 486 501 489 512 462 | 500 < 0.0006 3 5 5 3 4 | 5 | 3 4 4 5 5 > 0.9994 || = 0.48 505 472 500 503 518 | 500 < 0.0007 1 8 6 5 8 | 5 | 5 7 6 9 4 > 0.9993 || = 0.47 463 530 485 535 521 | 500 < 0.0008 3 5 1 6 2 | 5 | 3 6 8 3 4 > 0.9992 || = 0.46 447 506 524 498 529 | 500 < 0.0009 1 5 2 7 4 | 5 | 9 8 2 4 3 > 0.9991 || = 0.45 485 497 529 483 492 | 500 < 0.001 5 4 7 8 7 | 5 | 5 5 4 7 3 > 0.999 || = 0.44 484 497 489 481 524 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 506 515 486 537 499 | 500 < 0.001 32 49 53 52 46 | 50 | 45 51 45 45 52 > 0.999 || = 0.42 480 463 519 490 545 | 500 < 0.002 42 61 59 53 45 | 50 | 60 47 51 52 49 > 0.998 || = 0.41 536 445 500 516 510 | 500 < 0.003 46 49 51 50 46 | 50 | 53 38 39 41 44 > 0.997 || = 0.40 497 514 498 505 496 | 500 < 0.004 62 54 52 44 49 | 50 | 52 41 50 53 42 > 0.996 || = 0.39 527 446 516 478 514 | 500 < 0.005 44 35 50 62 43 | 50 | 44 58 47 47 44 > 0.995 || = 0.38 503 476 522 468 456 | 500 < 0.006 43 41 55 56 41 | 50 | 46 54 44 41 51 > 0.994 || = 0.37 478 490 487 529 493 | 500 < 0.007 47 44 52 44 60 | 50 | 52 55 48 43 42 > 0.993 || = 0.36 492 501 517 500 483 | 500 < 0.008 46 49 51 53 48 | 50 | 58 53 46 43 49 > 0.992 || = 0.35 480 503 519 548 501 | 500 < 0.009 39 61 50 58 53 | 50 | 44 56 44 45 55 > 0.991 || = 0.34 484 506 507 535 507 | 500 < 0.01 41 58 39 52 59 | 50 | 43 50 45 58 48 > 0.99 || = 0.33 513 479 523 500 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 501 501 524 504 516 | 500 < 0.01 442 501 512 524 490 | 497.5 | 497 503 459 468 476 > 0.99 || = 0.31 479 506 470 497 497 | 500 = 0.01 246 289 219 256 248 | 252.5 | 238 244 237 245 270 = 0.99 || = 0.30 531 513 509 480 513 | 500 = 0.02 513 503 487 493 502 | 500 | 534 497 480 512 530 = 0.98 || = 0.29 473 542 505 485 494 | 500 =================================================================| 500 | 551 519 501 475 492 = 0.97 || = 0.28 504 507 534 472 505 | 500 swalk_RandomWalk1 test: | 500 | 469 507 494 502 502 = 0.96 || = 0.27 480 489 536 506 531 | 500 ----------------------------------------------- | 500 | 501 469 517 498 517 = 0.95 || = 0.26 522 496 503 518 527 | 500 N = 1, n = 1000000, r = 0, s = 15, L0 = 10000, L1 = 10000 | 500 | 518 505 537 538 486 = 0.94 || = 0.25 499 503 522 497 512 | 500 Test on the values of the Statistic J | 500 | 494 554 504 481 515 = 0.93 || = 0.24 486 487 497 517 468 | 500 | 500 | 520 539 487 521 527 = 0.92 || = 0.23 485 495 508 506 474 | 500 =================================================================| 500 | 507 481 503 462 507 = 0.91 || = 0.22 534 502 489 522 473 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 469 517 468 522 480 = 0.90 || = 0.21 546 492 451 517 493 | 500 -----------------------------------------------------------------| 500 | 504 514 485 486 474 = 0.89 || = 0.20 533 518 489 480 524 | 500 SD Bern.: d 0.96927 1.31213 0.82865 | 500 | 536 482 470 489 540 = 0.88 || = 0.19 515 496 500 482 475 | 500 s 1.02066 1.15556 0.87792 | 500 | 481 502 486 487 502 = 0.87 || = 0.18 488 493 468 520 476 | 500 t 0.87125 0.70176 0.73927 | 500 | 500 451 484 513 484 = 0.86 || = 0.17 506 527 481 487 554 | 500 m 0.88978 0.82745 0.89037 | 500 | 476 490 523 501 539 = 0.85 || = 0.16 498 489 493 475 518 | 500 x 0.94951 0.87449 0.68735 | 500 | 490 500 488 509 477 = 0.84 || = 0.15 500 516 512 466 511 | 500 | 500 | 495 486 500 514 529 = 0.83 || = 0.14 529 468 480 471 514 | 500 Changes: d 58 2 4 | 500 | 514 460 518 502 487 = 0.82 || = 0.13 524 516 521 478 511 | 500 s 52 5 3 | 500 | 495 466 488 520 519 = 0.81 || = 0.12 518 510 498 496 477 | 500 t 53 3 2 | 500 | 551 538 524 498 464 = 0.80 || = 0.11 497 525 494 510 496 | 500 m 49 4 5 | 500 | 485 464 511 522 459 = 0.79 || = 0.10 510 508 511 502 482 | 500 x 52 3 5 | 500 | 485 491 518 483 479 = 0.78 || = 0.09 490 468 487 510 503 | 500 -----------------------------------------------------------------| 500 | 489 499 462 523 514 = 0.77 || = 0.08 502 522 530 493 495 | 500 Aver./ d 0.49988 498 > 500: 5 6 5 5 3 4 3 4 3 6 | 500 | 536 484 491 496 525 = 0.76 || = 0.07 498 534 479 528 467 | 500 median s 0.49888 501 ----- 7 6 5 6 5 5 4 4 3 6 | 500 | 492 555 506 448 521 = 0.75 || = 0.06 509 497 496 467 482 | 500 t 0.49912 500 4 3 6 8 3 6 6 6 2 5 | 500 | 502 546 494 485 506 = 0.74 || = 0.05 515 508 518 518 500 | 500 m 0.49918 498 7 3 6 4 6 3 3 2 7 4 | 500 | 522 500 491 481 510 = 0.73 || = 0.04 487 522 479 515 499 | 500 x 0.50062 501 3 5 5 5 6 4 7 5 5 7 | 500 | 457 473 508 496 470 = 0.72 || = 0.03 511 496 528 515 506 | 500 -----------------------------------------------------------------| 500 | 493 506 517 497 451 = 0.71 || = 0.02 513 503 487 493 502 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 482 512 478 497 516 = 0.70 || = 0.01 246 289 219 256 248 | 252.5 d 0 0 2 8 74 14 3 0 0 | 500 | 526 478 502 473 471 = 0.69 || < 0.01 442 501 512 524 490 | 497.5 s 0 0 4 11 73 9 4 0 0 | 500 | 490 539 499 513 503 = 0.68 ||========================================================================= t 0 0 2 8 79 11 1 0 0 | 500 | 494 529 511 497 514 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 10 77 12 1 0 0 | 500 | 509 513 465 498 504 = 0.66 ||========================================================================= x 0 0 1 17 68 13 2 0 0 | 500 | 479 470 513 506 501 = 0.65 || swalk_RandomWalk1 test: no 168 test no 169 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 169 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 2 1 0 1 | 0.5 | 1 0 0 1 0 > 0.99999 || = 0.64 489 528 484 488 511 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 1 0 1 0 0 > 0.99998 || = 0.63 494 509 485 464 517 | 500 < 0.00003 0 0 0 0 1 | 0.5 | 1 0 0 0 1 > 0.99997 || = 0.62 489 488 533 485 483 | 500 < 0.00004 1 1 0 0 0 | 0.5 | 0 1 0 1 0 > 0.99996 || = 0.61 480 488 467 485 505 | 500 < 0.00005 0 1 1 0 0 | 0.5 | 0 0 1 0 2 > 0.99995 || = 0.60 489 501 487 532 495 | 500 < 0.00006 0 1 1 1 1 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 529 476 494 471 453 | 500 < 0.00007 0 0 1 1 1 | 0.5 | 0 0 1 0 1 > 0.99993 || = 0.58 505 499 486 530 508 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 1 1 0 1 > 0.99992 || = 0.57 503 496 508 503 494 | 500 < 0.00009 2 0 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 502 539 478 531 510 | 500 < 0.0001 0 3 1 0 0 | 0.5 | 1 0 1 1 0 > 0.9999 || = 0.55 484 521 503 492 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 502 490 526 509 496 | 500 < 0.0001 5 8 5 3 5 | 5 | 4 3 6 3 5 > 0.9999 || = 0.53 511 500 474 497 507 | 500 < 0.0002 4 8 3 8 3 | 5 | 6 5 4 2 3 > 0.9998 || = 0.52 524 503 510 502 474 | 500 < 0.0003 5 8 6 8 9 | 5 | 4 5 3 2 4 > 0.9997 || = 0.51 530 467 516 492 503 | 500 < 0.0004 2 5 2 8 6 | 5 | 6 4 6 5 6 > 0.9996 || = 0.50 499 466 472 487 515 | 500 < 0.0005 3 2 6 2 6 | 5 | 6 1 3 8 3 > 0.9995 || = 0.49 517 491 525 509 519 | 500 < 0.0006 5 4 5 5 4 | 5 | 8 5 3 3 3 > 0.9994 || = 0.48 501 447 504 501 493 | 500 < 0.0007 6 4 3 8 1 | 5 | 1 6 6 2 4 > 0.9993 || = 0.47 527 510 535 513 505 | 500 < 0.0008 4 4 2 4 8 | 5 | 6 3 4 7 8 > 0.9992 || = 0.46 511 539 473 484 496 | 500 < 0.0009 2 4 8 3 8 | 5 | 9 4 2 4 1 > 0.9991 || = 0.45 511 467 470 501 500 | 500 < 0.001 4 7 6 4 5 | 5 | 4 7 3 9 10 > 0.999 || = 0.44 477 502 483 469 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 492 535 492 525 477 | 500 < 0.001 40 54 46 53 55 | 50 | 54 43 40 45 47 > 0.999 || = 0.42 466 498 485 486 514 | 500 < 0.002 42 48 54 56 48 | 50 | 41 71 50 41 67 > 0.998 || = 0.41 549 504 506 462 497 | 500 < 0.003 51 52 53 56 58 | 50 | 64 41 54 51 49 > 0.997 || = 0.40 500 485 467 546 480 | 500 < 0.004 39 42 49 43 46 | 50 | 57 47 57 50 47 > 0.996 || = 0.39 484 526 516 522 461 | 500 < 0.005 64 35 49 59 65 | 50 | 51 68 50 41 50 > 0.995 || = 0.38 499 501 521 516 536 | 500 < 0.006 48 55 54 43 52 | 50 | 56 38 48 50 46 > 0.994 || = 0.37 483 488 481 504 484 | 500 < 0.007 46 53 49 56 36 | 50 | 53 44 50 50 59 > 0.993 || = 0.36 510 492 464 496 516 | 500 < 0.008 40 50 55 45 77 | 50 | 46 57 46 50 53 > 0.992 || = 0.35 478 523 507 524 465 | 500 < 0.009 47 54 54 66 59 | 50 | 56 57 65 54 44 > 0.991 || = 0.34 531 528 466 492 460 | 500 < 0.01 52 50 45 59 48 | 50 | 48 51 49 44 60 > 0.99 || = 0.33 523 542 523 506 458 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 512 513 506 522 504 | 500 < 0.01 469 493 508 536 544 | 497.5 | 526 517 509 476 522 > 0.99 || = 0.31 492 497 502 487 518 | 500 = 0.01 265 254 253 264 245 | 252.5 | 240 256 245 258 249 = 0.99 || = 0.30 490 494 524 501 479 | 500 = 0.02 532 438 447 531 516 | 500 | 473 492 510 505 495 = 0.98 || = 0.29 497 561 515 476 494 | 500 =================================================================| 500 | 520 561 482 492 506 = 0.97 || = 0.28 516 485 492 515 448 | 500 swalk_RandomWalk1 test: | 500 | 541 513 533 527 497 = 0.96 || = 0.27 489 475 483 497 517 | 500 ----------------------------------------------- | 500 | 483 505 499 483 496 = 0.95 || = 0.26 481 496 525 507 489 | 500 N = 1, n = 1000000, r = 0, s = 15, L0 = 10000, L1 = 10000 | 500 | 537 512 475 510 512 = 0.94 || = 0.25 498 488 458 483 484 | 500 Test on the values of the Statistic R | 500 | 505 488 513 514 495 = 0.93 || = 0.24 482 490 521 542 521 | 500 | 500 | 510 480 490 512 513 = 0.92 || = 0.23 511 490 466 499 501 | 500 =================================================================| 500 | 516 505 502 467 493 = 0.91 || = 0.22 478 495 479 498 515 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 480 475 515 479 471 = 0.90 || = 0.21 550 525 486 505 519 | 500 -----------------------------------------------------------------| 500 | 464 518 519 492 497 = 0.89 || = 0.20 491 491 491 541 558 | 500 SD Bern.: d 1.05342 1.10960 0.94279 | 500 | 503 487 487 524 480 = 0.88 || = 0.19 453 535 515 511 539 | 500 s 0.95191 0.85247 1.53894 | 500 | 522 499 540 493 497 = 0.87 || = 0.18 533 533 480 518 492 | 500 t 0.98462 0.50223 0.90708 | 500 | 497 507 483 499 506 = 0.86 || = 0.17 494 508 481 519 543 | 500 m 0.90778 1.14773 0.69315 | 500 | 487 490 463 485 460 = 0.85 || = 0.16 533 532 500 474 512 | 500 x 0.98650 1.64276 1.04932 | 500 | 510 465 499 509 485 = 0.84 || = 0.15 488 508 505 536 514 | 500 | 500 | 550 478 474 523 501 = 0.83 || = 0.14 481 502 494 497 523 | 500 Changes: d 51 5 5 | 500 | 490 497 504 475 509 = 0.82 || = 0.13 484 496 542 503 485 | 500 s 51 7 5 | 500 | 530 482 502 471 488 = 0.81 || = 0.12 527 495 521 487 488 | 500 t 53 6 4 | 500 | 475 474 534 488 509 = 0.80 || = 0.11 454 515 542 511 516 | 500 m 55 6 4 | 500 | 464 514 497 490 512 = 0.79 || = 0.10 488 486 529 506 490 | 500 x 56 7 5 | 500 | 465 470 540 499 503 = 0.78 || = 0.09 500 471 504 495 520 | 500 -----------------------------------------------------------------| 500 | 505 484 539 464 486 = 0.77 || = 0.08 435 517 480 481 497 | 500 Aver./ d 0.50070 498 > 500: 4 3 3 4 6 8 3 3 5 7 | 500 | 497 488 545 491 466 = 0.76 || = 0.07 494 501 521 446 574 | 500 median s 0.49994 497 ----- 4 7 2 6 5 4 4 4 2 7 | 500 | 476 528 515 497 468 = 0.75 || = 0.06 554 494 527 494 491 | 500 t 0.50058 500 6 6 3 7 4 5 3 6 5 5 | 500 | 510 494 530 497 505 = 0.74 || = 0.05 488 483 498 477 483 | 500 m 0.49837 499 4 7 5 7 6 6 3 1 3 6 | 500 | 492 518 478 497 489 = 0.73 || = 0.04 495 502 478 473 514 | 500 x 0.49743 500 6 6 6 4 3 4 7 6 3 4 | 500 | 520 517 485 524 507 = 0.72 || = 0.03 514 491 512 519 508 | 500 -----------------------------------------------------------------| 500 | 467 491 488 480 508 = 0.71 || = 0.02 532 438 447 531 516 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 535 515 483 518 533 = 0.70 || = 0.01 265 254 253 264 245 | 252.5 d 0 0 3 11 67 16 4 0 0 | 500 | 484 499 496 488 513 = 0.69 || < 0.01 469 493 508 536 544 | 497.5 s 0 0 2 10 74 13 2 0 0 | 500 | 527 495 501 529 480 = 0.68 ||========================================================================= t 0 0 1 13 69 17 1 0 0 | 500 | 461 511 500 484 528 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 13 71 15 1 0 0 | 500 | 501 478 510 514 506 = 0.66 ||========================================================================= x 0 0 3 10 78 7 2 1 0 | 500 | 480 494 489 471 450 = 0.65 || swalk_RandomWalk1 test: no 169 test no 170 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 170 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 0 | 0.5 | 0 1 0 0 1 > 0.99999 || = 0.64 521 497 491 521 483 | 500 < 0.00002 0 0 1 1 1 | 0.5 | 1 1 3 0 1 > 0.99998 || = 0.63 478 515 519 502 445 | 500 < 0.00003 1 2 0 0 1 | 0.5 | 2 1 0 0 0 > 0.99997 || = 0.62 510 488 538 487 494 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 1 3 1 1 1 > 0.99996 || = 0.61 554 488 453 479 523 | 500 < 0.00005 1 2 1 0 1 | 0.5 | 0 2 0 2 0 > 0.99995 || = 0.60 513 502 474 492 462 | 500 < 0.00006 0 0 1 1 0 | 0.5 | 1 1 1 0 0 > 0.99994 || = 0.59 485 504 541 512 516 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 2 0 > 0.99993 || = 0.58 505 472 485 517 509 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 0 0 1 2 0 > 0.99992 || = 0.57 489 542 548 499 517 | 500 < 0.00009 1 1 1 2 1 | 0.5 | 0 0 1 0 0 > 0.99991 || = 0.56 510 496 488 508 449 | 500 < 0.0001 1 0 0 0 0 | 0.5 | 0 1 0 0 1 > 0.9999 || = 0.55 460 528 472 485 527 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 514 515 475 485 516 | 500 < 0.0001 4 7 4 5 4 | 5 | 5 10 7 7 4 > 0.9999 || = 0.53 521 505 490 545 508 | 500 < 0.0002 3 4 5 3 3 | 5 | 3 1 2 2 4 > 0.9998 || = 0.52 459 501 504 478 552 | 500 < 0.0003 5 4 5 7 7 | 5 | 2 8 8 5 1 > 0.9997 || = 0.51 486 513 492 484 485 | 500 < 0.0004 3 3 8 6 7 | 5 | 2 6 4 3 6 > 0.9996 || = 0.50 514 474 499 474 490 | 500 < 0.0005 4 7 7 6 7 | 5 | 3 4 7 4 7 > 0.9995 || = 0.49 506 500 470 505 534 | 500 < 0.0006 11 0 4 7 7 | 5 | 5 2 5 7 3 > 0.9994 || = 0.48 553 526 471 484 502 | 500 < 0.0007 4 6 6 7 10 | 5 | 2 6 2 3 10 > 0.9993 || = 0.47 513 527 472 525 488 | 500 < 0.0008 7 2 1 2 12 | 5 | 2 5 2 5 6 > 0.9992 || = 0.46 486 470 501 489 493 | 500 < 0.0009 5 7 4 2 8 | 5 | 3 4 4 5 10 > 0.9991 || = 0.45 510 507 471 461 490 | 500 < 0.001 9 4 5 5 4 | 5 | 5 6 7 7 5 > 0.999 || = 0.44 471 511 533 491 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 506 494 488 476 526 | 500 < 0.001 55 44 49 50 69 | 50 | 32 52 48 48 56 > 0.999 || = 0.42 481 504 513 496 484 | 500 < 0.002 50 49 55 55 36 | 50 | 59 35 46 60 53 > 0.998 || = 0.41 532 496 462 469 492 | 500 < 0.003 58 61 49 54 32 | 50 | 40 61 54 55 60 > 0.997 || = 0.40 511 511 483 485 497 | 500 < 0.004 40 48 37 39 44 | 50 | 40 40 44 60 54 > 0.996 || = 0.39 509 513 520 493 517 | 500 < 0.005 43 56 58 43 41 | 50 | 49 48 51 48 49 > 0.995 || = 0.38 471 483 498 510 487 | 500 < 0.006 51 53 41 58 60 | 50 | 54 45 48 59 47 > 0.994 || = 0.37 503 510 484 500 517 | 500 < 0.007 41 55 41 50 57 | 50 | 45 60 43 53 42 > 0.993 || = 0.36 452 431 489 530 467 | 500 < 0.008 43 50 54 64 52 | 50 | 63 45 63 60 56 > 0.992 || = 0.35 460 488 512 487 509 | 500 < 0.009 47 39 57 43 42 | 50 | 54 55 50 60 53 > 0.991 || = 0.34 541 472 498 455 509 | 500 < 0.01 51 61 43 66 53 | 50 | 55 46 51 57 59 > 0.99 || = 0.33 485 495 472 482 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 471 470 506 485 508 | 500 < 0.01 479 516 484 522 486 | 497.5 | 491 487 498 560 529 > 0.99 || = 0.31 502 507 501 481 504 | 500 = 0.01 268 277 264 263 258 | 252.5 | 220 276 252 243 212 = 0.99 || = 0.30 469 505 530 536 492 | 500 = 0.02 495 510 534 508 516 | 500 | 539 510 515 465 486 = 0.98 || = 0.29 513 471 502 539 509 | 500 =================================================================| 500 | 522 511 503 500 514 = 0.97 || = 0.28 480 500 478 520 488 | 500 swalk_RandomWalk1 test: | 500 | 484 491 536 486 462 = 0.96 || = 0.27 522 473 509 527 486 | 500 ----------------------------------------------- | 500 | 476 493 482 504 496 = 0.95 || = 0.26 477 507 499 478 495 | 500 N = 1, n = 1000000, r = 0, s = 15, L0 = 10000, L1 = 10000 | 500 | 504 483 528 483 512 = 0.94 || = 0.25 523 517 477 508 500 | 500 Test on the values of the Statistic C | 500 | 530 483 533 503 464 = 0.93 || = 0.24 514 486 494 507 498 | 500 | 500 | 535 535 530 478 524 = 0.92 || = 0.23 508 510 493 490 505 | 500 =================================================================| 500 | 500 522 495 506 526 = 0.91 || = 0.22 462 530 471 463 486 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 514 500 507 521 524 = 0.90 || = 0.21 470 514 504 494 512 | 500 -----------------------------------------------------------------| 500 | 513 535 481 519 513 = 0.89 || = 0.20 459 514 505 507 480 | 500 SD Bern.: d 1.18852 0.87106 1.30984 | 500 | 553 507 455 510 538 = 0.88 || = 0.19 467 494 512 488 459 | 500 s 1.01285 0.97413 1.13634 | 500 | 481 461 529 508 529 = 0.87 || = 0.18 463 486 547 495 492 | 500 t 1.05234 1.03588 0.76979 | 500 | 488 473 498 502 507 = 0.86 || = 0.17 522 493 501 467 511 | 500 m 0.97994 1.24641 1.07010 | 500 | 501 500 432 503 485 = 0.85 || = 0.16 497 497 495 512 556 | 500 x 1.02681 1.56538 0.85011 | 500 | 485 473 500 499 495 = 0.84 || = 0.15 492 512 534 516 511 | 500 | 500 | 487 519 489 503 503 = 0.83 || = 0.14 514 554 480 502 513 | 500 Changes: d 62 6 5 | 500 | 493 488 515 530 512 = 0.82 || = 0.13 491 527 511 526 517 | 500 s 47 5 7 | 500 | 452 525 470 495 520 = 0.81 || = 0.12 503 537 497 510 476 | 500 t 51 6 7 | 500 | 486 477 538 488 516 = 0.80 || = 0.11 496 509 467 488 475 | 500 m 44 7 3 | 500 | 451 481 480 510 543 = 0.79 || = 0.10 509 486 519 526 467 | 500 x 47 4 2 | 500 | 517 533 474 512 469 = 0.78 || = 0.09 522 520 494 512 474 | 500 -----------------------------------------------------------------| 500 | 552 480 497 539 488 = 0.77 || = 0.08 534 471 463 459 495 | 500 Aver./ d 0.50132 503 > 500: 6 4 5 4 7 5 7 5 4 5 | 500 | 528 434 496 512 466 = 0.76 || = 0.07 505 465 518 538 528 | 500 median s 0.49979 502 ----- 5 5 6 4 6 8 5 5 4 5 | 500 | 500 447 470 508 481 = 0.75 || = 0.06 448 479 523 520 500 | 500 t 0.50031 498 5 6 4 5 3 3 7 4 3 7 | 500 | 525 519 495 459 481 = 0.74 || = 0.05 534 471 520 489 506 | 500 m 0.49992 500 7 6 6 3 2 4 5 5 8 4 | 500 | 447 501 556 455 521 = 0.73 || = 0.04 492 508 491 493 533 | 500 x 0.49993 500 6 5 3 6 3 7 3 4 8 5 | 500 | 506 503 507 473 479 = 0.72 || = 0.03 533 477 498 506 526 | 500 -----------------------------------------------------------------| 500 | 496 510 512 496 506 = 0.71 || = 0.02 495 510 534 508 516 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 511 524 518 555 484 = 0.70 || = 0.01 268 277 264 263 258 | 252.5 d 0 0 6 16 61 13 5 0 0 | 500 | 546 499 516 473 516 = 0.69 || < 0.01 479 516 484 522 486 | 497.5 s 0 1 2 15 67 15 1 0 0 | 500 | 472 505 497 514 492 = 0.68 ||========================================================================= t 0 1 2 16 65 13 4 0 0 | 500 | 544 534 545 526 533 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 11 73 12 3 0 0 | 500 | 534 514 518 500 456 = 0.66 ||========================================================================= x 0 0 3 12 69 15 2 0 0 | 500 | 474 496 506 481 483 = 0.65 || swalk_RandomWalk1 test: no 170 test no 171 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 171 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 1 0 | 0.5 | 0 0 2 0 0 > 0.99999 || = 0.64 502 458 496 485 499 | 500 < 0.00002 1 0 1 1 0 | 0.5 | 0 0 0 1 0 > 0.99998 || = 0.63 496 508 503 532 548 | 500 < 0.00003 0 0 0 3 1 | 0.5 | 2 0 0 0 0 > 0.99997 || = 0.62 483 478 536 520 478 | 500 < 0.00004 0 0 0 0 1 | 0.5 | 0 1 1 1 0 > 0.99996 || = 0.61 478 501 536 488 497 | 500 < 0.00005 0 0 2 0 1 | 0.5 | 1 0 0 0 0 > 0.99995 || = 0.60 514 494 483 520 521 | 500 < 0.00006 0 1 1 0 0 | 0.5 | 0 0 0 0 1 > 0.99994 || = 0.59 532 475 487 525 525 | 500 < 0.00007 0 0 1 0 1 | 0.5 | 0 3 2 0 0 > 0.99993 || = 0.58 478 526 479 524 487 | 500 < 0.00008 1 0 1 0 2 | 0.5 | 0 0 2 0 1 > 0.99992 || = 0.57 501 506 459 502 501 | 500 < 0.00009 0 2 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99991 || = 0.56 498 493 483 475 487 | 500 < 0.0001 4 1 0 1 0 | 0.5 | 4 0 0 2 0 > 0.9999 || = 0.55 521 462 478 518 530 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 519 526 483 517 487 | 500 < 0.0001 7 4 7 6 6 | 5 | 8 4 8 4 2 > 0.9999 || = 0.53 521 518 498 497 472 | 500 < 0.0002 10 7 5 5 7 | 5 | 3 5 4 8 2 > 0.9998 || = 0.52 497 485 512 473 498 | 500 < 0.0003 7 6 1 5 6 | 5 | 6 4 6 8 5 > 0.9997 || = 0.51 521 496 569 491 503 | 500 < 0.0004 4 5 5 8 8 | 5 | 3 2 12 6 6 > 0.9996 || = 0.50 505 514 521 497 515 | 500 < 0.0005 2 13 2 7 3 | 5 | 1 6 5 3 3 > 0.9995 || = 0.49 485 500 508 465 494 | 500 < 0.0006 2 4 7 8 5 | 5 | 6 6 4 3 8 > 0.9994 || = 0.48 498 554 486 519 514 | 500 < 0.0007 6 1 12 4 2 | 5 | 8 7 7 6 2 > 0.9993 || = 0.47 522 499 512 500 515 | 500 < 0.0008 2 7 4 6 6 | 5 | 6 1 1 6 3 > 0.9992 || = 0.46 500 518 484 477 496 | 500 < 0.0009 3 4 8 5 8 | 5 | 3 4 8 7 5 > 0.9991 || = 0.45 453 519 485 482 506 | 500 < 0.001 6 5 3 4 1 | 5 | 6 4 6 6 4 > 0.999 || = 0.44 491 491 497 528 515 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 520 496 531 503 473 | 500 < 0.001 49 56 54 58 52 | 50 | 50 43 61 57 40 > 0.999 || = 0.42 520 520 502 510 507 | 500 < 0.002 59 56 49 49 40 | 50 | 38 50 44 45 40 > 0.998 || = 0.41 515 504 518 495 531 | 500 < 0.003 44 44 40 41 58 | 50 | 71 60 48 43 48 > 0.997 || = 0.40 471 480 511 469 523 | 500 < 0.004 50 51 62 60 55 | 50 | 62 40 58 57 57 > 0.996 || = 0.39 520 486 542 499 479 | 500 < 0.005 49 38 54 53 39 | 50 | 52 48 51 62 50 > 0.995 || = 0.38 479 510 494 548 489 | 500 < 0.006 53 64 41 59 44 | 50 | 62 43 61 45 47 > 0.994 || = 0.37 489 516 525 497 502 | 500 < 0.007 49 53 52 51 52 | 50 | 37 54 40 41 52 > 0.993 || = 0.36 509 466 516 514 497 | 500 < 0.008 47 53 51 50 52 | 50 | 58 53 68 39 48 > 0.992 || = 0.35 508 481 471 503 514 | 500 < 0.009 42 43 44 39 51 | 50 | 47 52 47 54 66 > 0.991 || = 0.34 502 508 491 506 497 | 500 < 0.01 64 46 51 47 31 | 50 | 56 40 56 56 53 > 0.99 || = 0.33 527 538 518 488 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 506 493 495 509 504 | 500 < 0.01 506 504 498 507 474 | 497.5 | 533 483 534 499 501 > 0.99 || = 0.31 503 480 491 513 503 | 500 = 0.01 258 274 256 231 249 | 252.5 | 273 248 256 229 249 = 0.99 || = 0.30 478 517 460 512 474 | 500 = 0.02 483 490 494 432 512 | 500 | 493 478 483 489 525 = 0.98 || = 0.29 512 519 473 476 469 | 500 =================================================================| 500 | 492 499 484 539 498 = 0.97 || = 0.28 523 519 527 492 557 | 500 swalk_RandomWalk1 test: | 500 | 535 491 511 503 506 = 0.96 || = 0.27 474 499 500 484 495 | 500 ----------------------------------------------- | 500 | 549 520 499 473 482 = 0.95 || = 0.26 484 525 484 505 509 | 500 N = 1, n = 1000000, r = 15, s = 15, L0 = 10000, L1 = 10000 | 500 | 493 511 487 529 535 = 0.94 || = 0.25 485 501 494 501 487 | 500 Test on the values of the Statistic H | 500 | 493 471 515 471 490 = 0.93 || = 0.24 501 512 508 540 530 | 500 | 500 | 498 513 503 485 499 = 0.92 || = 0.23 494 498 484 477 491 | 500 =================================================================| 500 | 513 503 541 502 501 = 0.91 || = 0.22 487 462 530 524 514 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 520 493 512 509 431 = 0.90 || = 0.21 500 476 473 552 461 | 500 -----------------------------------------------------------------| 500 | 497 502 469 514 555 = 0.89 || = 0.20 514 450 491 483 473 | 500 SD Bern.: d 0.85083 0.89263 1.52062 | 500 | 487 516 503 447 497 = 0.88 || = 0.19 487 508 498 483 493 | 500 s 0.84997 1.03201 0.92889 | 500 | 488 488 541 516 503 = 0.87 || = 0.18 473 473 495 474 500 | 500 t 0.98762 0.89486 1.27812 | 500 | 520 525 517 521 520 = 0.86 || = 0.17 519 500 491 523 525 | 500 m 0.99848 0.96691 1.09140 | 500 | 496 488 475 490 507 = 0.85 || = 0.16 481 522 489 529 491 | 500 x 1.01190 1.20059 1.03492 | 500 | 463 501 493 494 498 = 0.84 || = 0.15 499 521 495 449 511 | 500 | 500 | 494 508 535 482 499 = 0.83 || = 0.14 461 523 458 497 460 | 500 Changes: d 48 5 5 | 500 | 509 492 503 506 465 = 0.82 || = 0.13 523 529 477 512 507 | 500 s 51 5 4 | 500 | 493 503 482 467 443 = 0.81 || = 0.12 489 500 451 506 484 | 500 t 41 6 6 | 500 | 488 524 525 523 482 = 0.80 || = 0.11 471 503 468 476 539 | 500 m 50 3 4 | 500 | 499 471 517 500 487 = 0.79 || = 0.10 480 468 492 497 523 | 500 x 63 5 5 | 500 | 496 512 484 500 481 = 0.78 || = 0.09 499 505 494 543 534 | 500 -----------------------------------------------------------------| 500 | 504 507 496 496 473 = 0.77 || = 0.08 501 505 507 466 506 | 500 Aver./ d 0.50242 499 > 500: 4 2 4 7 4 7 5 5 3 5 | 500 | 514 508 457 526 508 = 0.76 || = 0.07 453 518 507 478 494 | 500 median s 0.49971 501 ----- 5 6 5 5 5 4 3 7 6 4 | 500 | 509 478 520 508 478 = 0.75 || = 0.06 493 482 489 476 477 | 500 t 0.50236 497 5 0 3 4 6 2 7 5 6 6 | 500 | 467 491 494 494 484 = 0.74 || = 0.05 499 496 545 529 509 | 500 m 0.50110 501 3 4 5 7 4 6 6 6 5 5 | 500 | 508 521 482 506 482 = 0.73 || = 0.04 499 483 492 485 513 | 500 x 0.49940 499 5 5 4 5 7 5 5 2 4 5 | 500 | 501 511 527 514 501 = 0.72 || = 0.03 511 484 488 490 478 | 500 -----------------------------------------------------------------| 500 | 496 531 530 502 498 = 0.71 || = 0.02 483 490 494 432 512 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 515 499 497 524 496 = 0.70 || = 0.01 258 274 256 231 249 | 252.5 d 0 0 2 7 82 8 2 0 0 | 500 | 531 483 513 503 502 = 0.69 || < 0.01 506 504 498 507 474 | 497.5 s 0 0 1 10 79 10 1 0 0 | 500 | 503 485 522 493 521 = 0.68 ||========================================================================= t 0 0 1 12 72 14 1 1 0 | 500 | 548 488 510 527 503 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 2 16 64 16 2 0 0 | 500 | 479 502 509 493 474 = 0.66 ||========================================================================= x 0 1 1 12 72 11 3 1 0 | 500 | 482 491 466 508 574 = 0.65 || swalk_RandomWalk1 test: no 171 test no 172 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 172 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 2 2 1 0 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 479 498 481 459 526 | 500 < 0.00002 0 0 1 2 0 | 0.5 | 0 2 1 1 1 > 0.99998 || = 0.63 489 512 547 500 492 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 1 0 2 0 3 > 0.99997 || = 0.62 528 541 508 482 479 | 500 < 0.00004 0 1 0 1 2 | 0.5 | 0 0 0 1 0 > 0.99996 || = 0.61 481 510 469 470 507 | 500 < 0.00005 2 0 0 0 0 | 0.5 | 0 1 0 1 1 > 0.99995 || = 0.60 467 500 488 487 471 | 500 < 0.00006 0 1 0 2 2 | 0.5 | 0 2 0 0 2 > 0.99994 || = 0.59 544 487 502 516 475 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 503 449 535 485 517 | 500 < 0.00008 1 0 0 0 0 | 0.5 | 0 2 0 1 0 > 0.99992 || = 0.57 534 471 493 495 506 | 500 < 0.00009 1 0 0 1 0 | 0.5 | 0 2 1 1 0 > 0.99991 || = 0.56 488 531 492 556 509 | 500 < 0.0001 2 0 0 0 0 | 0.5 | 1 3 0 0 0 > 0.9999 || = 0.55 500 490 522 502 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 489 547 510 539 490 | 500 < 0.0001 6 4 3 7 4 | 5 | 2 12 4 6 7 > 0.9999 || = 0.53 485 495 529 494 510 | 500 < 0.0002 2 6 3 4 2 | 5 | 2 0 2 4 0 > 0.9998 || = 0.52 528 489 482 492 518 | 500 < 0.0003 4 3 6 8 6 | 5 | 8 6 5 4 3 > 0.9997 || = 0.51 525 487 469 474 452 | 500 < 0.0004 4 5 5 9 3 | 5 | 8 4 8 6 8 > 0.9996 || = 0.50 484 454 467 507 512 | 500 < 0.0005 4 7 7 4 3 | 5 | 3 7 9 4 7 > 0.9995 || = 0.49 498 510 532 479 500 | 500 < 0.0006 5 3 5 8 1 | 5 | 5 3 10 9 7 > 0.9994 || = 0.48 507 509 526 489 489 | 500 < 0.0007 2 9 7 4 0 | 5 | 6 8 4 5 7 > 0.9993 || = 0.47 458 495 493 485 504 | 500 < 0.0008 15 8 2 3 5 | 5 | 2 10 5 4 5 > 0.9992 || = 0.46 489 496 511 522 490 | 500 < 0.0009 6 6 3 4 7 | 5 | 7 6 8 5 5 > 0.9991 || = 0.45 502 505 495 505 545 | 500 < 0.001 8 5 7 3 5 | 5 | 8 2 7 11 4 > 0.999 || = 0.44 505 516 503 486 481 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 477 468 481 495 466 | 500 < 0.001 56 56 48 54 36 | 50 | 51 58 62 58 53 > 0.999 || = 0.42 512 490 474 519 502 | 500 < 0.002 47 52 54 50 40 | 50 | 49 50 47 40 53 > 0.998 || = 0.41 506 502 459 506 468 | 500 < 0.003 50 51 62 61 55 | 50 | 49 63 46 57 69 > 0.997 || = 0.40 510 512 539 528 506 | 500 < 0.004 57 42 56 58 63 | 50 | 55 37 51 51 54 > 0.996 || = 0.39 503 510 546 519 513 | 500 < 0.005 53 63 42 59 50 | 50 | 42 65 53 55 46 > 0.995 || = 0.38 504 506 492 469 498 | 500 < 0.006 62 56 52 44 56 | 50 | 44 66 44 45 52 > 0.994 || = 0.37 497 463 490 507 508 | 500 < 0.007 40 47 47 49 50 | 50 | 51 44 45 46 44 > 0.993 || = 0.36 522 512 511 491 485 | 500 < 0.008 54 43 46 62 39 | 50 | 50 52 42 46 62 > 0.992 || = 0.35 502 481 503 484 475 | 500 < 0.009 39 63 52 44 41 | 50 | 53 55 53 54 63 > 0.991 || = 0.34 479 489 476 483 480 | 500 < 0.01 56 49 55 58 59 | 50 | 44 52 44 39 57 > 0.99 || = 0.33 482 527 491 537 558 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 474 503 495 486 484 | 500 < 0.01 514 522 514 539 489 | 497.5 | 488 542 487 491 553 > 0.99 || = 0.31 498 514 472 527 513 | 500 = 0.01 262 246 248 275 285 | 252.5 | 289 241 227 269 216 = 0.99 || = 0.30 502 497 519 489 527 | 500 = 0.02 484 512 498 527 498 | 500 | 498 519 530 538 527 = 0.98 || = 0.29 494 484 478 531 496 | 500 =================================================================| 500 | 475 512 497 518 505 = 0.97 || = 0.28 502 494 526 476 518 | 500 swalk_RandomWalk1 test: | 500 | 537 470 509 530 517 = 0.96 || = 0.27 528 467 513 465 477 | 500 ----------------------------------------------- | 500 | 510 496 506 534 519 = 0.95 || = 0.26 493 476 489 522 491 | 500 N = 1, n = 1000000, r = 15, s = 15, L0 = 10000, L1 = 10000 | 500 | 500 476 506 546 509 = 0.94 || = 0.25 485 511 495 476 475 | 500 Test on the values of the Statistic M | 500 | 468 493 492 477 505 = 0.93 || = 0.24 547 486 501 477 483 | 500 | 500 | 524 474 475 492 469 = 0.92 || = 0.23 513 529 498 477 489 | 500 =================================================================| 500 | 485 536 493 524 492 = 0.91 || = 0.22 490 511 501 517 472 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 508 493 510 502 529 = 0.90 || = 0.21 491 515 491 489 521 | 500 -----------------------------------------------------------------| 500 | 514 540 500 545 470 = 0.89 || = 0.20 512 510 480 517 509 | 500 SD Bern.: d 0.95585 1.02030 0.59019 | 500 | 487 503 510 501 512 = 0.88 || = 0.19 509 547 485 504 517 | 500 s 1.01405 1.03781 1.38053 | 500 | 523 524 506 448 495 = 0.87 || = 0.18 475 503 491 525 508 | 500 t 0.98203 0.80289 0.83587 | 500 | 462 515 472 491 494 = 0.86 || = 0.17 494 497 460 481 501 | 500 m 1.05516 1.06165 0.93104 | 500 | 523 485 462 516 506 = 0.85 || = 0.16 498 501 533 477 485 | 500 x 1.03289 1.27263 1.27577 | 500 | 469 511 554 502 480 = 0.84 || = 0.15 513 535 534 480 507 | 500 | 500 | 508 518 537 506 505 = 0.83 || = 0.14 478 456 487 490 502 | 500 Changes: d 57 6 7 | 500 | 509 500 501 503 475 = 0.82 || = 0.13 524 462 528 476 520 | 500 s 46 5 6 | 500 | 510 515 520 468 489 = 0.81 || = 0.12 519 507 510 479 483 | 500 t 49 5 5 | 500 | 471 519 494 466 506 = 0.80 || = 0.11 517 486 509 532 491 | 500 m 43 6 5 | 500 | 479 510 504 495 503 = 0.79 || = 0.10 484 492 528 551 511 | 500 x 57 5 4 | 500 | 511 504 536 514 506 = 0.78 || = 0.09 531 472 484 490 480 | 500 -----------------------------------------------------------------| 500 | 536 466 498 514 501 = 0.77 || = 0.08 509 506 467 480 500 | 500 Aver./ d 0.49922 502 > 500: 6 5 5 5 6 5 3 5 7 4 | 500 | 437 478 515 464 513 = 0.76 || = 0.07 485 517 506 484 528 | 500 median s 0.50067 502 ----- 6 5 5 6 6 2 5 6 7 4 | 500 | 530 524 454 511 470 = 0.75 || = 0.06 515 514 514 519 496 | 500 t 0.50076 498 4 6 4 4 5 5 3 6 7 4 | 500 | 502 540 521 473 537 = 0.74 || = 0.05 499 524 503 478 533 | 500 m 0.50073 495 4 4 4 4 5 4 3 4 7 7 | 500 | 477 469 515 485 485 = 0.73 || = 0.04 479 493 474 498 513 | 500 x 0.49967 502 5 7 3 5 4 6 5 7 4 7 | 500 | 455 511 510 520 512 = 0.72 || = 0.03 517 468 465 488 507 | 500 -----------------------------------------------------------------| 500 | 533 476 494 467 448 = 0.71 || = 0.02 484 512 498 527 498 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 492 531 483 517 519 = 0.70 || = 0.01 262 246 248 275 285 | 252.5 d 0 0 2 12 70 15 2 0 0 | 500 | 505 520 487 519 550 = 0.69 || < 0.01 514 522 514 539 489 | 497.5 s 0 0 2 18 65 13 3 0 0 | 500 | 487 457 476 523 541 = 0.68 ||========================================================================= t 0 0 1 16 67 14 3 0 0 | 500 | 476 468 530 483 459 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 18 62 16 4 0 0 | 500 | 519 475 495 464 480 = 0.66 ||========================================================================= x 0 0 4 13 71 8 5 0 0 | 500 | 491 480 482 500 445 = 0.65 || swalk_RandomWalk1 test: no 172 test no 173 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 173 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 1 | 0.5 | 1 1 0 0 0 > 0.99999 || = 0.64 533 502 488 531 537 | 500 < 0.00002 0 1 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 477 467 490 537 490 | 500 < 0.00003 0 2 1 1 1 | 0.5 | 1 1 1 0 0 > 0.99997 || = 0.62 484 507 519 442 494 | 500 < 0.00004 0 0 0 0 1 | 0.5 | 2 0 0 0 0 > 0.99996 || = 0.61 482 519 528 509 515 | 500 < 0.00005 2 0 0 2 0 | 0.5 | 1 0 2 0 0 > 0.99995 || = 0.60 500 539 479 465 450 | 500 < 0.00006 1 3 1 0 0 | 0.5 | 0 0 2 0 0 > 0.99994 || = 0.59 547 530 521 471 488 | 500 < 0.00007 3 1 0 0 0 | 0.5 | 1 1 0 0 0 > 0.99993 || = 0.58 492 478 506 499 461 | 500 < 0.00008 1 0 0 0 1 | 0.5 | 0 0 0 1 1 > 0.99992 || = 0.57 473 537 482 533 475 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 0 1 0 1 1 > 0.99991 || = 0.56 512 515 492 522 484 | 500 < 0.0001 0 1 0 1 2 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 497 457 514 427 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 518 507 470 495 498 | 500 < 0.0001 7 8 3 6 6 | 5 | 6 4 7 2 2 > 0.9999 || = 0.53 499 539 516 480 478 | 500 < 0.0002 4 5 12 3 4 | 5 | 4 5 3 1 5 > 0.9998 || = 0.52 502 496 538 506 465 | 500 < 0.0003 4 7 4 6 4 | 5 | 4 5 10 5 3 > 0.9997 || = 0.51 508 475 459 485 488 | 500 < 0.0004 5 4 9 3 5 | 5 | 8 4 6 3 3 > 0.9996 || = 0.50 495 482 521 477 512 | 500 < 0.0005 2 7 0 8 4 | 5 | 8 6 4 6 4 > 0.9995 || = 0.49 506 489 470 503 497 | 500 < 0.0006 2 3 4 5 6 | 5 | 7 5 9 6 9 > 0.9994 || = 0.48 491 512 499 503 486 | 500 < 0.0007 7 5 4 7 2 | 5 | 3 5 4 6 6 > 0.9993 || = 0.47 504 515 505 472 496 | 500 < 0.0008 5 5 2 6 4 | 5 | 3 3 4 5 10 > 0.9992 || = 0.46 486 479 553 512 458 | 500 < 0.0009 5 2 6 7 9 | 5 | 2 8 6 6 5 > 0.9991 || = 0.45 486 493 532 523 502 | 500 < 0.001 4 4 4 4 2 | 5 | 7 5 3 2 10 > 0.999 || = 0.44 511 487 555 525 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 492 460 490 508 458 | 500 < 0.001 45 50 48 55 46 | 50 | 52 50 56 42 57 > 0.999 || = 0.42 501 515 551 482 470 | 500 < 0.002 46 44 60 41 46 | 50 | 44 49 57 53 48 > 0.998 || = 0.41 477 522 504 481 500 | 500 < 0.003 56 54 49 57 57 | 50 | 44 57 58 56 57 > 0.997 || = 0.40 468 510 501 499 499 | 500 < 0.004 41 33 48 56 43 | 50 | 50 54 48 47 51 > 0.996 || = 0.39 512 476 508 535 563 | 500 < 0.005 53 42 50 58 40 | 50 | 51 50 48 57 48 > 0.995 || = 0.38 475 524 494 505 509 | 500 < 0.006 59 42 55 52 38 | 50 | 55 48 61 41 51 > 0.994 || = 0.37 503 494 482 481 475 | 500 < 0.007 42 58 65 66 45 | 50 | 50 48 43 33 50 > 0.993 || = 0.36 500 492 471 527 512 | 500 < 0.008 55 51 48 36 44 | 50 | 50 39 44 64 49 > 0.992 || = 0.35 515 482 471 507 492 | 500 < 0.009 46 44 40 50 53 | 50 | 57 52 38 53 60 > 0.991 || = 0.34 493 506 469 501 481 | 500 < 0.01 43 70 55 64 48 | 50 | 47 52 51 39 42 > 0.99 || = 0.33 531 493 503 486 537 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 501 489 521 491 513 | 500 < 0.01 486 488 518 535 460 | 497.5 | 500 499 504 485 513 > 0.99 || = 0.31 507 528 507 528 494 | 500 = 0.01 253 243 248 255 251 | 252.5 | 258 251 255 252 259 = 0.99 || = 0.30 448 446 500 539 475 | 500 = 0.02 530 442 453 513 521 | 500 | 492 506 508 506 502 = 0.98 || = 0.29 522 507 505 501 535 | 500 =================================================================| 500 | 490 518 469 491 500 = 0.97 || = 0.28 531 516 505 525 443 | 500 swalk_RandomWalk1 test: | 500 | 483 523 502 436 588 = 0.96 || = 0.27 469 520 500 517 539 | 500 ----------------------------------------------- | 500 | 500 489 487 512 480 = 0.95 || = 0.26 534 499 535 496 489 | 500 N = 1, n = 1000000, r = 15, s = 15, L0 = 10000, L1 = 10000 | 500 | 478 472 516 482 507 = 0.94 || = 0.25 515 511 471 506 524 | 500 Test on the values of the Statistic J | 500 | 507 474 489 524 493 = 0.93 || = 0.24 492 487 491 521 514 | 500 | 500 | 505 507 510 517 499 = 0.92 || = 0.23 511 528 479 516 501 | 500 =================================================================| 500 | 516 529 529 519 537 = 0.91 || = 0.22 528 512 508 512 496 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 502 496 526 474 474 = 0.90 || = 0.21 502 494 519 498 511 | 500 -----------------------------------------------------------------| 500 | 494 511 500 480 515 = 0.89 || = 0.20 503 479 503 483 532 | 500 SD Bern.: d 0.82186 0.89710 0.56595 | 500 | 494 514 515 559 522 = 0.88 || = 0.19 495 476 447 509 516 | 500 s 1.01696 1.39353 0.63748 | 500 | 479 493 463 484 496 = 0.87 || = 0.18 499 498 497 515 525 | 500 t 1.04114 0.98841 1.00846 | 500 | 504 484 525 506 528 = 0.86 || = 0.17 524 513 485 506 518 | 500 m 1.03038 1.34751 1.31442 | 500 | 489 464 503 452 481 = 0.85 || = 0.16 503 461 514 528 526 | 500 x 1.08682 0.94704 0.73927 | 500 | 534 508 541 516 451 = 0.84 || = 0.15 538 496 527 516 516 | 500 | 500 | 491 530 460 500 487 = 0.83 || = 0.14 529 501 502 471 476 | 500 Changes: d 54 6 5 | 500 | 487 531 495 517 473 = 0.82 || = 0.13 513 505 462 488 480 | 500 s 49 5 3 | 500 | 482 474 475 524 467 = 0.81 || = 0.12 486 523 475 490 511 | 500 t 50 5 4 | 500 | 484 494 506 476 497 = 0.80 || = 0.11 491 499 486 514 499 | 500 m 49 4 6 | 500 | 509 498 485 506 511 = 0.79 || = 0.10 479 520 526 487 496 | 500 x 49 4 7 | 500 | 490 502 490 500 476 = 0.78 || = 0.09 485 484 500 498 505 | 500 -----------------------------------------------------------------| 500 | 491 538 524 503 499 = 0.77 || = 0.08 494 462 464 511 497 | 500 Aver./ d 0.49882 500 > 500: 5 5 8 6 4 5 5 3 3 5 | 500 | 529 470 478 513 484 = 0.76 || = 0.07 482 466 483 467 501 | 500 median s 0.50183 501 ----- 2 5 6 3 5 6 7 6 5 6 | 500 | 506 521 492 470 515 = 0.75 || = 0.06 508 521 501 498 472 | 500 t 0.50137 502 4 4 6 4 7 5 4 6 5 7 | 500 | 455 517 515 486 515 = 0.74 || = 0.05 486 498 534 496 503 | 500 m 0.49871 503 4 6 7 7 6 3 6 5 5 5 | 500 | 496 505 512 508 505 = 0.73 || = 0.04 503 530 459 490 487 | 500 x 0.50052 499 4 6 7 5 2 0 6 6 3 6 | 500 | 469 469 523 490 560 = 0.72 || = 0.03 505 488 517 472 499 | 500 -----------------------------------------------------------------| 500 | 486 508 521 508 511 = 0.71 || = 0.02 530 442 453 513 521 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 521 501 518 541 522 = 0.70 || = 0.01 253 243 248 255 251 | 252.5 d 0 0 2 7 79 12 1 0 0 | 500 | 516 506 461 487 494 = 0.69 || < 0.01 486 488 518 535 460 | 497.5 s 0 0 2 15 69 14 0 1 0 | 500 | 496 478 517 482 509 = 0.68 ||========================================================================= t 0 0 2 17 66 13 3 0 0 | 500 | 513 498 496 457 534 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 3 11 70 15 1 0 0 | 500 | 536 517 473 513 505 = 0.66 ||========================================================================= x 0 0 3 15 69 11 2 1 0 | 500 | 496 576 494 503 491 = 0.65 || swalk_RandomWalk1 test: no 173 test no 174 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 174 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 1 0 | 0.5 | 3 1 0 0 0 > 0.99999 || = 0.64 475 478 521 487 498 | 500 < 0.00002 0 0 2 1 1 | 0.5 | 1 1 1 0 2 > 0.99998 || = 0.63 485 529 480 512 500 | 500 < 0.00003 0 2 0 0 0 | 0.5 | 0 1 0 1 0 > 0.99997 || = 0.62 493 491 499 507 508 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 1 2 0 2 1 > 0.99996 || = 0.61 505 502 529 525 488 | 500 < 0.00005 2 0 2 0 0 | 0.5 | 1 1 2 0 0 > 0.99995 || = 0.60 488 499 493 482 487 | 500 < 0.00006 0 0 0 2 0 | 0.5 | 0 1 0 0 1 > 0.99994 || = 0.59 529 484 531 496 494 | 500 < 0.00007 1 1 0 0 2 | 0.5 | 0 1 0 0 3 > 0.99993 || = 0.58 535 510 518 529 483 | 500 < 0.00008 0 1 0 0 1 | 0.5 | 0 1 1 1 1 > 0.99992 || = 0.57 495 514 436 492 462 | 500 < 0.00009 1 1 1 0 1 | 0.5 | 0 1 0 1 0 > 0.99991 || = 0.56 513 518 507 531 487 | 500 < 0.0001 1 0 1 0 1 | 0.5 | 1 0 1 2 0 > 0.9999 || = 0.55 518 500 535 492 472 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 492 489 512 458 466 | 500 < 0.0001 5 7 6 4 6 | 5 | 7 10 5 7 8 > 0.9999 || = 0.53 496 488 485 491 446 | 500 < 0.0002 0 6 5 7 2 | 5 | 2 2 2 0 2 > 0.9998 || = 0.52 490 487 519 555 539 | 500 < 0.0003 4 3 7 7 6 | 5 | 5 2 5 4 4 > 0.9997 || = 0.51 525 492 506 507 493 | 500 < 0.0004 6 6 4 4 3 | 5 | 6 6 12 6 4 > 0.9996 || = 0.50 490 491 510 496 506 | 500 < 0.0005 9 5 3 4 9 | 5 | 6 8 9 6 7 > 0.9995 || = 0.49 497 509 517 497 506 | 500 < 0.0006 3 6 5 4 6 | 5 | 5 5 3 2 4 > 0.9994 || = 0.48 531 531 476 512 489 | 500 < 0.0007 5 4 1 4 3 | 5 | 3 7 9 2 6 > 0.9993 || = 0.47 503 488 526 504 487 | 500 < 0.0008 6 4 6 12 6 | 5 | 5 9 5 8 0 > 0.9992 || = 0.46 487 477 480 486 488 | 500 < 0.0009 9 6 9 10 6 | 5 | 4 3 3 4 7 > 0.9991 || = 0.45 497 503 499 502 509 | 500 < 0.001 8 3 5 7 5 | 5 | 2 4 7 6 7 > 0.999 || = 0.44 470 525 482 474 520 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 502 493 492 469 479 | 500 < 0.001 55 50 51 63 52 | 50 | 45 56 60 45 49 > 0.999 || = 0.42 514 514 523 522 522 | 500 < 0.002 64 45 54 41 43 | 50 | 47 49 46 47 51 > 0.998 || = 0.41 490 511 493 471 486 | 500 < 0.003 45 54 43 60 48 | 50 | 54 52 50 44 52 > 0.997 || = 0.40 453 457 483 491 477 | 500 < 0.004 53 56 40 42 45 | 50 | 54 46 37 55 46 > 0.996 || = 0.39 485 505 525 493 505 | 500 < 0.005 52 53 54 54 38 | 50 | 47 43 51 48 68 > 0.995 || = 0.38 532 496 457 509 505 | 500 < 0.006 38 54 57 50 53 | 50 | 54 55 36 48 54 > 0.994 || = 0.37 484 525 537 469 495 | 500 < 0.007 54 63 34 53 55 | 50 | 53 43 59 51 53 > 0.993 || = 0.36 467 486 533 504 549 | 500 < 0.008 51 48 47 59 50 | 50 | 61 56 58 37 44 > 0.992 || = 0.35 517 507 510 536 511 | 500 < 0.009 60 44 57 51 61 | 50 | 53 55 50 46 59 > 0.991 || = 0.34 506 556 520 522 482 | 500 < 0.01 51 48 48 41 47 | 50 | 56 43 39 39 43 > 0.99 || = 0.33 505 501 488 477 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 516 490 515 525 527 | 500 < 0.01 523 515 485 514 492 | 497.5 | 524 498 486 460 519 > 0.99 || = 0.31 495 464 466 493 519 | 500 = 0.01 231 265 249 226 239 | 252.5 | 256 248 249 250 240 = 0.99 || = 0.30 474 518 482 501 485 | 500 = 0.02 497 499 492 509 461 | 500 | 503 537 508 503 474 = 0.98 || = 0.29 456 510 477 494 560 | 500 =================================================================| 500 | 516 490 504 503 532 = 0.97 || = 0.28 501 532 532 481 506 | 500 swalk_RandomWalk1 test: | 500 | 488 515 499 502 505 = 0.96 || = 0.27 521 475 470 506 500 | 500 ----------------------------------------------- | 500 | 495 508 511 495 473 = 0.95 || = 0.26 506 552 487 531 498 | 500 N = 1, n = 1000000, r = 15, s = 15, L0 = 10000, L1 = 10000 | 500 | 489 493 516 496 492 = 0.94 || = 0.25 480 493 486 487 520 | 500 Test on the values of the Statistic R | 500 | 490 507 492 480 488 = 0.93 || = 0.24 489 500 499 525 502 | 500 | 500 | 469 510 468 483 512 = 0.92 || = 0.23 510 496 488 478 529 | 500 =================================================================| 500 | 530 498 550 429 465 = 0.91 || = 0.22 452 513 527 513 502 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 508 489 511 443 489 = 0.90 || = 0.21 468 473 507 546 511 | 500 -----------------------------------------------------------------| 500 | 515 492 522 484 496 = 0.89 || = 0.20 525 472 482 539 516 | 500 SD Bern.: d 0.89886 1.02128 0.72973 | 500 | 519 487 474 474 497 = 0.88 || = 0.19 503 507 498 473 458 | 500 s 0.89946 0.79411 0.76195 | 500 | 520 475 501 498 513 = 0.87 || = 0.18 528 501 530 500 509 | 500 t 0.96736 1.04837 1.22371 | 500 | 490 518 486 487 494 = 0.86 || = 0.17 468 517 506 483 526 | 500 m 1.05010 1.09781 0.90598 | 500 | 486 506 490 521 508 = 0.85 || = 0.16 475 512 476 521 485 | 500 x 0.91733 0.88361 1.03684 | 500 | 506 503 498 561 518 = 0.84 || = 0.15 530 509 507 499 513 | 500 | 500 | 492 518 481 494 530 = 0.83 || = 0.14 487 522 495 500 487 | 500 Changes: d 42 4 3 | 500 | 502 476 489 470 543 = 0.82 || = 0.13 511 514 530 499 476 | 500 s 48 2 7 | 500 | 489 499 449 530 510 = 0.81 || = 0.12 512 481 492 518 507 | 500 t 50 5 5 | 500 | 486 497 511 511 480 = 0.80 || = 0.11 513 465 500 499 512 | 500 m 53 7 4 | 500 | 498 465 488 515 496 = 0.79 || = 0.10 526 494 507 520 485 | 500 x 49 5 6 | 500 | 458 497 506 497 497 = 0.78 || = 0.09 507 508 497 484 480 | 500 -----------------------------------------------------------------| 500 | 514 512 514 512 492 = 0.77 || = 0.08 520 470 495 497 521 | 500 Aver./ d 0.49969 501 > 500: 6 7 5 5 4 5 6 2 6 5 | 500 | 537 461 538 475 536 = 0.76 || = 0.07 519 525 482 474 500 | 500 median s 0.49977 501 ----- 6 7 4 6 6 3 5 5 4 6 | 500 | 482 508 516 470 498 = 0.75 || = 0.06 522 504 508 501 502 | 500 t 0.49977 499 3 5 3 6 3 7 5 7 3 5 | 500 | 485 506 484 458 514 = 0.74 || = 0.05 496 456 517 494 532 | 500 m 0.49780 499 5 3 6 6 4 4 6 6 3 3 | 500 | 491 536 498 545 520 = 0.73 || = 0.04 487 494 473 533 513 | 500 x 0.49982 498 4 5 8 6 4 1 4 4 6 4 | 500 | 473 512 502 508 480 = 0.72 || = 0.03 523 505 550 523 482 | 500 -----------------------------------------------------------------| 500 | 475 476 507 508 507 = 0.71 || = 0.02 497 499 492 509 461 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 509 531 508 544 514 = 0.70 || = 0.01 231 265 249 226 239 | 252.5 d 0 0 2 13 71 15 0 0 0 | 500 | 512 503 514 489 478 = 0.69 || < 0.01 523 515 485 514 492 | 497.5 s 0 0 1 15 74 9 2 0 0 | 500 | 494 509 467 515 512 = 0.68 ||========================================================================= t 0 0 3 11 72 13 2 0 0 | 500 | 522 498 473 496 491 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 1 15 68 12 4 0 0 | 500 | 533 454 449 488 489 = 0.66 ||========================================================================= x 0 0 1 10 79 9 2 0 0 | 500 | 504 461 512 522 519 = 0.65 || swalk_RandomWalk1 test: no 174 test no 175 TestU01 250000 runs BigCrush Test smarsa_S swalk_RandomWalk1 test: test no 175 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 2 0 0 | 0.5 | 2 0 1 1 0 > 0.99999 || = 0.64 511 485 497 459 513 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 521 487 506 483 506 | 500 < 0.00003 0 0 1 0 1 | 0.5 | 0 0 1 1 2 > 0.99997 || = 0.62 500 497 547 492 491 | 500 < 0.00004 0 0 0 3 0 | 0.5 | 0 0 0 1 1 > 0.99996 || = 0.61 518 476 460 518 521 | 500 < 0.00005 0 2 1 0 0 | 0.5 | 1 1 0 0 0 > 0.99995 || = 0.60 508 520 548 484 488 | 500 < 0.00006 0 1 1 0 1 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 480 441 526 538 478 | 500 < 0.00007 1 1 1 1 1 | 0.5 | 0 2 0 0 0 > 0.99993 || = 0.58 488 518 488 490 470 | 500 < 0.00008 0 0 1 1 0 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 481 530 497 487 474 | 500 < 0.00009 0 2 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 488 515 536 476 541 | 500 < 0.0001 0 0 1 0 2 | 0.5 | 0 1 1 0 1 > 0.9999 || = 0.55 520 485 511 524 490 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 512 487 473 505 460 | 500 < 0.0001 1 7 9 6 6 | 5 | 4 5 3 3 5 > 0.9999 || = 0.53 462 531 504 496 514 | 500 < 0.0002 6 5 6 8 6 | 5 | 2 1 2 0 4 > 0.9998 || = 0.52 513 462 480 538 506 | 500 < 0.0003 3 4 6 5 4 | 5 | 1 3 7 2 3 > 0.9997 || = 0.51 450 498 518 502 513 | 500 < 0.0004 9 5 3 3 7 | 5 | 7 3 3 5 8 > 0.9996 || = 0.50 502 483 499 537 506 | 500 < 0.0005 7 10 3 9 3 | 5 | 6 8 3 6 6 > 0.9995 || = 0.49 493 521 489 527 475 | 500 < 0.0006 3 4 3 4 2 | 5 | 9 3 5 2 10 > 0.9994 || = 0.48 501 468 475 479 494 | 500 < 0.0007 10 3 3 4 8 | 5 | 10 6 4 7 7 > 0.9993 || = 0.47 525 544 504 467 492 | 500 < 0.0008 5 4 7 6 8 | 5 | 8 5 6 8 3 > 0.9992 || = 0.46 540 547 493 508 514 | 500 < 0.0009 5 6 11 6 5 | 5 | 1 7 3 4 5 > 0.9991 || = 0.45 450 515 476 479 501 | 500 < 0.001 7 8 7 6 6 | 5 | 5 12 4 5 7 > 0.999 || = 0.44 519 491 513 487 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 518 491 481 495 542 | 500 < 0.001 56 56 58 57 55 | 50 | 53 53 40 42 58 > 0.999 || = 0.42 521 478 505 508 495 | 500 < 0.002 47 49 48 44 58 | 50 | 57 46 37 46 49 > 0.998 || = 0.41 547 490 509 477 540 | 500 < 0.003 59 53 52 43 56 | 50 | 40 50 50 53 50 > 0.997 || = 0.40 502 484 465 512 457 | 500 < 0.004 68 59 50 59 47 | 50 | 63 49 54 44 50 > 0.996 || = 0.39 494 502 510 524 497 | 500 < 0.005 58 46 51 55 44 | 50 | 52 56 50 41 55 > 0.995 || = 0.38 471 507 506 450 523 | 500 < 0.006 49 48 49 50 49 | 50 | 69 49 56 45 51 > 0.994 || = 0.37 483 522 487 494 522 | 500 < 0.007 43 41 55 57 47 | 50 | 64 49 41 43 46 > 0.993 || = 0.36 495 515 462 481 498 | 500 < 0.008 53 53 49 51 55 | 50 | 50 54 51 52 47 > 0.992 || = 0.35 502 476 475 497 488 | 500 < 0.009 62 47 50 53 48 | 50 | 57 48 41 42 47 > 0.991 || = 0.34 538 502 474 481 484 | 500 < 0.01 45 45 69 61 43 | 50 | 50 47 51 47 42 > 0.99 || = 0.33 483 471 524 523 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 526 507 497 526 526 | 500 < 0.01 540 497 531 530 502 | 497.5 | 555 501 471 455 495 > 0.99 || = 0.31 509 517 491 461 488 | 500 = 0.01 221 261 273 273 237 | 252.5 | 251 287 257 243 271 = 0.99 || = 0.30 502 475 523 465 497 | 500 = 0.02 535 506 514 483 500 | 500 | 521 520 514 519 481 = 0.98 || = 0.29 478 478 468 472 506 | 500 =================================================================| 500 | 495 533 512 515 503 = 0.97 || = 0.28 502 505 506 469 487 | 500 swalk_RandomWalk1 test: | 500 | 522 505 510 522 521 = 0.96 || = 0.27 540 437 494 506 491 | 500 ----------------------------------------------- | 500 | 478 507 516 519 470 = 0.95 || = 0.26 499 507 543 546 477 | 500 N = 1, n = 1000000, r = 15, s = 15, L0 = 10000, L1 = 10000 | 500 | 463 532 496 470 498 = 0.94 || = 0.25 521 476 480 496 491 | 500 Test on the values of the Statistic C | 500 | 500 523 505 519 524 = 0.93 || = 0.24 496 502 454 528 482 | 500 | 500 | 456 509 510 544 483 = 0.92 || = 0.23 548 510 542 534 523 | 500 =================================================================| 500 | 492 521 517 528 489 = 0.91 || = 0.22 501 465 520 481 499 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 522 505 453 498 501 = 0.90 || = 0.21 503 534 459 474 490 | 500 -----------------------------------------------------------------| 500 | 472 508 511 495 517 = 0.89 || = 0.20 516 470 485 543 512 | 500 SD Bern.: d 1.04162 1.21880 1.36961 | 500 | 518 522 476 464 515 = 0.88 || = 0.19 497 517 490 487 476 | 500 s 1.12768 0.73656 0.43147 | 500 | 527 434 524 484 487 = 0.87 || = 0.18 510 516 489 534 476 | 500 t 1.01882 0.96068 0.98536 | 500 | 437 522 489 507 490 = 0.86 || = 0.17 482 461 495 507 453 | 500 m 1.10315 0.91696 0.84539 | 500 | 499 485 468 475 518 = 0.85 || = 0.16 502 469 494 470 453 | 500 x 0.97854 0.71867 0.61510 | 500 | 517 465 520 489 472 = 0.84 || = 0.15 475 483 519 489 497 | 500 | 500 | 517 478 508 490 497 = 0.83 || = 0.14 482 466 498 503 501 | 500 Changes: d 54 5 5 | 500 | 515 518 543 481 480 = 0.82 || = 0.13 515 496 527 515 517 | 500 s 45 5 5 | 500 | 500 563 536 508 468 = 0.81 || = 0.12 507 517 485 494 516 | 500 t 51 8 7 | 500 | 473 499 531 513 521 = 0.80 || = 0.11 498 479 533 488 492 | 500 m 47 4 4 | 500 | 493 527 479 480 496 = 0.79 || = 0.10 476 504 476 503 498 | 500 x 51 3 3 | 500 | 475 492 496 527 469 = 0.78 || = 0.09 507 511 517 489 541 | 500 -----------------------------------------------------------------| 500 | 513 493 497 459 512 = 0.77 || = 0.08 471 490 468 474 497 | 500 Aver./ d 0.49937 500 > 500: 4 4 7 5 8 4 5 3 6 3 | 500 | 501 489 462 526 534 = 0.76 || = 0.07 500 492 499 531 506 | 500 median s 0.50305 502 ----- 5 4 5 7 4 5 3 4 6 10 | 500 | 491 564 526 475 498 = 0.75 || = 0.06 521 499 499 516 581 | 500 t 0.50086 499 5 3 4 4 4 6 5 5 6 8 | 500 | 491 503 517 478 488 = 0.74 || = 0.05 487 482 493 562 513 | 500 m 0.49813 495 6 5 5 3 4 5 3 5 2 7 | 500 | 489 562 512 482 495 = 0.73 || = 0.04 496 525 477 565 526 | 500 x 0.49916 498 7 3 3 4 4 4 7 4 4 4 | 500 | 480 489 510 507 504 = 0.72 || = 0.03 455 506 508 495 507 | 500 -----------------------------------------------------------------| 500 | 531 492 486 522 470 = 0.71 || = 0.02 535 506 514 483 500 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 473 511 528 517 511 = 0.70 || = 0.01 221 261 273 273 237 | 252.5 d 0 0 4 12 73 9 3 0 0 | 500 | 505 501 507 487 493 = 0.69 || < 0.01 540 497 531 530 502 | 497.5 s 0 0 3 15 69 9 5 0 0 | 500 | 513 487 510 484 518 = 0.68 ||========================================================================= t 0 0 2 19 62 16 2 0 0 | 500 | 484 471 468 485 481 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 17 61 19 3 0 0 | 500 | 490 514 471 491 554 = 0.66 ||========================================================================= x 0 0 2 13 73 11 1 1 0 | 500 | 487 469 479 515 515 = 0.65 || swalk_RandomWalk1 test: no 175 test no 176 TestU01 250000 runs BigCrush Test smarsa_S scomp_LinearComp test: test no 176 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 2 1 | 0.5 | 0 0 1 0 1 > 0.99999 || = 0.64 505 496 505 543 519 | 500 < 0.00002 0 0 0 2 1 | 0.5 | 0 0 3 0 0 > 0.99998 || = 0.63 478 493 534 512 514 | 500 < 0.00003 0 1 1 4 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 494 525 509 515 534 | 500 < 0.00004 0 0 0 1 1 | 0.5 | 0 2 0 0 0 > 0.99996 || = 0.61 513 455 469 488 515 | 500 < 0.00005 0 0 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 497 508 491 506 542 | 500 < 0.00006 0 1 0 2 1 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 495 473 501 537 483 | 500 < 0.00007 0 1 0 3 0 | 0.5 | 0 0 1 0 0 > 0.99993 || = 0.58 506 465 508 510 507 | 500 < 0.00008 0 0 2 1 0 | 0.5 | 1 0 1 0 0 > 0.99992 || = 0.57 520 517 458 525 514 | 500 < 0.00009 1 2 0 0 0 | 0.5 | 0 0 0 2 0 > 0.99991 || = 0.56 498 482 505 538 487 | 500 < 0.0001 0 1 0 2 0 | 0.5 | 0 2 2 0 2 > 0.9999 || = 0.55 511 522 529 486 538 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 471 470 516 487 527 | 500 < 0.0001 1 7 4 19 5 | 5 | 1 4 8 3 3 > 0.9999 || = 0.53 525 491 489 513 523 | 500 < 0.0002 5 2 3 4 6 | 5 | 0 2 1 3 4 > 0.9998 || = 0.52 542 500 480 492 496 | 500 < 0.0003 5 4 4 12 6 | 5 | 8 7 6 7 2 > 0.9997 || = 0.51 502 502 519 500 520 | 500 < 0.0004 5 3 9 12 6 | 5 | 9 4 3 8 1 > 0.9996 || = 0.50 538 515 482 522 478 | 500 < 0.0005 8 2 4 15 6 | 5 | 5 2 11 4 6 > 0.9995 || = 0.49 497 490 538 514 484 | 500 < 0.0006 2 7 1 11 9 | 5 | 5 8 5 11 6 > 0.9994 || = 0.48 479 478 493 488 523 | 500 < 0.0007 4 4 8 11 4 | 5 | 7 5 4 7 2 > 0.9993 || = 0.47 504 499 534 527 524 | 500 < 0.0008 6 9 9 4 5 | 5 | 6 5 8 8 7 > 0.9992 || = 0.46 503 513 487 504 540 | 500 < 0.0009 2 4 10 7 6 | 5 | 7 6 1 5 9 > 0.9991 || = 0.45 521 501 481 497 490 | 500 < 0.001 6 2 10 4 6 | 5 | 4 2 6 6 6 > 0.999 || = 0.44 491 492 486 481 509 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 518 513 483 462 480 | 500 < 0.001 44 44 62 99 59 | 50 | 52 45 53 62 46 > 0.999 || = 0.42 480 504 527 509 480 | 500 < 0.002 52 61 47 58 49 | 50 | 50 39 56 51 53 > 0.998 || = 0.41 501 513 490 530 541 | 500 < 0.003 53 58 48 69 44 | 50 | 54 42 46 47 63 > 0.997 || = 0.40 550 497 512 517 482 | 500 < 0.004 48 52 51 62 47 | 50 | 58 51 58 53 55 > 0.996 || = 0.39 512 500 535 485 481 | 500 < 0.005 47 51 45 61 57 | 50 | 52 47 42 58 48 > 0.995 || = 0.38 468 499 476 492 514 | 500 < 0.006 58 51 46 54 42 | 50 | 50 57 41 50 56 > 0.994 || = 0.37 477 481 514 536 502 | 500 < 0.007 54 61 35 53 50 | 50 | 51 51 51 40 49 > 0.993 || = 0.36 502 477 535 506 499 | 500 < 0.008 57 43 52 64 48 | 50 | 52 44 43 50 59 > 0.992 || = 0.35 521 535 514 506 462 | 500 < 0.009 53 42 63 47 48 | 50 | 55 50 45 48 57 > 0.991 || = 0.34 477 526 499 513 498 | 500 < 0.01 40 46 37 58 56 | 50 | 33 49 48 53 49 > 0.99 || = 0.33 498 527 510 483 469 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 536 496 516 488 543 | 500 < 0.01 506 509 486 625 500 | 497.5 | 507 475 483 512 535 > 0.99 || = 0.31 516 485 498 472 524 | 500 = 0.01 240 249 282 258 274 | 252.5 | 247 221 256 268 251 = 0.99 || = 0.30 517 474 517 479 497 | 500 = 0.02 525 494 529 516 471 | 500 | 527 495 536 485 493 = 0.98 || = 0.29 479 493 510 488 480 | 500 =================================================================| 500 | 490 540 487 486 498 = 0.97 || = 0.28 519 470 508 491 503 | 500 scomp_LinearComp test: | 500 | 499 509 507 535 487 = 0.96 || = 0.27 495 542 479 477 512 | 500 ----------------------------------------------- | 500 | 540 474 484 494 532 = 0.95 || = 0.26 500 503 480 457 552 | 500 N = 1, n = 400020, r = 0, s = 1 | 500 | 458 494 478 464 471 = 0.94 || = 0.25 465 521 486 470 526 | 500 Number of degrees of freedom : 12 | 500 | 484 484 561 501 551 = 0.93 || = 0.24 499 465 516 504 487 | 500 Chi2 statistic for size of jumps | 500 | 516 495 520 516 493 = 0.92 || = 0.23 516 571 496 481 488 | 500 =================================================================| 500 | 484 496 490 459 486 = 0.91 || = 0.22 486 483 509 485 492 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 489 496 518 562 489 = 0.90 || = 0.21 476 532 489 470 511 | 500 -----------------------------------------------------------------| 500 | 523 484 521 514 435 = 0.89 || = 0.20 496 506 472 465 485 | 500 SD Bern.: d 0.93445 0.77497 0.90266 | 500 | 508 506 486 447 524 = 0.88 || = 0.19 466 487 497 494 479 | 500 s 0.98867 0.97721 0.78396 | 500 | 553 495 482 485 491 = 0.87 || = 0.18 466 528 488 466 524 | 500 t 0.93192 1.23835 0.83587 | 500 | 525 483 503 464 508 = 0.86 || = 0.17 527 510 495 492 484 | 500 m 1.23464 2.60322 0.82502 | 500 | 463 554 499 528 486 = 0.85 || = 0.16 511 463 500 473 549 | 500 x 1.07377 0.75402 0.88473 | 500 | 515 486 452 521 543 = 0.84 || = 0.15 502 502 532 489 477 | 500 | 500 | 494 510 464 534 515 = 0.83 || = 0.14 477 489 469 527 500 | 500 Changes: d 54 4 5 | 500 | 491 496 519 487 490 = 0.82 || = 0.13 489 506 531 449 461 | 500 s 45 2 4 | 500 | 484 527 488 503 508 = 0.81 || = 0.12 502 529 487 461 462 | 500 t 58 5 5 | 500 | 477 508 472 483 492 = 0.80 || = 0.11 460 522 503 467 472 | 500 m 42 2 4 | 500 | 511 504 530 522 514 = 0.79 || = 0.10 520 512 493 455 495 | 500 x 50 4 6 | 500 | 476 526 486 491 493 = 0.78 || = 0.09 506 546 498 473 486 | 500 -----------------------------------------------------------------| 500 | 492 457 478 507 516 = 0.77 || = 0.08 512 479 478 503 475 | 500 Aver./ d 0.50043 499 > 500: 6 5 2 6 6 6 5 2 5 4 | 500 | 498 485 513 488 463 = 0.76 || = 0.07 503 469 498 506 479 | 500 median s 0.49805 499 ----- 5 7 6 3 5 4 5 4 4 2 | 500 | 487 470 524 562 538 = 0.75 || = 0.06 490 518 482 487 462 | 500 t 0.50027 498 3 3 4 7 4 6 6 4 4 5 | 500 | 500 477 493 552 498 = 0.74 || = 0.05 543 520 489 499 497 | 500 m 0.50247 500 7 1 1 4 6 6 7 6 6 5 | 500 | 490 477 471 535 482 = 0.73 || = 0.04 460 503 507 525 497 | 500 x 0.50181 497 2 2 5 4 5 7 5 4 5 3 | 500 | 516 505 511 476 493 = 0.72 || = 0.03 493 489 457 501 497 | 500 -----------------------------------------------------------------| 500 | 499 484 495 509 509 = 0.71 || = 0.02 525 494 529 516 471 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 504 494 491 509 480 = 0.70 || = 0.01 240 249 282 258 274 | 252.5 d 0 0 0 17 70 12 2 0 0 | 500 | 476 519 513 511 474 = 0.69 || < 0.01 506 509 486 625 500 | 497.5 s 0 0 1 16 69 12 2 1 0 | 500 | 506 512 495 507 513 = 0.68 ||========================================================================= t 0 0 1 9 76 14 1 0 0 | 500 | 483 501 511 474 462 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 17 64 13 3 0 1 | 500 | 473 538 487 501 472 = 0.66 ||========================================================================= x 0 0 1 14 64 19 3 0 0 | 500 | 523 499 510 491 499 = 0.65 || scomp_LinearComp test: no 176 test no 177 TestU01 250000 runs BigCrush Test smarsa_S scomp_LinearComp test: test no 177 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 2 | 0.5 | 1 0 1 0 2 > 0.99999 || = 0.64 486 520 486 0 502 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 0 1 1 0 0 > 0.99998 || = 0.63 537 495 489 0 483 | 500 < 0.00003 0 0 2 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 438 376 392 0 408 | 500 < 0.00004 1 0 0 0 0 | 0.5 | 0 3 0 0 2 > 0.99996 || = 0.61 516 513 528 0 551 | 500 < 0.00005 1 0 1 0 1 | 0.5 | 1 1 0 0 1 > 0.99995 || = 0.60 538 559 507 0 504 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 540 516 521 0 502 | 500 < 0.00007 1 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 550 555 561 0 567 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 431 446 439 0 442 | 500 < 0.00009 1 0 0 0 0 | 0.5 | 0 1 0 0 1 > 0.99991 || = 0.56 590 516 547 0 537 | 500 < 0.0001 2 0 0 0 0 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 496 535 544 0 549 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 440 392 459 0 422 | 500 < 0.0001 6 1 5 0 5 | 5 | 3 7 2 0 6 > 0.9999 || = 0.53 488 509 504 0 500 | 500 < 0.0002 3 6 4 0 5 | 5 | 2 1 4 0 5 > 0.9998 || = 0.52 445 475 429 0 455 | 500 < 0.0003 6 3 4 0 2 | 5 | 5 4 3 0 2 > 0.9997 || = 0.51 556 539 537 0 516 | 500 < 0.0004 7 6 7 0 3 | 5 | 10 7 4 0 6 > 0.9996 || = 0.50 587 534 537 0 557 | 500 < 0.0005 7 3 9 0 3 | 5 | 4 9 5 0 5 > 0.9995 || = 0.49 484 444 454 0 433 | 500 < 0.0006 4 2 4 0 5 | 5 | 10 9 5 0 6 > 0.9994 || = 0.48 556 550 510 0 549 | 500 < 0.0007 3 6 7 0 4 | 5 | 7 3 7 0 6 > 0.9993 || = 0.47 450 446 435 0 417 | 500 < 0.0008 8 6 2 0 1 | 5 | 3 9 5 0 6 > 0.9992 || = 0.46 571 505 541 0 531 | 500 < 0.0009 9 4 7 0 9 | 5 | 5 4 3 0 5 > 0.9991 || = 0.45 525 557 557 0 522 | 500 < 0.001 2 3 4 0 1 | 5 | 6 4 2 0 4 > 0.999 || = 0.44 462 461 431 0 479 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 528 573 524 0 524 | 500 < 0.001 55 40 53 0 38 | 50 | 55 57 40 0 51 > 0.999 || = 0.42 535 528 515 0 520 | 500 < 0.002 47 44 35 0 44 | 50 | 51 54 55 0 48 > 0.998 || = 0.41 503 543 515 0 521 | 500 < 0.003 35 43 44 0 51 | 50 | 50 52 51 0 45 > 0.997 || = 0.40 446 400 445 0 436 | 500 < 0.004 58 55 36 0 48 | 50 | 53 52 52 0 54 > 0.996 || = 0.39 491 541 530 0 539 | 500 < 0.005 46 42 54 0 43 | 50 | 51 44 47 0 40 > 0.995 || = 0.38 519 524 534 0 544 | 500 < 0.006 42 52 41 0 53 | 50 | 44 50 45 0 41 > 0.994 || = 0.37 486 467 515 0 461 | 500 < 0.007 65 47 35 0 48 | 50 | 47 60 48 0 57 > 0.993 || = 0.36 487 487 518 0 554 | 500 < 0.008 41 70 58 0 50 | 50 | 54 49 51 0 55 > 0.992 || = 0.35 484 441 476 0 473 | 500 < 0.009 49 48 54 0 45 | 50 | 41 45 41 0 38 > 0.991 || = 0.34 505 490 454 0 481 | 500 < 0.01 52 44 49 0 51 | 50 | 55 65 51 0 34 > 0.99 || = 0.33 480 469 495 0 484 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 630 575 574 0 533 | 500 < 0.01 490 485 459 0 471 | 497.5 | 501 528 481 0 463 > 0.99 || = 0.31 476 489 507 0 460 | 500 = 0.01 271 246 242 0 256 | 252.5 | 244 234 254 0 262 = 0.99 || = 0.30 423 441 481 0 467 | 500 = 0.02 510 517 516 0 510 | 500 | 505 520 496 0 487 = 0.98 || = 0.29 545 551 565 0 536 | 500 =================================================================| 500 | 473 496 536 0 550 = 0.97 || = 0.28 420 457 465 0 457 | 500 scomp_LinearComp test: | 500 | 476 519 502 0 511 = 0.96 || = 0.27 499 510 496 0 522 | 500 ----------------------------------------------- | 500 | 474 482 488 0 521 = 0.95 || = 0.26 513 521 472 0 489 | 500 N = 1, n = 400020, r = 0, s = 1 | 500 | 456 478 513 0 489 = 0.94 || = 0.25 465 493 462 0 536 | 500 Normal statistic for number of jumps | 500 | 498 480 495 0 512 = 0.93 || = 0.24 508 490 454 0 468 | 500 | 500 | 445 474 505 0 469 = 0.92 || = 0.23 518 529 528 0 564 | 500 =================================================================| 500 | 479 568 484 0 472 = 0.91 || = 0.22 445 438 460 0 476 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 546 509 532 0 502 = 0.90 || = 0.21 534 501 527 0 526 | 500 -----------------------------------------------------------------| 500 | 433 461 452 0 442 = 0.89 || = 0.20 459 523 505 0 457 | 500 SD Bern.: d 1.74831 1.19558 0.63748 | 500 | 501 567 541 0 529 = 0.88 || = 0.19 494 450 476 0 503 | 500 s 1.86508 1.20641 0.95964 | 500 | 472 494 456 0 455 = 0.87 || = 0.18 533 530 579 0 552 | 500 t 1.72133 1.31898 0.70886 | 500 | 478 443 484 0 491 = 0.86 || = 0.17 525 463 494 0 508 | 500 m n.a. n.a. n.a. | 500 | 518 556 513 0 492 = 0.85 || = 0.16 497 498 489 0 511 | 500 x 1.70154 0.73928 1.18464 | 500 | 508 519 478 0 476 = 0.84 || = 0.15 468 464 460 0 474 | 500 | 500 | 506 489 511 0 489 = 0.83 || = 0.14 535 509 483 0 504 | 500 Changes: d 59 6 6 | 500 | 467 464 460 0 485 = 0.82 || = 0.13 536 478 531 0 512 | 500 s 61 6 4 | 500 | 529 536 573 0 542 = 0.81 || = 0.12 461 509 491 0 465 | 500 t 66 5 5 | 500 | 512 528 472 0 510 = 0.80 || = 0.11 506 514 526 0 534 | 500 m - - - | 500 | 451 475 458 0 459 = 0.79 || = 0.10 497 522 506 0 456 | 500 x 64 5 5 | 500 | 506 556 527 0 550 = 0.78 || = 0.09 521 525 483 0 520 | 500 -----------------------------------------------------------------| 500 | 511 432 491 0 422 = 0.77 || = 0.08 520 456 536 0 514 | 500 Aver./ d 0.49734 503 > 500: 8 5 5 3 6 5 6 5 6 2 | 500 | 466 526 499 0 534 = 0.76 || = 0.07 439 454 488 0 476 | 500 median s 0.50204 505 ----- 4 5 6 3 6 7 7 5 5 4 | 500 | 551 575 569 0 580 = 0.75 || = 0.06 520 528 520 0 517 | 500 t 0.49958 502 5 4 4 6 6 7 5 4 5 5 | 500 | 450 440 432 0 437 = 0.74 || = 0.05 506 497 542 0 541 | 500 m - - - - - - - - - - - - | 500 | 521 551 518 0 543 = 0.73 || = 0.04 543 503 507 0 458 | 500 x 0.49923 504 7 7 5 4 6 6 6 6 3 5 | 500 | 499 489 545 0 560 = 0.72 || = 0.03 523 486 483 0 521 | 500 -----------------------------------------------------------------| 500 | 467 418 428 0 474 = 0.71 || = 0.02 510 517 516 0 510 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 519 539 575 0 539 = 0.70 || = 0.01 271 246 242 0 256 | 252.5 d 0 4 10 15 46 15 6 3 2 | 500 | 506 505 509 0 470 = 0.69 || < 0.01 490 485 459 0 471 | 497.5 s 3 2 10 13 41 18 9 5 0 | 500 | 467 530 461 0 540 = 0.68 ||========================================================================= t 1 4 8 14 45 18 5 6 0 | 500 | 586 560 570 0 510 = 0.67 || Total 50000 50000 50000 0 50000 | 497.5 m - - - - - - - - - | 500 | 507 509 445 0 475 = 0.66 ||========================================================================= x 1 4 6 22 39 17 10 2 0 | 500 | 492 492 511 0 501 = 0.65 || scomp_LinearComp test: no 177 test no 178 TestU01 250000 runs BigCrush Test smarsa_S scomp_LinearComp test: test no 178 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 3 1 0 | 0.5 | 2 1 0 0 0 > 0.99999 || = 0.64 475 500 458 499 459 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 526 510 491 530 499 | 500 < 0.00003 3 0 0 2 0 | 0.5 | 0 1 0 1 0 > 0.99997 || = 0.62 478 528 513 507 512 | 500 < 0.00004 0 0 0 4 0 | 0.5 | 0 0 2 0 1 > 0.99996 || = 0.61 460 449 477 496 519 | 500 < 0.00005 0 2 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99995 || = 0.60 501 504 499 516 504 | 500 < 0.00006 0 0 2 0 0 | 0.5 | 1 0 1 1 0 > 0.99994 || = 0.59 459 466 494 532 507 | 500 < 0.00007 1 1 0 2 0 | 0.5 | 1 0 0 0 1 > 0.99993 || = 0.58 504 543 532 503 474 | 500 < 0.00008 0 1 1 1 1 | 0.5 | 1 1 0 1 1 > 0.99992 || = 0.57 511 506 519 479 487 | 500 < 0.00009 0 1 2 2 0 | 0.5 | 0 0 2 0 0 > 0.99991 || = 0.56 494 469 511 553 533 | 500 < 0.0001 1 0 1 2 2 | 0.5 | 1 0 3 0 1 > 0.9999 || = 0.55 497 474 519 540 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 482 471 465 509 483 | 500 < 0.0001 5 5 9 14 4 | 5 | 6 4 8 3 4 > 0.9999 || = 0.53 467 458 450 496 516 | 500 < 0.0002 7 4 4 14 6 | 5 | 1 4 4 3 5 > 0.9998 || = 0.52 494 508 507 478 471 | 500 < 0.0003 6 5 7 11 6 | 5 | 5 7 7 4 3 > 0.9997 || = 0.51 474 470 460 514 530 | 500 < 0.0004 5 1 9 6 0 | 5 | 8 2 7 8 8 > 0.9996 || = 0.50 505 503 496 486 470 | 500 < 0.0005 5 5 5 8 3 | 5 | 9 3 7 5 2 > 0.9995 || = 0.49 522 493 538 473 476 | 500 < 0.0006 9 7 5 11 3 | 5 | 8 8 3 8 6 > 0.9994 || = 0.48 507 481 522 506 507 | 500 < 0.0007 2 4 4 9 4 | 5 | 4 4 8 5 5 > 0.9993 || = 0.47 438 488 483 518 545 | 500 < 0.0008 4 4 2 7 3 | 5 | 6 5 4 8 3 > 0.9992 || = 0.46 491 527 503 469 472 | 500 < 0.0009 7 3 6 6 6 | 5 | 3 4 5 5 4 > 0.9991 || = 0.45 499 545 494 487 521 | 500 < 0.001 4 5 2 9 3 | 5 | 7 8 6 4 2 > 0.999 || = 0.44 483 500 472 491 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 567 497 514 473 516 | 500 < 0.001 54 43 53 95 38 | 50 | 57 49 59 53 42 > 0.999 || = 0.42 485 547 519 538 516 | 500 < 0.002 45 46 58 63 47 | 50 | 53 51 44 60 34 > 0.998 || = 0.41 516 501 490 528 492 | 500 < 0.003 58 48 58 70 39 | 50 | 44 34 46 43 55 > 0.997 || = 0.40 511 503 527 506 468 | 500 < 0.004 63 47 52 65 30 | 50 | 55 39 49 32 48 > 0.996 || = 0.39 514 488 456 512 480 | 500 < 0.005 57 40 50 57 64 | 50 | 56 56 61 56 45 > 0.995 || = 0.38 471 542 478 506 475 | 500 < 0.006 46 53 57 51 47 | 50 | 48 59 56 55 54 > 0.994 || = 0.37 522 506 529 464 522 | 500 < 0.007 51 57 44 62 44 | 50 | 33 60 57 38 68 > 0.993 || = 0.36 525 501 532 497 486 | 500 < 0.008 56 67 61 61 45 | 50 | 46 51 52 58 67 > 0.992 || = 0.35 511 506 504 519 522 | 500 < 0.009 49 52 61 63 56 | 50 | 49 47 43 60 40 > 0.991 || = 0.34 474 522 521 503 517 | 500 < 0.01 66 56 51 56 54 | 50 | 36 37 36 51 53 > 0.99 || = 0.33 496 511 536 504 511 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 503 497 515 489 454 | 500 < 0.01 545 509 545 643 464 | 497.5 | 477 483 503 506 506 > 0.99 || = 0.31 507 476 493 484 525 | 500 = 0.01 246 255 249 277 270 | 252.5 | 279 234 261 261 241 = 0.99 || = 0.30 499 469 493 440 499 | 500 = 0.02 492 496 512 535 549 | 500 | 488 486 547 509 461 = 0.98 || = 0.29 483 530 503 464 494 | 500 =================================================================| 500 | 504 490 484 528 487 = 0.97 || = 0.28 486 478 502 468 482 | 500 scomp_LinearComp test: | 500 | 518 504 514 570 480 = 0.96 || = 0.27 513 496 489 474 513 | 500 ----------------------------------------------- | 500 | 511 516 488 491 517 = 0.95 || = 0.26 491 517 485 458 492 | 500 N = 1, n = 400020, r = 29, s = 1 | 500 | 539 521 478 456 476 = 0.94 || = 0.25 449 466 471 475 490 | 500 Number of degrees of freedom : 12 | 500 | 458 535 477 527 533 = 0.93 || = 0.24 468 517 529 523 448 | 500 Chi2 statistic for size of jumps | 500 | 511 484 508 502 492 = 0.92 || = 0.23 449 501 503 466 505 | 500 =================================================================| 500 | 482 510 513 487 502 = 0.91 || = 0.22 493 489 485 496 508 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 495 450 495 511 457 = 0.90 || = 0.21 527 543 493 473 499 | 500 -----------------------------------------------------------------| 500 | 495 516 486 518 502 = 0.89 || = 0.20 499 489 497 524 494 | 500 SD Bern.: d 1.10877 1.12572 1.15034 | 500 | 500 508 474 508 512 = 0.88 || = 0.19 488 485 542 462 496 | 500 s 0.98383 1.06354 1.24560 | 500 | 497 510 510 516 507 = 0.87 || = 0.18 517 479 527 479 454 | 500 t 1.04396 0.96898 1.08589 | 500 | 495 534 494 511 503 = 0.86 || = 0.17 480 507 483 447 482 | 500 m 1.28813 2.58547 1.30601 | 500 | 546 520 499 496 499 = 0.85 || = 0.16 488 480 473 503 502 | 500 x 0.99741 1.40924 1.49204 | 500 | 468 516 532 506 515 = 0.84 || = 0.15 482 531 471 474 507 | 500 | 500 | 549 489 467 531 504 = 0.83 || = 0.14 465 488 493 468 483 | 500 Changes: d 49 6 3 | 500 | 496 485 505 520 493 = 0.82 || = 0.13 524 474 531 458 513 | 500 s 53 1 4 | 500 | 528 514 493 498 472 = 0.81 || = 0.12 512 515 514 451 528 | 500 t 50 4 3 | 500 | 514 494 496 505 509 = 0.80 || = 0.11 502 529 475 478 464 | 500 m 40 0 4 | 500 | 480 495 464 513 516 = 0.79 || = 0.10 531 484 539 467 480 | 500 x 47 3 5 | 500 | 507 538 525 498 492 = 0.78 || = 0.09 538 518 513 499 560 | 500 -----------------------------------------------------------------| 500 | 506 513 514 497 499 = 0.77 || = 0.08 512 483 504 492 502 | 500 Aver./ d 0.50029 499 > 500: 6 5 2 6 5 3 4 7 3 6 | 500 | 471 502 497 509 485 = 0.76 || = 0.07 481 480 480 462 518 | 500 median s 0.50042 501 ----- 4 4 5 6 5 4 5 6 7 5 | 500 | 504 482 488 546 504 = 0.75 || = 0.06 520 473 527 485 511 | 500 t 0.49837 499 7 5 4 6 6 5 4 3 3 6 | 500 | 472 519 515 492 490 = 0.74 || = 0.05 521 492 527 503 513 | 500 m 0.50421 503 5 1 2 5 5 7 6 6 8 7 | 500 | 515 483 494 526 531 = 0.73 || = 0.04 489 536 453 474 522 | 500 x 0.49890 502 9 4 3 5 6 5 6 6 6 4 | 500 | 549 504 467 508 510 = 0.72 || = 0.03 517 486 517 524 525 | 500 -----------------------------------------------------------------| 500 | 525 516 478 474 526 = 0.71 || = 0.02 492 496 512 535 549 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 518 520 517 480 526 = 0.70 || = 0.01 246 255 249 277 270 | 252.5 d 0 0 3 15 66 11 5 1 0 | 500 | 474 480 499 506 521 = 0.69 || < 0.01 545 509 545 643 464 | 497.5 s 0 0 2 13 72 12 2 0 0 | 500 | 493 462 454 514 507 = 0.68 ||========================================================================= t 0 0 3 16 63 17 2 0 0 | 500 | 526 504 532 522 495 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 20 60 14 2 1 1 | 500 | 557 491 525 494 472 = 0.66 ||========================================================================= x 0 0 3 15 69 11 3 0 0 | 500 | 477 507 465 517 509 = 0.65 || scomp_LinearComp test: no 178 test no 179 TestU01 250000 runs BigCrush Test smarsa_S scomp_LinearComp test: test no 179 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 2 | 0.5 | 1 0 1 0 0 > 0.99999 || = 0.64 483 482 497 0 486 | 500 < 0.00002 1 0 0 0 1 | 0.5 | 1 1 0 0 1 > 0.99998 || = 0.63 501 500 516 0 505 | 500 < 0.00003 0 0 1 0 1 | 0.5 | 0 2 0 0 3 > 0.99997 || = 0.62 407 426 435 0 388 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 2 1 0 0 0 > 0.99996 || = 0.61 557 545 492 0 512 | 500 < 0.00005 1 0 0 0 2 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 487 513 566 0 532 | 500 < 0.00006 0 1 1 0 2 | 0.5 | 0 1 0 0 0 > 0.99994 || = 0.59 532 535 505 0 549 | 500 < 0.00007 1 0 2 0 1 | 0.5 | 0 1 0 0 3 > 0.99993 || = 0.58 538 572 516 0 545 | 500 < 0.00008 2 1 0 0 1 | 0.5 | 1 0 0 0 0 > 0.99992 || = 0.57 446 453 441 0 463 | 500 < 0.00009 0 0 1 0 0 | 0.5 | 1 0 2 0 0 > 0.99991 || = 0.56 524 520 526 0 534 | 500 < 0.0001 1 0 3 0 0 | 0.5 | 1 1 1 0 3 > 0.9999 || = 0.55 509 506 516 0 524 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 448 434 413 0 449 | 500 < 0.0001 6 4 8 0 10 | 5 | 7 7 5 0 10 > 0.9999 || = 0.53 530 543 493 0 533 | 500 < 0.0002 5 5 1 0 10 | 5 | 6 3 4 0 2 > 0.9998 || = 0.52 397 431 455 0 462 | 500 < 0.0003 6 5 4 0 2 | 5 | 9 6 7 0 3 > 0.9997 || = 0.51 538 522 547 0 527 | 500 < 0.0004 6 7 5 0 3 | 5 | 4 4 7 0 2 > 0.9996 || = 0.50 536 512 556 0 554 | 500 < 0.0005 5 8 5 0 4 | 5 | 7 4 6 0 3 > 0.9995 || = 0.49 432 466 477 0 468 | 500 < 0.0006 5 9 4 0 5 | 5 | 8 6 11 0 4 > 0.9994 || = 0.48 547 530 506 0 593 | 500 < 0.0007 4 4 8 0 8 | 5 | 2 5 3 0 3 > 0.9993 || = 0.47 453 471 405 0 448 | 500 < 0.0008 7 7 9 0 7 | 5 | 2 5 4 0 4 > 0.9992 || = 0.46 541 562 515 0 501 | 500 < 0.0009 7 6 6 0 7 | 5 | 6 8 5 0 5 > 0.9991 || = 0.45 493 496 590 0 494 | 500 < 0.001 4 7 5 0 6 | 5 | 4 6 4 0 6 > 0.999 || = 0.44 499 456 464 0 439 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 497 532 573 0 540 | 500 < 0.001 55 62 55 0 62 | 50 | 55 54 56 0 42 > 0.999 || = 0.42 484 499 538 0 531 | 500 < 0.002 45 47 42 0 56 | 50 | 48 54 51 0 46 > 0.998 || = 0.41 505 502 506 0 491 | 500 < 0.003 33 43 47 0 52 | 50 | 47 41 41 0 61 > 0.997 || = 0.40 422 426 431 0 438 | 500 < 0.004 45 60 55 0 60 | 50 | 62 46 52 0 41 > 0.996 || = 0.39 536 509 486 0 510 | 500 < 0.005 57 38 52 0 58 | 50 | 40 48 58 0 43 > 0.995 || = 0.38 509 480 536 0 541 | 500 < 0.006 56 46 65 0 49 | 50 | 51 53 48 0 49 > 0.994 || = 0.37 486 525 492 0 540 | 500 < 0.007 37 55 51 0 51 | 50 | 58 48 58 0 60 > 0.993 || = 0.36 485 494 512 0 500 | 500 < 0.008 46 50 46 0 54 | 50 | 45 48 54 0 50 > 0.992 || = 0.35 520 517 469 0 462 | 500 < 0.009 65 48 58 0 58 | 50 | 50 49 56 0 56 > 0.991 || = 0.34 486 515 452 0 485 | 500 < 0.01 41 55 64 0 59 | 50 | 61 43 34 0 51 > 0.99 || = 0.33 455 507 470 0 450 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 592 572 547 0 491 | 500 < 0.01 480 504 535 0 559 | 497.5 | 517 484 508 0 499 > 0.99 || = 0.31 482 497 451 0 492 | 500 = 0.01 267 249 230 0 245 | 252.5 | 240 277 258 0 260 = 0.99 || = 0.30 457 442 466 0 462 | 500 = 0.02 503 491 485 0 508 | 500 | 529 482 516 0 526 = 0.98 || = 0.29 531 547 540 0 532 | 500 =================================================================| 500 | 509 527 500 0 511 = 0.97 || = 0.28 427 475 456 0 447 | 500 scomp_LinearComp test: | 500 | 511 475 500 0 479 = 0.96 || = 0.27 524 538 467 0 506 | 500 ----------------------------------------------- | 500 | 461 488 476 0 507 = 0.95 || = 0.26 478 509 492 0 435 | 500 N = 1, n = 400020, r = 29, s = 1 | 500 | 480 518 546 0 490 = 0.94 || = 0.25 518 521 472 0 511 | 500 Normal statistic for number of jumps | 500 | 492 551 492 0 524 = 0.93 || = 0.24 501 481 497 0 478 | 500 | 500 | 540 516 508 0 487 = 0.92 || = 0.23 555 482 613 0 512 | 500 =================================================================| 500 | 526 512 516 0 494 = 0.91 || = 0.22 486 446 486 0 462 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 539 521 524 0 478 = 0.90 || = 0.21 502 511 460 0 550 | 500 -----------------------------------------------------------------| 500 | 503 515 506 0 504 = 0.89 || = 0.20 455 492 510 0 534 | 500 SD Bern.: d 1.64599 1.37181 0.99346 | 500 | 560 567 484 0 481 = 0.88 || = 0.19 469 490 499 0 501 | 500 s 1.66275 1.01637 0.63275 | 500 | 503 456 484 0 478 = 0.87 || = 0.18 554 538 513 0 547 | 500 t 1.71482 1.12216 1.06070 | 500 | 483 476 474 0 483 = 0.86 || = 0.17 503 486 529 0 522 | 500 m n.a. n.a. n.a. | 500 | 460 521 540 0 550 = 0.85 || = 0.16 482 497 484 0 490 | 500 x 1.62245 1.01143 0.96897 | 500 | 520 469 536 0 506 = 0.84 || = 0.15 478 506 466 0 472 | 500 | 500 | 487 513 534 0 528 = 0.83 || = 0.14 521 461 493 0 471 | 500 Changes: d 63 5 6 | 500 | 458 451 448 0 471 = 0.82 || = 0.13 551 513 522 0 527 | 500 s 63 6 3 | 500 | 555 544 536 0 532 = 0.81 || = 0.12 464 537 505 0 493 | 500 t 54 4 5 | 500 | 532 492 500 0 490 = 0.80 || = 0.11 516 527 474 0 449 | 500 m - - - | 500 | 434 400 449 0 443 = 0.79 || = 0.10 500 509 485 0 499 | 500 x 58 2 5 | 500 | 509 531 557 0 577 = 0.78 || = 0.09 519 464 521 0 515 | 500 -----------------------------------------------------------------| 500 | 508 453 480 0 424 = 0.77 || = 0.08 512 452 485 0 482 | 500 Aver./ d 0.50044 501 > 500: 6 5 6 4 3 6 4 5 6 6 | 500 | 491 498 495 0 480 = 0.76 || = 0.07 496 502 471 0 502 | 500 median s 0.50113 501 ----- 3 6 5 6 4 7 4 3 6 6 | 500 | 535 542 573 0 552 = 0.75 || = 0.06 521 499 530 0 484 | 500 t 0.50145 499 4 4 3 3 6 6 3 3 6 6 | 500 | 430 472 431 0 429 = 0.74 || = 0.05 533 482 531 0 522 | 500 m - - - - - - - - - - - - | 500 | 499 489 513 0 477 = 0.73 || = 0.04 484 485 488 0 503 | 500 x 0.50006 501 7 4 6 3 4 7 6 4 5 6 | 500 | 539 581 482 0 537 = 0.72 || = 0.03 485 501 500 0 512 | 500 -----------------------------------------------------------------| 500 | 449 422 452 0 502 = 0.71 || = 0.02 503 491 485 0 508 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 557 589 591 0 515 = 0.70 || = 0.01 267 249 230 0 245 | 252.5 d 2 4 7 7 53 18 9 0 1 | 500 | 469 479 470 0 489 = 0.69 || < 0.01 480 504 535 0 559 | 497.5 s 1 5 7 11 53 14 5 4 1 | 500 | 498 430 484 0 506 = 0.68 ||========================================================================= t 1 3 8 16 48 13 7 2 3 | 500 | 562 559 559 0 588 = 0.67 || Total 50000 50000 50000 0 50000 | 497.5 m - - - - - - - - - | 500 | 497 499 480 0 490 = 0.66 ||========================================================================= x 1 2 9 10 51 17 8 2 1 | 500 | 489 514 499 0 504 = 0.65 || scomp_LinearComp test: no 179 test no 180 TestU01 250000 runs BigCrush Test smarsa_S scomp_LempelZiv test: test no 180 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 2 0 1 | 0.5 | 1 1 1 0 0 > 0.99999 || = 0.64 702 692 740 678 706 | 500 < 0.00002 0 1 1 3 2 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 276 294 293 292 310 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 0 0 0 2 0 > 0.99997 || = 0.62 720 725 727 669 683 | 500 < 0.00004 1 1 1 0 0 | 0.5 | 1 0 0 1 1 > 0.99996 || = 0.61 306 243 286 305 310 | 500 < 0.00005 2 1 1 0 0 | 0.5 | 0 0 1 1 0 > 0.99995 || = 0.60 525 501 481 493 500 | 500 < 0.00006 0 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 586 584 577 554 593 | 500 < 0.00007 0 0 0 0 1 | 0.5 | 0 2 0 0 1 > 0.99993 || = 0.58 341 295 326 339 321 | 500 < 0.00008 0 1 0 2 0 | 0.5 | 0 1 1 0 0 > 0.99992 || = 0.57 666 713 684 679 745 | 500 < 0.00009 1 0 3 1 0 | 0.5 | 0 1 1 0 0 > 0.99991 || = 0.56 470 413 424 431 476 | 500 < 0.0001 1 0 1 0 2 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 541 480 528 529 527 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 505 515 508 492 483 | 500 < 0.0001 5 5 9 8 6 | 5 | 3 5 5 4 2 > 0.9999 || = 0.53 411 394 367 378 380 | 500 < 0.0002 9 6 4 7 6 | 5 | 2 3 0 2 2 > 0.9998 || = 0.52 416 395 385 428 377 | 500 < 0.0003 4 6 5 6 2 | 5 | 3 5 1 2 3 > 0.9997 || = 0.51 635 587 602 634 632 | 500 < 0.0004 6 5 10 7 4 | 5 | 5 6 6 3 11 > 0.9996 || = 0.50 651 620 671 627 663 | 500 < 0.0005 5 3 8 5 7 | 5 | 5 6 7 6 7 > 0.9995 || = 0.49 454 487 450 499 459 | 500 < 0.0006 13 6 3 6 7 | 5 | 5 1 3 5 1 > 0.9994 || = 0.48 177 201 178 189 171 | 500 < 0.0007 4 6 7 1 7 | 5 | 4 7 9 4 5 > 0.9993 || = 0.47 725 717 714 712 739 | 500 < 0.0008 13 6 9 8 14 | 5 | 5 5 3 6 7 > 0.9992 || = 0.46 403 374 383 401 404 | 500 < 0.0009 8 7 6 9 5 | 5 | 4 3 3 5 7 > 0.9991 || = 0.45 726 725 749 797 728 | 500 < 0.001 1 0 1 1 2 | 5 | 7 5 4 4 6 > 0.999 || = 0.44 340 363 324 353 300 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 666 669 636 639 687 | 500 < 0.001 68 50 62 58 60 | 50 | 43 46 41 41 51 > 0.999 || = 0.42 218 235 228 223 205 | 500 < 0.002 50 49 51 58 56 | 50 | 45 34 31 33 45 > 0.998 || = 0.41 700 760 675 680 706 | 500 < 0.003 72 62 60 68 52 | 50 | 50 43 41 57 54 > 0.997 || = 0.40 540 563 547 527 621 | 500 < 0.004 44 60 72 58 65 | 50 | 46 42 48 25 27 > 0.996 || = 0.39 483 443 470 444 438 | 500 < 0.005 58 51 42 38 50 | 50 | 50 77 53 64 55 > 0.995 || = 0.38 411 430 451 417 442 | 500 < 0.006 54 45 58 68 71 | 50 | 34 34 43 50 39 > 0.994 || = 0.37 628 667 646 675 671 | 500 < 0.007 54 63 53 51 62 | 50 | 33 39 40 32 40 > 0.993 || = 0.36 363 364 361 372 364 | 500 < 0.008 64 76 62 51 57 | 50 | 58 52 46 59 36 > 0.992 || = 0.35 798 768 786 710 750 | 500 < 0.009 27 43 52 56 49 | 50 | 28 36 47 42 36 > 0.991 || = 0.34 267 261 255 253 247 | 500 < 0.01 59 67 74 61 69 | 50 | 44 39 48 62 42 > 0.99 || = 0.33 649 674 631 652 700 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 353 389 408 372 375 | 500 < 0.01 550 566 586 567 591 | 497.5 | 431 442 438 465 425 > 0.99 || = 0.31 646 622 667 644 670 | 500 = 0.01 274 289 300 290 255 | 252.5 | 206 213 207 219 189 = 0.99 || = 0.30 476 429 519 462 480 | 500 = 0.02 569 540 547 582 566 | 500 | 462 488 487 468 467 = 0.98 || = 0.29 568 510 593 570 526 | 500 =================================================================| 500 | 460 412 439 405 418 = 0.97 || = 0.28 353 382 363 365 373 | 500 scomp_LempelZiv test: | 500 | 451 440 434 443 444 = 0.96 || = 0.27 600 598 595 538 558 | 500 ----------------------------------------------- | 500 | 419 481 432 448 427 = 0.95 || = 0.26 478 486 438 447 418 | 500 N = 10, n = 134217728, r = 0, s = 30, k = 27 | 500 | 455 458 463 463 452 = 0.94 || = 0.25 615 614 602 584 583 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 537 532 532 533 566 = 0.93 || = 0.24 560 582 555 576 537 | 500 | 500 | 478 480 432 477 451 = 0.92 || = 0.23 456 376 411 405 417 | 500 =================================================================| 500 | 439 447 426 463 450 = 0.91 || = 0.22 664 678 637 674 668 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 442 490 451 478 421 = 0.90 || = 0.21 484 478 535 517 529 | 500 -----------------------------------------------------------------| 500 | 386 376 356 344 403 = 0.89 || = 0.20 447 469 452 500 433 | 500 SD Bern.: d 5.61316 1.86962 1.56218 | 500 | 588 617 565 611 556 = 0.88 || = 0.19 440 517 476 523 463 | 500 s 5.67569 1.70613 1.90462 | 500 | 425 449 426 368 404 = 0.87 || = 0.18 506 502 512 533 477 | 500 t 5.67211 1.78414 1.19557 | 500 | 553 501 522 529 553 = 0.86 || = 0.17 429 435 473 441 402 | 500 m 5.45220 1.51270 1.92605 | 500 | 278 277 295 246 266 = 0.85 || = 0.16 636 655 616 620 648 | 500 x 5.79012 1.65066 1.59640 | 500 | 607 595 606 591 577 = 0.84 || = 0.15 475 480 505 490 512 | 500 | 500 | 304 318 302 306 311 = 0.83 || = 0.14 641 660 647 633 651 | 500 Changes: d 65 6 2 | 500 | 590 628 589 610 626 = 0.82 || = 0.13 446 447 436 464 447 | 500 s 67 5 4 | 500 | 313 354 344 373 335 = 0.81 || = 0.12 536 509 565 530 538 | 500 t 63 2 2 | 500 | 617 658 640 610 594 = 0.80 || = 0.11 583 562 579 572 534 | 500 m 65 2 7 | 500 | 298 296 288 284 277 = 0.79 || = 0.10 568 501 582 520 538 | 500 x 61 4 5 | 500 | 625 650 691 683 684 = 0.78 || = 0.09 540 502 528 529 545 | 500 -----------------------------------------------------------------| 500 | 361 365 372 426 407 = 0.77 || = 0.08 559 573 591 534 611 | 500 Aver./ d 0.48362 506 > 500: 9 6 5 4 5 6 6 5 4 1 | 500 | 477 520 475 467 500 = 0.76 || = 0.07 424 401 415 471 477 | 500 median s 0.48482 501 ----- 9 7 5 4 5 5 5 6 4 1 | 500 | 624 572 573 588 593 = 0.75 || = 0.06 660 644 660 635 651 | 500 t 0.48048 508 9 7 6 5 5 5 4 5 4 1 | 500 | 338 342 337 354 352 = 0.74 || = 0.05 529 548 535 553 559 | 500 m 0.48296 507 9 7 6 4 5 4 5 5 4 1 | 500 | 576 557 521 555 582 = 0.73 || = 0.04 519 541 585 555 534 | 500 x 0.48234 504 9 6 6 4 5 4 6 5 4 1 | 500 | 285 296 289 318 295 = 0.72 || = 0.03 598 642 608 608 618 | 500 -----------------------------------------------------------------| 500 | 566 569 564 577 543 = 0.71 || = 0.02 569 540 547 582 566 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 508 439 472 507 522 = 0.70 || = 0.01 274 289 300 290 255 | 252.5 d 22 5 10 8 10 8 5 8 25 | 500 | 587 568 565 568 526 = 0.69 || < 0.01 550 566 586 567 591 | 497.5 s 24 4 10 2 19 4 6 8 24 | 500 | 522 553 553 551 550 = 0.68 ||========================================================================= t 23 6 10 7 9 5 9 6 26 | 500 | 511 527 474 494 517 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 23 4 6 9 11 10 6 9 23 | 500 | 326 358 350 308 321 = 0.66 ||========================================================================= x 25 7 7 7 8 10 8 3 26 | 500 | 474 453 486 495 474 = 0.65 || scomp_LempelZiv test: no 180 test no 181 TestU01 250000 runs BigCrush Test smarsa_S scomp_LempelZiv test: test no 181 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 0 | 0.5 | 0 1 0 0 1 > 0.99999 || = 0.64 737 628 740 708 725 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 0 0 1 1 0 > 0.99998 || = 0.63 294 301 279 296 305 | 500 < 0.00003 0 1 0 0 0 | 0.5 | 1 1 0 0 1 > 0.99997 || = 0.62 767 751 735 723 703 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99996 || = 0.61 283 300 335 312 306 | 500 < 0.00005 1 0 1 0 1 | 0.5 | 1 1 1 0 1 > 0.99995 || = 0.60 531 544 519 524 541 | 500 < 0.00006 0 1 0 0 1 | 0.5 | 1 2 2 0 0 > 0.99994 || = 0.59 598 582 588 597 536 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 351 298 361 332 360 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 3 0 0 0 > 0.99992 || = 0.57 719 699 704 742 734 | 500 < 0.00009 1 0 1 1 0 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 493 456 439 468 436 | 500 < 0.0001 1 0 0 1 0 | 0.5 | 0 1 0 3 1 > 0.9999 || = 0.55 533 525 527 542 548 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 534 547 506 484 528 | 500 < 0.0001 3 3 2 5 2 | 5 | 3 10 4 5 4 > 0.9999 || = 0.53 352 396 376 393 392 | 500 < 0.0002 6 6 2 6 2 | 5 | 0 4 5 3 3 > 0.9998 || = 0.52 392 405 396 406 405 | 500 < 0.0003 0 5 3 2 4 | 5 | 7 10 4 2 5 > 0.9997 || = 0.51 624 628 664 555 640 | 500 < 0.0004 5 3 3 6 5 | 5 | 5 8 7 4 2 > 0.9996 || = 0.50 608 645 606 677 617 | 500 < 0.0005 5 1 0 7 3 | 5 | 5 5 4 4 4 > 0.9995 || = 0.49 499 461 439 464 481 | 500 < 0.0006 7 8 3 2 2 | 5 | 3 10 4 7 5 > 0.9994 || = 0.48 190 167 210 199 180 | 500 < 0.0007 2 0 3 2 1 | 5 | 6 5 6 5 5 > 0.9993 || = 0.47 717 702 695 714 716 | 500 < 0.0008 1 4 8 6 4 | 5 | 7 7 5 6 11 > 0.9992 || = 0.46 388 354 385 371 389 | 500 < 0.0009 7 3 3 4 5 | 5 | 4 9 9 3 10 > 0.9991 || = 0.45 688 715 759 753 723 | 500 < 0.001 0 0 2 0 0 | 5 | 3 11 7 10 7 > 0.999 || = 0.44 358 337 348 370 305 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 600 655 625 664 629 | 500 < 0.001 36 33 29 40 28 | 50 | 43 79 55 49 56 > 0.999 || = 0.42 215 196 217 221 185 | 500 < 0.002 41 43 43 39 32 | 50 | 60 50 54 72 68 > 0.998 || = 0.41 606 628 681 645 691 | 500 < 0.003 41 51 55 55 50 | 50 | 57 55 53 68 51 > 0.997 || = 0.40 538 559 584 556 544 | 500 < 0.004 58 46 44 50 35 | 50 | 64 54 57 67 68 > 0.996 || = 0.39 416 407 409 411 420 | 500 < 0.005 47 50 44 38 40 | 50 | 54 80 71 84 59 > 0.995 || = 0.38 395 422 403 386 402 | 500 < 0.006 52 42 39 50 38 | 50 | 59 47 59 62 62 > 0.994 || = 0.37 671 637 636 613 654 | 500 < 0.007 47 45 47 55 47 | 50 | 46 52 64 46 47 > 0.993 || = 0.36 373 366 348 391 366 | 500 < 0.008 36 42 38 38 47 | 50 | 66 73 77 64 78 > 0.992 || = 0.35 747 689 698 737 717 | 500 < 0.009 38 35 30 28 35 | 50 | 50 48 66 39 48 > 0.991 || = 0.34 242 244 276 279 263 | 500 < 0.01 50 51 54 62 53 | 50 | 59 68 51 61 65 > 0.99 || = 0.33 662 631 620 653 662 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 354 351 349 348 359 | 500 < 0.01 446 438 423 455 405 | 497.5 | 558 606 607 612 602 > 0.99 || = 0.31 597 573 639 576 584 | 500 = 0.01 217 209 217 206 224 | 252.5 | 279 274 280 279 268 = 0.99 || = 0.30 430 446 415 438 418 | 500 = 0.02 415 435 422 409 467 | 500 | 618 632 610 583 607 = 0.98 || = 0.29 520 520 503 532 549 | 500 =================================================================| 500 | 566 521 515 551 571 = 0.97 || = 0.28 328 360 348 326 335 | 500 scomp_LempelZiv test: | 500 | 590 577 552 559 543 = 0.96 || = 0.27 548 505 531 559 572 | 500 ----------------------------------------------- | 500 | 537 535 556 527 524 = 0.95 || = 0.26 413 426 377 408 404 | 500 N = 10, n = 134217728, r = 0, s = 30, k = 27 | 500 | 581 585 546 485 582 = 0.94 || = 0.25 543 521 570 529 476 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 595 624 690 696 648 = 0.93 || = 0.24 515 529 467 499 556 | 500 | 500 | 511 505 535 522 540 = 0.92 || = 0.23 382 390 372 355 376 | 500 =================================================================| 500 | 543 547 544 521 539 = 0.91 || = 0.22 620 642 595 605 634 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 523 505 519 513 525 = 0.90 || = 0.21 450 470 458 451 458 | 500 -----------------------------------------------------------------| 500 | 448 453 412 439 476 = 0.89 || = 0.20 383 438 439 438 428 | 500 SD Bern.: d 5.77155 1.25282 1.29987 | 500 | 698 651 711 703 668 = 0.88 || = 0.19 426 425 465 445 440 | 500 s 5.63232 1.21221 2.30418 | 500 | 504 477 502 499 529 = 0.87 || = 0.18 456 460 436 449 437 | 500 t 5.65419 1.59891 1.89988 | 500 | 622 617 601 631 593 = 0.86 || = 0.17 408 383 426 405 410 | 500 m 5.60228 1.54154 2.38949 | 500 | 293 332 286 291 307 = 0.85 || = 0.16 577 600 591 607 591 | 500 x 5.76078 1.74958 1.96668 | 500 | 669 679 682 636 692 = 0.84 || = 0.15 395 419 432 443 438 | 500 | 500 | 344 360 364 353 316 = 0.83 || = 0.14 571 580 547 599 575 | 500 Changes: d 63 4 5 | 500 | 711 670 690 700 691 = 0.82 || = 0.13 379 378 392 401 371 | 500 s 65 3 6 | 500 | 371 382 376 393 412 = 0.81 || = 0.12 400 444 440 457 436 | 500 t 61 3 0 | 500 | 694 709 712 681 680 = 0.80 || = 0.11 478 467 492 453 500 | 500 m 67 5 5 | 500 | 320 354 333 337 344 = 0.79 || = 0.10 442 481 469 488 461 | 500 x 61 1 4 | 500 | 729 761 692 692 741 = 0.78 || = 0.09 441 463 449 443 431 | 500 -----------------------------------------------------------------| 500 | 420 432 446 416 441 = 0.77 || = 0.08 525 510 517 515 475 | 500 Aver./ d 0.51791 511 > 500: 3 2 5 4 5 6 6 6 6 10 | 500 | 555 563 566 561 539 = 0.76 || = 0.07 364 362 368 401 356 | 500 median s 0.51781 505 ----- 3 2 5 4 5 6 5 6 5 10 | 500 | 661 635 627 632 616 = 0.75 || = 0.06 550 537 521 545 570 | 500 t 0.51832 503 2 2 4 4 5 6 6 6 6 10 | 500 | 341 388 353 342 347 = 0.74 || = 0.05 467 464 436 440 431 | 500 m 0.51536 499 3 2 4 4 5 5 5 6 5 9 | 500 | 582 636 601 609 558 = 0.73 || = 0.04 427 403 412 424 379 | 500 x 0.51787 514 2 2 4 4 5 6 6 6 6 10 | 500 | 327 292 318 324 309 = 0.72 || = 0.03 549 501 490 509 514 | 500 -----------------------------------------------------------------| 500 | 652 610 609 613 596 = 0.71 || = 0.02 415 435 422 409 467 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 505 540 530 506 546 = 0.70 || = 0.01 217 209 217 206 224 | 252.5 d 28 7 6 2 10 10 7 4 27 | 500 | 595 595 561 544 643 = 0.69 || < 0.01 446 438 423 455 405 | 497.5 s 26 5 7 8 11 7 4 5 28 | 500 | 566 622 592 580 557 = 0.68 ||========================================================================= t 26 7 9 4 12 6 6 3 28 | 500 | 502 499 512 491 504 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 28 2 11 5 12 7 7 3 26 | 500 | 372 345 354 359 306 = 0.66 ||========================================================================= x 27 6 6 8 5 11 6 6 26 | 500 | 481 482 500 476 477 = 0.65 || scomp_LempelZiv test: no 181 test no 182 TestU01 250000 runs BigCrush Test smarsa_S scomp_LempelZiv test: test no 182 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 523 533 489 489 512 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 515 492 494 522 504 | 500 < 0.00003 0 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 490 525 520 472 516 | 500 < 0.00004 0 1 1 0 0 | 0.5 | 0 1 0 0 0 > 0.99996 || = 0.61 499 485 511 515 486 | 500 < 0.00005 1 0 1 2 0 | 0.5 | 1 0 0 1 0 > 0.99995 || = 0.60 542 513 465 498 509 | 500 < 0.00006 0 1 1 0 0 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 467 496 521 526 505 | 500 < 0.00007 1 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 501 494 515 507 495 | 500 < 0.00008 0 1 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99992 || = 0.57 462 498 473 500 525 | 500 < 0.00009 1 0 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99991 || = 0.56 491 515 532 488 497 | 500 < 0.0001 2 2 0 1 0 | 0.5 | 0 0 0 1 0 > 0.9999 || = 0.55 482 503 508 503 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 488 506 493 457 498 | 500 < 0.0001 5 7 3 7 2 | 5 | 2 1 3 2 0 > 0.9999 || = 0.53 536 482 491 523 501 | 500 < 0.0002 2 5 4 5 6 | 5 | 4 3 2 0 0 > 0.9998 || = 0.52 527 518 514 493 493 | 500 < 0.0003 5 6 9 6 2 | 5 | 9 2 4 3 8 > 0.9997 || = 0.51 527 521 518 534 467 | 500 < 0.0004 6 3 4 7 7 | 5 | 4 3 4 8 2 > 0.9996 || = 0.50 491 485 512 500 498 | 500 < 0.0005 2 3 3 0 7 | 5 | 6 2 1 1 2 > 0.9995 || = 0.49 536 480 496 534 500 | 500 < 0.0006 6 5 6 5 7 | 5 | 4 1 6 4 2 > 0.9994 || = 0.48 508 468 484 530 495 | 500 < 0.0007 3 6 6 4 6 | 5 | 7 7 6 0 7 > 0.9993 || = 0.47 496 462 482 477 470 | 500 < 0.0008 6 7 4 5 8 | 5 | 3 2 4 5 0 > 0.9992 || = 0.46 447 484 506 496 482 | 500 < 0.0009 1 3 2 11 8 | 5 | 5 5 4 7 6 > 0.9991 || = 0.45 499 453 509 507 511 | 500 < 0.001 10 5 10 5 8 | 5 | 2 6 4 2 7 > 0.999 || = 0.44 472 491 507 489 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 477 496 505 497 453 | 500 < 0.001 46 50 51 55 61 | 50 | 46 32 38 32 34 > 0.999 || = 0.42 492 489 483 475 510 | 500 < 0.002 55 40 47 54 41 | 50 | 39 36 49 43 40 > 0.998 || = 0.41 479 529 535 522 460 | 500 < 0.003 54 67 53 53 51 | 50 | 35 39 43 39 53 > 0.997 || = 0.40 490 506 496 497 501 | 500 < 0.004 49 62 50 58 57 | 50 | 40 44 51 56 46 > 0.996 || = 0.39 494 495 498 531 516 | 500 < 0.005 49 44 52 46 52 | 50 | 54 42 40 42 42 > 0.995 || = 0.38 494 502 518 507 537 | 500 < 0.006 53 61 59 54 51 | 50 | 46 42 47 51 42 > 0.994 || = 0.37 487 494 484 485 481 | 500 < 0.007 55 50 64 57 39 | 50 | 40 48 57 39 49 > 0.993 || = 0.36 494 511 479 497 480 | 500 < 0.008 49 59 46 65 53 | 50 | 54 43 45 46 51 > 0.992 || = 0.35 487 510 507 508 514 | 500 < 0.009 52 52 54 43 53 | 50 | 51 52 52 58 60 > 0.991 || = 0.34 506 479 539 494 471 | 500 < 0.01 38 53 51 61 48 | 50 | 40 47 56 43 46 > 0.99 || = 0.33 507 470 500 503 494 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 504 494 508 486 488 | 500 < 0.01 500 538 527 546 506 | 497.5 | 445 425 478 449 463 > 0.99 || = 0.31 496 457 509 541 495 | 500 = 0.01 265 266 259 237 254 | 252.5 | 280 289 242 250 257 = 0.99 || = 0.30 489 510 466 488 551 | 500 = 0.02 523 473 557 506 519 | 500 | 539 504 540 511 456 = 0.98 || = 0.29 474 478 491 486 508 | 500 =================================================================| 500 | 491 531 512 507 518 = 0.97 || = 0.28 515 473 468 491 487 | 500 scomp_LempelZiv test: | 500 | 500 484 505 531 525 = 0.96 || = 0.27 462 478 528 495 502 | 500 ----------------------------------------------- | 500 | 517 493 472 461 503 = 0.95 || = 0.26 520 520 500 478 524 | 500 N = 10, n = 134217728, r = 0, s = 30, k = 27 | 500 | 524 524 456 465 552 = 0.94 || = 0.25 493 504 510 511 493 | 500 Anderson-Darling statistic = A2 | 500 | 527 524 476 517 477 = 0.93 || = 0.24 493 508 482 543 497 | 500 | 500 | 482 498 492 489 482 = 0.92 || = 0.23 501 535 474 515 515 | 500 =================================================================| 500 | 495 502 481 510 513 = 0.91 || = 0.22 462 499 522 466 528 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 517 471 464 461 468 = 0.90 || = 0.21 536 501 500 491 536 | 500 -----------------------------------------------------------------| 500 | 516 503 474 516 484 = 0.89 || = 0.20 516 493 531 470 481 | 500 SD Bern.: d 1.06334 0.69603 1.19306 | 500 | 471 525 522 495 514 = 0.88 || = 0.19 492 526 473 524 531 | 500 s 0.97220 1.25282 1.32049 | 500 | 459 492 497 447 498 = 0.87 || = 0.18 479 512 513 500 482 | 500 t 1.06791 0.81649 0.91477 | 500 | 483 478 494 510 507 = 0.86 || = 0.17 498 464 512 513 519 | 500 m 0.99611 1.08681 1.30064 | 500 | 519 486 475 468 476 = 0.85 || = 0.16 464 518 511 505 507 | 500 x 0.99437 0.89486 1.12037 | 500 | 500 490 537 479 514 = 0.84 || = 0.15 508 521 528 480 498 | 500 | 500 | 462 500 457 510 527 = 0.83 || = 0.14 487 492 495 508 509 | 500 Changes: d 43 6 4 | 500 | 480 495 567 513 504 = 0.82 || = 0.13 536 487 556 531 494 | 500 s 47 5 2 | 500 | 529 498 492 500 483 = 0.81 || = 0.12 485 550 511 494 486 | 500 t 47 6 5 | 500 | 514 482 467 501 484 = 0.80 || = 0.11 537 510 504 527 527 | 500 m 59 4 6 | 500 | 510 509 521 472 513 = 0.79 || = 0.10 504 495 526 505 499 | 500 x 53 5 4 | 500 | 525 526 485 500 503 = 0.78 || = 0.09 516 497 488 509 570 | 500 -----------------------------------------------------------------| 500 | 553 498 490 462 481 = 0.77 || = 0.08 495 509 451 545 498 | 500 Aver./ d 0.49929 499 > 500: 8 4 5 3 2 5 5 5 4 5 | 500 | 511 477 499 471 519 = 0.76 || = 0.07 523 516 498 522 541 | 500 median s 0.49803 499 ----- 8 6 5 4 2 6 5 4 2 6 | 500 | 492 499 466 518 447 = 0.75 || = 0.06 550 513 487 499 511 | 500 t 0.49642 499 5 8 4 5 5 6 5 2 3 3 | 500 | 468 502 467 469 497 = 0.74 || = 0.05 474 513 526 558 534 | 500 m 0.49602 500 8 7 3 5 4 5 3 4 4 5 | 500 | 483 506 529 487 492 = 0.73 || = 0.04 520 537 485 501 487 | 500 x 0.49731 498 7 5 6 4 3 4 5 3 5 6 | 500 | 500 493 488 512 491 = 0.72 || = 0.03 532 549 541 503 475 | 500 -----------------------------------------------------------------| 500 | 486 488 480 505 483 = 0.71 || = 0.02 523 473 557 506 519 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 527 464 479 497 498 = 0.70 || = 0.01 265 266 259 237 254 | 252.5 d 0 0 3 13 64 19 2 0 0 | 500 | 518 501 454 517 474 = 0.69 || < 0.01 500 538 527 546 506 | 497.5 s 0 1 1 10 73 13 3 0 0 | 500 | 448 512 511 498 537 = 0.68 ||========================================================================= t 0 0 2 16 67 13 2 1 0 | 500 | 510 493 516 498 489 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 69 12 3 0 0 | 500 | 478 529 510 482 456 = 0.66 ||========================================================================= x 0 0 2 12 72 12 2 1 0 | 500 | 486 488 484 472 506 = 0.65 || scomp_LempelZiv test: no 182 test no 183 TestU01 250000 runs BigCrush Test smarsa_S scomp_LempelZiv test: test no 183 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 507 511 541 527 511 | 500 < 0.00002 0 1 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99998 || = 0.63 506 505 520 517 500 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 526 497 531 504 554 | 500 < 0.00004 1 2 1 2 0 | 0.5 | 0 0 2 2 0 > 0.99996 || = 0.61 468 389 447 397 437 | 500 < 0.00005 0 1 0 1 0 | 0.5 | 2 0 1 2 0 > 0.99995 || = 0.60 572 536 520 509 538 | 500 < 0.00006 0 0 0 1 1 | 0.5 | 2 0 1 0 2 > 0.99994 || = 0.59 536 498 548 516 565 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 1 3 3 0 1 > 0.99993 || = 0.58 515 513 575 512 539 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 0 0 1 0 1 > 0.99992 || = 0.57 448 432 452 458 449 | 500 < 0.00009 1 3 0 2 1 | 0.5 | 0 1 1 0 0 > 0.99991 || = 0.56 543 522 531 543 523 | 500 < 0.0001 0 0 0 1 1 | 0.5 | 0 1 2 1 1 > 0.9999 || = 0.55 534 548 566 517 525 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 415 476 407 419 413 | 500 < 0.0001 2 7 1 9 4 | 5 | 5 6 11 6 5 > 0.9999 || = 0.53 597 561 520 527 501 | 500 < 0.0002 1 3 2 3 5 | 5 | 5 3 4 5 5 > 0.9998 || = 0.52 543 521 538 611 495 | 500 < 0.0003 7 4 5 3 4 | 5 | 4 9 7 6 16 > 0.9997 || = 0.51 431 425 467 418 429 | 500 < 0.0004 2 3 2 6 4 | 5 | 5 6 6 6 4 > 0.9996 || = 0.50 531 554 562 489 536 | 500 < 0.0005 5 2 4 4 4 | 5 | 7 5 3 7 3 > 0.9995 || = 0.49 424 423 469 421 428 | 500 < 0.0006 8 4 4 5 3 | 5 | 5 4 9 8 7 > 0.9994 || = 0.48 557 497 531 496 534 | 500 < 0.0007 4 6 2 4 4 | 5 | 1 8 6 6 4 > 0.9993 || = 0.47 533 560 584 521 554 | 500 < 0.0008 1 3 3 6 5 | 5 | 4 7 4 7 9 > 0.9992 || = 0.46 450 434 417 434 401 | 500 < 0.0009 8 5 5 6 3 | 5 | 8 6 4 7 7 > 0.9991 || = 0.45 524 496 514 521 531 | 500 < 0.001 6 4 7 2 3 | 5 | 8 5 11 9 8 > 0.999 || = 0.44 530 507 551 518 542 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 430 403 473 440 422 | 500 < 0.001 44 41 35 48 39 | 50 | 52 59 65 67 68 > 0.999 || = 0.42 499 513 520 509 518 | 500 < 0.002 47 55 36 36 42 | 50 | 70 63 81 66 56 > 0.998 || = 0.41 535 484 484 487 495 | 500 < 0.003 33 45 58 48 43 | 50 | 47 65 53 64 64 > 0.997 || = 0.40 534 515 456 536 522 | 500 < 0.004 48 45 53 43 25 | 50 | 63 61 70 74 58 > 0.996 || = 0.39 414 445 391 411 377 | 500 < 0.005 43 36 45 39 42 | 50 | 53 63 63 61 64 > 0.995 || = 0.38 460 483 498 528 511 | 500 < 0.006 46 34 48 40 43 | 50 | 47 49 56 67 65 > 0.994 || = 0.37 475 509 495 455 502 | 500 < 0.007 41 48 38 34 37 | 50 | 60 67 71 54 59 > 0.993 || = 0.36 492 475 473 493 492 | 500 < 0.008 34 53 45 47 49 | 50 | 67 69 60 46 58 > 0.992 || = 0.35 507 510 420 503 517 | 500 < 0.009 37 51 42 43 43 | 50 | 62 56 60 52 73 > 0.991 || = 0.34 467 476 497 474 481 | 500 < 0.01 43 44 35 42 44 | 50 | 68 62 56 43 46 > 0.99 || = 0.33 459 451 458 494 481 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 485 432 441 485 485 | 500 < 0.01 416 452 435 420 407 | 497.5 | 589 614 635 594 611 > 0.99 || = 0.31 445 489 505 519 460 | 500 = 0.01 234 206 205 213 213 | 252.5 | 312 309 295 314 285 = 0.99 || = 0.30 556 544 513 572 553 | 500 = 0.02 459 442 450 469 440 | 500 | 593 554 588 575 573 = 0.98 || = 0.29 410 464 440 466 444 | 500 =================================================================| 500 | 583 577 538 543 594 = 0.97 || = 0.28 542 492 521 535 543 | 500 scomp_LempelZiv test: | 500 | 585 606 597 610 602 = 0.96 || = 0.27 393 419 413 418 446 | 500 ----------------------------------------------- | 500 | 500 533 572 522 560 = 0.95 || = 0.26 501 515 499 517 552 | 500 N = 10, n = 134217728, r = 0, s = 30, k = 27 | 500 | 591 567 616 586 628 = 0.94 || = 0.25 478 456 470 512 489 | 500 Tests on the sum of all N observations | 500 | 582 626 599 582 613 = 0.93 || = 0.24 429 431 384 421 427 | 500 | 500 | 508 523 514 511 525 = 0.92 || = 0.23 554 566 541 562 516 | 500 =================================================================| 500 | 514 573 525 510 535 = 0.91 || = 0.22 465 503 473 440 446 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 568 560 589 566 556 = 0.90 || = 0.21 426 436 475 413 427 | 500 -----------------------------------------------------------------| 500 | 548 555 567 572 542 = 0.89 || = 0.20 511 508 516 471 477 | 500 SD Bern.: d 2.54236 1.38488 1.70789 | 500 | 531 476 533 545 515 = 0.88 || = 0.19 391 392 450 441 443 | 500 s 2.36679 1.14773 1.78750 | 500 | 604 549 559 565 540 = 0.87 || = 0.18 441 502 491 445 450 | 500 t 2.50523 1.40141 2.22686 | 500 | 484 530 523 486 469 = 0.86 || = 0.17 541 553 497 499 516 | 500 m 2.42560 1.30602 1.90462 | 500 | 575 545 526 533 546 = 0.85 || = 0.16 433 401 403 441 433 | 500 x 2.44784 1.56730 1.86156 | 500 | 485 490 526 505 475 = 0.84 || = 0.15 445 450 460 467 482 | 500 | 500 | 623 585 566 629 587 = 0.83 || = 0.14 429 456 443 454 436 | 500 Changes: d 51 0 4 | 500 | 537 516 524 506 529 = 0.82 || = 0.13 483 504 453 452 499 | 500 s 51 4 2 | 500 | 457 451 458 455 480 = 0.81 || = 0.12 430 441 439 460 441 | 500 t 37 2 0 | 500 | 595 516 547 589 529 = 0.80 || = 0.11 490 472 441 511 503 | 500 m 45 0 3 | 500 | 454 494 479 479 505 = 0.79 || = 0.10 481 469 471 479 484 | 500 x 51 0 1 | 500 | 495 524 488 536 511 = 0.78 || = 0.09 426 455 420 447 440 | 500 -----------------------------------------------------------------| 500 | 617 597 610 596 587 = 0.77 || = 0.08 423 461 456 464 409 | 500 Aver./ d 0.51942 499 > 500: 1 1 4 2 6 7 6 5 7 9 | 500 | 450 436 434 427 457 = 0.76 || = 0.07 515 474 468 477 467 | 500 median s 0.51835 502 ----- 0 3 4 3 4 6 7 6 7 10 | 500 | 514 545 550 549 547 = 0.75 || = 0.06 468 456 441 469 436 | 500 t 0.52133 498 0 0 3 2 5 7 7 5 9 10 | 500 | 528 591 533 536 581 = 0.74 || = 0.05 445 444 411 396 446 | 500 m 0.51811 504 0 1 4 4 5 7 7 6 8 10 | 500 | 489 468 467 442 421 = 0.73 || = 0.04 457 442 464 489 449 | 500 x 0.51968 502 0 2 3 4 6 6 6 7 7 10 | 500 | 506 558 542 562 543 = 0.72 || = 0.03 430 486 459 419 442 | 500 -----------------------------------------------------------------| 500 | 492 498 452 478 467 = 0.71 || = 0.02 459 442 450 469 440 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 609 583 600 600 591 = 0.70 || = 0.01 234 206 205 213 213 | 252.5 d 3 14 8 12 27 16 5 7 9 | 500 | 481 506 467 497 490 = 0.69 || < 0.01 416 452 435 420 407 | 497.5 s 4 6 14 13 32 8 13 6 5 | 500 | 503 536 519 514 538 = 0.68 ||========================================================================= t 5 4 15 18 21 16 10 5 7 | 500 | 469 497 525 481 512 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 3 9 13 10 36 11 6 6 7 | 500 | 484 506 552 538 492 = 0.66 ||========================================================================= x 4 8 16 7 28 18 10 4 6 | 500 | 551 524 481 519 540 = 0.65 || scomp_LempelZiv test: no 183 test no 184 TestU01 250000 runs BigCrush Test smarsa_S scomp_LempelZiv test: test no 184 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 0 0 2 0 1 > 0.99999 || = 0.64 470 471 491 476 517 | 500 < 0.00002 0 0 1 0 2 | 0.5 | 3 0 0 0 0 > 0.99998 || = 0.63 497 449 505 529 486 | 500 < 0.00003 0 1 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 517 514 501 465 467 | 500 < 0.00004 3 1 0 2 0 | 0.5 | 0 1 0 1 2 > 0.99996 || = 0.61 494 538 511 469 501 | 500 < 0.00005 1 1 1 0 0 | 0.5 | 1 0 0 1 0 > 0.99995 || = 0.60 508 490 493 488 512 | 500 < 0.00006 0 0 1 1 0 | 0.5 | 1 0 0 0 1 > 0.99994 || = 0.59 502 466 490 518 501 | 500 < 0.00007 1 0 1 0 0 | 0.5 | 1 0 0 1 0 > 0.99993 || = 0.58 476 523 475 469 517 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 1 1 1 0 0 > 0.99992 || = 0.57 482 499 498 543 463 | 500 < 0.00009 0 1 0 2 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 570 446 456 483 484 | 500 < 0.0001 1 0 2 0 1 | 0.5 | 1 1 2 0 1 > 0.9999 || = 0.55 503 469 477 516 452 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 513 477 504 524 504 | 500 < 0.0001 6 5 7 5 5 | 5 | 8 3 5 3 5 > 0.9999 || = 0.53 495 531 528 483 535 | 500 < 0.0002 2 7 6 5 5 | 5 | 0 4 5 0 1 > 0.9998 || = 0.52 528 444 483 489 523 | 500 < 0.0003 3 2 6 11 8 | 5 | 3 4 3 3 5 > 0.9997 || = 0.51 511 552 512 484 480 | 500 < 0.0004 8 3 6 2 6 | 5 | 4 8 7 7 5 > 0.9996 || = 0.50 503 517 499 482 533 | 500 < 0.0005 5 6 3 6 10 | 5 | 3 8 10 9 6 > 0.9995 || = 0.49 521 489 469 494 486 | 500 < 0.0006 7 4 5 3 5 | 5 | 9 2 4 8 6 > 0.9994 || = 0.48 489 491 500 502 514 | 500 < 0.0007 3 6 2 6 5 | 5 | 1 6 6 4 1 > 0.9993 || = 0.47 528 503 496 498 510 | 500 < 0.0008 6 4 6 3 6 | 5 | 3 3 2 6 5 > 0.9992 || = 0.46 509 529 520 527 477 | 500 < 0.0009 4 5 6 4 4 | 5 | 5 4 7 5 4 > 0.9991 || = 0.45 530 510 518 522 475 | 500 < 0.001 3 5 8 7 4 | 5 | 4 2 5 6 6 > 0.999 || = 0.44 503 462 498 511 463 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 527 493 526 488 469 | 500 < 0.001 47 47 55 52 58 | 50 | 40 44 54 51 44 > 0.999 || = 0.42 470 504 498 511 470 | 500 < 0.002 37 52 44 69 49 | 50 | 53 42 60 48 51 > 0.998 || = 0.41 488 531 507 451 481 | 500 < 0.003 66 57 53 38 49 | 50 | 52 49 54 50 42 > 0.997 || = 0.40 515 535 502 488 499 | 500 < 0.004 49 60 62 57 57 | 50 | 40 51 50 49 40 > 0.996 || = 0.39 484 524 517 482 490 | 500 < 0.005 48 66 41 50 50 | 50 | 42 48 56 37 53 > 0.995 || = 0.38 522 537 531 531 521 | 500 < 0.006 60 51 57 59 63 | 50 | 40 44 56 49 30 > 0.994 || = 0.37 520 520 506 523 520 | 500 < 0.007 58 51 57 42 61 | 50 | 53 41 50 46 50 > 0.993 || = 0.36 489 513 504 502 498 | 500 < 0.008 68 46 52 61 49 | 50 | 40 46 53 49 50 > 0.992 || = 0.35 489 536 508 508 516 | 500 < 0.009 53 48 50 46 48 | 50 | 48 40 51 56 42 > 0.991 || = 0.34 524 532 504 513 477 | 500 < 0.01 56 55 44 55 56 | 50 | 56 40 47 38 47 > 0.99 || = 0.33 517 493 495 509 515 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 533 468 524 487 510 | 500 < 0.01 542 533 515 529 540 | 497.5 | 464 445 531 473 449 > 0.99 || = 0.31 509 517 528 530 480 | 500 = 0.01 292 281 276 274 259 | 252.5 | 257 258 237 257 243 = 0.99 || = 0.30 485 495 480 512 492 | 500 = 0.02 534 511 521 533 500 | 500 | 469 465 449 497 513 = 0.98 || = 0.29 473 521 509 558 521 | 500 =================================================================| 500 | 453 522 472 447 472 = 0.97 || = 0.28 493 537 495 484 490 | 500 scomp_LempelZiv test: | 500 | 481 458 479 496 503 = 0.96 || = 0.27 481 520 537 532 515 | 500 ----------------------------------------------- | 500 | 478 478 498 489 495 = 0.95 || = 0.26 495 494 487 523 499 | 500 N = 10, n = 134217728, r = 0, s = 30, k = 27 | 500 | 477 527 466 541 495 = 0.94 || = 0.25 501 533 482 505 478 | 500 Sample variance | 500 | 500 482 485 517 501 = 0.93 || = 0.24 486 490 504 546 509 | 500 | 500 | 486 455 465 513 495 = 0.92 || = 0.23 483 516 470 525 489 | 500 =================================================================| 500 | 489 481 478 472 462 = 0.91 || = 0.22 483 490 491 530 544 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 515 494 493 537 469 = 0.90 || = 0.21 505 489 529 501 508 | 500 -----------------------------------------------------------------| 500 | 482 453 509 466 491 = 0.89 || = 0.20 526 539 544 540 504 | 500 SD Bern.: d 1.02656 1.39496 1.02617 | 500 | 523 475 474 474 491 = 0.88 || = 0.19 538 517 537 523 509 | 500 s 1.33421 0.96484 0.93747 | 500 | 484 477 471 455 483 = 0.87 || = 0.18 503 490 511 475 515 | 500 t 0.97055 0.93105 0.66815 | 500 | 476 446 525 474 503 = 0.86 || = 0.17 511 547 496 500 494 | 500 m 1.14846 1.31594 0.86413 | 500 | 500 440 486 466 489 = 0.85 || = 0.16 492 516 518 494 517 | 500 x 1.04404 0.94492 1.16933 | 500 | 484 529 508 472 471 = 0.84 || = 0.15 512 542 490 502 525 | 500 | 500 | 491 512 506 483 492 = 0.83 || = 0.14 531 529 476 515 495 | 500 Changes: d 43 3 5 | 500 | 459 479 515 489 508 = 0.82 || = 0.13 538 492 509 472 533 | 500 s 41 3 2 | 500 | 485 498 512 482 521 = 0.81 || = 0.12 498 489 518 541 538 | 500 t 42 5 5 | 500 | 531 450 486 503 503 = 0.80 || = 0.11 536 511 539 514 503 | 500 m 39 8 3 | 500 | 503 464 498 461 512 = 0.79 || = 0.10 498 516 489 505 533 | 500 x 47 6 4 | 500 | 465 474 495 478 478 = 0.78 || = 0.09 480 505 502 522 562 | 500 -----------------------------------------------------------------| 500 | 523 471 484 481 473 = 0.77 || = 0.08 481 529 512 524 550 | 500 Aver./ d 0.49518 498 > 500: 6 7 3 6 7 7 2 6 2 1 | 500 | 482 457 499 513 472 = 0.76 || = 0.07 488 524 503 562 517 | 500 median s 0.49153 499 ----- 9 7 6 7 6 3 5 1 2 3 | 500 | 514 465 497 470 505 = 0.75 || = 0.06 510 540 496 531 532 | 500 t 0.49468 500 8 6 5 8 5 3 4 3 6 1 | 500 | 441 467 514 491 472 = 0.74 || = 0.05 498 514 539 511 487 | 500 m 0.49279 501 9 6 9 8 5 4 2 3 1 4 | 500 | 533 559 511 470 546 = 0.73 || = 0.04 502 485 565 504 518 | 500 x 0.49462 501 7 8 6 5 2 6 6 5 3 3 | 500 | 521 491 501 509 454 = 0.72 || = 0.03 514 539 496 496 496 | 500 -----------------------------------------------------------------| 500 | 484 469 487 452 501 = 0.71 || = 0.02 534 511 521 533 500 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 486 510 508 477 518 = 0.70 || = 0.01 292 281 276 274 259 | 252.5 d 0 0 2 12 68 16 2 1 0 | 500 | 483 470 442 486 511 = 0.69 || < 0.01 542 533 515 529 540 | 497.5 s 0 0 9 18 46 24 4 0 0 | 500 | 473 547 472 448 492 = 0.68 ||========================================================================= t 0 0 2 14 70 14 1 0 0 | 500 | 507 536 500 484 452 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 5 17 55 21 3 0 0 | 500 | 476 493 475 488 526 = 0.66 ||========================================================================= x 0 0 4 15 68 11 3 0 0 | 500 | 480 496 462 511 521 = 0.65 || scomp_LempelZiv test: no 184 test no 185 TestU01 250000 runs BigCrush Test smarsa_S scomp_LempelZiv test: test no 185 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 2 0 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 763 686 691 725 732 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 1 1 0 2 1 > 0.99998 || = 0.63 271 290 284 307 294 | 500 < 0.00003 1 2 1 0 0 | 0.5 | 0 1 2 1 0 > 0.99997 || = 0.62 798 755 743 706 706 | 500 < 0.00004 0 0 1 2 0 | 0.5 | 0 1 0 1 0 > 0.99996 || = 0.61 304 280 304 305 294 | 500 < 0.00005 1 0 3 0 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 502 549 519 486 533 | 500 < 0.00006 0 2 0 1 0 | 0.5 | 0 0 0 1 1 > 0.99994 || = 0.59 566 614 538 564 621 | 500 < 0.00007 2 0 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 331 292 316 333 313 | 500 < 0.00008 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 717 695 683 719 755 | 500 < 0.00009 0 2 2 1 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 440 421 437 442 468 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 1 1 0 0 1 > 0.9999 || = 0.55 526 490 540 508 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 514 544 465 489 480 | 500 < 0.0001 5 9 8 8 3 | 5 | 2 5 2 5 3 > 0.9999 || = 0.53 406 397 353 398 363 | 500 < 0.0002 4 5 10 3 3 | 5 | 2 3 3 1 2 > 0.9998 || = 0.52 409 394 410 436 406 | 500 < 0.0003 9 7 3 4 4 | 5 | 6 3 3 1 1 > 0.9997 || = 0.51 647 669 630 615 617 | 500 < 0.0004 2 8 6 6 6 | 5 | 4 0 4 8 4 > 0.9996 || = 0.50 601 614 666 652 603 | 500 < 0.0005 8 4 4 7 3 | 5 | 7 7 1 6 3 > 0.9995 || = 0.49 518 487 468 460 473 | 500 < 0.0006 2 10 7 11 8 | 5 | 4 5 7 3 5 > 0.9994 || = 0.48 213 165 166 177 184 | 500 < 0.0007 10 4 3 6 5 | 5 | 4 4 5 7 6 > 0.9993 || = 0.47 713 693 753 711 755 | 500 < 0.0008 12 9 7 8 4 | 5 | 4 3 5 10 6 > 0.9992 || = 0.46 399 392 379 396 365 | 500 < 0.0009 9 9 5 8 13 | 5 | 7 6 5 3 4 > 0.9991 || = 0.45 737 720 685 739 799 | 500 < 0.001 1 0 0 0 0 | 5 | 3 3 4 6 5 > 0.999 || = 0.44 313 368 328 317 366 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 602 629 621 651 641 | 500 < 0.001 62 65 53 61 49 | 50 | 43 39 39 50 39 > 0.999 || = 0.42 207 213 226 229 238 | 500 < 0.002 63 56 57 48 48 | 50 | 35 50 38 43 49 > 0.998 || = 0.41 707 697 721 660 682 | 500 < 0.003 57 79 53 55 64 | 50 | 40 55 46 32 33 > 0.997 || = 0.40 602 541 560 558 570 | 500 < 0.004 60 57 62 71 59 | 50 | 26 37 45 39 39 > 0.996 || = 0.39 444 436 478 441 429 | 500 < 0.005 45 64 67 45 64 | 50 | 58 48 50 54 57 > 0.995 || = 0.38 398 449 438 419 462 | 500 < 0.006 64 60 58 61 60 | 50 | 45 43 43 50 38 > 0.994 || = 0.37 631 661 654 674 625 | 500 < 0.007 54 59 51 53 67 | 50 | 39 43 37 40 30 > 0.993 || = 0.36 372 369 373 390 356 | 500 < 0.008 55 53 59 61 60 | 50 | 52 51 48 48 38 > 0.992 || = 0.35 730 779 733 793 797 | 500 < 0.009 43 49 48 42 32 | 50 | 36 44 46 40 42 > 0.991 || = 0.34 249 268 271 276 239 | 500 < 0.01 74 66 61 68 62 | 50 | 52 41 50 49 32 > 0.99 || = 0.33 641 644 667 691 683 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 362 374 378 381 398 | 500 < 0.01 577 608 569 565 565 | 497.5 | 426 451 442 445 397 > 0.99 || = 0.31 661 639 636 657 677 | 500 = 0.01 291 283 248 286 290 | 252.5 | 212 193 204 199 185 = 0.99 || = 0.30 492 457 467 466 425 | 500 = 0.02 574 519 540 554 556 | 500 | 429 482 499 448 465 = 0.98 || = 0.29 567 588 529 558 562 | 500 =================================================================| 500 | 441 453 399 458 435 = 0.97 || = 0.28 399 380 377 379 365 | 500 scomp_LempelZiv test: | 500 | 483 477 473 454 484 = 0.96 || = 0.27 618 579 580 601 552 | 500 ----------------------------------------------- | 500 | 409 430 432 423 455 = 0.95 || = 0.26 464 422 445 431 405 | 500 N = 10, n = 134217728, r = 15, s = 15, k = 27 | 500 | 467 445 464 455 476 = 0.94 || = 0.25 557 588 590 584 552 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 520 564 475 522 518 = 0.93 || = 0.24 525 580 586 535 579 | 500 | 500 | 457 447 453 450 452 = 0.92 || = 0.23 409 428 467 384 408 | 500 =================================================================| 500 | 429 465 428 474 410 = 0.91 || = 0.22 633 639 679 634 678 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 436 443 412 472 449 = 0.90 || = 0.21 467 451 474 506 480 | 500 -----------------------------------------------------------------| 500 | 376 363 407 363 405 = 0.89 || = 0.20 458 483 478 448 451 | 500 SD Bern.: d 5.69353 1.64337 1.65248 | 500 | 570 628 578 609 622 = 0.88 || = 0.19 487 467 514 465 534 | 500 s 5.58581 1.89514 1.03491 | 500 | 415 443 437 394 446 = 0.87 || = 0.18 486 520 470 505 509 | 500 t 5.61043 1.24239 1.04358 | 500 | 559 510 517 529 510 = 0.86 || = 0.17 418 433 426 440 375 | 500 m 5.65055 1.58508 1.19641 | 500 | 283 254 259 268 260 = 0.85 || = 0.16 657 627 613 668 655 | 500 x 5.89580 1.69495 1.82134 | 500 | 565 646 556 637 603 = 0.84 || = 0.15 477 562 516 458 462 | 500 | 500 | 321 301 334 296 285 = 0.83 || = 0.14 622 606 654 640 689 | 500 Changes: d 67 4 5 | 500 | 618 626 660 662 631 = 0.82 || = 0.13 426 477 438 439 467 | 500 s 67 2 4 | 500 | 354 366 349 358 338 = 0.81 || = 0.12 576 504 517 513 485 | 500 t 65 2 0 | 500 | 615 595 661 606 620 = 0.80 || = 0.11 550 552 604 599 579 | 500 m 65 6 2 | 500 | 325 309 303 314 312 = 0.79 || = 0.10 528 564 571 528 550 | 500 x 67 3 2 | 500 | 682 594 653 677 678 = 0.78 || = 0.09 506 554 563 588 533 | 500 -----------------------------------------------------------------| 500 | 389 353 365 356 402 = 0.77 || = 0.08 609 611 588 586 574 | 500 Aver./ d 0.48355 492 > 500: 8 5 5 4 6 6 4 5 4 1 | 500 | 500 507 471 529 552 = 0.76 || = 0.07 462 453 438 447 448 | 500 median s 0.48368 490 ----- 8 7 5 4 5 5 4 6 4 1 | 500 | 635 583 621 593 615 = 0.75 || = 0.06 667 631 638 642 632 | 500 t 0.48274 491 7 7 5 4 5 5 6 5 4 0 | 500 | 316 344 355 363 338 = 0.74 || = 0.05 574 564 591 535 536 | 500 m 0.48391 505 9 6 6 4 5 4 6 6 4 1 | 500 | 578 550 531 555 577 = 0.73 || = 0.04 490 489 484 516 502 | 500 x 0.48450 485 9 6 5 4 5 5 4 6 4 1 | 500 | 260 299 304 266 258 = 0.72 || = 0.03 623 602 621 609 602 | 500 -----------------------------------------------------------------| 500 | 610 517 611 543 561 = 0.71 || = 0.02 574 519 540 554 556 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 469 478 509 505 477 = 0.70 || = 0.01 291 283 248 286 290 | 252.5 d 25 6 5 8 14 4 6 7 26 | 500 | 519 553 525 554 572 = 0.69 || < 0.01 577 608 569 565 565 | 497.5 s 22 6 10 6 13 3 9 5 27 | 500 | 529 590 597 516 532 = 0.68 ||========================================================================= t 23 5 8 11 11 7 3 6 27 | 500 | 485 486 526 501 479 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 23 4 13 7 11 6 7 4 26 | 500 | 347 355 338 348 327 = 0.66 ||========================================================================= x 28 2 8 8 10 5 8 7 25 | 500 | 488 465 463 444 444 = 0.65 || scomp_LempelZiv test: no 185 test no 186 TestU01 250000 runs BigCrush Test smarsa_S scomp_LempelZiv test: test no 186 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99999 || = 0.64 735 725 767 739 751 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 0 1 0 1 1 > 0.99998 || = 0.63 291 305 324 336 268 | 500 < 0.00003 0 0 1 1 0 | 0.5 | 1 2 1 1 0 > 0.99997 || = 0.62 752 703 762 739 709 | 500 < 0.00004 3 1 1 0 1 | 0.5 | 0 1 1 0 1 > 0.99996 || = 0.61 288 303 311 302 282 | 500 < 0.00005 1 1 2 0 0 | 0.5 | 0 0 1 1 0 > 0.99995 || = 0.60 569 527 562 523 546 | 500 < 0.00006 2 0 0 0 0 | 0.5 | 1 1 0 0 0 > 0.99994 || = 0.59 609 592 606 604 612 | 500 < 0.00007 0 0 0 0 1 | 0.5 | 1 1 0 0 0 > 0.99993 || = 0.58 337 351 315 312 337 | 500 < 0.00008 0 2 0 1 0 | 0.5 | 1 0 0 1 0 > 0.99992 || = 0.57 731 710 730 742 745 | 500 < 0.00009 0 0 1 1 0 | 0.5 | 0 0 0 3 0 > 0.99991 || = 0.56 403 451 444 455 497 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 2 2 4 0 0 > 0.9999 || = 0.55 498 530 510 527 525 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 566 488 464 508 518 | 500 < 0.0001 6 6 5 3 3 | 5 | 6 8 8 7 2 > 0.9999 || = 0.53 387 400 389 384 396 | 500 < 0.0002 5 4 5 3 3 | 5 | 3 5 3 2 3 > 0.9998 || = 0.52 395 406 400 350 427 | 500 < 0.0003 4 4 2 4 7 | 5 | 3 10 10 5 7 > 0.9997 || = 0.51 605 658 646 610 635 | 500 < 0.0004 4 4 2 6 4 | 5 | 7 3 10 7 5 > 0.9996 || = 0.50 679 646 614 661 618 | 500 < 0.0005 4 9 6 3 4 | 5 | 5 4 6 6 5 > 0.9995 || = 0.49 456 464 455 442 457 | 500 < 0.0006 2 2 5 7 9 | 5 | 5 7 10 5 5 > 0.9994 || = 0.48 179 184 200 194 166 | 500 < 0.0007 4 3 3 3 4 | 5 | 5 7 10 8 4 > 0.9993 || = 0.47 724 725 683 725 786 | 500 < 0.0008 6 4 3 6 7 | 5 | 9 10 9 6 19 > 0.9992 || = 0.46 366 369 347 382 389 | 500 < 0.0009 4 5 3 7 7 | 5 | 7 5 7 7 4 > 0.9991 || = 0.45 687 683 713 749 701 | 500 < 0.001 3 0 1 0 0 | 5 | 7 11 2 9 5 > 0.999 || = 0.44 348 356 356 342 319 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 622 617 602 617 615 | 500 < 0.001 42 41 35 42 48 | 50 | 57 70 75 62 59 > 0.999 || = 0.42 215 212 200 235 211 | 500 < 0.002 43 54 35 46 40 | 50 | 54 68 56 52 55 > 0.998 || = 0.41 683 642 673 607 660 | 500 < 0.003 37 50 43 54 51 | 50 | 39 58 60 73 62 > 0.997 || = 0.40 534 568 570 585 512 | 500 < 0.004 40 48 45 47 40 | 50 | 60 55 53 47 55 > 0.996 || = 0.39 428 410 409 437 434 | 500 < 0.005 41 31 36 38 38 | 50 | 86 78 79 69 57 > 0.995 || = 0.38 412 391 419 364 429 | 500 < 0.006 37 62 38 40 39 | 50 | 45 47 64 65 51 > 0.994 || = 0.37 700 591 613 644 628 | 500 < 0.007 51 48 42 40 54 | 50 | 58 61 60 51 50 > 0.993 || = 0.36 355 357 379 329 350 | 500 < 0.008 42 45 45 50 42 | 50 | 60 74 80 67 70 > 0.992 || = 0.35 754 736 758 779 737 | 500 < 0.009 33 36 49 27 32 | 50 | 42 49 38 38 46 > 0.991 || = 0.34 234 260 297 279 223 | 500 < 0.01 53 53 50 48 54 | 50 | 61 62 60 57 81 > 0.99 || = 0.33 639 661 643 640 624 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 358 383 388 367 381 | 500 < 0.01 419 468 418 432 438 | 497.5 | 562 622 625 581 586 > 0.99 || = 0.31 603 599 602 593 628 | 500 = 0.01 215 199 208 215 218 | 252.5 | 301 276 240 269 256 = 0.99 || = 0.30 442 427 434 469 421 | 500 = 0.02 436 445 473 406 414 | 500 | 606 599 612 630 644 = 0.98 || = 0.29 516 543 542 501 517 | 500 =================================================================| 500 | 532 530 536 539 510 = 0.97 || = 0.28 357 366 321 360 317 | 500 scomp_LempelZiv test: | 500 | 565 531 566 582 587 = 0.96 || = 0.27 508 535 572 535 510 | 500 ----------------------------------------------- | 500 | 532 517 511 530 512 = 0.95 || = 0.26 404 426 403 420 445 | 500 N = 10, n = 134217728, r = 15, s = 15, k = 27 | 500 | 530 540 584 576 546 = 0.94 || = 0.25 493 567 514 545 544 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 605 629 646 656 663 = 0.93 || = 0.24 490 499 511 507 525 | 500 | 500 | 526 519 548 529 555 = 0.92 || = 0.23 359 378 386 356 365 | 500 =================================================================| 500 | 534 559 512 559 510 = 0.91 || = 0.22 648 587 593 608 587 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 554 511 526 510 524 = 0.90 || = 0.21 461 403 430 499 461 | 500 -----------------------------------------------------------------| 500 | 454 463 469 452 478 = 0.89 || = 0.20 422 433 409 386 443 | 500 SD Bern.: d 5.78712 1.41137 1.97886 | 500 | 682 659 717 672 644 = 0.88 || = 0.19 448 413 428 451 430 | 500 s 5.57678 1.29679 2.21379 | 500 | 489 489 502 450 497 = 0.87 || = 0.18 425 452 445 463 437 | 500 t 5.70961 1.38199 2.47145 | 500 | 572 605 598 607 643 = 0.86 || = 0.17 380 370 390 400 405 | 500 m 5.79868 1.40212 1.87442 | 500 | 296 310 323 300 332 = 0.85 || = 0.16 605 638 563 605 614 | 500 x 5.70008 1.33482 1.84590 | 500 | 639 680 661 641 618 = 0.84 || = 0.15 444 451 452 449 412 | 500 | 500 | 352 378 383 333 357 = 0.83 || = 0.14 551 537 563 580 530 | 500 Changes: d 65 3 6 | 500 | 724 706 689 699 678 = 0.82 || = 0.13 397 395 384 430 410 | 500 s 63 5 4 | 500 | 399 404 403 371 384 = 0.81 || = 0.12 437 460 384 462 452 | 500 t 63 0 2 | 500 | 714 634 662 698 649 = 0.80 || = 0.11 459 483 524 514 463 | 500 m 67 2 4 | 500 | 336 332 281 327 315 = 0.79 || = 0.10 504 461 532 414 488 | 500 x 65 5 4 | 500 | 722 757 749 750 710 = 0.78 || = 0.09 462 465 447 454 475 | 500 -----------------------------------------------------------------| 500 | 415 418 419 417 461 = 0.77 || = 0.08 524 487 495 499 457 | 500 Aver./ d 0.51666 504 > 500: 3 3 3 4 5 5 6 6 5 10 | 500 | 529 576 532 553 552 = 0.76 || = 0.07 368 380 377 355 373 | 500 median s 0.51633 489 ----- 1 2 4 4 5 5 4 6 5 10 | 500 | 637 617 617 650 699 = 0.75 || = 0.06 524 518 529 562 556 | 500 t 0.51788 510 1 4 5 4 5 5 6 6 6 9 | 500 | 415 366 384 347 359 = 0.74 || = 0.05 458 493 457 448 478 | 500 m 0.51628 504 2 3 5 4 5 6 5 6 5 10 | 500 | 577 602 597 578 572 = 0.73 || = 0.04 420 430 423 384 408 | 500 x 0.51700 497 2 2 5 4 5 6 4 6 5 10 | 500 | 313 307 264 291 350 = 0.72 || = 0.03 513 490 439 504 519 | 500 -----------------------------------------------------------------| 500 | 574 691 578 626 600 = 0.71 || = 0.02 436 445 473 406 414 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 536 483 556 453 488 = 0.70 || = 0.01 215 199 208 215 218 | 252.5 d 25 8 7 6 8 11 5 5 26 | 500 | 608 572 565 563 565 = 0.69 || < 0.01 419 468 418 432 438 | 497.5 s 27 7 4 7 13 9 1 5 28 | 500 | 615 633 587 576 613 = 0.68 ||========================================================================= t 28 6 8 5 8 7 8 5 26 | 500 | 528 489 554 513 489 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 27 4 12 3 10 7 5 7 26 | 500 | 322 326 336 370 339 = 0.66 ||========================================================================= x 24 6 7 6 17 5 6 4 26 | 500 | 474 468 471 487 487 = 0.65 || scomp_LempelZiv test: no 186 test no 187 TestU01 250000 runs BigCrush Test smarsa_S scomp_LempelZiv test: test no 187 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 1 1 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 509 510 520 502 476 | 500 < 0.00002 1 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 487 500 525 486 485 | 500 < 0.00003 2 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 510 471 525 530 518 | 500 < 0.00004 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 480 488 543 534 507 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 455 506 497 485 465 | 500 < 0.00006 1 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 487 509 487 495 507 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 502 496 481 475 514 | 500 < 0.00008 1 1 1 2 0 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 494 481 482 485 491 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99991 || = 0.56 511 460 465 494 493 | 500 < 0.0001 0 0 0 1 0 | 0.5 | 1 0 1 0 0 > 0.9999 || = 0.55 496 478 516 521 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 459 509 455 522 491 | 500 < 0.0001 6 7 2 5 2 | 5 | 1 0 3 1 1 > 0.9999 || = 0.53 528 471 504 466 519 | 500 < 0.0002 4 4 6 4 3 | 5 | 4 2 1 3 2 > 0.9998 || = 0.52 535 504 561 499 504 | 500 < 0.0003 6 5 4 5 5 | 5 | 3 3 5 4 3 > 0.9997 || = 0.51 481 489 492 526 527 | 500 < 0.0004 11 8 6 4 8 | 5 | 3 2 4 4 4 > 0.9996 || = 0.50 509 524 485 501 497 | 500 < 0.0005 5 4 7 5 9 | 5 | 2 1 3 6 3 > 0.9995 || = 0.49 512 517 479 523 495 | 500 < 0.0006 7 4 5 7 2 | 5 | 3 1 6 7 3 > 0.9994 || = 0.48 474 472 506 510 492 | 500 < 0.0007 12 4 8 6 9 | 5 | 4 4 2 1 4 > 0.9993 || = 0.47 506 471 489 465 488 | 500 < 0.0008 5 7 4 8 6 | 5 | 6 7 4 5 4 > 0.9992 || = 0.46 478 545 497 523 506 | 500 < 0.0009 6 5 5 2 8 | 5 | 2 4 4 10 3 > 0.9991 || = 0.45 480 481 542 482 512 | 500 < 0.001 2 6 1 4 3 | 5 | 2 4 6 6 2 > 0.999 || = 0.44 509 533 498 487 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 492 459 499 514 519 | 500 < 0.001 64 54 48 50 55 | 50 | 30 28 38 47 29 > 0.999 || = 0.42 490 517 485 507 493 | 500 < 0.002 44 65 48 50 54 | 50 | 47 35 36 47 48 > 0.998 || = 0.41 465 516 479 477 526 | 500 < 0.003 57 57 49 63 57 | 50 | 49 46 35 41 45 > 0.997 || = 0.40 528 514 502 505 498 | 500 < 0.004 43 50 47 48 53 | 50 | 47 43 37 31 46 > 0.996 || = 0.39 523 515 485 474 488 | 500 < 0.005 45 52 53 47 38 | 50 | 42 40 50 47 42 > 0.995 || = 0.38 514 507 517 484 476 | 500 < 0.006 63 61 55 70 55 | 50 | 51 50 46 42 51 > 0.994 || = 0.37 553 484 520 505 522 | 500 < 0.007 62 51 48 40 47 | 50 | 51 39 56 53 37 > 0.993 || = 0.36 509 493 503 509 472 | 500 < 0.008 50 49 42 44 55 | 50 | 44 54 47 48 56 > 0.992 || = 0.35 490 522 511 490 523 | 500 < 0.009 57 59 48 54 48 | 50 | 57 58 45 58 51 > 0.991 || = 0.34 476 556 488 492 481 | 500 < 0.01 64 53 41 45 66 | 50 | 58 63 58 44 47 > 0.99 || = 0.33 509 548 494 486 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 492 475 498 521 474 | 500 < 0.01 549 551 479 511 528 | 497.5 | 476 456 448 458 452 > 0.99 || = 0.31 491 499 487 472 479 | 500 = 0.01 263 273 256 270 273 | 252.5 | 253 257 259 221 281 = 0.99 || = 0.30 486 526 541 463 535 | 500 = 0.02 504 531 539 519 514 | 500 | 541 530 521 525 506 = 0.98 || = 0.29 519 497 476 517 544 | 500 =================================================================| 500 | 551 532 525 531 512 = 0.97 || = 0.28 473 485 555 508 461 | 500 scomp_LempelZiv test: | 500 | 498 497 496 507 483 = 0.96 || = 0.27 481 526 464 520 529 | 500 ----------------------------------------------- | 500 | 470 481 475 494 527 = 0.95 || = 0.26 505 531 517 479 512 | 500 N = 10, n = 134217728, r = 15, s = 15, k = 27 | 500 | 505 487 500 479 543 = 0.94 || = 0.25 497 502 486 511 498 | 500 Anderson-Darling statistic = A2 | 500 | 517 522 504 513 470 = 0.93 || = 0.24 456 517 502 526 496 | 500 | 500 | 480 478 503 505 519 = 0.92 || = 0.23 524 490 499 496 514 | 500 =================================================================| 500 | 467 508 487 458 544 = 0.91 || = 0.22 507 479 499 502 489 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 462 485 464 500 486 = 0.90 || = 0.21 557 521 497 461 501 | 500 -----------------------------------------------------------------| 500 | 481 504 522 501 510 = 0.89 || = 0.20 500 509 492 497 480 | 500 SD Bern.: d 1.13036 1.35196 1.12660 | 500 | 503 484 502 516 473 = 0.88 || = 0.19 455 491 487 526 475 | 500 s 1.06018 1.00747 1.57812 | 500 | 467 509 484 488 496 = 0.87 || = 0.18 498 540 534 516 493 | 500 t 1.04591 0.64062 1.33031 | 500 | 496 496 480 514 477 = 0.86 || = 0.17 507 520 518 513 507 | 500 m 0.94770 1.23268 1.13722 | 500 | 500 465 515 494 506 = 0.85 || = 0.16 508 500 524 474 504 | 500 x 1.06373 1.06071 1.23834 | 500 | 585 462 473 519 517 = 0.84 || = 0.15 483 525 540 508 505 | 500 | 500 | 532 470 479 485 475 = 0.83 || = 0.14 471 520 446 507 484 | 500 Changes: d 48 6 3 | 500 | 470 529 457 511 491 = 0.82 || = 0.13 470 479 519 559 529 | 500 s 49 4 1 | 500 | 496 505 469 497 482 = 0.81 || = 0.12 542 537 521 513 458 | 500 t 46 2 3 | 500 | 473 472 476 491 469 = 0.80 || = 0.11 536 512 512 494 489 | 500 m 43 6 4 | 500 | 505 513 532 481 533 = 0.79 || = 0.10 522 524 498 526 506 | 500 x 53 6 4 | 500 | 475 480 514 490 521 = 0.78 || = 0.09 503 499 483 506 531 | 500 -----------------------------------------------------------------| 500 | 494 478 515 496 489 = 0.77 || = 0.08 540 460 514 511 560 | 500 Aver./ d 0.49789 499 > 500: 8 5 5 5 4 4 4 4 3 5 | 500 | 499 477 522 455 484 = 0.76 || = 0.07 513 516 498 547 468 | 500 median s 0.49515 500 ----- 7 7 6 6 6 4 2 1 4 5 | 500 | 473 478 491 484 450 = 0.75 || = 0.06 497 531 524 509 463 | 500 t 0.49705 498 6 7 3 5 3 3 5 5 3 5 | 500 | 524 483 475 489 468 = 0.74 || = 0.05 497 478 537 489 511 | 500 m 0.49712 502 8 8 6 3 6 3 9 0 5 5 | 500 | 531 485 498 462 481 = 0.73 || = 0.04 527 511 475 499 549 | 500 x 0.49869 498 7 5 5 4 5 6 5 3 3 7 | 500 | 493 461 521 474 461 = 0.72 || = 0.03 509 502 542 510 477 | 500 -----------------------------------------------------------------| 500 | 504 476 470 457 523 = 0.71 || = 0.02 504 531 539 519 514 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 474 492 484 532 545 = 0.70 || = 0.01 263 273 256 270 273 | 252.5 d 0 0 3 17 63 13 4 1 0 | 500 | 499 524 506 501 488 = 0.69 || < 0.01 549 551 479 511 528 | 497.5 s 0 0 0 18 63 16 4 0 0 | 500 | 512 470 484 522 504 = 0.68 ||========================================================================= t 0 0 3 12 70 14 2 0 0 | 500 | 521 486 490 508 490 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 15 71 12 2 0 0 | 500 | 447 493 485 504 513 = 0.66 ||========================================================================= x 0 0 2 18 62 16 3 0 0 | 500 | 493 472 483 504 479 = 0.65 || scomp_LempelZiv test: no 187 test no 188 TestU01 250000 runs BigCrush Test smarsa_S scomp_LempelZiv test: test no 188 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 2 0 1 1 | 0.5 | 2 0 1 1 1 > 0.99999 || = 0.64 522 534 516 502 499 | 500 < 0.00002 1 0 0 1 0 | 0.5 | 0 2 0 1 0 > 0.99998 || = 0.63 529 531 538 523 516 | 500 < 0.00003 1 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99997 || = 0.62 529 540 505 540 530 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 0 2 1 0 1 > 0.99996 || = 0.61 436 450 431 398 432 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 524 545 563 533 592 | 500 < 0.00006 0 1 0 0 0 | 0.5 | 1 0 2 0 1 > 0.99994 || = 0.59 518 537 529 540 528 | 500 < 0.00007 0 1 0 1 0 | 0.5 | 1 1 1 1 1 > 0.99993 || = 0.58 511 503 544 528 503 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 1 1 1 0 0 > 0.99992 || = 0.57 415 486 447 422 438 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 547 541 497 539 516 | 500 < 0.0001 1 2 0 2 0 | 0.5 | 0 0 0 1 1 > 0.9999 || = 0.55 553 499 507 517 573 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 421 443 408 434 434 | 500 < 0.0001 4 7 0 7 1 | 5 | 5 7 6 4 5 > 0.9999 || = 0.53 552 506 508 548 517 | 500 < 0.0002 5 6 3 5 7 | 5 | 4 7 5 8 3 > 0.9998 || = 0.52 518 517 521 565 553 | 500 < 0.0003 6 5 3 4 2 | 5 | 12 4 6 3 8 > 0.9997 || = 0.51 465 412 425 465 451 | 500 < 0.0004 2 6 5 4 7 | 5 | 7 5 7 9 5 > 0.9996 || = 0.50 535 529 553 551 538 | 500 < 0.0005 4 4 5 5 7 | 5 | 10 3 2 4 10 > 0.9995 || = 0.49 468 441 458 438 425 | 500 < 0.0006 6 4 5 0 5 | 5 | 5 5 10 5 2 > 0.9994 || = 0.48 532 537 541 537 545 | 500 < 0.0007 6 1 4 3 5 | 5 | 4 0 6 5 4 > 0.9993 || = 0.47 521 548 523 562 533 | 500 < 0.0008 5 5 2 4 2 | 5 | 7 9 5 7 3 > 0.9992 || = 0.46 424 443 440 384 425 | 500 < 0.0009 4 3 2 6 8 | 5 | 9 7 5 12 7 > 0.9991 || = 0.45 543 521 498 536 533 | 500 < 0.001 5 2 8 8 7 | 5 | 4 15 6 5 8 > 0.999 || = 0.44 524 494 526 542 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 422 392 436 409 429 | 500 < 0.001 47 43 37 46 51 | 50 | 67 62 58 62 55 > 0.999 || = 0.42 518 527 527 522 543 | 500 < 0.002 43 41 43 44 47 | 50 | 63 66 61 55 65 > 0.998 || = 0.41 533 540 511 529 501 | 500 < 0.003 57 56 39 38 49 | 50 | 63 65 61 58 62 > 0.997 || = 0.40 498 481 530 465 478 | 500 < 0.004 46 42 46 43 40 | 50 | 64 59 64 64 66 > 0.996 || = 0.39 402 424 405 449 389 | 500 < 0.005 40 44 35 44 34 | 50 | 55 53 67 63 62 > 0.995 || = 0.38 495 473 487 506 541 | 500 < 0.006 42 50 51 42 43 | 50 | 67 72 57 54 75 > 0.994 || = 0.37 447 515 476 493 517 | 500 < 0.007 40 47 41 40 44 | 50 | 60 46 59 63 55 > 0.993 || = 0.36 521 497 513 487 492 | 500 < 0.008 27 42 46 40 49 | 50 | 56 52 64 59 57 > 0.992 || = 0.35 492 532 512 544 473 | 500 < 0.009 47 42 47 50 38 | 50 | 71 85 63 55 52 > 0.991 || = 0.34 493 447 490 501 495 | 500 < 0.01 26 56 35 33 46 | 50 | 53 59 43 55 46 > 0.99 || = 0.33 437 478 467 487 473 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 498 468 465 495 470 | 500 < 0.01 415 463 420 420 441 | 497.5 | 619 619 597 588 595 > 0.99 || = 0.31 453 448 461 475 493 | 500 = 0.01 185 233 209 211 210 | 252.5 | 304 315 304 319 264 = 0.99 || = 0.30 546 506 525 541 561 | 500 = 0.02 437 419 449 448 469 | 500 | 588 552 606 591 623 = 0.98 || = 0.29 437 450 446 434 427 | 500 =================================================================| 500 | 588 551 562 606 585 = 0.97 || = 0.28 514 521 525 522 511 | 500 scomp_LempelZiv test: | 500 | 567 611 555 624 551 = 0.96 || = 0.27 434 447 460 411 441 | 500 ----------------------------------------------- | 500 | 541 544 544 518 537 = 0.95 || = 0.26 467 455 501 476 511 | 500 N = 10, n = 134217728, r = 15, s = 15, k = 27 | 500 | 611 557 613 588 547 = 0.94 || = 0.25 486 466 467 492 457 | 500 Tests on the sum of all N observations | 500 | 531 518 523 577 545 = 0.93 || = 0.24 398 407 411 372 406 | 500 | 500 | 533 520 515 533 533 = 0.92 || = 0.23 554 578 531 567 512 | 500 =================================================================| 500 | 497 542 488 522 553 = 0.91 || = 0.22 463 456 471 426 446 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 557 579 623 548 585 = 0.90 || = 0.21 439 397 452 485 428 | 500 -----------------------------------------------------------------| 500 | 544 555 623 547 528 = 0.89 || = 0.20 518 518 498 541 554 | 500 SD Bern.: d 2.42165 1.73349 1.85726 | 500 | 553 547 516 539 518 = 0.88 || = 0.19 416 417 419 433 436 | 500 s 2.24595 0.93748 2.24833 | 500 | 539 552 590 577 567 = 0.87 || = 0.18 465 458 440 482 488 | 500 t 2.36758 1.35122 1.63482 | 500 | 502 507 532 508 536 = 0.86 || = 0.17 520 519 508 531 511 | 500 m 2.54684 1.29215 1.35270 | 500 | 584 529 537 540 583 = 0.85 || = 0.16 418 406 421 406 422 | 500 x 2.38576 1.10779 1.74040 | 500 | 482 517 488 473 464 = 0.84 || = 0.15 469 471 432 480 495 | 500 | 500 | 544 594 601 559 630 = 0.83 || = 0.14 442 454 454 438 437 | 500 Changes: d 41 2 0 | 500 | 523 521 536 529 533 = 0.82 || = 0.13 479 484 458 487 466 | 500 s 45 3 2 | 500 | 458 489 459 455 470 = 0.81 || = 0.12 438 420 439 459 473 | 500 t 45 2 1 | 500 | 599 561 528 560 559 = 0.80 || = 0.11 484 501 477 485 459 | 500 m 45 0 0 | 500 | 466 527 544 463 481 = 0.79 || = 0.10 499 526 517 475 491 | 500 x 45 1 1 | 500 | 488 514 495 481 518 = 0.78 || = 0.09 437 500 463 433 451 | 500 -----------------------------------------------------------------| 500 | 587 587 590 632 554 = 0.77 || = 0.08 478 468 423 420 412 | 500 Aver./ d 0.51956 502 > 500: 0 1 3 2 6 7 9 5 8 9 | 500 | 459 438 449 421 399 = 0.76 || = 0.07 497 484 458 488 485 | 500 median s 0.51765 506 ----- 0 3 3 3 5 6 6 7 9 10 | 500 | 528 536 544 499 522 = 0.75 || = 0.06 454 484 496 460 483 | 500 t 0.51967 501 0 2 3 3 6 6 7 6 8 9 | 500 | 542 513 581 533 524 = 0.74 || = 0.05 422 471 447 433 411 | 500 m 0.51842 501 0 1 3 4 6 7 7 4 8 10 | 500 | 474 453 458 470 466 = 0.73 || = 0.04 443 447 483 443 442 | 500 x 0.51826 501 0 1 4 3 5 7 6 6 8 10 | 500 | 588 572 572 591 572 = 0.72 || = 0.03 448 431 425 425 428 | 500 -----------------------------------------------------------------| 500 | 469 471 462 451 496 = 0.71 || = 0.02 437 419 449 448 469 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 633 571 553 573 590 = 0.70 || = 0.01 185 233 209 211 210 | 252.5 d 3 8 14 11 29 17 8 7 4 | 500 | 520 479 515 501 508 = 0.69 || < 0.01 415 463 420 420 441 | 497.5 s 4 6 13 11 31 18 9 6 3 | 500 | 512 525 474 484 470 = 0.68 ||========================================================================= t 3 8 12 16 26 19 6 3 8 | 500 | 512 493 482 513 493 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 6 9 11 10 25 19 9 5 7 | 500 | 558 523 509 448 518 = 0.66 ||========================================================================= x 4 9 11 12 30 13 11 6 5 | 500 | 502 482 549 549 545 = 0.65 || scomp_LempelZiv test: no 188 test no 189 TestU01 250000 runs BigCrush Test smarsa_S scomp_LempelZiv test: test no 189 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 1 | 0.5 | 0 1 1 0 1 > 0.99999 || = 0.64 466 489 515 515 510 | 500 < 0.00002 3 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 501 473 501 483 494 | 500 < 0.00003 2 0 1 2 0 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 508 494 466 523 535 | 500 < 0.00004 1 0 0 3 1 | 0.5 | 0 1 0 1 0 > 0.99996 || = 0.61 466 490 474 486 509 | 500 < 0.00005 0 0 1 2 0 | 0.5 | 0 0 0 3 0 > 0.99995 || = 0.60 491 499 460 476 468 | 500 < 0.00006 3 1 3 0 0 | 0.5 | 0 0 0 2 1 > 0.99994 || = 0.59 495 418 529 519 478 | 500 < 0.00007 1 1 0 1 0 | 0.5 | 0 0 1 1 1 > 0.99993 || = 0.58 483 508 535 436 501 | 500 < 0.00008 2 0 0 0 1 | 0.5 | 1 0 0 0 1 > 0.99992 || = 0.57 463 471 525 510 548 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 485 489 517 479 514 | 500 < 0.0001 0 0 2 0 0 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 497 526 481 542 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 460 506 505 489 509 | 500 < 0.0001 13 3 7 9 4 | 5 | 1 3 3 8 4 > 0.9999 || = 0.53 455 479 455 517 486 | 500 < 0.0002 5 2 4 5 4 | 5 | 6 2 1 2 2 > 0.9998 || = 0.52 462 488 513 492 495 | 500 < 0.0003 5 8 2 3 5 | 5 | 4 2 5 3 3 > 0.9997 || = 0.51 469 485 472 481 497 | 500 < 0.0004 8 6 2 7 8 | 5 | 6 8 4 0 7 > 0.9996 || = 0.50 491 512 524 520 497 | 500 < 0.0005 6 9 10 6 7 | 5 | 2 7 2 7 3 > 0.9995 || = 0.49 496 452 506 454 521 | 500 < 0.0006 8 2 4 2 1 | 5 | 2 3 4 3 8 > 0.9994 || = 0.48 473 479 487 501 461 | 500 < 0.0007 7 6 4 5 3 | 5 | 2 1 3 2 5 > 0.9993 || = 0.47 542 469 479 497 493 | 500 < 0.0008 7 4 8 8 6 | 5 | 4 4 6 2 2 > 0.9992 || = 0.46 515 530 488 477 506 | 500 < 0.0009 3 7 7 4 4 | 5 | 3 5 3 4 7 > 0.9991 || = 0.45 513 473 476 456 526 | 500 < 0.001 6 3 7 4 4 | 5 | 2 6 4 6 8 > 0.999 || = 0.44 481 501 502 504 482 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 505 483 515 486 515 | 500 < 0.001 68 50 55 53 46 | 50 | 32 41 35 37 49 > 0.999 || = 0.42 494 495 511 473 479 | 500 < 0.002 50 64 43 54 42 | 50 | 42 44 56 50 59 > 0.998 || = 0.41 492 537 499 488 500 | 500 < 0.003 60 51 47 57 48 | 50 | 41 51 50 49 46 > 0.997 || = 0.40 520 497 492 517 518 | 500 < 0.004 49 54 50 66 46 | 50 | 48 54 56 51 47 > 0.996 || = 0.39 506 464 499 446 514 | 500 < 0.005 60 56 48 40 46 | 50 | 46 54 35 43 48 > 0.995 || = 0.38 519 497 520 468 496 | 500 < 0.006 65 55 54 51 54 | 50 | 39 62 49 47 48 > 0.994 || = 0.37 501 541 449 487 470 | 500 < 0.007 57 52 58 52 57 | 50 | 50 48 46 58 55 > 0.993 || = 0.36 536 560 484 528 533 | 500 < 0.008 51 52 63 52 51 | 50 | 49 45 46 52 46 > 0.992 || = 0.35 557 514 536 481 516 | 500 < 0.009 53 66 60 46 41 | 50 | 44 43 52 59 52 > 0.991 || = 0.34 502 543 500 495 527 | 500 < 0.01 65 62 65 60 59 | 50 | 42 47 46 51 39 > 0.99 || = 0.33 508 546 490 515 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 515 505 521 482 501 | 500 < 0.01 578 562 543 531 490 | 497.5 | 433 489 471 497 489 > 0.99 || = 0.31 514 524 501 527 506 | 500 = 0.01 255 303 277 265 260 | 252.5 | 251 241 246 228 226 = 0.99 || = 0.30 497 491 488 466 500 | 500 = 0.02 516 513 530 555 543 | 500 | 486 479 450 493 489 = 0.98 || = 0.29 486 471 541 534 492 | 500 =================================================================| 500 | 491 473 464 467 490 = 0.97 || = 0.28 520 506 493 523 501 | 500 scomp_LempelZiv test: | 500 | 472 489 500 472 441 = 0.96 || = 0.27 500 548 527 532 497 | 500 ----------------------------------------------- | 500 | 484 500 470 440 507 = 0.95 || = 0.26 496 501 465 518 529 | 500 N = 10, n = 134217728, r = 15, s = 15, k = 27 | 500 | 481 469 460 460 466 = 0.94 || = 0.25 509 528 518 505 493 | 500 Sample variance | 500 | 502 462 506 466 478 = 0.93 || = 0.24 464 496 487 520 482 | 500 | 500 | 479 478 495 463 516 = 0.92 || = 0.23 518 489 493 529 454 | 500 =================================================================| 500 | 492 465 450 526 528 = 0.91 || = 0.22 551 555 474 515 486 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 512 501 504 468 465 = 0.90 || = 0.21 512 466 518 532 520 | 500 -----------------------------------------------------------------| 500 | 437 528 517 490 489 = 0.89 || = 0.20 524 540 480 543 464 | 500 SD Bern.: d 1.10089 1.43877 1.19306 | 500 | 495 501 499 509 455 = 0.88 || = 0.19 514 507 516 530 506 | 500 s 1.29285 1.16848 0.87334 | 500 | 524 517 502 469 482 = 0.87 || = 0.18 528 474 498 528 514 | 500 t 1.13007 1.15035 1.07291 | 500 | 469 475 505 507 495 = 0.86 || = 0.17 541 509 516 529 554 | 500 m 1.27644 1.05408 0.87105 | 500 | 478 484 500 542 486 = 0.85 || = 0.16 495 488 533 496 484 | 500 x 1.18712 0.82986 0.75003 | 500 | 500 486 517 459 546 = 0.84 || = 0.15 532 526 523 492 516 | 500 | 500 | 489 488 444 514 479 = 0.83 || = 0.14 495 502 546 525 489 | 500 Changes: d 37 4 0 | 500 | 493 531 473 456 513 = 0.82 || = 0.13 506 544 531 466 545 | 500 s 37 1 2 | 500 | 505 449 517 511 486 = 0.81 || = 0.12 524 545 530 518 494 | 500 t 45 2 6 | 500 | 500 495 480 485 472 = 0.80 || = 0.11 511 501 525 495 500 | 500 m 53 4 3 | 500 | 463 479 467 516 434 = 0.79 || = 0.10 552 543 560 513 565 | 500 x 50 3 6 | 500 | 484 471 490 433 473 = 0.78 || = 0.09 526 511 466 533 523 | 500 -----------------------------------------------------------------| 500 | 514 501 479 502 504 = 0.77 || = 0.08 478 526 553 566 550 | 500 Aver./ d 0.49331 500 > 500: 9 8 6 9 5 0 5 4 3 1 | 500 | 500 497 499 485 460 = 0.76 || = 0.07 520 567 512 519 525 | 500 median s 0.49192 497 ----- 9 8 6 7 3 3 2 2 5 0 | 500 | 509 477 461 529 531 = 0.75 || = 0.06 503 481 528 497 492 | 500 t 0.49307 501 9 9 4 4 4 6 5 2 6 1 | 500 | 505 483 504 545 466 = 0.74 || = 0.05 503 518 515 529 523 | 500 m 0.49222 499 9 6 10 3 3 4 4 4 5 1 | 500 | 489 480 475 488 510 = 0.73 || = 0.04 506 519 531 542 545 | 500 x 0.49350 497 8 6 3 6 5 4 3 4 2 3 | 500 | 548 518 490 471 524 = 0.72 || = 0.03 512 534 502 554 579 | 500 -----------------------------------------------------------------| 500 | 482 480 510 493 474 = 0.71 || = 0.02 516 513 530 555 543 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 501 498 512 498 492 = 0.70 || = 0.01 255 303 277 265 260 | 252.5 d 0 0 3 12 71 10 4 1 0 | 500 | 482 512 491 512 495 = 0.69 || < 0.01 578 562 543 531 490 | 497.5 s 0 2 2 15 59 15 6 2 0 | 500 | 482 479 491 503 471 = 0.68 ||========================================================================= t 0 0 5 16 59 17 4 0 0 | 500 | 476 512 485 491 497 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 4 19 52 21 4 0 0 | 500 | 511 479 504 495 487 = 0.66 ||========================================================================= x 0 0 4 14 63 12 7 1 0 | 500 | 528 433 526 467 475 = 0.65 || scomp_LempelZiv test: no 189 test no 190 TestU01 250000 runs BigCrush Test smarsa_S sspectral_Fourier3 test: test no 190 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 586 584 623 601 655 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 573 598 660 612 631 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 634 627 612 613 569 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 595 602 613 569 632 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 618 620 630 635 600 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 1 1 1 0 > 0.99994 || = 0.59 598 635 668 614 619 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 654 603 614 579 621 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 619 582 622 651 668 | 500 < 0.00009 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 615 620 620 585 605 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.9999 || = 0.55 586 632 624 647 606 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 654 638 675 643 580 | 500 < 0.0001 0 0 0 0 1 | 5 | 0 2 1 2 0 > 0.9999 || = 0.53 616 662 641 584 611 | 500 < 0.0002 0 0 0 0 0 | 5 | 0 0 1 1 1 > 0.9998 || = 0.52 679 655 625 574 575 | 500 < 0.0003 1 0 0 1 0 | 5 | 0 1 0 1 1 > 0.9997 || = 0.51 640 619 645 644 600 | 500 < 0.0004 0 1 2 1 1 | 5 | 3 1 1 0 1 > 0.9996 || = 0.50 657 595 662 688 647 | 500 < 0.0005 1 1 1 2 0 | 5 | 2 0 1 0 2 > 0.9995 || = 0.49 620 685 624 650 674 | 500 < 0.0006 0 0 1 0 0 | 5 | 0 0 2 0 1 > 0.9994 || = 0.48 623 624 614 583 604 | 500 < 0.0007 0 0 0 0 1 | 5 | 0 0 0 3 0 > 0.9993 || = 0.47 642 645 585 664 639 | 500 < 0.0008 0 1 1 0 2 | 5 | 1 0 2 1 2 > 0.9992 || = 0.46 625 649 646 612 645 | 500 < 0.0009 0 1 0 0 1 | 5 | 1 1 3 1 1 > 0.9991 || = 0.45 552 616 642 638 656 | 500 < 0.001 0 0 1 0 1 | 5 | 1 0 1 1 0 > 0.999 || = 0.44 628 646 620 621 610 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 652 623 641 637 591 | 500 < 0.001 2 4 6 4 7 | 50 | 8 5 12 10 9 > 0.999 || = 0.42 642 618 616 599 638 | 500 < 0.002 6 10 6 5 10 | 50 | 11 9 10 9 10 > 0.998 || = 0.41 637 657 598 661 639 | 500 < 0.003 5 8 16 11 12 | 50 | 8 13 16 8 9 > 0.997 || = 0.40 606 634 581 649 607 | 500 < 0.004 11 17 15 12 5 | 50 | 6 8 17 10 10 > 0.996 || = 0.39 593 596 610 606 603 | 500 < 0.005 18 15 11 8 16 | 50 | 18 12 13 7 15 > 0.995 || = 0.38 624 569 579 626 569 | 500 < 0.006 9 10 15 13 7 | 50 | 13 11 16 14 7 > 0.994 || = 0.37 586 539 591 636 573 | 500 < 0.007 11 14 11 18 12 | 50 | 11 17 12 10 9 > 0.993 || = 0.36 606 608 576 604 627 | 500 < 0.008 12 13 12 9 20 | 50 | 12 13 9 13 11 > 0.992 || = 0.35 623 576 634 595 597 | 500 < 0.009 16 13 20 11 17 | 50 | 10 13 13 13 16 > 0.991 || = 0.34 630 568 605 595 593 | 500 < 0.01 16 22 11 16 6 | 50 | 13 12 12 11 17 > 0.99 || = 0.33 619 628 538 575 564 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 602 615 576 584 614 | 500 < 0.01 106 126 123 107 112 | 497.5 | 110 113 130 105 113 > 0.99 || = 0.31 610 605 634 603 598 | 500 = 0.01 92 90 83 94 92 | 252.5 | 73 83 78 77 82 = 0.99 || = 0.30 580 576 605 562 546 | 500 = 0.02 204 188 211 192 240 | 500 | 177 191 175 186 191 = 0.98 || = 0.29 593 609 623 579 595 | 500 =================================================================| 500 | 227 207 234 197 218 = 0.97 || = 0.28 563 626 579 608 631 | 500 sspectral_Fourier3 test: | 500 | 254 221 273 245 233 = 0.96 || = 0.27 589 602 580 566 588 | 500 ----------------------------------------------- | 500 | 239 290 245 279 239 = 0.95 || = 0.26 572 565 551 554 586 | 500 N = 100000, n = 16384, r = 0, s = 3, k = 14 | 500 | 300 317 304 287 307 = 0.94 || = 0.25 546 570 569 574 572 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 286 304 314 330 314 = 0.93 || = 0.24 568 580 523 531 575 | 500 | 500 | 349 345 315 337 320 = 0.92 || = 0.23 552 502 568 546 562 | 500 =================================================================| 500 | 334 375 371 355 346 = 0.91 || = 0.22 550 536 517 510 514 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 334 373 384 335 324 = 0.90 || = 0.21 537 518 547 546 577 | 500 -----------------------------------------------------------------| 500 | 366 339 354 378 373 = 0.89 || = 0.20 541 511 517 491 537 | 500 SD Bern.: d 6.17638 5.61850 5.53665 | 500 | 387 399 373 397 424 = 0.88 || = 0.19 477 545 476 515 531 | 500 s 6.04041 5.33408 5.49363 | 500 | 442 429 438 412 408 = 0.87 || = 0.18 511 541 523 475 515 | 500 t 6.02793 5.36644 5.24704 | 500 | 432 402 431 423 393 = 0.86 || = 0.17 504 477 501 486 560 | 500 m 6.08323 5.59225 5.59725 | 500 | 428 461 417 432 439 = 0.85 || = 0.16 470 497 432 472 492 | 500 x 6.05683 5.53304 5.49510 | 500 | 472 451 475 453 453 = 0.84 || = 0.15 470 503 484 477 479 | 500 | 500 | 469 449 451 497 446 = 0.83 || = 0.14 446 452 479 452 478 | 500 Changes: d 6 0 0 | 500 | 549 484 452 506 492 = 0.82 || = 0.13 471 462 445 439 470 | 500 s 8 0 0 | 500 | 486 483 502 539 479 = 0.81 || = 0.12 446 425 451 466 422 | 500 t 8 0 0 | 500 | 458 518 510 475 491 = 0.80 || = 0.11 412 412 450 460 407 | 500 m 6 0 0 | 500 | 466 510 498 499 470 = 0.79 || = 0.10 403 415 451 448 367 | 500 x 4 0 0 | 500 | 511 525 508 515 513 = 0.78 || = 0.09 422 380 388 378 377 | 500 -----------------------------------------------------------------| 500 | 506 489 474 525 498 = 0.77 || = 0.08 358 385 393 393 361 | 500 Aver./ d 0.49235 549 > 500: 0 2 10 10 10 10 10 8 1 0 | 500 | 510 483 516 540 516 = 0.76 || = 0.07 325 367 331 344 377 | 500 median s 0.49167 536 ----- 0 3 10 10 10 10 10 7 0 0 | 500 | 522 508 577 522 552 = 0.75 || = 0.06 348 343 323 326 355 | 500 t 0.49286 523 0 2 10 10 10 10 10 8 1 0 | 500 | 527 500 567 532 562 = 0.74 || = 0.05 322 331 318 333 291 | 500 m 0.49326 539 0 1 9 10 10 10 10 8 2 0 | 500 | 560 532 576 535 563 = 0.73 || = 0.04 279 280 294 254 314 | 500 x 0.49049 559 0 3 10 10 10 10 10 7 0 0 | 500 | 541 558 520 555 543 = 0.72 || = 0.03 238 252 250 280 263 | 500 -----------------------------------------------------------------| 500 | 557 542 509 554 570 = 0.71 || = 0.02 204 188 211 192 240 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 576 534 517 536 579 = 0.70 || = 0.01 92 90 83 94 92 | 252.5 d 23 4 3 8 7 4 9 8 35 | 500 | 603 601 566 656 559 = 0.69 || < 0.01 106 126 123 107 112 | 497.5 s 24 4 3 3 13 7 3 10 34 | 500 | 595 582 586 582 551 = 0.68 ||========================================================================= t 23 3 7 3 13 3 4 14 31 | 500 | 634 589 550 576 583 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 23 3 4 6 9 7 7 13 29 | 500 | 563 579 587 578 596 = 0.66 ||========================================================================= x 26 2 3 2 11 3 9 13 32 | 500 | 618 595 594 615 614 = 0.65 || sspectral_Fourier3 test: no 190 test no 191 TestU01 250000 runs BigCrush Test smarsa_S sspectral_Fourier3 test: test no 191 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 663 623 608 623 667 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 625 654 634 692 674 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 629 623 656 620 650 | 500 < 0.00004 0 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 675 644 635 648 608 | 500 < 0.00005 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 676 668 641 621 634 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 620 655 701 625 679 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 654 638 685 674 666 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 671 622 658 686 666 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 706 665 671 651 649 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 683 589 604 626 631 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 673 650 641 698 649 | 500 < 0.0001 0 1 1 0 0 | 5 | 0 0 0 0 0 > 0.9999 || = 0.53 684 680 647 692 677 | 500 < 0.0002 0 0 0 1 0 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 729 652 640 638 646 | 500 < 0.0003 0 0 0 0 0 | 5 | 0 0 0 1 0 > 0.9997 || = 0.51 655 659 660 651 656 | 500 < 0.0004 0 0 0 0 0 | 5 | 1 0 0 0 0 > 0.9996 || = 0.50 637 649 698 646 657 | 500 < 0.0005 2 0 0 0 1 | 5 | 0 0 1 0 0 > 0.9995 || = 0.49 641 651 668 681 655 | 500 < 0.0006 0 1 0 1 0 | 5 | 0 0 0 0 0 > 0.9994 || = 0.48 644 632 652 701 668 | 500 < 0.0007 1 0 0 1 1 | 5 | 0 2 0 1 0 > 0.9993 || = 0.47 627 629 621 628 618 | 500 < 0.0008 0 0 1 0 0 | 5 | 1 0 0 1 0 > 0.9992 || = 0.46 664 621 610 620 642 | 500 < 0.0009 0 0 0 0 0 | 5 | 0 1 1 0 0 > 0.9991 || = 0.45 623 642 607 675 609 | 500 < 0.001 1 0 0 0 0 | 5 | 2 1 0 0 1 > 0.999 || = 0.44 600 631 648 661 650 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 645 594 620 678 645 | 500 < 0.001 4 2 2 3 2 | 50 | 4 4 2 3 1 > 0.999 || = 0.42 657 605 625 596 561 | 500 < 0.002 2 7 5 2 4 | 50 | 8 5 8 5 6 > 0.998 || = 0.41 624 653 623 615 632 | 500 < 0.003 6 9 4 7 8 | 50 | 4 7 6 7 9 > 0.997 || = 0.40 618 654 633 603 657 | 500 < 0.004 10 7 8 9 7 | 50 | 5 7 8 8 10 > 0.996 || = 0.39 584 610 583 571 643 | 500 < 0.005 8 9 8 3 9 | 50 | 5 11 6 8 8 > 0.995 || = 0.38 638 619 623 674 642 | 500 < 0.006 9 10 6 4 6 | 50 | 7 8 6 9 10 > 0.994 || = 0.37 610 608 589 564 539 | 500 < 0.007 11 13 7 8 16 | 50 | 13 15 9 8 9 > 0.993 || = 0.36 595 569 581 595 602 | 500 < 0.008 15 7 12 9 7 | 50 | 10 14 10 13 12 > 0.992 || = 0.35 600 604 586 599 598 | 500 < 0.009 14 16 11 10 12 | 50 | 13 12 15 7 11 > 0.991 || = 0.34 608 596 581 600 626 | 500 < 0.01 9 18 8 7 5 | 50 | 16 12 15 8 14 > 0.99 || = 0.33 630 573 582 587 600 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 546 628 564 602 578 | 500 < 0.01 88 98 71 62 76 | 497.5 | 85 95 85 76 90 > 0.99 || = 0.31 559 548 532 563 548 | 500 = 0.01 73 77 61 69 63 | 252.5 | 66 77 58 62 71 = 0.99 || = 0.30 575 562 587 573 526 | 500 = 0.02 159 180 160 169 155 | 500 | 151 163 159 185 160 = 0.98 || = 0.29 513 577 574 578 534 | 500 =================================================================| 500 | 201 177 233 204 188 = 0.97 || = 0.28 529 541 562 565 562 | 500 sspectral_Fourier3 test: | 500 | 226 254 233 230 267 = 0.96 || = 0.27 534 536 566 532 500 | 500 ----------------------------------------------- | 500 | 268 254 292 254 262 = 0.95 || = 0.26 526 516 535 537 552 | 500 N = 100000, n = 16384, r = 0, s = 3, k = 14 | 500 | 290 301 331 293 284 = 0.94 || = 0.25 526 536 563 481 546 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 312 299 309 300 309 = 0.93 || = 0.24 499 498 521 505 529 | 500 | 500 | 334 355 325 308 323 = 0.92 || = 0.23 528 503 482 501 501 | 500 =================================================================| 500 | 365 379 356 336 367 = 0.91 || = 0.22 490 527 487 531 525 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 381 372 392 424 374 = 0.90 || = 0.21 495 508 494 534 496 | 500 -----------------------------------------------------------------| 500 | 406 432 410 364 434 = 0.89 || = 0.20 466 455 462 481 467 | 500 SD Bern.: d 7.04699 5.85510 5.90023 | 500 | 434 404 438 432 419 = 0.88 || = 0.19 438 470 455 480 457 | 500 s 6.72697 5.72335 5.75317 | 500 | 434 456 463 447 446 = 0.87 || = 0.18 457 467 459 415 471 | 500 t 6.81725 6.08366 5.89717 | 500 | 414 452 434 434 435 = 0.86 || = 0.17 453 432 416 459 432 | 500 m 7.04786 6.20987 6.00932 | 500 | 450 467 496 421 469 = 0.85 || = 0.16 374 453 409 417 422 | 500 x 6.94439 6.02364 5.82080 | 500 | 502 495 514 526 525 = 0.84 || = 0.15 430 434 392 410 431 | 500 | 500 | 512 507 494 470 489 = 0.83 || = 0.14 395 411 412 379 382 | 500 Changes: d 6 0 0 | 500 | 481 520 530 496 539 = 0.82 || = 0.13 392 387 377 391 391 | 500 s 4 0 0 | 500 | 492 541 586 513 536 = 0.81 || = 0.12 358 351 376 395 372 | 500 t 4 0 0 | 500 | 529 550 539 583 497 = 0.80 || = 0.11 367 390 367 364 360 | 500 m 6 0 0 | 500 | 546 537 526 520 517 = 0.79 || = 0.10 351 364 336 349 351 | 500 x 8 0 0 | 500 | 538 551 551 591 550 = 0.78 || = 0.09 338 340 325 331 328 | 500 -----------------------------------------------------------------| 500 | 578 551 560 552 567 = 0.77 || = 0.08 324 315 325 321 312 | 500 Aver./ d 0.50940 534 > 500: 0 0 6 10 10 10 10 10 2 0 | 500 | 579 583 584 546 570 = 0.76 || = 0.07 285 297 318 288 275 | 500 median s 0.50816 548 ----- 0 0 8 10 10 10 10 10 3 0 | 500 | 584 604 591 630 584 = 0.75 || = 0.06 278 297 295 277 292 | 500 t 0.51087 562 0 0 6 10 10 10 10 10 3 0 | 500 | 598 608 564 597 595 = 0.74 || = 0.05 269 263 240 245 272 | 500 m 0.50817 552 0 0 8 10 10 10 10 10 2 0 | 500 | 613 595 585 592 635 = 0.73 || = 0.04 214 187 249 236 226 | 500 x 0.50975 539 0 0 7 10 10 10 10 9 3 0 | 500 | 590 551 597 601 607 = 0.72 || = 0.03 188 217 200 192 187 | 500 -----------------------------------------------------------------| 500 | 618 610 627 585 576 = 0.71 || = 0.02 159 180 160 169 155 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 620 568 602 594 627 = 0.70 || = 0.01 73 77 61 69 63 | 252.5 d 28 2 5 2 8 7 3 5 41 | 500 | 651 637 632 639 671 = 0.69 || < 0.01 88 98 71 62 76 | 497.5 s 27 2 4 4 7 6 6 5 40 | 500 | 658 601 607 633 637 = 0.68 ||========================================================================= t 28 2 3 3 7 5 7 10 36 | 500 | 654 612 651 651 604 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 27 5 2 2 8 5 5 6 41 | 500 | 621 637 625 610 628 = 0.66 ||========================================================================= x 26 4 3 4 6 8 6 5 39 | 500 | 614 678 638 630 633 = 0.65 || sspectral_Fourier3 test: no 191 test no 192 TestU01 250000 runs BigCrush Test smarsa_S sspectral_Fourier3 test: test no 192 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 2 1 2 1 > 0.99999 || = 0.64 601 580 578 626 595 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 611 575 614 565 621 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 2 0 0 0 0 > 0.99997 || = 0.62 601 625 601 592 601 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 1 2 1 0 2 > 0.99996 || = 0.61 598 612 592 586 620 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 1 1 0 1 2 > 0.99995 || = 0.60 594 613 629 629 595 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 1 0 0 0 1 > 0.99994 || = 0.59 603 622 563 619 581 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 2 0 0 0 > 0.99993 || = 0.58 566 546 574 601 562 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 3 1 1 0 2 > 0.99992 || = 0.57 578 572 547 590 555 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 2 0 0 0 > 0.99991 || = 0.56 541 567 572 596 588 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 584 574 565 531 582 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 554 555 553 525 561 | 500 < 0.0001 0 0 0 0 0 | 5 | 8 10 4 3 8 > 0.9999 || = 0.53 593 581 572 551 495 | 500 < 0.0002 0 0 0 0 0 | 5 | 5 2 7 1 3 > 0.9998 || = 0.52 536 539 510 537 545 | 500 < 0.0003 0 0 0 0 0 | 5 | 8 9 7 6 7 > 0.9997 || = 0.51 539 549 576 512 548 | 500 < 0.0004 0 0 0 1 0 | 5 | 10 11 6 7 4 > 0.9996 || = 0.50 510 593 592 511 576 | 500 < 0.0005 0 0 0 0 0 | 5 | 6 15 10 6 7 > 0.9995 || = 0.49 618 538 520 498 547 | 500 < 0.0006 0 0 0 0 0 | 5 | 6 8 8 4 14 > 0.9994 || = 0.48 567 569 500 570 549 | 500 < 0.0007 0 0 1 0 0 | 5 | 6 5 5 5 8 > 0.9993 || = 0.47 561 537 576 564 514 | 500 < 0.0008 0 0 0 0 0 | 5 | 7 7 1 8 5 > 0.9992 || = 0.46 518 545 493 521 545 | 500 < 0.0009 0 0 0 0 0 | 5 | 7 8 10 7 3 > 0.9991 || = 0.45 572 548 491 557 519 | 500 < 0.001 0 0 0 0 0 | 5 | 8 11 3 5 9 > 0.999 || = 0.44 544 530 507 494 575 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 560 510 524 524 524 | 500 < 0.001 0 0 1 1 0 | 50 | 71 86 61 52 68 > 0.999 || = 0.42 501 541 503 549 552 | 500 < 0.002 1 1 1 0 2 | 50 | 72 71 72 73 63 > 0.998 || = 0.41 478 537 546 518 525 | 500 < 0.003 2 1 0 1 5 | 50 | 64 53 69 65 79 > 0.997 || = 0.40 470 520 516 527 491 | 500 < 0.004 0 2 2 1 2 | 50 | 66 59 70 65 61 > 0.996 || = 0.39 534 489 496 517 481 | 500 < 0.005 1 1 5 2 2 | 50 | 69 76 70 76 67 > 0.995 || = 0.38 479 482 481 501 484 | 500 < 0.006 5 4 0 3 1 | 50 | 66 76 72 71 72 > 0.994 || = 0.37 489 539 506 486 515 | 500 < 0.007 2 4 5 0 3 | 50 | 83 65 74 52 67 > 0.993 || = 0.36 499 468 494 505 514 | 500 < 0.008 1 5 4 3 4 | 50 | 76 67 72 70 71 > 0.992 || = 0.35 473 502 508 509 494 | 500 < 0.009 6 5 6 3 5 | 50 | 67 67 86 72 79 > 0.991 || = 0.34 484 441 467 451 492 | 500 < 0.01 5 3 2 5 3 | 50 | 85 80 70 87 68 > 0.99 || = 0.33 445 452 484 449 468 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 467 462 454 462 473 | 500 < 0.01 23 26 26 19 27 | 497.5 | 719 700 716 683 695 > 0.99 || = 0.31 419 409 463 450 452 | 500 = 0.01 20 35 17 26 23 | 252.5 | 341 345 290 339 341 = 0.99 || = 0.30 462 444 416 462 452 | 500 = 0.02 67 74 76 70 68 | 500 | 710 693 720 633 699 = 0.98 || = 0.29 414 448 465 425 458 | 500 =================================================================| 500 | 666 694 699 712 713 = 0.97 || = 0.28 423 431 475 409 420 | 500 sspectral_Fourier3 test: | 500 | 694 641 690 711 686 = 0.96 || = 0.27 402 435 406 435 412 | 500 ----------------------------------------------- | 500 | 718 691 664 695 624 = 0.95 || = 0.26 387 391 411 452 430 | 500 N = 100000, n = 16384, r = 0, s = 3, k = 14 | 500 | 717 675 708 679 674 = 0.94 || = 0.25 420 408 409 414 411 | 500 Anderson-Darling statistic = A2 | 500 | 706 643 686 666 638 = 0.93 || = 0.24 355 437 435 404 398 | 500 | 500 | 658 622 659 639 674 = 0.92 || = 0.23 375 390 409 365 392 | 500 =================================================================| 500 | 697 673 672 679 682 = 0.91 || = 0.22 369 401 342 404 395 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 619 632 675 684 677 = 0.90 || = 0.21 366 336 378 365 370 | 500 -----------------------------------------------------------------| 500 | 650 669 687 655 698 = 0.89 || = 0.20 370 374 374 370 393 | 500 SD Bern.: d 7.54104 6.75571 3.24907 | 500 | 669 655 695 624 662 = 0.88 || = 0.19 357 346 381 311 348 | 500 s 7.25677 6.71126 3.12629 | 500 | 669 635 651 674 614 = 0.87 || = 0.18 354 356 325 366 323 | 500 t 7.48372 6.71335 3.16575 | 500 | 683 610 632 643 636 = 0.86 || = 0.17 343 318 296 317 323 | 500 m 7.51902 6.80913 2.95341 | 500 | 638 656 638 664 645 = 0.85 || = 0.16 317 342 301 284 353 | 500 x 7.32644 6.69618 2.87301 | 500 | 667 669 666 664 644 = 0.84 || = 0.15 308 293 294 304 334 | 500 | 500 | 637 695 686 711 672 = 0.83 || = 0.14 285 332 314 297 289 | 500 Changes: d 3 0 0 | 500 | 656 630 660 663 647 = 0.82 || = 0.13 289 327 280 258 312 | 500 s 5 0 0 | 500 | 639 631 700 592 648 = 0.81 || = 0.12 278 252 254 282 264 | 500 t 9 0 0 | 500 | 605 614 654 665 640 = 0.80 || = 0.11 290 263 226 250 260 | 500 m 7 0 0 | 500 | 667 647 615 630 630 = 0.79 || = 0.10 245 266 250 259 236 | 500 x 5 0 0 | 500 | 658 624 699 635 663 = 0.78 || = 0.09 210 216 254 213 238 | 500 -----------------------------------------------------------------| 500 | 664 629 626 634 664 = 0.77 || = 0.08 205 214 209 193 218 | 500 Aver./ d 0.59094 560 > 500: 0 0 0 1 8 10 10 10 10 10 | 500 | 631 626 619 617 655 = 0.76 || = 0.07 184 191 184 182 184 | 500 median s 0.58663 548 ----- 0 0 0 2 10 10 10 10 10 10 | 500 | 565 647 626 649 593 = 0.75 || = 0.06 166 169 177 155 152 | 500 t 0.59000 547 0 0 0 2 7 10 10 10 10 10 | 500 | 608 651 567 622 611 = 0.74 || = 0.05 156 168 151 165 151 | 500 m 0.59012 537 0 0 0 4 8 10 10 10 10 10 | 500 | 617 595 580 661 641 = 0.73 || = 0.04 115 133 133 118 130 | 500 x 0.58751 549 0 0 0 2 9 9 10 10 10 10 | 500 | 588 640 671 617 605 = 0.72 || = 0.03 98 103 104 114 98 | 500 -----------------------------------------------------------------| 500 | 642 596 625 643 556 = 0.71 || = 0.02 67 74 76 70 68 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 605 610 595 598 585 = 0.70 || = 0.01 20 35 17 26 23 | 252.5 d 27 4 1 4 8 5 5 5 42 | 500 | 603 621 610 600 611 = 0.69 || < 0.01 23 26 26 19 27 | 497.5 s 27 1 6 2 5 7 5 8 40 | 500 | 630 592 596 640 581 = 0.68 ||========================================================================= t 27 1 2 4 14 1 6 9 37 | 500 | 602 620 595 603 585 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 26 2 5 2 11 5 5 2 43 | 500 | 603 604 585 639 614 = 0.66 ||========================================================================= x 26 3 2 3 10 2 10 8 37 | 500 | 619 584 604 626 596 = 0.65 || sspectral_Fourier3 test: no 192 test no 193 TestU01 250000 runs BigCrush Test smarsa_S sspectral_Fourier3 test: test no 193 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 603 566 590 619 613 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 669 623 614 573 598 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 620 604 596 569 633 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 620 593 580 624 602 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 641 676 605 663 642 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 534 624 631 605 609 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 588 625 679 631 594 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 657 598 602 617 571 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 621 620 640 615 652 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 653 623 665 605 643 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 627 611 653 624 587 | 500 < 0.0001 0 0 0 0 0 | 5 | 0 0 1 0 0 > 0.9999 || = 0.53 619 605 677 671 665 | 500 < 0.0002 1 0 0 0 1 | 5 | 0 0 0 1 0 > 0.9998 || = 0.52 661 583 634 597 609 | 500 < 0.0003 0 1 0 1 1 | 5 | 0 1 1 2 1 > 0.9997 || = 0.51 614 636 638 596 645 | 500 < 0.0004 0 0 0 0 0 | 5 | 1 2 2 0 0 > 0.9996 || = 0.50 600 622 669 616 591 | 500 < 0.0005 0 1 0 1 0 | 5 | 0 0 0 1 2 > 0.9995 || = 0.49 638 633 630 663 600 | 500 < 0.0006 1 1 1 0 0 | 5 | 0 0 0 2 2 > 0.9994 || = 0.48 588 641 641 603 609 | 500 < 0.0007 0 1 1 0 0 | 5 | 1 2 1 1 0 > 0.9993 || = 0.47 602 626 602 654 647 | 500 < 0.0008 0 0 0 0 0 | 5 | 0 0 2 1 0 > 0.9992 || = 0.46 634 622 597 619 600 | 500 < 0.0009 1 1 0 0 0 | 5 | 1 1 1 0 1 > 0.9991 || = 0.45 608 609 642 591 665 | 500 < 0.001 1 1 0 1 0 | 5 | 2 1 0 0 3 > 0.999 || = 0.44 637 609 612 608 613 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 639 628 619 641 646 | 500 < 0.001 4 6 2 3 2 | 50 | 5 7 8 8 9 > 0.999 || = 0.42 629 580 639 584 619 | 500 < 0.002 4 7 4 10 7 | 50 | 8 7 6 11 13 > 0.998 || = 0.41 606 661 649 598 598 | 500 < 0.003 9 10 3 7 6 | 50 | 16 11 10 13 15 > 0.997 || = 0.40 635 637 612 639 610 | 500 < 0.004 7 6 15 11 16 | 50 | 10 9 10 11 13 > 0.996 || = 0.39 620 595 640 594 575 | 500 < 0.005 15 12 13 20 7 | 50 | 16 13 12 9 12 > 0.995 || = 0.38 578 609 607 634 652 | 500 < 0.006 7 8 13 18 13 | 50 | 18 11 9 10 7 > 0.994 || = 0.37 633 600 609 615 648 | 500 < 0.007 15 16 8 21 16 | 50 | 7 9 15 16 12 > 0.993 || = 0.36 650 660 593 577 612 | 500 < 0.008 17 13 13 9 11 | 50 | 16 14 12 10 12 > 0.992 || = 0.35 618 613 621 647 617 | 500 < 0.009 17 14 13 17 17 | 50 | 14 7 9 14 14 > 0.991 || = 0.34 605 635 589 582 612 | 500 < 0.01 14 17 16 14 20 | 50 | 16 9 9 14 19 > 0.99 || = 0.33 659 592 605 640 554 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 553 618 641 600 567 | 500 < 0.01 109 109 100 130 115 | 497.5 | 126 97 100 116 126 > 0.99 || = 0.31 554 585 578 580 604 | 500 = 0.01 72 100 87 94 92 | 252.5 | 71 83 85 67 91 = 0.99 || = 0.30 583 545 612 575 594 | 500 = 0.02 212 211 218 245 226 | 500 | 175 158 215 179 183 = 0.98 || = 0.29 581 568 572 579 612 | 500 =================================================================| 500 | 194 235 215 211 202 = 0.97 || = 0.28 574 574 607 617 554 | 500 sspectral_Fourier3 test: | 500 | 227 264 247 234 248 = 0.96 || = 0.27 600 619 595 575 621 | 500 ----------------------------------------------- | 500 | 248 245 268 260 263 = 0.95 || = 0.26 546 535 567 582 534 | 500 N = 100000, n = 16384, r = 27, s = 3, k = 14 | 500 | 306 295 303 311 304 = 0.94 || = 0.25 548 575 568 585 557 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 294 296 313 296 295 = 0.93 || = 0.24 549 534 542 526 538 | 500 | 500 | 310 333 315 338 333 = 0.92 || = 0.23 529 555 508 537 523 | 500 =================================================================| 500 | 363 308 350 375 321 = 0.91 || = 0.22 521 528 560 555 547 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 362 365 351 369 383 = 0.90 || = 0.21 558 548 531 537 553 | 500 -----------------------------------------------------------------| 500 | 402 369 366 385 349 = 0.89 || = 0.20 502 557 526 505 486 | 500 SD Bern.: d 6.19806 5.57683 5.32844 | 500 | 371 384 400 421 386 = 0.88 || = 0.19 529 491 507 505 560 | 500 s 6.04146 5.55957 5.71196 | 500 | 411 446 415 420 368 = 0.87 || = 0.18 550 545 508 533 493 | 500 t 6.14856 5.70372 5.66957 | 500 | 417 399 400 411 429 = 0.86 || = 0.17 509 553 487 517 509 | 500 m 5.93812 5.29603 5.44403 | 500 | 445 458 448 477 442 = 0.85 || = 0.16 488 519 458 459 526 | 500 x 5.99302 5.50347 5.30962 | 500 | 419 444 455 443 444 = 0.84 || = 0.15 467 482 494 443 477 | 500 | 500 | 465 481 430 466 457 = 0.83 || = 0.14 462 474 462 450 527 | 500 Changes: d 2 0 0 | 500 | 457 440 447 477 463 = 0.82 || = 0.13 464 449 453 451 473 | 500 s 8 0 0 | 500 | 462 507 464 519 483 = 0.81 || = 0.12 454 473 471 460 434 | 500 t 2 0 0 | 500 | 487 444 482 499 510 = 0.80 || = 0.11 459 434 404 418 424 | 500 m 6 0 0 | 500 | 493 495 478 500 476 = 0.79 || = 0.10 416 367 389 411 418 | 500 x 10 0 0 | 500 | 504 526 536 535 507 = 0.78 || = 0.09 417 409 395 387 383 | 500 -----------------------------------------------------------------| 500 | 548 484 509 542 531 = 0.77 || = 0.08 344 357 385 373 382 | 500 Aver./ d 0.49142 546 > 500: 0 3 10 10 10 10 10 8 0 0 | 500 | 522 537 526 466 518 = 0.76 || = 0.07 399 356 358 366 338 | 500 median s 0.48950 545 ----- 0 3 10 10 10 10 10 7 1 0 | 500 | 534 545 534 556 539 = 0.75 || = 0.06 351 341 342 333 333 | 500 t 0.49167 540 0 2 10 10 10 10 10 8 0 0 | 500 | 553 552 572 517 575 = 0.74 || = 0.05 297 357 313 330 367 | 500 m 0.49204 537 0 3 10 10 10 10 10 7 1 0 | 500 | 537 529 551 503 536 = 0.73 || = 0.04 279 305 267 283 310 | 500 x 0.49020 547 0 4 9 10 10 10 10 9 0 0 | 500 | 585 572 524 537 563 = 0.72 || = 0.03 219 270 251 267 248 | 500 -----------------------------------------------------------------| 500 | 591 535 546 560 567 = 0.71 || = 0.02 212 211 218 245 226 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 578 594 582 571 577 = 0.70 || = 0.01 72 100 87 94 92 | 252.5 d 23 4 2 7 8 6 9 9 33 | 500 | 529 588 540 596 571 = 0.69 || < 0.01 109 109 100 130 115 | 497.5 s 25 0 6 3 7 8 9 10 33 | 500 | 583 538 558 602 605 = 0.68 ||========================================================================= t 26 2 4 4 8 8 4 9 36 | 500 | 613 571 571 565 562 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 24 3 4 6 8 7 4 14 31 | 500 | 618 583 594 585 558 = 0.66 ||========================================================================= x 24 3 3 5 7 8 9 9 33 | 500 | 599 598 574 569 579 = 0.65 || sspectral_Fourier3 test: no 193 test no 194 TestU01 250000 runs BigCrush Test smarsa_S sspectral_Fourier3 test: test no 194 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 590 668 613 661 664 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 635 688 671 676 691 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 628 622 657 646 624 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 646 633 634 661 636 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 679 617 670 624 626 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 649 656 646 639 660 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 663 684 677 688 661 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99992 || = 0.57 637 666 655 656 648 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 694 645 687 640 651 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 699 637 644 659 616 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 641 660 652 659 620 | 500 < 0.0001 0 0 0 0 0 | 5 | 0 0 1 0 1 > 0.9999 || = 0.53 661 658 645 633 657 | 500 < 0.0002 0 0 0 0 1 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 638 658 665 650 649 | 500 < 0.0003 1 0 0 0 0 | 5 | 1 1 0 1 0 > 0.9997 || = 0.51 625 700 663 646 608 | 500 < 0.0004 1 0 0 0 0 | 5 | 0 1 1 0 3 > 0.9996 || = 0.50 664 632 645 649 623 | 500 < 0.0005 2 0 0 0 2 | 5 | 0 1 1 0 2 > 0.9995 || = 0.49 677 632 621 699 670 | 500 < 0.0006 0 0 0 0 0 | 5 | 0 0 0 0 1 > 0.9994 || = 0.48 625 666 665 670 632 | 500 < 0.0007 0 0 0 0 0 | 5 | 2 2 0 0 0 > 0.9993 || = 0.47 623 634 637 637 659 | 500 < 0.0008 0 0 1 0 0 | 5 | 0 1 0 1 0 > 0.9992 || = 0.46 627 646 620 610 667 | 500 < 0.0009 0 1 0 1 0 | 5 | 0 0 2 1 0 > 0.9991 || = 0.45 645 599 645 602 666 | 500 < 0.001 1 0 1 0 1 | 5 | 0 1 0 0 3 > 0.999 || = 0.44 640 667 651 611 645 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 654 574 633 609 632 | 500 < 0.001 5 1 2 1 4 | 50 | 3 7 5 3 10 > 0.999 || = 0.42 653 622 568 647 632 | 500 < 0.002 4 6 3 9 1 | 50 | 4 8 8 6 3 > 0.998 || = 0.41 603 584 608 575 601 | 500 < 0.003 4 8 11 7 6 | 50 | 11 7 8 5 7 > 0.997 || = 0.40 642 616 640 654 621 | 500 < 0.004 7 7 7 9 7 | 50 | 3 6 8 10 7 > 0.996 || = 0.39 602 609 643 646 605 | 500 < 0.005 9 9 6 12 6 | 50 | 6 6 8 7 17 > 0.995 || = 0.38 634 584 633 576 644 | 500 < 0.006 7 5 7 9 8 | 50 | 8 21 7 13 3 > 0.994 || = 0.37 591 565 592 572 616 | 500 < 0.007 8 9 9 4 13 | 50 | 9 10 10 15 6 > 0.993 || = 0.36 556 606 536 637 601 | 500 < 0.008 7 11 11 10 9 | 50 | 8 10 10 15 13 > 0.992 || = 0.35 601 591 554 582 599 | 500 < 0.009 15 9 9 12 8 | 50 | 11 9 8 13 13 > 0.991 || = 0.34 585 583 577 618 561 | 500 < 0.01 7 15 14 17 13 | 50 | 12 9 12 9 12 > 0.99 || = 0.33 604 563 576 586 545 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 581 540 578 551 566 | 500 < 0.01 73 80 79 90 75 | 497.5 | 75 93 84 96 91 > 0.99 || = 0.31 543 625 566 630 559 | 500 = 0.01 60 62 81 66 53 | 252.5 | 71 70 60 71 58 = 0.99 || = 0.30 559 577 552 523 570 | 500 = 0.02 136 173 174 158 159 | 500 | 172 164 170 173 168 = 0.98 || = 0.29 545 559 595 565 547 | 500 =================================================================| 500 | 200 191 213 184 207 = 0.97 || = 0.28 540 544 551 580 571 | 500 sspectral_Fourier3 test: | 500 | 227 237 227 246 245 = 0.96 || = 0.27 587 505 542 533 574 | 500 ----------------------------------------------- | 500 | 266 278 271 283 263 = 0.95 || = 0.26 533 516 562 529 527 | 500 N = 100000, n = 16384, r = 27, s = 3, k = 14 | 500 | 302 292 293 273 297 = 0.94 || = 0.25 535 550 523 528 535 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 344 310 331 333 308 = 0.93 || = 0.24 532 493 498 486 496 | 500 | 500 | 342 368 314 366 339 = 0.92 || = 0.23 530 493 522 506 544 | 500 =================================================================| 500 | 348 373 360 360 349 = 0.91 || = 0.22 500 460 516 450 491 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 399 412 366 367 353 = 0.90 || = 0.21 453 489 490 506 478 | 500 -----------------------------------------------------------------| 500 | 408 382 423 390 390 = 0.89 || = 0.20 423 457 475 479 494 | 500 SD Bern.: d 6.98066 6.05662 6.03044 | 500 | 396 467 420 426 432 = 0.88 || = 0.19 478 443 476 446 513 | 500 s 6.87301 5.96351 5.78856 | 500 | 435 429 444 456 438 = 0.87 || = 0.18 481 455 469 473 447 | 500 t 6.85763 5.97743 5.89157 | 500 | 482 438 466 427 449 = 0.86 || = 0.17 491 455 459 448 471 | 500 m 6.84873 5.83146 5.74533 | 500 | 455 439 464 469 474 = 0.85 || = 0.16 417 404 418 453 451 | 500 x 6.93911 6.03377 5.82063 | 500 | 544 508 515 465 454 = 0.84 || = 0.15 410 440 451 382 433 | 500 | 500 | 501 508 497 528 505 = 0.83 || = 0.14 402 413 390 397 399 | 500 Changes: d 2 0 0 | 500 | 518 510 482 548 512 = 0.82 || = 0.13 408 383 411 430 383 | 500 s 2 0 0 | 500 | 541 532 564 547 512 = 0.81 || = 0.12 374 361 395 393 372 | 500 t 6 0 0 | 500 | 520 530 513 488 499 = 0.80 || = 0.11 368 352 354 365 385 | 500 m 8 0 0 | 500 | 606 544 557 581 558 = 0.79 || = 0.10 335 358 309 355 355 | 500 x 8 0 0 | 500 | 531 577 556 552 562 = 0.78 || = 0.09 306 344 331 338 335 | 500 -----------------------------------------------------------------| 500 | 583 590 573 599 605 = 0.77 || = 0.08 296 345 316 301 319 | 500 Aver./ d 0.51075 544 > 500: 0 0 7 10 10 10 10 10 4 0 | 500 | 596 559 577 541 588 = 0.76 || = 0.07 261 267 285 325 296 | 500 median s 0.51156 544 ----- 0 0 5 10 10 10 10 10 4 0 | 500 | 578 636 561 570 606 = 0.75 || = 0.06 280 281 267 286 266 | 500 t 0.50899 554 0 0 7 10 10 10 10 10 2 0 | 500 | 553 631 572 581 608 = 0.74 || = 0.05 246 255 239 218 234 | 500 m 0.50938 548 0 0 7 10 10 10 10 9 3 0 | 500 | 610 606 623 593 598 = 0.73 || = 0.04 226 259 232 205 235 | 500 x 0.50863 549 0 1 6 10 10 10 10 9 3 0 | 500 | 613 605 603 661 549 = 0.72 || = 0.03 203 179 214 228 171 | 500 -----------------------------------------------------------------| 500 | 598 622 619 601 647 = 0.71 || = 0.02 136 173 174 158 159 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 604 649 606 595 642 = 0.70 || = 0.01 60 62 81 66 53 | 252.5 d 29 2 3 0 8 9 4 5 41 | 500 | 648 596 603 632 645 = 0.69 || < 0.01 73 80 79 90 75 | 497.5 s 26 3 6 3 8 5 5 6 39 | 500 | 597 660 671 612 634 = 0.68 ||========================================================================= t 26 3 2 6 8 3 9 7 37 | 500 | 634 632 601 609 613 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 27 3 4 4 5 6 5 9 38 | 500 | 639 658 594 613 633 = 0.66 ||========================================================================= x 27 2 5 2 9 3 8 4 41 | 500 | 641 622 664 623 635 = 0.65 || sspectral_Fourier3 test: no 194 test no 195 TestU01 250000 runs BigCrush Test smarsa_S sspectral_Fourier3 test: test no 195 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 1 1 0 0 > 0.99999 || = 0.64 623 599 582 579 626 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 1 2 0 1 0 > 0.99998 || = 0.63 597 601 584 633 556 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99997 || = 0.62 607 593 591 572 594 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 3 1 1 1 > 0.99996 || = 0.61 549 582 575 579 590 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 582 568 588 639 554 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 1 0 0 1 2 > 0.99994 || = 0.59 626 555 573 581 547 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 1 0 0 2 0 > 0.99993 || = 0.58 606 587 574 615 594 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 1 1 1 1 > 0.99992 || = 0.57 555 564 595 550 538 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 1 0 0 1 0 > 0.99991 || = 0.56 524 596 592 585 581 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 1 0 0 1 > 0.9999 || = 0.55 575 541 561 625 578 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 590 566 557 590 576 | 500 < 0.0001 0 0 0 0 0 | 5 | 4 9 3 7 5 > 0.9999 || = 0.53 578 540 593 563 585 | 500 < 0.0002 0 0 0 0 0 | 5 | 1 4 4 6 6 > 0.9998 || = 0.52 514 561 555 589 521 | 500 < 0.0003 0 0 0 0 0 | 5 | 2 4 6 7 9 > 0.9997 || = 0.51 584 536 571 517 545 | 500 < 0.0004 0 0 0 0 0 | 5 | 6 6 4 9 11 > 0.9996 || = 0.50 549 565 532 516 607 | 500 < 0.0005 0 0 0 0 0 | 5 | 4 4 3 7 2 > 0.9995 || = 0.49 537 490 517 528 570 | 500 < 0.0006 0 0 0 0 0 | 5 | 7 8 4 11 9 > 0.9994 || = 0.48 531 542 563 559 536 | 500 < 0.0007 0 0 0 0 0 | 5 | 8 6 13 8 7 > 0.9993 || = 0.47 543 556 557 498 553 | 500 < 0.0008 0 0 1 0 0 | 5 | 7 4 6 2 9 > 0.9992 || = 0.46 564 566 569 492 540 | 500 < 0.0009 0 0 0 0 1 | 5 | 4 11 3 8 9 > 0.9991 || = 0.45 532 522 525 517 519 | 500 < 0.001 0 0 0 0 0 | 5 | 7 5 8 7 7 > 0.999 || = 0.44 487 543 558 539 523 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 556 518 542 506 538 | 500 < 0.001 0 0 1 0 1 | 50 | 50 61 54 72 74 > 0.999 || = 0.42 494 526 538 495 503 | 500 < 0.002 0 0 1 0 1 | 50 | 72 58 79 80 53 > 0.998 || = 0.41 493 491 500 531 513 | 500 < 0.003 1 1 1 2 3 | 50 | 69 63 63 68 64 > 0.997 || = 0.40 532 525 528 486 497 | 500 < 0.004 2 2 0 1 2 | 50 | 74 62 71 75 82 > 0.996 || = 0.39 483 492 468 482 499 | 500 < 0.005 3 0 3 1 3 | 50 | 65 56 74 80 66 > 0.995 || = 0.38 493 484 525 500 506 | 500 < 0.006 5 2 3 4 1 | 50 | 69 62 65 64 68 > 0.994 || = 0.37 511 483 497 513 498 | 500 < 0.007 2 0 3 2 1 | 50 | 89 64 61 63 64 > 0.993 || = 0.36 467 451 442 490 496 | 500 < 0.008 4 4 7 6 1 | 50 | 76 57 90 71 63 > 0.992 || = 0.35 496 481 454 474 488 | 500 < 0.009 6 6 2 6 2 | 50 | 72 66 57 84 80 > 0.991 || = 0.34 489 483 470 464 467 | 500 < 0.01 7 5 3 8 4 | 50 | 65 63 60 73 70 > 0.99 || = 0.33 466 502 490 499 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 434 454 462 494 457 | 500 < 0.01 30 20 24 30 19 | 497.5 | 701 612 674 730 684 > 0.99 || = 0.31 452 491 481 433 449 | 500 = 0.01 26 27 25 24 24 | 252.5 | 341 360 349 352 353 = 0.99 || = 0.30 410 440 450 421 446 | 500 = 0.02 67 83 74 85 66 | 500 | 700 710 679 692 666 = 0.98 || = 0.29 467 422 423 404 470 | 500 =================================================================| 500 | 649 696 689 697 708 = 0.97 || = 0.28 455 429 415 417 436 | 500 sspectral_Fourier3 test: | 500 | 672 701 694 690 674 = 0.96 || = 0.27 430 448 414 443 435 | 500 ----------------------------------------------- | 500 | 654 666 656 657 650 = 0.95 || = 0.26 417 425 403 428 405 | 500 N = 100000, n = 16384, r = 27, s = 3, k = 14 | 500 | 690 656 678 666 599 = 0.94 || = 0.25 421 436 411 407 426 | 500 Anderson-Darling statistic = A2 | 500 | 678 696 652 671 689 = 0.93 || = 0.24 430 384 387 446 379 | 500 | 500 | 697 682 669 686 688 = 0.92 || = 0.23 407 401 411 389 396 | 500 =================================================================| 500 | 649 674 663 668 679 = 0.91 || = 0.22 365 374 402 403 371 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 697 655 678 667 675 = 0.90 || = 0.21 380 377 347 392 421 | 500 -----------------------------------------------------------------| 500 | 717 677 686 680 667 = 0.89 || = 0.20 365 357 366 344 384 | 500 SD Bern.: d 7.58028 6.65825 3.13620 | 500 | 639 708 688 689 665 = 0.88 || = 0.19 357 377 371 398 380 | 500 s 7.32311 6.79839 1.64276 | 500 | 665 616 642 621 624 = 0.87 || = 0.18 370 346 327 351 333 | 500 t 7.38529 6.74013 2.87823 | 500 | 681 647 634 585 635 = 0.86 || = 0.17 338 319 336 359 314 | 500 m 7.33762 6.66095 3.38517 | 500 | 654 643 641 627 653 = 0.85 || = 0.16 323 288 321 326 329 | 500 x 7.37010 6.80737 2.84746 | 500 | 664 626 646 605 669 = 0.84 || = 0.15 309 333 342 316 311 | 500 | 500 | 685 656 664 627 626 = 0.83 || = 0.14 269 303 298 279 309 | 500 Changes: d 7 0 1 | 500 | 640 686 667 668 636 = 0.82 || = 0.13 249 321 288 276 230 | 500 s 7 0 0 | 500 | 640 614 668 702 662 = 0.81 || = 0.12 284 283 259 248 296 | 500 t 5 0 0 | 500 | 630 618 643 657 664 = 0.80 || = 0.11 246 264 268 263 244 | 500 m 7 0 0 | 500 | 638 653 643 629 642 = 0.79 || = 0.10 223 234 248 243 215 | 500 x 3 0 0 | 500 | 670 678 640 635 623 = 0.78 || = 0.09 198 222 229 252 228 | 500 -----------------------------------------------------------------| 500 | 609 662 617 638 593 = 0.77 || = 0.08 202 204 206 201 215 | 500 Aver./ d 0.59086 549 > 500: 0 0 0 1 7 10 10 10 10 10 | 500 | 611 662 656 576 699 = 0.76 || = 0.07 181 224 174 181 205 | 500 median s 0.58791 543 ----- 0 0 0 1 8 10 10 10 10 10 | 500 | 613 605 610 632 618 = 0.75 || = 0.06 158 168 165 184 175 | 500 t 0.58866 558 0 0 0 1 9 10 10 10 10 10 | 500 | 616 602 613 576 623 = 0.74 || = 0.05 121 157 149 167 143 | 500 m 0.58782 539 0 0 0 1 6 10 10 10 10 10 | 500 | 629 624 598 652 660 = 0.73 || = 0.04 104 106 121 116 128 | 500 x 0.58786 545 0 0 0 1 9 10 10 10 10 10 | 500 | 630 611 622 654 607 = 0.72 || = 0.03 92 111 100 106 113 | 500 -----------------------------------------------------------------| 500 | 629 628 633 592 601 = 0.71 || = 0.02 67 83 74 85 66 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 643 610 608 603 635 = 0.70 || = 0.01 26 27 25 24 24 | 252.5 d 25 4 3 3 9 6 5 5 41 | 500 | 614 624 641 622 585 = 0.69 || < 0.01 30 20 24 30 19 | 497.5 s 25 3 5 0 11 7 7 4 39 | 500 | 645 599 609 606 610 = 0.68 ||========================================================================= t 27 3 3 3 5 6 6 9 39 | 500 | 618 594 611 599 642 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 26 4 2 2 14 3 3 9 38 | 500 | 607 634 572 638 603 = 0.66 ||========================================================================= x 25 2 4 3 11 5 5 6 40 | 500 | 572 578 604 579 620 = 0.65 || sspectral_Fourier3 test: no 195 test no 196 TestU01 250000 runs BigCrush Test smarsa_S sstring_LongestHeadRun test: test no 196 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 0 2 | 0.5 | 1 1 0 1 1 > 0.99999 || = 0.64 525 518 517 491 512 | 500 < 0.00002 0 1 1 1 0 | 0.5 | 2 1 0 0 1 > 0.99998 || = 0.63 472 506 473 523 456 | 500 < 0.00003 1 0 1 2 2 | 0.5 | 0 1 1 0 0 > 0.99997 || = 0.62 499 476 501 501 495 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 2 0 0 0 0 > 0.99996 || = 0.61 499 495 490 495 498 | 500 < 0.00005 0 0 1 0 3 | 0.5 | 0 0 1 2 0 > 0.99995 || = 0.60 519 464 513 475 476 | 500 < 0.00006 1 0 1 1 0 | 0.5 | 1 0 1 0 0 > 0.99994 || = 0.59 482 517 491 504 482 | 500 < 0.00007 0 0 0 1 1 | 0.5 | 0 1 0 0 2 > 0.99993 || = 0.58 467 539 497 477 493 | 500 < 0.00008 2 2 1 1 1 | 0.5 | 0 2 2 0 1 > 0.99992 || = 0.57 499 478 523 505 520 | 500 < 0.00009 0 0 0 1 1 | 0.5 | 1 0 0 1 0 > 0.99991 || = 0.56 511 512 495 517 499 | 500 < 0.0001 0 0 0 0 1 | 0.5 | 0 0 1 1 0 > 0.9999 || = 0.55 491 443 525 476 473 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 474 529 486 504 494 | 500 < 0.0001 5 3 7 7 12 | 5 | 7 6 6 5 5 > 0.9999 || = 0.53 515 506 523 521 468 | 500 < 0.0002 4 2 7 8 6 | 5 | 3 1 1 3 3 > 0.9998 || = 0.52 495 516 521 446 557 | 500 < 0.0003 4 6 4 4 5 | 5 | 4 4 4 8 7 > 0.9997 || = 0.51 475 503 481 487 466 | 500 < 0.0004 6 11 5 4 4 | 5 | 4 8 4 7 7 > 0.9996 || = 0.50 521 487 531 517 486 | 500 < 0.0005 6 9 3 4 4 | 5 | 7 8 4 4 5 > 0.9995 || = 0.49 505 553 498 486 478 | 500 < 0.0006 7 3 5 5 8 | 5 | 6 4 7 6 1 > 0.9994 || = 0.48 516 498 513 497 527 | 500 < 0.0007 6 7 3 3 5 | 5 | 3 10 5 7 6 > 0.9993 || = 0.47 533 479 488 533 472 | 500 < 0.0008 5 5 7 6 5 | 5 | 4 5 5 4 8 > 0.9992 || = 0.46 469 484 461 537 492 | 500 < 0.0009 6 9 10 7 7 | 5 | 6 4 6 4 3 > 0.9991 || = 0.45 528 493 524 479 537 | 500 < 0.001 3 5 5 5 9 | 5 | 6 7 4 1 7 > 0.999 || = 0.44 493 494 521 468 501 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 517 532 475 517 448 | 500 < 0.001 52 60 56 53 65 | 50 | 50 57 46 49 52 > 0.999 || = 0.42 522 528 503 475 482 | 500 < 0.002 54 54 45 52 47 | 50 | 53 51 59 46 65 > 0.998 || = 0.41 481 555 500 496 506 | 500 < 0.003 66 45 54 60 56 | 50 | 49 42 50 46 37 > 0.997 || = 0.40 524 484 505 507 482 | 500 < 0.004 62 58 54 49 48 | 50 | 61 53 51 53 58 > 0.996 || = 0.39 480 513 493 472 526 | 500 < 0.005 57 51 49 46 51 | 50 | 55 49 53 50 50 > 0.995 || = 0.38 455 518 487 494 510 | 500 < 0.006 59 45 41 44 50 | 50 | 58 51 35 43 47 > 0.994 || = 0.37 438 483 478 530 486 | 500 < 0.007 46 45 44 46 51 | 50 | 57 46 52 40 37 > 0.993 || = 0.36 480 487 492 493 519 | 500 < 0.008 45 48 42 51 45 | 50 | 51 51 55 55 41 > 0.992 || = 0.35 495 479 473 506 512 | 500 < 0.009 53 45 71 43 54 | 50 | 49 54 53 57 52 > 0.991 || = 0.34 515 511 508 492 499 | 500 < 0.01 49 52 45 53 53 | 50 | 47 52 43 51 41 > 0.99 || = 0.33 533 491 506 510 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 490 508 499 525 501 | 500 < 0.01 543 503 501 497 520 | 497.5 | 530 506 497 490 480 > 0.99 || = 0.31 473 523 505 507 554 | 500 = 0.01 265 231 295 245 274 | 252.5 | 233 269 216 240 253 = 0.99 || = 0.30 505 488 501 491 478 | 500 = 0.02 493 462 485 491 544 | 500 | 439 477 502 510 526 = 0.98 || = 0.29 479 471 483 497 482 | 500 =================================================================| 500 | 529 484 457 479 489 = 0.97 || = 0.28 540 514 504 526 500 | 500 sstring_LongestHeadRun test: | 500 | 502 502 538 519 496 = 0.96 || = 0.27 488 514 518 545 531 | 500 ----------------------------------------------- | 500 | 506 525 510 489 452 = 0.95 || = 0.26 505 512 510 507 487 | 500 N = 1, n = 1000, r = 0, s = 3, L = 10000020 | 500 | 485 500 492 519 468 = 0.94 || = 0.25 502 498 479 517 495 | 500 Number of degrees of freedom : 8 | 500 | 507 482 549 529 477 = 0.93 || = 0.24 495 493 510 569 489 | 500 Chi-square statistic | 500 | 523 459 531 474 518 = 0.92 || = 0.23 498 518 467 515 505 | 500 =================================================================| 500 | 525 510 497 492 479 = 0.91 || = 0.22 534 546 482 486 518 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 492 457 484 525 508 = 0.90 || = 0.21 542 469 502 502 515 | 500 -----------------------------------------------------------------| 500 | 512 474 464 503 508 = 0.89 || = 0.20 514 501 485 481 498 | 500 SD Bern.: d 1.09456 1.09690 0.74869 | 500 | 511 502 513 504 503 = 0.88 || = 0.19 497 491 479 457 499 | 500 s 1.02213 0.76063 0.56948 | 500 | 506 504 480 495 510 = 0.87 || = 0.18 454 486 497 507 520 | 500 t 1.01933 1.21797 0.91587 | 500 | 473 494 493 475 512 = 0.86 || = 0.17 528 516 503 510 491 | 500 m 0.96911 0.69460 0.72973 | 500 | 453 522 504 505 497 = 0.85 || = 0.16 460 496 512 488 482 | 500 x 0.99085 0.80786 1.27027 | 500 | 482 485 487 509 545 = 0.84 || = 0.15 492 522 473 524 485 | 500 | 500 | 500 460 513 508 506 = 0.83 || = 0.14 518 499 514 463 459 | 500 Changes: d 50 3 4 | 500 | 501 504 497 491 515 = 0.82 || = 0.13 507 489 503 505 479 | 500 s 50 4 6 | 500 | 492 531 491 504 512 = 0.81 || = 0.12 497 528 503 447 520 | 500 t 57 5 6 | 500 | 511 506 496 488 504 = 0.80 || = 0.11 473 475 550 558 525 | 500 m 58 4 3 | 500 | 481 503 538 532 494 = 0.79 || = 0.10 474 464 501 500 475 | 500 x 46 8 5 | 500 | 501 513 495 510 528 = 0.78 || = 0.09 469 517 499 485 504 | 500 -----------------------------------------------------------------| 500 | 495 514 463 506 493 = 0.77 || = 0.08 528 541 528 501 480 | 500 Aver./ d 0.49997 501 > 500: 7 3 6 3 7 3 3 8 4 7 | 500 | 537 458 552 524 469 = 0.76 || = 0.07 508 510 501 475 471 | 500 median s 0.49958 501 ----- 5 3 6 5 4 7 5 6 5 5 | 500 | 504 518 533 466 493 = 0.75 || = 0.06 507 478 513 479 528 | 500 t 0.50069 500 5 7 5 4 5 5 4 6 3 5 | 500 | 542 499 519 520 511 = 0.74 || = 0.05 444 508 490 532 505 | 500 m 0.49960 501 4 5 7 5 4 5 4 5 7 4 | 500 | 530 500 547 500 534 = 0.73 || = 0.04 518 496 467 511 495 | 500 x 0.49932 499 7 3 4 6 4 2 6 5 9 3 | 500 | 528 497 482 478 505 = 0.72 || = 0.03 533 476 446 511 515 | 500 -----------------------------------------------------------------| 500 | 502 535 538 483 493 = 0.71 || = 0.02 493 462 485 491 544 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 541 477 512 502 531 = 0.70 || = 0.01 265 231 295 245 274 | 252.5 d 0 0 6 13 61 20 1 0 0 | 500 | 478 472 488 493 512 = 0.69 || < 0.01 543 503 501 497 520 | 497.5 s 0 0 1 17 68 11 4 0 0 | 500 | 492 485 469 500 521 = 0.68 ||========================================================================= t 0 0 2 13 70 11 5 0 0 | 500 | 482 548 475 478 504 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 13 71 12 2 1 0 | 500 | 472 509 470 510 519 = 0.66 ||========================================================================= x 0 0 2 13 70 13 3 0 0 | 500 | 502 505 511 465 467 = 0.65 || sstring_LongestHeadRun test: no 196 test no 197 TestU01 250000 runs BigCrush Test smarsa_S sstring_LongestHeadRun test: test no 197 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 0 0 0 0 0 | 500 < 0.00002 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 0 0 0 0 0 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 0 0 0 0 0 | 500 < 0.00004 0 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 0 0 0 0 0 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 0 0 0 0 0 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 0 0 0 0 0 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 0 0 0 0 0 | 500 < 0.00008 4 2 2 1 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 0 0 0 0 0 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 0 0 0 0 0 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 8 4 5 4 6 > 0.9999 || = 0.55 0 0 0 0 0 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 0 0 0 0 0 | 500 < 0.0001 4 2 3 3 3 | 5 | 8 4 5 4 6 > 0.9999 || = 0.53 0 0 0 0 0 | 500 < 0.0002 9 2 3 4 4 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 0 0 0 0 0 | 500 < 0.0003 11 4 9 7 5 | 5 | 0 0 0 0 0 > 0.9997 || = 0.51 0 0 0 0 0 | 500 < 0.0004 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9996 || = 0.50 12227 12329 12236 12481 12307 | 500 < 0.0005 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 12 7 12 14 14 | 5 | 0 0 0 0 0 > 0.9994 || = 0.48 0 0 0 0 0 | 500 < 0.0007 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9993 || = 0.47 0 0 0 0 0 | 500 < 0.0008 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9992 || = 0.46 0 0 0 0 0 | 500 < 0.0009 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9991 || = 0.45 0 0 0 0 0 | 500 < 0.001 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.999 || = 0.44 9554 9326 9438 9508 9330 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 0 0 0 0 0 | 500 < 0.001 36 15 27 28 26 | 50 | 8 4 5 4 6 > 0.999 || = 0.42 0 0 0 0 0 | 500 < 0.002 33 30 31 27 29 | 50 | 0 0 0 0 0 > 0.998 || = 0.41 0 0 0 0 0 | 500 < 0.003 67 54 69 72 54 | 50 | 0 0 0 0 0 > 0.997 || = 0.40 0 0 0 0 0 | 500 < 0.004 0 0 0 0 0 | 50 | 0 0 0 0 0 > 0.996 || = 0.39 0 0 0 0 0 | 500 < 0.005 120 127 117 119 120 | 50 | 0 0 0 0 0 > 0.995 || = 0.38 0 0 0 0 0 | 500 < 0.006 0 0 0 0 0 | 50 | 0 0 0 0 0 > 0.994 || = 0.37 0 0 0 0 0 | 500 < 0.007 0 0 0 0 0 | 50 | 0 0 0 0 0 > 0.993 || = 0.36 0 0 0 0 0 | 500 < 0.008 0 0 0 0 0 | 50 | 0 0 0 0 0 > 0.992 || = 0.35 0 0 0 0 0 | 500 < 0.009 0 0 0 0 0 | 50 | 0 0 0 0 0 > 0.991 || = 0.34 0 0 0 0 0 | 500 < 0.01 215 239 225 234 251 | 50 | 477 473 494 449 439 > 0.99 || = 0.33 0 0 0 0 0 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 0 0 0 0 0 | 500 < 0.01 471 465 469 480 480 | 497.5 | 485 477 499 453 445 > 0.99 || = 0.31 0 0 0 0 0 | 500 = 0.01 0 0 0 0 0 | 252.5 | 0 0 0 0 0 = 0.99 || = 0.30 0 0 0 0 0 | 500 = 0.02 437 457 453 454 463 | 500 | 0 0 0 0 0 = 0.98 || = 0.29 0 0 0 0 0 | 500 =================================================================| 500 | 0 0 0 0 0 = 0.97 || = 0.28 0 0 0 0 0 | 500 sstring_LongestHeadRun test: | 500 | 0 0 0 0 0 = 0.96 || = 0.27 0 0 0 0 0 | 500 ----------------------------------------------- | 500 | 0 0 0 0 0 = 0.95 || = 0.26 0 0 0 0 0 | 500 N = 1, n = 1000, r = 0, s = 3, L = 10000020 | 500 | 0 0 0 0 0 = 0.94 || = 0.25 5796 5868 5911 5858 5856 | 500 Global longest run of 1 | 500 | 0 0 0 0 0 = 0.93 || = 0.24 0 0 0 0 0 | 500 | 500 | 0 0 0 0 0 = 0.92 || = 0.23 0 0 0 0 0 | 500 =================================================================| 500 | 0 0 0 0 0 = 0.91 || = 0.22 0 0 0 0 0 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 4414 4405 4497 4276 4266 = 0.90 || = 0.21 0 0 0 0 0 | 500 -----------------------------------------------------------------| 500 | 0 0 0 0 0 = 0.89 || = 0.20 0 0 0 0 0 | 500 SD Bern.: d 89.45768 9.53356 20.21371 | 500 | 0 0 0 0 0 = 0.88 || = 0.19 0 0 0 0 0 | 500 s 89.59160 10.56852 20.06221 | 500 | 0 0 0 0 0 = 0.87 || = 0.18 0 0 0 0 0 | 500 t 89.12460 9.89079 20.94661 | 500 | 0 0 0 0 0 = 0.86 || = 0.17 0 0 0 0 0 | 500 m 89.62178 10.26320 19.05247 | 500 | 0 0 0 0 0 = 0.85 || = 0.16 0 0 0 0 0 | 500 x 89.27991 10.85291 18.62419 | 500 | 0 0 0 0 0 = 0.84 || = 0.15 0 0 0 0 0 | 500 | 500 | 0 0 0 0 0 = 0.83 || = 0.14 3312 3173 3191 3268 3380 | 500 Changes: d 16 5 1 | 500 | 0 0 0 0 0 = 0.82 || = 0.13 0 0 0 0 0 | 500 s 16 5 1 | 500 | 0 0 0 0 0 = 0.81 || = 0.12 0 0 0 0 0 | 500 t 17 5 1 | 500 | 0 0 0 0 0 = 0.80 || = 0.11 0 0 0 0 0 | 500 m 16 5 1 | 500 | 0 0 0 0 0 = 0.79 || = 0.10 0 0 0 0 0 | 500 x 16 5 1 | 500 | 0 0 0 0 0 = 0.78 || = 0.09 0 0 0 0 0 | 500 -----------------------------------------------------------------| 500 | 0 0 0 0 0 = 0.77 || = 0.08 0 0 0 0 0 | 500 Aver./ d 0.48559 0 > 500: 2 1 1 0 1 0 1 0 1 0 | 500 | 0 0 0 0 0 = 0.76 || = 0.07 1701 1703 1793 1743 1761 | 500 median s 0.48624 0 ----- 2 1 1 0 1 0 1 0 1 0 | 500 | 0 0 0 0 0 = 0.75 || = 0.06 0 0 0 0 0 | 500 t 0.48509 0 2 1 1 0 1 0 1 0 1 1 | 500 | 0 0 0 0 0 = 0.74 || = 0.05 0 0 0 0 0 | 500 m 0.48272 0 2 1 1 0 1 0 1 0 1 0 | 500 | 0 0 0 0 0 = 0.73 || = 0.04 831 885 867 864 919 | 500 x 0.48191 0 2 1 1 0 1 0 1 0 1 0 | 500 | 0 0 0 0 0 = 0.72 || = 0.03 0 0 0 0 0 | 500 -----------------------------------------------------------------| 500 | 0 0 0 0 0 = 0.71 || = 0.02 437 457 453 454 463 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 0 0 0 0 0 = 0.70 || = 0.01 0 0 0 0 0 | 252.5 d 90 0 1 1 1 0 0 0 8 | 500 | 10772 10912 10646 10615 10793 = 0.69 || < 0.01 471 465 469 480 480 | 497.5 s 90 0 0 2 1 0 0 0 8 | 500 | 0 0 0 0 0 = 0.68 ||========================================================================= t 90 0 1 1 1 0 0 0 8 | 500 | 0 0 0 0 0 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 90 0 2 0 1 0 0 0 8 | 500 | 0 0 0 0 0 = 0.66 ||========================================================================= x 90 0 1 1 1 0 0 0 8 | 500 | 0 0 0 0 0 = 0.65 || sstring_LongestHeadRun test: no 197 test no 198 TestU01 250000 runs BigCrush Test smarsa_S sstring_LongestHeadRun test: test no 198 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 2 0 1 | 0.5 | 0 1 0 2 2 > 0.99999 || = 0.64 478 509 488 501 531 | 500 < 0.00002 1 1 1 1 0 | 0.5 | 0 2 0 0 0 > 0.99998 || = 0.63 502 501 550 496 519 | 500 < 0.00003 0 1 0 1 0 | 0.5 | 1 0 1 1 0 > 0.99997 || = 0.62 546 496 485 518 481 | 500 < 0.00004 1 0 0 0 2 | 0.5 | 0 2 1 0 0 > 0.99996 || = 0.61 488 489 496 529 511 | 500 < 0.00005 2 2 0 1 1 | 0.5 | 0 0 0 1 2 > 0.99995 || = 0.60 505 513 512 508 496 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 1 1 0 1 0 > 0.99994 || = 0.59 481 505 457 534 520 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99993 || = 0.58 512 503 478 521 476 | 500 < 0.00008 0 0 1 0 0 | 0.5 | 2 1 0 0 1 > 0.99992 || = 0.57 539 508 518 500 526 | 500 < 0.00009 2 1 2 0 0 | 0.5 | 1 0 0 0 0 > 0.99991 || = 0.56 524 484 480 512 522 | 500 < 0.0001 0 3 0 2 1 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 484 478 497 497 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 491 478 518 480 512 | 500 < 0.0001 7 8 6 6 5 | 5 | 6 7 2 5 5 > 0.9999 || = 0.53 503 542 468 517 502 | 500 < 0.0002 8 4 5 11 4 | 5 | 4 0 2 2 4 > 0.9998 || = 0.52 499 515 497 509 525 | 500 < 0.0003 9 4 0 6 5 | 5 | 4 4 5 6 7 > 0.9997 || = 0.51 509 500 547 547 470 | 500 < 0.0004 5 4 6 6 4 | 5 | 3 7 6 4 6 > 0.9996 || = 0.50 499 482 502 462 510 | 500 < 0.0005 9 4 5 4 5 | 5 | 7 7 6 2 7 > 0.9995 || = 0.49 492 508 506 492 504 | 500 < 0.0006 4 7 2 6 6 | 5 | 3 4 3 5 6 > 0.9994 || = 0.48 508 500 474 451 524 | 500 < 0.0007 5 2 6 3 4 | 5 | 7 10 4 5 5 > 0.9993 || = 0.47 516 499 494 458 445 | 500 < 0.0008 4 6 6 3 7 | 5 | 6 4 6 6 3 > 0.9992 || = 0.46 481 451 473 488 521 | 500 < 0.0009 4 11 4 6 1 | 5 | 6 5 4 4 1 > 0.9991 || = 0.45 483 498 521 477 496 | 500 < 0.001 2 5 6 6 8 | 5 | 10 9 11 5 3 > 0.999 || = 0.44 519 489 520 508 486 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 496 530 497 521 515 | 500 < 0.001 57 55 46 57 49 | 50 | 56 57 49 44 47 > 0.999 || = 0.42 507 506 504 478 478 | 500 < 0.002 34 41 53 44 61 | 50 | 39 48 44 43 46 > 0.998 || = 0.41 499 481 482 523 531 | 500 < 0.003 55 42 44 43 51 | 50 | 46 49 49 43 51 > 0.997 || = 0.40 481 500 510 529 485 | 500 < 0.004 56 62 47 44 49 | 50 | 37 51 53 45 36 > 0.996 || = 0.39 495 492 540 469 539 | 500 < 0.005 50 47 52 51 53 | 50 | 47 45 49 62 45 > 0.995 || = 0.38 483 495 522 479 500 | 500 < 0.006 54 47 60 49 63 | 50 | 56 58 36 54 52 > 0.994 || = 0.37 510 507 516 496 497 | 500 < 0.007 64 47 65 58 46 | 50 | 54 49 47 48 46 > 0.993 || = 0.36 486 519 516 479 494 | 500 < 0.008 44 48 43 67 54 | 50 | 60 47 55 45 43 > 0.992 || = 0.35 550 504 522 474 481 | 500 < 0.009 54 61 50 47 59 | 50 | 41 53 49 55 58 > 0.991 || = 0.34 538 450 504 516 473 | 500 < 0.01 48 60 50 63 48 | 50 | 52 42 37 53 52 > 0.99 || = 0.33 504 505 520 481 478 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 471 494 468 531 443 | 500 < 0.01 516 510 510 523 533 | 497.5 | 488 499 468 492 476 > 0.99 || = 0.31 515 521 462 494 482 | 500 = 0.01 253 239 249 238 251 | 252.5 | 242 257 230 226 248 = 0.99 || = 0.30 511 472 498 514 477 | 500 = 0.02 503 497 511 496 467 | 500 | 509 465 470 480 487 = 0.98 || = 0.29 510 513 475 511 500 | 500 =================================================================| 500 | 501 516 486 436 515 = 0.97 || = 0.28 453 498 504 485 486 | 500 sstring_LongestHeadRun test: | 500 | 481 481 477 497 509 = 0.96 || = 0.27 484 493 542 497 507 | 500 ----------------------------------------------- | 500 | 509 498 508 512 516 = 0.95 || = 0.26 514 498 472 492 467 | 500 N = 1, n = 1000, r = 27, s = 3, L = 10000020 | 500 | 508 513 523 520 495 = 0.94 || = 0.25 508 528 537 476 534 | 500 Number of degrees of freedom : 8 | 500 | 461 452 512 521 473 = 0.93 || = 0.24 465 510 498 503 539 | 500 Chi-square statistic | 500 | 524 513 532 525 512 = 0.92 || = 0.23 495 448 483 500 511 | 500 =================================================================| 500 | 507 498 490 490 464 = 0.91 || = 0.22 475 499 528 514 522 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 520 471 506 488 488 = 0.90 || = 0.21 482 507 496 505 525 | 500 -----------------------------------------------------------------| 500 | 526 485 500 473 491 = 0.89 || = 0.20 512 509 459 483 477 | 500 SD Bern.: d 0.91560 1.12661 1.08497 | 500 | 480 485 501 540 498 = 0.88 || = 0.19 462 520 504 464 503 | 500 s 0.88367 1.06448 0.67412 | 500 | 496 513 486 485 498 = 0.87 || = 0.18 506 485 478 510 505 | 500 t 1.01625 0.94704 0.94703 | 500 | 525 511 504 509 466 = 0.86 || = 0.17 527 488 501 520 514 | 500 m 1.03901 1.18633 0.87449 | 500 | 505 499 474 504 504 = 0.85 || = 0.16 468 487 499 486 527 | 500 x 1.03599 0.91587 0.87678 | 500 | 484 501 462 488 510 = 0.84 || = 0.15 464 511 500 479 470 | 500 | 500 | 472 485 524 517 504 = 0.83 || = 0.14 482 487 491 498 500 | 500 Changes: d 55 7 4 | 500 | 524 505 499 535 506 = 0.82 || = 0.13 538 524 494 468 534 | 500 s 52 4 7 | 500 | 499 491 531 505 477 = 0.81 || = 0.12 473 507 505 544 482 | 500 t 61 4 4 | 500 | 483 516 568 470 527 = 0.80 || = 0.11 520 483 464 514 528 | 500 m 43 6 3 | 500 | 491 516 497 483 527 = 0.79 || = 0.10 487 493 541 518 485 | 500 x 53 6 5 | 500 | 510 465 495 471 553 = 0.78 || = 0.09 511 505 496 495 465 | 500 -----------------------------------------------------------------| 500 | 557 559 530 492 501 = 0.77 || = 0.08 511 546 503 493 505 | 500 Aver./ d 0.50082 502 > 500: 8 4 4 6 4 6 5 6 5 6 | 500 | 496 501 517 496 462 = 0.76 || = 0.07 495 489 484 537 498 | 500 median s 0.50003 500 ----- 5 4 5 5 3 6 7 6 4 5 | 500 | 513 486 480 510 474 = 0.75 || = 0.06 476 514 517 534 518 | 500 t 0.50012 499 5 4 4 7 5 4 4 5 5 4 | 500 | 511 521 539 481 503 = 0.74 || = 0.05 504 503 481 508 504 | 500 m 0.49919 497 6 5 4 3 4 7 5 3 6 4 | 500 | 501 524 492 493 508 = 0.73 || = 0.04 504 490 502 505 462 | 500 x 0.49992 501 5 6 6 1 5 6 6 7 4 4 | 500 | 449 481 514 508 475 = 0.72 || = 0.03 508 476 473 501 505 | 500 -----------------------------------------------------------------| 500 | 507 497 480 584 515 = 0.71 || = 0.02 503 497 511 496 467 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 520 520 520 483 541 = 0.70 || = 0.01 253 239 249 238 251 | 252.5 d 0 0 2 10 77 9 3 0 0 | 500 | 502 544 479 493 458 = 0.69 || < 0.01 516 510 510 523 533 | 497.5 s 0 0 4 5 82 8 2 0 0 | 500 | 487 523 509 490 527 = 0.68 ||========================================================================= t 0 0 0 18 69 11 2 1 0 | 500 | 517 527 512 533 489 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 12 72 13 1 1 0 | 500 | 494 491 466 503 542 = 0.66 ||========================================================================= x 0 0 2 18 62 18 1 0 0 | 500 | 490 510 480 481 491 = 0.65 || sstring_LongestHeadRun test: no 198 test no 199 TestU01 250000 runs BigCrush Test smarsa_S sstring_LongestHeadRun test: test no 199 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 3 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 0 0 0 0 0 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 0 0 0 0 0 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 0 0 0 0 0 | 500 < 0.00004 2 1 2 1 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 0 0 0 0 0 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 0 0 0 0 0 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 0 0 0 0 0 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 0 0 0 0 0 | 500 < 0.00008 1 4 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 0 0 0 0 0 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 0 0 0 0 0 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 5 7 4 6 3 > 0.9999 || = 0.55 0 0 0 0 0 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 0 0 0 0 0 | 500 < 0.0001 4 8 4 4 0 | 5 | 5 7 4 6 3 > 0.9999 || = 0.53 0 0 0 0 0 | 500 < 0.0002 6 2 7 6 4 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 0 0 0 0 0 | 500 < 0.0003 7 9 3 9 12 | 5 | 0 0 0 0 0 > 0.9997 || = 0.51 0 0 0 0 0 | 500 < 0.0004 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9996 || = 0.50 12437 12429 12093 12269 12313 | 500 < 0.0005 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9995 || = 0.49 0 0 0 0 0 | 500 < 0.0006 17 8 14 13 17 | 5 | 0 0 0 0 0 > 0.9994 || = 0.48 0 0 0 0 0 | 500 < 0.0007 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9993 || = 0.47 0 0 0 0 0 | 500 < 0.0008 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9992 || = 0.46 0 0 0 0 0 | 500 < 0.0009 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9991 || = 0.45 0 0 0 0 0 | 500 < 0.001 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.999 || = 0.44 9360 9410 9533 9611 9381 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 0 0 0 0 0 | 500 < 0.001 34 27 28 32 33 | 50 | 5 7 4 6 3 > 0.999 || = 0.42 0 0 0 0 0 | 500 < 0.002 28 32 36 30 29 | 50 | 0 0 0 0 0 > 0.998 || = 0.41 0 0 0 0 0 | 500 < 0.003 50 53 50 56 55 | 50 | 0 0 0 0 0 > 0.997 || = 0.40 0 0 0 0 0 | 500 < 0.004 0 0 0 0 0 | 50 | 0 0 0 0 0 > 0.996 || = 0.39 0 0 0 0 0 | 500 < 0.005 113 111 119 102 105 | 50 | 0 0 0 0 0 > 0.995 || = 0.38 0 0 0 0 0 | 500 < 0.006 0 0 0 0 0 | 50 | 0 0 0 0 0 > 0.994 || = 0.37 0 0 0 0 0 | 500 < 0.007 0 0 0 0 0 | 50 | 0 0 0 0 0 > 0.993 || = 0.36 0 0 0 0 0 | 500 < 0.008 0 0 0 0 0 | 50 | 0 0 0 0 0 > 0.992 || = 0.35 0 0 0 0 0 | 500 < 0.009 0 0 0 0 0 | 50 | 0 0 0 0 0 > 0.991 || = 0.34 0 0 0 0 0 | 500 < 0.01 221 213 240 209 248 | 50 | 478 498 470 485 447 > 0.99 || = 0.33 0 0 0 0 0 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 0 0 0 0 0 | 500 < 0.01 446 436 473 429 470 | 497.5 | 483 505 474 491 450 > 0.99 || = 0.31 0 0 0 0 0 | 500 = 0.01 0 0 0 0 0 | 252.5 | 0 0 0 0 0 = 0.99 || = 0.30 0 0 0 0 0 | 500 = 0.02 455 418 413 469 442 | 500 | 0 0 0 0 0 = 0.98 || = 0.29 0 0 0 0 0 | 500 =================================================================| 500 | 0 0 0 0 0 = 0.97 || = 0.28 0 0 0 0 0 | 500 sstring_LongestHeadRun test: | 500 | 0 0 0 0 0 = 0.96 || = 0.27 0 0 0 0 0 | 500 ----------------------------------------------- | 500 | 0 0 0 0 0 = 0.95 || = 0.26 0 0 0 0 0 | 500 N = 1, n = 1000, r = 27, s = 3, L = 10000020 | 500 | 0 0 0 0 0 = 0.94 || = 0.25 5782 5891 5940 5738 5931 | 500 Global longest run of 1 | 500 | 0 0 0 0 0 = 0.93 || = 0.24 0 0 0 0 0 | 500 | 500 | 0 0 0 0 0 = 0.92 || = 0.23 0 0 0 0 0 | 500 =================================================================| 500 | 0 0 0 0 0 = 0.91 || = 0.22 0 0 0 0 0 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 4330 4303 4313 4509 4506 = 0.90 || = 0.21 0 0 0 0 0 | 500 -----------------------------------------------------------------| 500 | 0 0 0 0 0 = 0.89 || = 0.20 0 0 0 0 0 | 500 SD Bern.: d 89.79926 9.64328 20.26890 | 500 | 0 0 0 0 0 = 0.88 || = 0.19 0 0 0 0 0 | 500 s 89.47538 9.34833 21.10808 | 500 | 0 0 0 0 0 = 0.87 || = 0.18 0 0 0 0 0 | 500 t 89.20089 10.40145 19.93562 | 500 | 0 0 0 0 0 = 0.86 || = 0.17 0 0 0 0 0 | 500 m 89.28805 9.08694 20.56075 | 500 | 0 0 0 0 0 = 0.85 || = 0.16 0 0 0 0 0 | 500 x 89.19518 10.53940 18.97355 | 500 | 0 0 0 0 0 = 0.84 || = 0.15 0 0 0 0 0 | 500 | 500 | 0 0 0 0 0 = 0.83 || = 0.14 3163 3257 3346 3205 3338 | 500 Changes: d 16 3 1 | 500 | 0 0 0 0 0 = 0.82 || = 0.13 0 0 0 0 0 | 500 s 17 5 1 | 500 | 0 0 0 0 0 = 0.81 || = 0.12 0 0 0 0 0 | 500 t 16 3 1 | 500 | 0 0 0 0 0 = 0.80 || = 0.11 0 0 0 0 0 | 500 m 16 5 1 | 500 | 0 0 0 0 0 = 0.79 || = 0.10 0 0 0 0 0 | 500 x 16 5 1 | 500 | 0 0 0 0 0 = 0.78 || = 0.09 0 0 0 0 0 | 500 -----------------------------------------------------------------| 500 | 0 0 0 0 0 = 0.77 || = 0.08 0 0 0 0 0 | 500 Aver./ d 0.48607 0 > 500: 2 1 1 0 1 0 1 0 1 0 | 500 | 0 0 0 0 0 = 0.76 || = 0.07 1755 1815 1753 1765 1703 | 500 median s 0.48375 0 ----- 2 1 1 0 1 0 1 0 1 1 | 500 | 0 0 0 0 0 = 0.75 || = 0.06 0 0 0 0 0 | 500 t 0.48301 0 2 1 1 0 1 0 1 0 1 0 | 500 | 0 0 0 0 0 = 0.74 || = 0.05 0 0 0 0 0 | 500 m 0.48567 0 2 1 1 0 1 0 1 0 1 0 | 500 | 0 0 0 0 0 = 0.73 || = 0.04 871 872 886 904 872 | 500 x 0.48422 0 2 1 1 0 1 0 1 0 1 0 | 500 | 0 0 0 0 0 = 0.72 || = 0.03 0 0 0 0 0 | 500 -----------------------------------------------------------------| 500 | 0 0 0 0 0 = 0.71 || = 0.02 455 418 413 469 442 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 0 0 0 0 0 = 0.70 || = 0.01 0 0 0 0 0 | 252.5 d 90 0 2 0 1 0 0 0 8 | 500 | 10918 10664 10776 10610 10594 = 0.69 || < 0.01 446 436 473 429 470 | 497.5 s 90 1 1 0 1 0 0 0 8 | 500 | 0 0 0 0 0 = 0.68 ||========================================================================= t 90 1 0 2 0 0 0 0 8 | 500 | 0 0 0 0 0 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 90 1 0 1 1 0 0 0 8 | 500 | 0 0 0 0 0 = 0.66 ||========================================================================= x 90 0 2 1 0 0 0 0 8 | 500 | 0 0 0 0 0 = 0.65 || sstring_LongestHeadRun test: no 199 test no 200 TestU01 250000 runs BigCrush Test smarsa_S sstring_PeriodsInStrings test: test no 200 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 0 2 | 0.5 | 1 0 2 1 1 > 0.99999 || = 0.64 485 524 464 472 475 | 500 < 0.00002 1 1 0 0 0 | 0.5 | 1 2 1 1 1 > 0.99998 || = 0.63 473 488 514 482 537 | 500 < 0.00003 1 0 0 0 2 | 0.5 | 0 0 0 0 1 > 0.99997 || = 0.62 510 540 508 487 484 | 500 < 0.00004 0 0 1 0 0 | 0.5 | 2 1 0 1 0 > 0.99996 || = 0.61 479 508 491 515 456 | 500 < 0.00005 1 1 0 0 0 | 0.5 | 1 3 0 1 1 > 0.99995 || = 0.60 505 489 489 479 495 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 1 1 1 0 1 > 0.99994 || = 0.59 524 519 478 515 511 | 500 < 0.00007 1 0 0 0 0 | 0.5 | 0 0 1 1 1 > 0.99993 || = 0.58 494 480 518 529 539 | 500 < 0.00008 1 1 2 0 1 | 0.5 | 0 0 0 1 2 > 0.99992 || = 0.57 499 504 532 529 457 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99991 || = 0.56 524 544 492 508 499 | 500 < 0.0001 0 0 1 2 1 | 0.5 | 0 3 0 0 1 > 0.9999 || = 0.55 543 486 474 490 557 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 511 503 486 452 544 | 500 < 0.0001 6 3 5 3 6 | 5 | 7 10 5 6 9 > 0.9999 || = 0.53 487 494 509 455 492 | 500 < 0.0002 8 3 10 7 3 | 5 | 1 5 0 1 0 > 0.9998 || = 0.52 565 485 484 522 501 | 500 < 0.0003 3 6 7 3 2 | 5 | 3 3 2 3 4 > 0.9997 || = 0.51 541 561 481 477 528 | 500 < 0.0004 4 4 3 3 9 | 5 | 5 3 9 6 5 > 0.9996 || = 0.50 479 513 495 485 461 | 500 < 0.0005 6 3 4 5 2 | 5 | 6 5 8 5 4 > 0.9995 || = 0.49 505 457 465 508 520 | 500 < 0.0006 4 3 11 5 4 | 5 | 3 6 3 3 7 > 0.9994 || = 0.48 498 521 502 477 531 | 500 < 0.0007 6 8 4 3 2 | 5 | 8 10 3 4 0 > 0.9993 || = 0.47 498 504 488 504 461 | 500 < 0.0008 4 5 2 4 6 | 5 | 8 4 6 5 5 > 0.9992 || = 0.46 505 465 508 501 474 | 500 < 0.0009 9 5 7 3 4 | 5 | 0 3 3 4 1 > 0.9991 || = 0.45 502 496 485 479 529 | 500 < 0.001 3 3 6 2 11 | 5 | 2 11 3 8 6 > 0.999 || = 0.44 482 503 498 477 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 520 540 475 505 511 | 500 < 0.001 53 43 59 38 49 | 50 | 43 60 42 45 41 > 0.999 || = 0.42 529 499 504 495 525 | 500 < 0.002 42 41 38 45 49 | 50 | 53 56 55 44 45 > 0.998 || = 0.41 512 542 494 485 479 | 500 < 0.003 54 40 54 52 58 | 50 | 47 52 61 51 51 > 0.997 || = 0.40 451 513 507 480 458 | 500 < 0.004 40 46 55 50 43 | 50 | 49 50 50 49 49 > 0.996 || = 0.39 489 494 512 497 501 | 500 < 0.005 49 55 57 61 53 | 50 | 55 57 48 61 63 > 0.995 || = 0.38 472 538 495 500 507 | 500 < 0.006 52 46 45 52 50 | 50 | 41 53 54 49 52 > 0.994 || = 0.37 494 455 491 565 531 | 500 < 0.007 37 45 31 41 38 | 50 | 51 53 36 51 44 > 0.993 || = 0.36 517 500 511 493 526 | 500 < 0.008 48 45 45 34 49 | 50 | 52 49 59 51 41 > 0.992 || = 0.35 522 494 537 509 505 | 500 < 0.009 56 56 47 43 47 | 50 | 44 49 43 47 48 > 0.991 || = 0.34 472 487 515 471 499 | 500 < 0.01 57 57 40 42 43 | 50 | 50 46 49 66 46 > 0.99 || = 0.33 521 432 505 521 490 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 482 520 511 524 505 | 500 < 0.01 488 474 471 458 479 | 497.5 | 485 525 497 514 480 > 0.99 || = 0.31 501 504 489 505 475 | 500 = 0.01 280 238 266 241 259 | 252.5 | 245 230 260 235 250 = 0.99 || = 0.30 513 538 515 513 480 | 500 = 0.02 500 507 473 497 562 | 500 | 505 525 488 453 483 = 0.98 || = 0.29 474 459 523 490 499 | 500 =================================================================| 500 | 485 519 521 497 435 = 0.97 || = 0.28 499 517 502 511 526 | 500 sstring_PeriodsInStrings test: | 500 | 520 492 512 468 481 = 0.96 || = 0.27 545 513 511 486 508 | 500 ----------------------------------------------- | 500 | 512 539 485 505 512 = 0.95 || = 0.26 515 500 505 482 505 | 500 N = 10, n = 500000000, r = 0, s = 10 | 500 | 517 458 505 542 493 = 0.94 || = 0.25 494 528 534 510 511 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 518 501 480 515 512 = 0.93 || = 0.24 482 516 544 510 517 | 500 | 500 | 496 520 527 444 479 = 0.92 || = 0.23 491 475 452 439 495 | 500 =================================================================| 500 | 513 500 513 479 524 = 0.91 || = 0.22 484 502 487 515 500 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 497 481 493 506 497 = 0.90 || = 0.21 487 476 478 543 484 | 500 -----------------------------------------------------------------| 500 | 500 517 493 574 503 = 0.89 || = 0.20 509 471 511 507 525 | 500 SD Bern.: d 0.92237 0.95125 0.65605 | 500 | 488 488 499 539 500 = 0.88 || = 0.19 510 502 520 490 529 | 500 s 1.05638 0.91914 0.67114 | 500 | 502 473 494 524 471 = 0.87 || = 0.18 521 476 472 501 477 | 500 t 0.97260 1.29292 1.05597 | 500 | 484 489 527 499 491 = 0.86 || = 0.17 533 490 530 543 518 | 500 m 1.13953 1.22371 0.95125 | 500 | 531 526 541 489 456 = 0.85 || = 0.16 519 507 470 499 506 | 500 x 1.08133 0.80910 0.91477 | 500 | 498 504 498 507 524 = 0.84 || = 0.15 502 537 491 512 525 | 500 | 500 | 497 498 528 529 491 = 0.83 || = 0.14 487 519 482 498 475 | 500 Changes: d 48 6 6 | 500 | 498 472 515 531 466 = 0.82 || = 0.13 509 510 564 513 490 | 500 s 53 3 3 | 500 | 483 496 467 469 521 = 0.81 || = 0.12 517 476 490 478 507 | 500 t 56 3 6 | 500 | 512 467 494 485 476 = 0.80 || = 0.11 477 534 470 499 509 | 500 m 51 4 7 | 500 | 496 489 504 510 483 = 0.79 || = 0.10 491 517 508 477 532 | 500 x 48 4 4 | 500 | 473 496 488 515 527 = 0.78 || = 0.09 466 502 478 499 517 | 500 -----------------------------------------------------------------| 500 | 490 477 498 513 519 = 0.77 || = 0.08 498 511 532 517 502 | 500 Aver./ d 0.49876 498 > 500: 5 7 3 5 6 7 1 4 2 6 | 500 | 527 517 520 477 486 = 0.76 || = 0.07 521 469 483 495 510 | 500 median s 0.49958 501 ----- 6 7 5 4 6 5 6 3 3 6 | 500 | 473 449 490 470 483 = 0.75 || = 0.06 496 501 489 473 522 | 500 t 0.50098 499 4 4 7 7 4 3 5 5 4 6 | 500 | 496 489 518 491 489 = 0.74 || = 0.05 518 484 516 513 509 | 500 m 0.50023 500 4 4 6 6 4 5 5 5 7 4 | 500 | 476 479 495 518 501 = 0.73 || = 0.04 519 531 475 529 481 | 500 x 0.49654 501 7 7 6 6 5 6 5 3 3 3 | 500 | 501 515 547 440 488 = 0.72 || = 0.03 505 504 501 516 492 | 500 -----------------------------------------------------------------| 500 | 515 511 518 547 480 = 0.71 || = 0.02 500 507 473 497 562 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 459 503 537 481 486 = 0.70 || = 0.01 280 238 266 241 259 | 252.5 d 0 0 2 13 75 9 2 0 0 | 500 | 477 479 511 511 515 = 0.69 || < 0.01 488 474 471 458 479 | 497.5 s 0 1 2 16 66 15 1 0 0 | 500 | 491 492 450 491 433 = 0.68 ||========================================================================= t 0 0 2 13 72 12 2 0 0 | 500 | 475 492 462 551 532 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 6 13 66 12 3 1 0 | 500 | 452 501 508 524 517 = 0.66 ||========================================================================= x 0 1 1 14 65 18 2 0 0 | 500 | 472 505 467 510 503 = 0.65 || sstring_PeriodsInStrings test: no 200 test no 201 TestU01 250000 runs BigCrush Test smarsa_S sstring_PeriodsInStrings test: test no 201 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 2 0 | 0.5 | 1 1 0 0 0 > 0.99999 || = 0.64 505 497 482 471 482 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99998 || = 0.63 496 482 532 508 495 | 500 < 0.00003 0 1 2 0 1 | 0.5 | 0 0 1 0 0 > 0.99997 || = 0.62 498 525 483 478 501 | 500 < 0.00004 0 0 0 0 1 | 0.5 | 1 1 0 0 0 > 0.99996 || = 0.61 451 472 492 544 487 | 500 < 0.00005 0 0 2 0 0 | 0.5 | 1 0 0 1 0 > 0.99995 || = 0.60 480 468 503 512 519 | 500 < 0.00006 1 1 0 0 0 | 0.5 | 0 0 0 1 2 > 0.99994 || = 0.59 493 481 469 521 482 | 500 < 0.00007 0 2 0 0 2 | 0.5 | 0 0 2 0 0 > 0.99993 || = 0.58 490 487 503 524 523 | 500 < 0.00008 0 0 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 521 486 474 486 522 | 500 < 0.00009 0 1 1 0 0 | 0.5 | 0 2 1 0 0 > 0.99991 || = 0.56 522 491 496 500 473 | 500 < 0.0001 0 0 1 1 1 | 0.5 | 2 0 0 0 0 > 0.9999 || = 0.55 493 492 514 470 514 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 477 513 533 541 481 | 500 < 0.0001 2 5 7 3 6 | 5 | 5 5 4 2 2 > 0.9999 || = 0.53 518 533 517 489 509 | 500 < 0.0002 7 5 7 4 3 | 5 | 0 1 2 5 4 > 0.9998 || = 0.52 528 505 499 524 513 | 500 < 0.0003 2 3 2 7 7 | 5 | 3 3 6 4 5 > 0.9997 || = 0.51 506 473 509 479 520 | 500 < 0.0004 7 4 10 5 5 | 5 | 8 5 6 5 2 > 0.9996 || = 0.50 514 518 531 514 503 | 500 < 0.0005 5 5 5 2 8 | 5 | 6 6 5 4 5 > 0.9995 || = 0.49 506 454 517 458 496 | 500 < 0.0006 3 5 7 1 3 | 5 | 4 5 7 3 10 > 0.9994 || = 0.48 509 483 452 496 485 | 500 < 0.0007 4 5 4 4 7 | 5 | 8 5 4 7 6 > 0.9993 || = 0.47 512 472 558 518 530 | 500 < 0.0008 3 2 2 9 5 | 5 | 6 3 10 3 4 > 0.9992 || = 0.46 465 504 514 534 504 | 500 < 0.0009 2 5 6 4 6 | 5 | 5 6 6 4 12 > 0.9991 || = 0.45 519 508 535 537 486 | 500 < 0.001 5 5 2 5 2 | 5 | 3 4 8 1 4 > 0.999 || = 0.44 462 500 486 514 502 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 475 460 490 474 475 | 500 < 0.001 40 44 52 44 52 | 50 | 48 43 58 38 54 > 0.999 || = 0.42 489 561 482 496 501 | 500 < 0.002 48 49 48 43 40 | 50 | 46 49 50 48 48 > 0.998 || = 0.41 495 480 430 522 484 | 500 < 0.003 45 45 64 49 39 | 50 | 60 50 38 45 36 > 0.997 || = 0.40 502 502 487 520 508 | 500 < 0.004 52 46 59 56 42 | 50 | 50 54 41 46 50 > 0.996 || = 0.39 477 473 510 498 458 | 500 < 0.005 43 52 45 45 33 | 50 | 60 47 57 49 53 > 0.995 || = 0.38 483 477 496 489 479 | 500 < 0.006 47 38 58 57 50 | 50 | 48 52 56 57 51 > 0.994 || = 0.37 516 544 486 500 482 | 500 < 0.007 48 49 36 47 47 | 50 | 48 57 53 40 48 > 0.993 || = 0.36 489 475 508 509 450 | 500 < 0.008 59 65 37 47 58 | 50 | 50 61 41 55 44 > 0.992 || = 0.35 464 503 525 487 548 | 500 < 0.009 63 47 56 45 55 | 50 | 54 49 54 46 45 > 0.991 || = 0.34 446 505 498 454 537 | 500 < 0.01 45 36 43 51 57 | 50 | 45 42 46 53 56 > 0.99 || = 0.33 511 479 496 481 518 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 523 493 486 504 502 | 500 < 0.01 490 471 498 484 473 | 497.5 | 509 504 494 477 485 > 0.99 || = 0.31 493 475 490 498 532 | 500 = 0.01 249 240 233 257 228 | 252.5 | 264 236 259 250 254 = 0.99 || = 0.30 500 483 479 470 494 | 500 = 0.02 519 496 503 508 450 | 500 | 495 492 533 491 516 = 0.98 || = 0.29 486 481 524 511 495 | 500 =================================================================| 500 | 484 478 478 494 512 = 0.97 || = 0.28 490 542 518 503 479 | 500 sstring_PeriodsInStrings test: | 500 | 542 474 488 496 535 = 0.96 || = 0.27 486 498 518 518 534 | 500 ----------------------------------------------- | 500 | 513 470 463 467 511 = 0.95 || = 0.26 443 470 512 493 470 | 500 N = 10, n = 500000000, r = 0, s = 10 | 500 | 482 486 504 455 517 = 0.94 || = 0.25 526 508 510 519 493 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 503 507 516 489 509 = 0.93 || = 0.24 503 522 462 455 504 | 500 | 500 | 534 535 509 489 494 = 0.92 || = 0.23 478 485 508 535 531 | 500 =================================================================| 500 | 486 516 470 496 514 = 0.91 || = 0.22 526 491 476 520 467 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 516 532 485 475 518 = 0.90 || = 0.21 515 499 517 552 491 | 500 -----------------------------------------------------------------| 500 | 472 533 472 497 528 = 0.89 || = 0.20 468 500 516 494 465 | 500 SD Bern.: d 1.00740 0.97001 0.73384 | 500 | 512 466 494 490 556 = 0.88 || = 0.19 472 528 538 528 522 | 500 s 1.04566 1.14686 0.79284 | 500 | 527 517 521 490 487 = 0.87 || = 0.18 501 543 510 486 487 | 500 t 1.03948 1.28438 0.99647 | 500 | 520 479 483 504 495 = 0.86 || = 0.17 532 466 481 519 437 | 500 m 0.97959 0.69315 0.88247 | 500 | 503 523 469 518 465 = 0.85 || = 0.16 484 512 501 512 472 | 500 x 1.05735 1.20475 0.80909 | 500 | 527 521 505 480 501 = 0.84 || = 0.15 514 497 542 537 517 | 500 | 500 | 493 548 464 515 522 = 0.83 || = 0.14 462 510 532 502 475 | 500 Changes: d 49 4 6 | 500 | 508 525 545 517 492 = 0.82 || = 0.13 538 484 499 461 490 | 500 s 43 4 4 | 500 | 518 514 484 514 509 = 0.81 || = 0.12 515 487 525 506 474 | 500 t 51 7 5 | 500 | 497 532 489 486 537 = 0.80 || = 0.11 537 485 472 485 496 | 500 m 50 5 5 | 500 | 466 514 460 482 526 = 0.79 || = 0.10 493 502 487 500 522 | 500 x 50 2 4 | 500 | 499 509 550 451 496 = 0.78 || = 0.09 533 495 487 501 489 | 500 -----------------------------------------------------------------| 500 | 521 527 488 528 496 = 0.77 || = 0.08 537 480 500 522 520 | 500 Aver./ d 0.50037 501 > 500: 6 6 4 3 5 5 5 3 8 6 | 500 | 482 521 478 495 545 = 0.76 || = 0.07 478 499 503 505 518 | 500 median s 0.50229 498 ----- 1 5 3 3 4 3 6 7 8 4 | 500 | 521 485 501 540 463 = 0.75 || = 0.06 480 540 517 484 497 | 500 t 0.49856 500 5 6 8 3 4 6 4 5 3 5 | 500 | 443 474 521 470 513 = 0.74 || = 0.05 514 476 524 526 494 | 500 m 0.49798 498 6 6 7 2 6 5 4 4 5 0 | 500 | 496 530 499 473 527 = 0.73 || = 0.04 530 485 486 482 521 | 500 x 0.50350 501 4 3 3 5 5 7 3 6 6 8 | 500 | 501 504 505 514 480 = 0.72 || = 0.03 512 492 489 488 504 | 500 -----------------------------------------------------------------| 500 | 492 500 504 531 518 = 0.71 || = 0.02 519 496 503 508 450 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 522 521 460 497 533 = 0.70 || = 0.01 249 240 233 257 228 | 252.5 d 0 0 4 12 69 16 0 0 0 | 500 | 485 482 495 500 460 = 0.69 || < 0.01 490 471 498 484 473 | 497.5 s 0 0 1 18 63 16 3 0 0 | 500 | 524 502 545 508 470 = 0.68 ||========================================================================= t 0 1 1 13 69 13 4 0 0 | 500 | 475 514 489 498 498 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 10 72 14 1 0 0 | 500 | 503 542 501 487 486 = 0.66 ||========================================================================= x 0 0 3 15 68 12 3 0 0 | 500 | 526 549 529 523 522 = 0.65 || sstring_PeriodsInStrings test: no 201 test no 202 TestU01 250000 runs BigCrush Test smarsa_S sstring_PeriodsInStrings test: test no 202 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 3 2 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 497 510 513 514 472 | 500 < 0.00002 1 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 505 489 500 474 507 | 500 < 0.00003 0 0 2 0 0 | 0.5 | 0 1 0 1 0 > 0.99997 || = 0.62 514 480 487 475 520 | 500 < 0.00004 2 2 2 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 507 534 471 471 462 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99995 || = 0.60 493 498 520 498 458 | 500 < 0.00006 0 0 1 0 0 | 0.5 | 1 0 1 1 0 > 0.99994 || = 0.59 491 508 534 490 480 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 475 513 478 526 476 | 500 < 0.00008 0 0 1 0 0 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 478 490 511 496 493 | 500 < 0.00009 0 0 0 1 2 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 501 516 490 500 473 | 500 < 0.0001 1 1 0 0 0 | 0.5 | 0 0 2 0 0 > 0.9999 || = 0.55 489 510 512 484 477 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 521 548 536 519 478 | 500 < 0.0001 5 4 7 5 5 | 5 | 1 3 3 4 1 > 0.9999 || = 0.53 509 471 533 495 477 | 500 < 0.0002 4 2 2 3 5 | 5 | 0 0 1 0 1 > 0.9998 || = 0.52 515 494 482 513 495 | 500 < 0.0003 4 4 5 3 7 | 5 | 1 4 1 4 2 > 0.9997 || = 0.51 457 503 505 528 516 | 500 < 0.0004 5 3 2 10 2 | 5 | 3 2 8 3 3 > 0.9996 || = 0.50 493 486 511 548 501 | 500 < 0.0005 5 4 8 6 5 | 5 | 3 5 2 5 5 > 0.9995 || = 0.49 497 473 531 515 539 | 500 < 0.0006 1 5 6 4 3 | 5 | 4 5 2 2 5 > 0.9994 || = 0.48 494 468 497 471 490 | 500 < 0.0007 7 6 5 7 3 | 5 | 4 4 4 1 3 > 0.9993 || = 0.47 521 518 508 502 547 | 500 < 0.0008 7 3 6 6 7 | 5 | 2 3 5 0 3 > 0.9992 || = 0.46 536 476 503 507 538 | 500 < 0.0009 1 6 9 4 1 | 5 | 4 7 5 6 3 > 0.9991 || = 0.45 499 503 525 498 520 | 500 < 0.001 3 6 5 5 8 | 5 | 2 9 3 4 4 > 0.999 || = 0.44 482 463 520 506 524 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 527 504 477 527 480 | 500 < 0.001 42 43 55 53 46 | 50 | 24 42 34 29 30 > 0.999 || = 0.42 492 548 538 482 538 | 500 < 0.002 55 47 38 39 42 | 50 | 39 55 42 49 38 > 0.998 || = 0.41 476 504 492 475 528 | 500 < 0.003 56 46 70 44 39 | 50 | 32 38 55 61 43 > 0.997 || = 0.40 506 504 483 513 469 | 500 < 0.004 51 38 44 36 58 | 50 | 45 48 43 55 53 > 0.996 || = 0.39 529 516 481 472 532 | 500 < 0.005 46 53 53 58 41 | 50 | 44 43 45 47 58 > 0.995 || = 0.38 515 505 521 538 517 | 500 < 0.006 49 57 62 53 63 | 50 | 41 40 44 41 50 > 0.994 || = 0.37 460 503 512 581 462 | 500 < 0.007 49 62 48 45 59 | 50 | 48 53 55 47 48 > 0.993 || = 0.36 481 500 494 491 492 | 500 < 0.008 46 40 46 48 48 | 50 | 55 58 55 58 57 > 0.992 || = 0.35 528 496 518 485 501 | 500 < 0.009 48 48 50 56 59 | 50 | 54 51 47 50 54 > 0.991 || = 0.34 512 513 496 519 514 | 500 < 0.01 50 61 45 40 45 | 50 | 49 49 59 46 48 > 0.99 || = 0.33 502 526 505 521 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 499 522 513 472 481 | 500 < 0.01 492 495 511 472 500 | 497.5 | 431 477 479 483 479 > 0.99 || = 0.31 527 516 506 539 494 | 500 = 0.01 225 241 278 246 227 | 252.5 | 271 235 250 240 221 = 0.99 || = 0.30 466 526 454 516 517 | 500 = 0.02 471 486 511 492 501 | 500 | 494 584 506 534 539 = 0.98 || = 0.29 487 512 508 460 533 | 500 =================================================================| 500 | 510 478 471 491 528 = 0.97 || = 0.28 504 487 455 498 458 | 500 sstring_PeriodsInStrings test: | 500 | 480 507 468 539 497 = 0.96 || = 0.27 573 484 530 470 473 | 500 ----------------------------------------------- | 500 | 493 508 525 500 467 = 0.95 || = 0.26 478 493 511 468 498 | 500 N = 10, n = 500000000, r = 0, s = 10 | 500 | 509 519 486 489 480 = 0.94 || = 0.25 501 492 472 479 508 | 500 Anderson-Darling statistic = A2 | 500 | 468 543 518 513 470 = 0.93 || = 0.24 490 516 503 525 487 | 500 | 500 | 526 516 514 480 510 = 0.92 || = 0.23 567 506 546 497 529 | 500 =================================================================| 500 | 479 506 518 485 522 = 0.91 || = 0.22 465 544 504 483 518 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 473 459 507 456 478 = 0.90 || = 0.21 487 498 495 483 473 | 500 -----------------------------------------------------------------| 500 | 553 488 513 485 484 = 0.89 || = 0.20 483 481 498 500 508 | 500 SD Bern.: d 1.10429 0.57299 1.61882 | 500 | 480 510 483 489 531 = 0.88 || = 0.19 501 529 501 514 493 | 500 s 1.02636 1.13634 0.96067 | 500 | 494 489 514 484 530 = 0.87 || = 0.18 527 496 515 490 544 | 500 t 1.01109 1.26791 1.09140 | 500 | 486 503 461 493 506 = 0.86 || = 0.17 536 473 484 528 481 | 500 m 1.05743 1.09598 1.23916 | 500 | 499 498 492 504 466 = 0.85 || = 0.16 504 481 531 515 513 | 500 x 1.00097 1.18886 1.21633 | 500 | 482 491 503 499 508 = 0.84 || = 0.15 528 493 492 495 492 | 500 | 500 | 479 554 474 484 502 = 0.83 || = 0.14 526 494 527 501 504 | 500 Changes: d 50 2 2 | 500 | 497 486 501 499 486 = 0.82 || = 0.13 508 478 470 525 512 | 500 s 46 3 4 | 500 | 474 468 461 504 518 = 0.81 || = 0.12 509 536 547 485 508 | 500 t 53 5 5 | 500 | 514 465 476 502 514 = 0.80 || = 0.11 487 506 500 509 489 | 500 m 46 5 4 | 500 | 549 535 527 456 468 = 0.79 || = 0.10 528 523 465 477 523 | 500 x 53 6 4 | 500 | 538 489 512 466 500 = 0.78 || = 0.09 522 483 485 473 491 | 500 -----------------------------------------------------------------| 500 | 453 519 488 507 514 = 0.77 || = 0.08 501 504 482 556 500 | 500 Aver./ d 0.49713 499 > 500: 5 9 4 6 4 4 5 6 1 4 | 500 | 502 485 451 541 504 = 0.76 || = 0.07 490 502 508 470 507 | 500 median s 0.50086 500 ----- 3 4 4 8 6 6 4 5 3 7 | 500 | 477 456 499 533 501 = 0.75 || = 0.06 535 466 508 467 510 | 500 t 0.49919 503 5 5 6 6 6 7 5 3 5 5 | 500 | 466 534 486 505 509 = 0.74 || = 0.05 523 459 431 517 500 | 500 m 0.49999 498 3 6 1 6 6 4 4 8 2 3 | 500 | 534 506 493 515 494 = 0.73 || = 0.04 499 475 500 513 518 | 500 x 0.49938 501 5 6 5 5 7 1 5 6 6 4 | 500 | 474 502 471 564 507 = 0.72 || = 0.03 517 514 474 492 459 | 500 -----------------------------------------------------------------| 500 | 509 476 502 506 497 = 0.71 || = 0.02 471 486 511 492 501 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 489 487 520 499 480 = 0.70 || = 0.01 225 241 278 246 227 | 252.5 d 0 0 2 15 64 16 2 2 0 | 500 | 508 477 514 485 497 = 0.69 || < 0.01 492 495 511 472 500 | 497.5 s 0 0 0 16 71 10 3 1 0 | 500 | 514 483 542 482 535 = 0.68 ||========================================================================= t 0 1 3 13 69 13 2 0 0 | 500 | 490 502 503 517 513 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 18 67 12 3 1 0 | 500 | 483 505 491 506 500 = 0.66 ||========================================================================= x 0 0 0 19 66 15 1 0 0 | 500 | 464 479 482 504 520 = 0.65 || sstring_PeriodsInStrings test: no 202 test no 203 TestU01 250000 runs BigCrush Test smarsa_S sstring_PeriodsInStrings test: test no 203 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 1 0 | 0.5 | 1 1 1 1 2 > 0.99999 || = 0.64 512 508 526 506 543 | 500 < 0.00002 0 1 1 1 0 | 0.5 | 1 0 0 1 0 > 0.99998 || = 0.63 516 520 508 497 479 | 500 < 0.00003 1 2 0 0 0 | 0.5 | 2 0 2 0 0 > 0.99997 || = 0.62 516 513 469 470 450 | 500 < 0.00004 0 0 1 0 0 | 0.5 | 0 2 0 0 0 > 0.99996 || = 0.61 528 485 457 529 510 | 500 < 0.00005 0 2 1 1 1 | 0.5 | 0 0 0 0 2 > 0.99995 || = 0.60 503 520 509 514 528 | 500 < 0.00006 0 0 0 1 2 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 495 513 516 476 458 | 500 < 0.00007 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 473 491 456 525 486 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 1 0 1 1 1 > 0.99992 || = 0.57 483 490 507 493 503 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99991 || = 0.56 512 480 479 532 473 | 500 < 0.0001 0 3 1 0 1 | 0.5 | 2 0 2 1 0 > 0.9999 || = 0.55 484 559 505 551 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 462 475 517 522 540 | 500 < 0.0001 2 8 5 4 4 | 5 | 8 3 7 4 5 > 0.9999 || = 0.53 494 502 522 517 542 | 500 < 0.0002 3 6 4 3 7 | 5 | 1 2 1 4 3 > 0.9998 || = 0.52 478 488 491 479 528 | 500 < 0.0003 8 1 4 8 6 | 5 | 3 5 2 5 3 > 0.9997 || = 0.51 505 466 479 468 501 | 500 < 0.0004 3 3 5 6 3 | 5 | 6 6 9 6 5 > 0.9996 || = 0.50 495 486 558 506 479 | 500 < 0.0005 7 5 5 3 4 | 5 | 7 5 7 2 5 > 0.9995 || = 0.49 502 519 504 503 498 | 500 < 0.0006 4 8 7 8 4 | 5 | 5 3 3 8 5 > 0.9994 || = 0.48 473 448 506 489 497 | 500 < 0.0007 4 5 12 1 4 | 5 | 2 2 7 6 3 > 0.9993 || = 0.47 502 491 549 514 497 | 500 < 0.0008 7 7 6 2 2 | 5 | 6 2 7 5 4 > 0.9992 || = 0.46 511 502 465 533 507 | 500 < 0.0009 1 4 7 4 5 | 5 | 3 6 7 6 2 > 0.9991 || = 0.45 473 519 516 511 503 | 500 < 0.001 3 6 7 4 5 | 5 | 5 2 4 2 4 > 0.999 || = 0.44 522 500 484 502 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 472 477 485 506 465 | 500 < 0.001 42 53 62 43 44 | 50 | 46 36 54 48 39 > 0.999 || = 0.42 469 514 502 514 506 | 500 < 0.002 48 50 42 52 44 | 50 | 43 40 58 37 55 > 0.998 || = 0.41 493 488 503 515 498 | 500 < 0.003 44 57 45 52 59 | 50 | 57 60 58 45 59 > 0.997 || = 0.40 512 482 504 446 492 | 500 < 0.004 38 55 49 54 45 | 50 | 43 54 42 53 45 > 0.996 || = 0.39 497 489 512 471 518 | 500 < 0.005 54 48 55 42 40 | 50 | 48 47 49 48 35 > 0.995 || = 0.38 504 485 494 521 515 | 500 < 0.006 43 55 42 39 57 | 50 | 44 51 50 62 63 > 0.994 || = 0.37 503 488 515 503 514 | 500 < 0.007 53 45 46 42 57 | 50 | 54 47 63 43 58 > 0.993 || = 0.36 472 493 468 490 504 | 500 < 0.008 50 43 48 65 51 | 50 | 47 58 39 36 46 > 0.992 || = 0.35 512 474 486 537 514 | 500 < 0.009 61 52 59 50 47 | 50 | 52 59 60 36 50 > 0.991 || = 0.34 459 527 484 480 459 | 500 < 0.01 57 48 47 40 53 | 50 | 57 41 50 45 52 > 0.99 || = 0.33 529 524 493 498 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 498 503 505 477 475 | 500 < 0.01 490 506 495 479 497 | 497.5 | 491 493 523 453 502 > 0.99 || = 0.31 466 475 513 505 504 | 500 = 0.01 239 247 249 253 242 | 252.5 | 247 236 258 257 248 = 0.99 || = 0.30 465 487 521 527 476 | 500 = 0.02 540 515 491 479 503 | 500 | 522 473 485 464 498 = 0.98 || = 0.29 479 491 511 501 501 | 500 =================================================================| 500 | 471 503 491 495 531 = 0.97 || = 0.28 509 498 495 459 486 | 500 sstring_PeriodsInStrings test: | 500 | 534 490 514 548 502 = 0.96 || = 0.27 507 504 478 487 487 | 500 ----------------------------------------------- | 500 | 513 496 460 541 489 = 0.95 || = 0.26 509 493 470 487 503 | 500 N = 10, n = 500000000, r = 0, s = 10 | 500 | 525 496 477 503 522 = 0.94 || = 0.25 496 504 514 496 516 | 500 Test on the sum of all N observations | 500 | 557 497 529 456 537 = 0.93 || = 0.24 506 478 506 499 509 | 500 | 500 | 519 503 481 481 535 = 0.92 || = 0.23 483 459 465 511 478 | 500 =================================================================| 500 | 513 509 467 462 505 = 0.91 || = 0.22 516 524 487 554 479 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 517 488 491 480 526 = 0.90 || = 0.21 507 491 512 480 508 | 500 -----------------------------------------------------------------| 500 | 472 518 521 503 523 = 0.89 || = 0.20 552 483 489 520 531 | 500 SD Bern.: d 1.05992 0.99246 0.75003 | 500 | 461 539 473 482 491 = 0.88 || = 0.19 515 496 525 468 492 | 500 s 0.89066 0.62320 1.14686 | 500 | 466 537 481 507 505 = 0.87 || = 0.18 450 520 501 545 497 | 500 t 0.94410 0.93105 1.09507 | 500 | 500 548 520 498 530 = 0.86 || = 0.17 490 498 515 566 487 | 500 m 1.08148 1.13810 1.28203 | 500 | 493 506 521 508 489 = 0.85 || = 0.16 509 507 531 493 494 | 500 x 1.02504 0.88925 1.20890 | 500 | 496 507 513 534 489 = 0.84 || = 0.15 533 488 518 481 512 | 500 | 500 | 512 501 490 490 502 = 0.83 || = 0.14 461 490 504 515 503 | 500 Changes: d 52 5 5 | 500 | 481 475 501 487 535 = 0.82 || = 0.13 536 512 516 462 466 | 500 s 49 7 6 | 500 | 548 500 522 519 526 = 0.81 || = 0.12 480 514 501 535 519 | 500 t 47 5 5 | 500 | 484 530 531 493 480 = 0.80 || = 0.11 531 473 514 514 542 | 500 m 56 4 4 | 500 | 443 522 514 525 543 = 0.79 || = 0.10 536 516 564 503 459 | 500 x 47 5 5 | 500 | 535 503 485 487 493 = 0.78 || = 0.09 514 512 487 505 477 | 500 -----------------------------------------------------------------| 500 | 509 482 492 498 543 = 0.77 || = 0.08 505 490 484 500 489 | 500 Aver./ d 0.50074 501 > 500: 4 6 7 4 5 3 7 6 3 7 | 500 | 537 500 467 490 527 = 0.76 || = 0.07 490 518 504 517 478 | 500 median s 0.50186 498 ----- 5 5 3 3 4 4 7 4 7 3 | 500 | 501 500 502 503 448 = 0.75 || = 0.06 505 487 526 500 489 | 500 t 0.49858 503 4 10 4 5 7 6 5 6 6 4 | 500 | 507 509 506 494 518 = 0.74 || = 0.05 472 466 509 466 471 | 500 m 0.49882 501 5 6 4 5 8 6 6 3 5 4 | 500 | 493 496 506 501 479 = 0.73 || = 0.04 490 508 477 502 478 | 500 x 0.50351 499 1 4 6 7 4 6 4 4 7 7 | 500 | 518 495 462 476 493 = 0.72 || = 0.03 491 476 502 506 470 | 500 -----------------------------------------------------------------| 500 | 485 484 502 472 485 = 0.71 || = 0.02 540 515 491 479 503 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 511 555 489 504 533 = 0.70 || = 0.01 239 247 249 253 242 | 252.5 d 0 0 2 17 67 11 4 0 0 | 500 | 501 529 503 524 516 = 0.69 || < 0.01 490 506 495 479 497 | 497.5 s 0 0 1 12 77 8 3 0 0 | 500 | 495 537 480 515 499 = 0.68 ||========================================================================= t 0 0 0 15 76 7 3 0 0 | 500 | 470 519 519 492 450 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 14 68 11 5 0 0 | 500 | 553 491 472 510 467 = 0.66 ||========================================================================= x 0 0 3 12 67 19 0 0 0 | 500 | 489 488 504 438 492 = 0.65 || sstring_PeriodsInStrings test: no 203 test no 204 TestU01 250000 runs BigCrush Test smarsa_S sstring_PeriodsInStrings test: test no 204 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 2 | 0.5 | 1 0 2 0 0 > 0.99999 || = 0.64 530 524 512 486 530 | 500 < 0.00002 0 0 0 1 1 | 0.5 | 0 0 0 4 1 > 0.99998 || = 0.63 486 489 497 490 488 | 500 < 0.00003 1 0 0 1 1 | 0.5 | 0 2 2 0 0 > 0.99997 || = 0.62 506 540 486 546 503 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99996 || = 0.61 515 450 503 511 527 | 500 < 0.00005 0 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 499 514 503 505 496 | 500 < 0.00006 4 0 1 0 0 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 489 520 502 496 489 | 500 < 0.00007 0 1 0 0 0 | 0.5 | 0 0 1 1 1 > 0.99993 || = 0.58 465 528 509 473 475 | 500 < 0.00008 0 2 1 0 1 | 0.5 | 2 2 0 1 0 > 0.99992 || = 0.57 487 514 489 491 452 | 500 < 0.00009 0 0 1 0 0 | 0.5 | 0 0 0 2 0 > 0.99991 || = 0.56 496 460 513 511 466 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 1 2 0 0 > 0.9999 || = 0.55 502 514 501 501 471 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 510 478 516 492 524 | 500 < 0.0001 5 5 3 3 5 | 5 | 3 5 8 8 3 > 0.9999 || = 0.53 494 529 512 481 493 | 500 < 0.0002 8 3 4 7 5 | 5 | 1 0 3 2 4 > 0.9998 || = 0.52 510 507 546 539 526 | 500 < 0.0003 3 4 4 4 5 | 5 | 4 8 4 7 1 > 0.9997 || = 0.51 490 510 501 495 487 | 500 < 0.0004 2 4 7 5 4 | 5 | 3 4 3 5 3 > 0.9996 || = 0.50 534 535 524 495 539 | 500 < 0.0005 6 8 3 3 3 | 5 | 6 5 1 7 7 > 0.9995 || = 0.49 536 489 539 523 519 | 500 < 0.0006 6 2 6 6 6 | 5 | 1 4 2 3 6 > 0.9994 || = 0.48 513 495 509 504 512 | 500 < 0.0007 7 2 7 4 3 | 5 | 3 7 5 6 7 > 0.9993 || = 0.47 485 451 509 552 487 | 500 < 0.0008 3 7 3 4 2 | 5 | 1 4 4 4 5 > 0.9992 || = 0.46 513 463 522 486 505 | 500 < 0.0009 6 11 6 1 7 | 5 | 5 5 2 6 4 > 0.9991 || = 0.45 536 488 492 504 496 | 500 < 0.001 6 6 8 4 2 | 5 | 7 6 3 5 5 > 0.999 || = 0.44 486 522 496 474 469 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 520 506 534 476 501 | 500 < 0.001 52 52 51 41 42 | 50 | 34 48 35 53 45 > 0.999 || = 0.42 476 483 459 519 525 | 500 < 0.002 55 55 41 40 53 | 50 | 58 43 54 35 62 > 0.998 || = 0.41 539 491 481 440 512 | 500 < 0.003 42 53 49 61 53 | 50 | 49 52 36 53 42 > 0.997 || = 0.40 520 523 536 474 496 | 500 < 0.004 52 32 44 64 47 | 50 | 52 64 64 52 44 > 0.996 || = 0.39 488 517 496 497 515 | 500 < 0.005 48 36 44 51 48 | 50 | 47 43 45 43 51 > 0.995 || = 0.38 513 521 509 496 490 | 500 < 0.006 37 66 49 43 45 | 50 | 50 52 58 51 43 > 0.994 || = 0.37 488 483 499 534 505 | 500 < 0.007 38 50 47 65 58 | 50 | 46 41 41 39 48 > 0.993 || = 0.36 509 478 514 472 495 | 500 < 0.008 35 53 43 57 48 | 50 | 50 48 41 55 51 > 0.992 || = 0.35 502 478 522 492 506 | 500 < 0.009 50 47 53 48 52 | 50 | 65 49 45 57 50 > 0.991 || = 0.34 525 493 472 493 517 | 500 < 0.01 44 50 45 56 52 | 50 | 52 46 50 44 46 > 0.99 || = 0.33 479 498 529 513 516 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 480 485 502 513 510 | 500 < 0.01 453 494 466 526 498 | 497.5 | 503 486 469 482 482 > 0.99 || = 0.31 500 488 499 501 497 | 500 = 0.01 259 259 281 235 272 | 252.5 | 232 260 266 260 237 = 0.99 || = 0.30 517 497 502 504 497 | 500 = 0.02 470 433 481 523 503 | 500 | 518 533 452 495 521 = 0.98 || = 0.29 527 467 505 490 504 | 500 =================================================================| 500 | 511 501 511 512 517 = 0.97 || = 0.28 485 509 498 531 512 | 500 sstring_PeriodsInStrings test: | 500 | 519 538 510 477 519 = 0.96 || = 0.27 522 491 495 477 482 | 500 ----------------------------------------------- | 500 | 495 475 493 468 516 = 0.95 || = 0.26 517 482 471 515 466 | 500 N = 10, n = 500000000, r = 20, s = 10 | 500 | 490 475 539 498 504 = 0.94 || = 0.25 516 485 503 492 477 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 505 485 472 479 520 = 0.93 || = 0.24 535 502 484 523 526 | 500 | 500 | 491 527 491 458 490 = 0.92 || = 0.23 502 484 448 485 489 | 500 =================================================================| 500 | 521 490 509 490 481 = 0.91 || = 0.22 539 517 498 549 515 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 508 499 523 481 497 = 0.90 || = 0.21 465 475 488 508 503 | 500 -----------------------------------------------------------------| 500 | 516 516 527 507 515 = 0.89 || = 0.20 493 534 550 497 479 | 500 SD Bern.: d 1.01324 1.16247 1.07663 | 500 | 501 485 513 473 518 = 0.88 || = 0.19 506 482 529 497 505 | 500 s 1.04210 1.29060 0.90376 | 500 | 457 525 488 471 500 = 0.87 || = 0.18 482 504 502 498 539 | 500 t 0.99295 0.70461 1.34899 | 500 | 518 549 469 515 509 = 0.86 || = 0.17 477 525 546 500 476 | 500 m 0.96996 1.31366 1.02812 | 500 | 505 520 507 488 502 = 0.85 || = 0.16 508 474 458 505 532 | 500 x 0.91635 0.62640 0.82502 | 500 | 468 490 493 476 532 = 0.84 || = 0.15 491 535 491 474 502 | 500 | 500 | 510 489 481 487 510 = 0.83 || = 0.14 511 483 518 529 482 | 500 Changes: d 55 3 5 | 500 | 535 522 511 484 508 = 0.82 || = 0.13 521 525 523 514 554 | 500 s 56 5 4 | 500 | 492 536 500 490 502 = 0.81 || = 0.12 509 491 516 541 495 | 500 t 48 3 6 | 500 | 436 493 504 507 458 = 0.80 || = 0.11 524 488 500 500 491 | 500 m 51 5 7 | 500 | 548 552 516 517 498 = 0.79 || = 0.10 485 528 516 550 499 | 500 x 48 5 6 | 500 | 461 475 513 531 444 = 0.78 || = 0.09 515 470 514 478 510 | 500 -----------------------------------------------------------------| 500 | 474 482 489 507 487 = 0.77 || = 0.08 478 531 480 522 506 | 500 Aver./ d 0.50023 502 > 500: 4 6 7 5 7 3 5 3 7 6 | 500 | 533 535 473 531 500 = 0.76 || = 0.07 465 525 499 523 439 | 500 median s 0.50187 496 ----- 4 5 4 2 3 8 4 5 6 5 | 500 | 476 505 453 475 497 = 0.75 || = 0.06 499 496 480 475 513 | 500 t 0.49963 502 2 7 3 6 6 9 4 5 5 5 | 500 | 475 488 521 492 504 = 0.74 || = 0.05 448 496 484 488 469 | 500 m 0.49659 497 6 5 5 5 5 4 5 6 2 2 | 500 | 486 504 489 513 501 = 0.73 || = 0.04 513 512 480 528 492 | 500 x 0.50064 502 6 5 5 6 6 2 7 2 8 6 | 500 | 492 480 503 476 497 = 0.72 || = 0.03 503 483 481 511 461 | 500 -----------------------------------------------------------------| 500 | 512 515 455 496 492 = 0.71 || = 0.02 470 433 481 523 503 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 484 468 509 490 507 = 0.70 || = 0.01 259 259 281 235 272 | 252.5 d 0 0 4 13 70 13 1 0 0 | 500 | 499 494 516 493 511 = 0.69 || < 0.01 453 494 466 526 498 | 497.5 s 0 1 2 11 66 19 2 0 0 | 500 | 451 495 491 529 489 = 0.68 ||========================================================================= t 0 0 5 9 73 11 3 0 0 | 500 | 529 501 491 471 482 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 18 64 14 4 0 0 | 500 | 492 506 451 511 524 = 0.66 ||========================================================================= x 0 0 3 10 75 12 1 0 0 | 500 | 501 465 482 507 502 = 0.65 || sstring_PeriodsInStrings test: no 204 test no 205 TestU01 250000 runs BigCrush Test smarsa_S sstring_PeriodsInStrings test: test no 205 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 1 0 | 0.5 | 3 0 0 1 0 > 0.99999 || = 0.64 502 505 458 510 491 | 500 < 0.00002 1 1 1 1 0 | 0.5 | 0 0 0 1 0 > 0.99998 || = 0.63 480 497 508 494 494 | 500 < 0.00003 0 0 1 0 1 | 0.5 | 0 0 1 2 1 > 0.99997 || = 0.62 522 470 499 491 496 | 500 < 0.00004 0 2 1 0 0 | 0.5 | 0 2 0 0 0 > 0.99996 || = 0.61 483 480 479 491 506 | 500 < 0.00005 1 0 0 0 1 | 0.5 | 0 0 1 1 0 > 0.99995 || = 0.60 549 515 496 499 479 | 500 < 0.00006 1 1 0 3 2 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 471 503 535 514 492 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 0 0 0 6 0 > 0.99993 || = 0.58 448 515 489 530 559 | 500 < 0.00008 2 0 0 0 0 | 0.5 | 1 1 0 0 2 > 0.99992 || = 0.57 528 503 507 480 436 | 500 < 0.00009 2 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 469 493 515 488 457 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 1 0 0 0 1 > 0.9999 || = 0.55 521 542 501 490 533 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 477 506 481 501 489 | 500 < 0.0001 7 4 5 5 4 | 5 | 5 3 2 11 4 > 0.9999 || = 0.53 470 498 523 502 460 | 500 < 0.0002 5 6 2 5 6 | 5 | 3 2 3 0 1 > 0.9998 || = 0.52 493 500 501 520 465 | 500 < 0.0003 5 3 3 2 3 | 5 | 3 1 6 0 7 > 0.9997 || = 0.51 521 471 515 488 529 | 500 < 0.0004 7 5 3 4 6 | 5 | 5 7 9 6 10 > 0.9996 || = 0.50 518 516 512 501 513 | 500 < 0.0005 3 6 7 4 7 | 5 | 5 5 6 3 3 > 0.9995 || = 0.49 553 472 509 498 496 | 500 < 0.0006 8 5 10 5 3 | 5 | 5 5 7 9 7 > 0.9994 || = 0.48 473 469 550 515 518 | 500 < 0.0007 5 5 4 5 3 | 5 | 5 6 9 7 5 > 0.9993 || = 0.47 528 494 486 504 506 | 500 < 0.0008 7 3 7 3 13 | 5 | 4 4 4 7 5 > 0.9992 || = 0.46 476 518 545 502 474 | 500 < 0.0009 7 6 6 8 6 | 5 | 4 4 3 9 5 > 0.9991 || = 0.45 559 485 482 476 494 | 500 < 0.001 1 4 6 7 4 | 5 | 2 4 5 5 4 > 0.999 || = 0.44 457 461 471 520 449 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 509 469 521 528 523 | 500 < 0.001 55 47 53 48 55 | 50 | 41 41 54 57 51 > 0.999 || = 0.42 476 481 480 516 472 | 500 < 0.002 52 44 52 45 49 | 50 | 55 53 56 56 54 > 0.998 || = 0.41 500 469 487 489 502 | 500 < 0.003 42 64 48 59 47 | 50 | 52 44 48 38 47 > 0.997 || = 0.40 514 490 514 496 498 | 500 < 0.004 50 56 51 42 51 | 50 | 39 62 49 48 45 > 0.996 || = 0.39 481 558 517 503 541 | 500 < 0.005 38 71 47 49 36 | 50 | 58 42 42 52 62 > 0.995 || = 0.38 494 532 507 507 501 | 500 < 0.006 54 52 58 37 53 | 50 | 60 57 38 49 51 > 0.994 || = 0.37 512 533 497 508 490 | 500 < 0.007 59 59 55 45 45 | 50 | 50 50 54 63 46 > 0.993 || = 0.36 497 524 503 532 471 | 500 < 0.008 46 49 45 55 50 | 50 | 53 42 59 53 48 > 0.992 || = 0.35 506 448 483 475 522 | 500 < 0.009 47 55 47 52 55 | 50 | 55 48 51 50 51 > 0.991 || = 0.34 506 544 500 434 510 | 500 < 0.01 54 36 52 52 49 | 50 | 54 54 57 44 43 > 0.99 || = 0.33 486 466 518 496 539 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 502 526 505 486 503 | 500 < 0.01 497 533 508 484 490 | 497.5 | 517 493 508 510 498 > 0.99 || = 0.31 494 511 491 503 480 | 500 = 0.01 212 264 264 262 250 | 252.5 | 230 277 252 276 231 = 0.99 || = 0.30 495 534 505 525 546 | 500 = 0.02 529 527 464 460 482 | 500 | 479 489 457 473 537 = 0.98 || = 0.29 541 487 511 486 469 | 500 =================================================================| 500 | 486 509 516 463 515 = 0.97 || = 0.28 531 519 444 479 513 | 500 sstring_PeriodsInStrings test: | 500 | 498 463 493 527 457 = 0.96 || = 0.27 468 534 508 523 476 | 500 ----------------------------------------------- | 500 | 469 501 552 501 467 = 0.95 || = 0.26 504 531 464 520 499 | 500 N = 10, n = 500000000, r = 20, s = 10 | 500 | 495 510 500 484 508 = 0.94 || = 0.25 522 476 484 519 518 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 532 444 441 511 521 = 0.93 || = 0.24 472 514 528 469 471 | 500 | 500 | 483 519 542 480 522 = 0.92 || = 0.23 486 495 507 523 498 | 500 =================================================================| 500 | 519 515 486 506 519 = 0.91 || = 0.22 494 515 504 505 522 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 513 496 540 513 517 = 0.90 || = 0.21 527 463 453 518 494 | 500 -----------------------------------------------------------------| 500 | 494 525 474 487 519 = 0.89 || = 0.20 509 499 499 484 515 | 500 SD Bern.: d 1.05965 0.86645 0.94385 | 500 | 478 512 494 497 539 = 0.88 || = 0.19 510 485 495 479 484 | 500 s 1.12031 1.43249 0.96691 | 500 | 498 515 464 509 473 = 0.87 || = 0.18 509 492 525 488 475 | 500 t 1.02398 0.55524 0.90819 | 500 | 496 451 476 492 481 = 0.86 || = 0.17 484 506 506 491 477 | 500 m 0.91516 0.89710 0.95125 | 500 | 479 511 510 500 508 = 0.85 || = 0.16 509 531 474 502 525 | 500 x 1.09754 0.76457 0.72973 | 500 | 482 530 473 491 512 = 0.84 || = 0.15 503 528 497 465 520 | 500 | 500 | 520 519 487 503 490 = 0.83 || = 0.14 502 485 505 510 503 | 500 Changes: d 55 4 5 | 500 | 484 522 473 544 502 = 0.82 || = 0.13 507 524 511 510 504 | 500 s 45 4 7 | 500 | 527 488 486 535 453 = 0.81 || = 0.12 514 524 471 471 498 | 500 t 50 6 2 | 500 | 552 502 511 506 514 = 0.80 || = 0.11 464 520 466 480 517 | 500 m 45 3 5 | 500 | 487 470 525 493 530 = 0.79 || = 0.10 504 463 525 487 473 | 500 x 55 7 5 | 500 | 499 486 510 500 534 = 0.78 || = 0.09 525 470 506 464 511 | 500 -----------------------------------------------------------------| 500 | 492 500 525 516 523 = 0.77 || = 0.08 456 525 552 495 556 | 500 Aver./ d 0.49935 499 > 500: 4 8 6 4 5 4 6 4 3 3 | 500 | 515 479 489 535 492 = 0.76 || = 0.07 540 510 508 474 475 | 500 median s 0.49828 501 ----- 7 6 5 8 1 6 3 2 7 6 | 500 | 502 492 511 517 503 = 0.75 || = 0.06 500 515 497 502 511 | 500 t 0.49986 501 6 5 5 6 5 7 2 8 2 4 | 500 | 493 495 539 548 497 = 0.74 || = 0.05 490 492 496 490 491 | 500 m 0.50258 501 3 3 6 6 6 5 4 6 5 6 | 500 | 456 496 524 507 517 = 0.73 || = 0.04 481 452 495 517 524 | 500 x 0.50038 501 4 5 4 7 4 3 3 8 6 7 | 500 | 494 485 478 482 533 = 0.72 || = 0.03 519 501 512 496 485 | 500 -----------------------------------------------------------------| 500 | 528 518 503 488 505 = 0.71 || = 0.02 529 527 464 460 482 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 497 516 532 492 471 = 0.70 || = 0.01 212 264 264 262 250 | 252.5 d 0 0 2 16 67 12 4 0 0 | 500 | 523 526 499 500 452 = 0.69 || < 0.01 497 533 508 484 490 | 497.5 s 0 1 4 14 61 20 1 0 0 | 500 | 515 479 488 502 503 = 0.68 ||========================================================================= t 0 0 3 13 69 12 4 0 0 | 500 | 505 431 492 511 516 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 11 76 11 2 0 0 | 500 | 515 480 488 562 492 = 0.66 ||========================================================================= x 0 0 4 18 63 13 3 0 0 | 500 | 469 478 493 474 489 = 0.65 || sstring_PeriodsInStrings test: no 205 test no 206 TestU01 250000 runs BigCrush Test smarsa_S sstring_PeriodsInStrings test: test no 206 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 489 551 505 525 502 | 500 < 0.00002 0 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 506 476 462 502 488 | 500 < 0.00003 0 0 0 0 2 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 522 461 485 449 519 | 500 < 0.00004 1 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99996 || = 0.61 548 517 519 524 484 | 500 < 0.00005 0 0 1 1 1 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 468 485 510 522 509 | 500 < 0.00006 0 1 1 2 1 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 512 520 545 525 479 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 1 0 0 0 0 > 0.99993 || = 0.58 521 529 514 518 479 | 500 < 0.00008 1 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 514 516 513 496 516 | 500 < 0.00009 1 1 0 1 1 | 0.5 | 1 0 0 0 1 > 0.99991 || = 0.56 502 494 502 485 499 | 500 < 0.0001 3 1 0 0 1 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 507 489 500 474 486 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 501 527 481 499 500 | 500 < 0.0001 7 7 3 6 7 | 5 | 2 0 1 1 2 > 0.9999 || = 0.53 505 475 509 512 510 | 500 < 0.0002 3 5 6 3 3 | 5 | 0 2 0 1 3 > 0.9998 || = 0.52 551 505 471 508 507 | 500 < 0.0003 3 7 7 4 2 | 5 | 4 2 2 2 3 > 0.9997 || = 0.51 461 502 526 529 530 | 500 < 0.0004 7 4 3 3 3 | 5 | 6 5 1 3 3 > 0.9996 || = 0.50 470 482 499 497 482 | 500 < 0.0005 6 13 4 4 8 | 5 | 3 1 5 3 4 > 0.9995 || = 0.49 510 484 508 482 490 | 500 < 0.0006 6 8 4 7 5 | 5 | 5 0 2 7 1 > 0.9994 || = 0.48 511 506 540 536 530 | 500 < 0.0007 7 2 2 2 8 | 5 | 4 2 3 6 3 > 0.9993 || = 0.47 492 533 505 517 511 | 500 < 0.0008 3 4 5 4 5 | 5 | 4 2 7 4 3 > 0.9992 || = 0.46 536 468 463 481 460 | 500 < 0.0009 6 4 0 3 7 | 5 | 6 2 2 5 1 > 0.9991 || = 0.45 528 537 530 533 508 | 500 < 0.001 4 7 5 2 5 | 5 | 1 4 5 6 5 > 0.999 || = 0.44 510 495 554 509 494 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 497 527 524 501 493 | 500 < 0.001 52 61 39 38 53 | 50 | 35 20 28 38 28 > 0.999 || = 0.42 502 514 492 532 502 | 500 < 0.002 41 40 48 44 58 | 50 | 44 49 47 49 54 > 0.998 || = 0.41 467 481 498 482 523 | 500 < 0.003 46 51 61 54 43 | 50 | 32 38 44 52 51 > 0.997 || = 0.40 495 522 504 527 523 | 500 < 0.004 52 46 53 53 44 | 50 | 42 58 45 53 42 > 0.996 || = 0.39 504 510 496 475 499 | 500 < 0.005 50 55 48 44 59 | 50 | 45 46 57 56 51 > 0.995 || = 0.38 531 543 507 461 513 | 500 < 0.006 44 67 61 60 36 | 50 | 58 37 48 51 46 > 0.994 || = 0.37 517 494 488 483 474 | 500 < 0.007 47 50 43 52 48 | 50 | 45 44 44 67 47 > 0.993 || = 0.36 514 490 522 549 509 | 500 < 0.008 49 59 53 47 52 | 50 | 59 53 53 42 50 > 0.992 || = 0.35 499 524 497 507 440 | 500 < 0.009 54 50 51 40 44 | 50 | 57 42 55 50 63 > 0.991 || = 0.34 490 511 482 527 473 | 500 < 0.01 40 64 56 57 61 | 50 | 57 56 55 47 38 > 0.99 || = 0.33 492 514 512 483 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 476 436 481 499 546 | 500 < 0.01 475 543 513 489 498 | 497.5 | 474 443 476 505 470 > 0.99 || = 0.31 512 540 514 504 519 | 500 = 0.01 247 262 227 249 254 | 252.5 | 235 249 254 281 241 = 0.99 || = 0.30 528 466 496 482 507 | 500 = 0.02 461 483 470 507 474 | 500 | 529 520 516 521 524 = 0.98 || = 0.29 493 529 469 493 502 | 500 =================================================================| 500 | 509 485 506 496 516 = 0.97 || = 0.28 536 507 528 471 479 | 500 sstring_PeriodsInStrings test: | 500 | 499 506 545 510 525 = 0.96 || = 0.27 506 497 497 471 524 | 500 ----------------------------------------------- | 500 | 492 502 508 513 504 = 0.95 || = 0.26 535 494 518 510 519 | 500 N = 10, n = 500000000, r = 20, s = 10 | 500 | 454 513 499 479 521 = 0.94 || = 0.25 550 501 497 449 476 | 500 Anderson-Darling statistic = A2 | 500 | 518 514 471 512 533 = 0.93 || = 0.24 508 523 491 520 502 | 500 | 500 | 499 500 521 536 469 = 0.92 || = 0.23 510 505 498 459 468 | 500 =================================================================| 500 | 544 492 500 496 487 = 0.91 || = 0.22 477 519 507 496 517 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 476 524 473 500 477 = 0.90 || = 0.21 475 491 514 478 489 | 500 -----------------------------------------------------------------| 500 | 530 509 517 503 508 = 0.89 || = 0.20 497 503 458 537 526 | 500 SD Bern.: d 0.99698 0.73110 1.37326 | 500 | 503 486 517 491 512 = 0.88 || = 0.19 515 481 492 485 505 | 500 s 1.01227 1.28827 1.69730 | 500 | 529 498 472 488 481 = 0.87 || = 0.18 477 500 530 510 488 | 500 t 0.94173 0.97516 1.18549 | 500 | 459 499 495 495 483 = 0.86 || = 0.17 482 481 522 488 502 | 500 m 0.91781 1.00349 1.05598 | 500 | 466 476 477 491 474 = 0.85 || = 0.16 503 502 486 508 516 | 500 x 0.98936 1.09598 1.34528 | 500 | 500 502 506 510 471 = 0.84 || = 0.15 470 534 471 499 506 | 500 | 500 | 485 519 494 484 523 = 0.83 || = 0.14 500 502 518 493 505 | 500 Changes: d 42 5 3 | 500 | 505 489 500 507 485 = 0.82 || = 0.13 461 522 511 498 491 | 500 s 51 8 5 | 500 | 511 499 504 474 457 = 0.81 || = 0.12 467 493 540 492 517 | 500 t 57 5 3 | 500 | 501 474 465 508 478 = 0.80 || = 0.11 517 492 466 503 526 | 500 m 53 5 2 | 500 | 499 454 532 500 517 = 0.79 || = 0.10 469 487 504 503 517 | 500 x 50 6 6 | 500 | 560 528 477 527 547 = 0.78 || = 0.09 481 499 493 509 513 | 500 -----------------------------------------------------------------| 500 | 494 498 512 490 509 = 0.77 || = 0.08 491 504 491 514 478 | 500 Aver./ d 0.50118 500 > 500: 2 3 6 6 6 8 4 4 5 4 | 500 | 506 515 480 523 539 = 0.76 || = 0.07 507 517 479 488 503 | 500 median s 0.49897 500 ----- 4 4 7 6 6 6 4 3 4 5 | 500 | 508 485 468 476 506 = 0.75 || = 0.06 500 494 509 521 470 | 500 t 0.50007 501 4 6 4 4 7 7 4 5 4 6 | 500 | 500 512 515 475 477 = 0.74 || = 0.05 485 488 478 534 542 | 500 m 0.50085 499 5 4 3 4 7 6 5 4 3 7 | 500 | 472 475 517 508 549 = 0.73 || = 0.04 498 471 512 487 490 | 500 x 0.49948 502 5 8 6 6 6 5 5 6 3 6 | 500 | 498 457 503 471 492 = 0.72 || = 0.03 520 464 510 477 486 | 500 -----------------------------------------------------------------| 500 | 494 482 483 493 484 = 0.71 || = 0.02 461 483 470 507 474 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 475 517 473 520 467 = 0.70 || = 0.01 247 262 227 249 254 | 252.5 d 0 0 1 21 65 10 4 0 0 | 500 | 494 462 501 513 469 = 0.69 || < 0.01 475 543 513 489 498 | 497.5 s 0 0 3 13 69 13 3 0 0 | 500 | 490 486 523 483 459 = 0.68 ||========================================================================= t 0 0 0 18 71 9 3 0 0 | 500 | 493 496 500 472 508 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 12 71 15 1 0 0 | 500 | 509 545 483 485 520 = 0.66 ||========================================================================= x 0 0 1 17 66 14 3 0 0 | 500 | 489 477 464 491 527 = 0.65 || sstring_PeriodsInStrings test: no 206 test no 207 TestU01 250000 runs BigCrush Test smarsa_S sstring_PeriodsInStrings test: test no 207 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 1 1 | 0.5 | 2 3 0 1 0 > 0.99999 || = 0.64 507 498 498 477 512 | 500 < 0.00002 1 1 0 0 3 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 512 520 519 476 484 | 500 < 0.00003 0 2 1 1 1 | 0.5 | 0 1 1 0 0 > 0.99997 || = 0.62 491 475 504 526 493 | 500 < 0.00004 0 1 0 1 0 | 0.5 | 1 0 0 1 0 > 0.99996 || = 0.61 500 504 497 482 503 | 500 < 0.00005 0 0 1 1 0 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 515 478 474 526 463 | 500 < 0.00006 0 0 1 1 0 | 0.5 | 1 0 0 1 2 > 0.99994 || = 0.59 482 484 512 536 499 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 1 0 2 1 1 > 0.99993 || = 0.58 509 517 519 518 495 | 500 < 0.00008 0 0 1 0 1 | 0.5 | 1 1 0 0 0 > 0.99992 || = 0.57 536 457 526 483 495 | 500 < 0.00009 0 1 1 1 1 | 0.5 | 1 1 0 1 0 > 0.99991 || = 0.56 549 476 482 509 506 | 500 < 0.0001 0 1 0 1 0 | 0.5 | 0 0 0 1 1 > 0.9999 || = 0.55 512 495 446 470 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 487 491 518 474 517 | 500 < 0.0001 1 7 5 7 7 | 5 | 7 6 4 6 5 > 0.9999 || = 0.53 521 475 499 570 510 | 500 < 0.0002 7 5 5 3 3 | 5 | 1 4 2 2 3 > 0.9998 || = 0.52 499 483 470 519 485 | 500 < 0.0003 6 11 1 3 2 | 5 | 4 4 6 2 9 > 0.9997 || = 0.51 538 471 486 507 468 | 500 < 0.0004 5 6 6 4 4 | 5 | 6 7 3 2 5 > 0.9996 || = 0.50 502 507 495 491 480 | 500 < 0.0005 9 5 8 2 4 | 5 | 9 3 2 7 7 > 0.9995 || = 0.49 526 489 520 512 497 | 500 < 0.0006 2 6 2 4 4 | 5 | 4 4 8 6 3 > 0.9994 || = 0.48 536 548 521 516 502 | 500 < 0.0007 7 5 6 5 7 | 5 | 7 1 5 10 2 > 0.9993 || = 0.47 513 453 526 499 512 | 500 < 0.0008 4 5 8 3 5 | 5 | 8 4 4 3 7 > 0.9992 || = 0.46 478 487 505 468 486 | 500 < 0.0009 5 4 4 1 8 | 5 | 1 4 7 6 2 > 0.9991 || = 0.45 484 478 482 485 471 | 500 < 0.001 1 5 6 3 6 | 5 | 4 5 1 3 8 > 0.999 || = 0.44 515 494 499 523 475 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 507 504 491 511 531 | 500 < 0.001 47 59 51 35 50 | 50 | 51 42 42 47 51 > 0.999 || = 0.42 484 506 498 521 533 | 500 < 0.002 43 45 48 42 37 | 50 | 34 49 49 38 52 > 0.998 || = 0.41 478 500 475 514 508 | 500 < 0.003 55 56 57 50 61 | 50 | 40 69 49 48 53 > 0.997 || = 0.40 482 520 500 477 470 | 500 < 0.004 52 62 51 46 46 | 50 | 42 42 42 40 53 > 0.996 || = 0.39 525 499 538 474 484 | 500 < 0.005 58 45 49 41 42 | 50 | 48 52 40 45 54 > 0.995 || = 0.38 537 493 491 514 473 | 500 < 0.006 44 47 41 50 47 | 50 | 57 43 48 52 38 > 0.994 || = 0.37 438 463 531 518 476 | 500 < 0.007 51 52 33 46 38 | 50 | 46 44 57 47 45 > 0.993 || = 0.36 500 518 460 486 491 | 500 < 0.008 48 53 42 48 46 | 50 | 56 44 39 63 58 > 0.992 || = 0.35 508 526 508 492 510 | 500 < 0.009 40 49 53 46 44 | 50 | 53 57 55 60 47 > 0.991 || = 0.34 486 495 490 488 513 | 500 < 0.01 42 69 49 48 61 | 50 | 54 38 52 46 49 > 0.99 || = 0.33 487 511 496 476 502 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 456 472 480 493 488 | 500 < 0.01 480 537 474 452 472 | 497.5 | 481 480 473 486 500 > 0.99 || = 0.31 544 527 490 465 450 | 500 = 0.01 256 244 268 258 246 | 252.5 | 241 212 242 284 244 = 0.99 || = 0.30 489 516 486 519 527 | 500 = 0.02 532 466 492 521 493 | 500 | 434 501 493 522 510 = 0.98 || = 0.29 502 535 484 543 491 | 500 =================================================================| 500 | 490 505 459 511 465 = 0.97 || = 0.28 488 518 519 543 507 | 500 sstring_PeriodsInStrings test: | 500 | 497 513 520 515 498 = 0.96 || = 0.27 488 533 498 500 528 | 500 ----------------------------------------------- | 500 | 497 493 517 505 501 = 0.95 || = 0.26 475 524 520 500 458 | 500 N = 10, n = 500000000, r = 20, s = 10 | 500 | 475 511 491 525 498 = 0.94 || = 0.25 515 479 521 470 527 | 500 Test on the sum of all N observations | 500 | 498 493 514 487 539 = 0.93 || = 0.24 501 547 516 470 495 | 500 | 500 | 506 497 513 483 514 = 0.92 || = 0.23 504 549 494 506 479 | 500 =================================================================| 500 | 521 515 481 497 553 = 0.91 || = 0.22 501 513 503 474 512 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 473 498 444 500 505 = 0.90 || = 0.21 467 525 512 518 504 | 500 -----------------------------------------------------------------| 500 | 490 529 482 496 516 = 0.89 || = 0.20 503 494 495 512 493 | 500 SD Bern.: d 0.93355 0.84421 1.05028 | 500 | 498 492 535 498 537 = 0.88 || = 0.19 505 490 504 445 477 | 500 s 0.95719 1.17956 1.27184 | 500 | 489 489 498 464 503 = 0.87 || = 0.18 490 498 455 525 491 | 500 t 0.90952 1.00049 0.93104 | 500 | 519 475 515 512 515 = 0.86 || = 0.17 495 509 494 518 524 | 500 m 1.04878 0.92349 1.07756 | 500 | 509 472 512 509 501 = 0.85 || = 0.16 518 498 500 472 543 | 500 x 0.98614 1.18041 0.75136 | 500 | 473 468 495 549 525 = 0.84 || = 0.15 504 514 480 500 511 | 500 | 500 | 517 504 506 519 476 = 0.83 || = 0.14 526 500 509 492 505 | 500 Changes: d 44 4 4 | 500 | 489 486 483 505 493 = 0.82 || = 0.13 522 511 511 462 499 | 500 s 51 6 6 | 500 | 489 507 505 517 466 = 0.81 || = 0.12 523 513 462 506 504 | 500 t 54 5 3 | 500 | 495 558 486 482 491 = 0.80 || = 0.11 466 521 498 466 541 | 500 m 40 0 4 | 500 | 515 520 508 507 480 = 0.79 || = 0.10 521 483 507 451 526 | 500 x 43 3 3 | 500 | 527 470 500 516 537 = 0.78 || = 0.09 503 526 477 484 498 | 500 -----------------------------------------------------------------| 500 | 480 507 504 487 518 = 0.77 || = 0.08 504 509 508 479 500 | 500 Aver./ d 0.49884 500 > 500: 5 7 6 4 5 7 5 5 3 2 | 500 | 478 509 489 490 488 = 0.76 || = 0.07 505 476 548 501 490 | 500 median s 0.49774 499 ----- 4 5 8 5 4 1 3 7 3 5 | 500 | 520 504 497 500 495 = 0.75 || = 0.06 483 499 518 508 504 | 500 t 0.50034 498 4 4 6 3 4 4 6 5 5 4 | 500 | 500 494 524 528 514 = 0.74 || = 0.05 499 504 497 464 480 | 500 m 0.50348 500 5 3 5 3 6 7 3 5 6 6 | 500 | 512 515 553 502 491 = 0.73 || = 0.04 485 499 485 511 551 | 500 x 0.50066 500 2 7 5 4 5 3 7 4 7 6 | 500 | 525 512 528 479 474 = 0.72 || = 0.03 496 493 488 482 471 | 500 -----------------------------------------------------------------| 500 | 469 491 492 537 519 = 0.71 || = 0.02 532 466 492 521 493 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 493 497 509 540 435 = 0.70 || = 0.01 256 244 268 258 246 | 252.5 d 0 0 2 8 77 13 1 0 0 | 500 | 481 492 497 522 529 = 0.69 || < 0.01 480 537 474 452 472 | 497.5 s 0 0 2 14 72 9 4 0 0 | 500 | 510 505 530 494 504 = 0.68 ||========================================================================= t 0 0 3 9 78 9 2 0 0 | 500 | 506 473 493 494 507 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 17 67 12 1 1 0 | 500 | 485 478 523 496 528 = 0.66 ||========================================================================= x 0 0 2 15 67 15 2 0 0 | 500 | 528 498 520 494 513 = 0.65 || sstring_PeriodsInStrings test: no 207 test no 208 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingWeight2 test: test no 208 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 1 | 0.5 | 1 1 0 0 0 > 0.99999 || = 0.64 476 492 528 493 487 | 500 < 0.00002 1 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 475 535 513 504 472 | 500 < 0.00003 0 0 1 0 1 | 0.5 | 2 1 0 1 1 > 0.99997 || = 0.62 530 486 491 510 476 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99996 || = 0.61 518 518 513 477 518 | 500 < 0.00005 0 1 0 1 0 | 0.5 | 0 0 1 1 0 > 0.99995 || = 0.60 517 524 480 508 492 | 500 < 0.00006 0 0 1 0 0 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 516 486 513 522 488 | 500 < 0.00007 0 0 1 0 1 | 0.5 | 1 2 0 0 0 > 0.99993 || = 0.58 491 512 463 514 516 | 500 < 0.00008 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 475 480 526 549 493 | 500 < 0.00009 0 1 1 2 1 | 0.5 | 0 0 1 1 1 > 0.99991 || = 0.56 529 453 485 544 484 | 500 < 0.0001 0 1 0 1 0 | 0.5 | 0 1 0 0 0 > 0.9999 || = 0.55 513 481 545 503 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 475 499 509 505 474 | 500 < 0.0001 1 3 4 6 5 | 5 | 4 5 2 4 3 > 0.9999 || = 0.53 483 511 523 519 501 | 500 < 0.0002 5 3 7 4 3 | 5 | 1 1 3 3 3 > 0.9998 || = 0.52 533 531 480 498 501 | 500 < 0.0003 7 2 4 5 8 | 5 | 1 5 3 3 5 > 0.9997 || = 0.51 513 484 479 502 492 | 500 < 0.0004 5 8 2 8 7 | 5 | 9 3 7 0 8 > 0.9996 || = 0.50 495 487 492 497 535 | 500 < 0.0005 2 1 3 7 3 | 5 | 1 5 12 6 8 > 0.9995 || = 0.49 518 514 513 511 545 | 500 < 0.0006 6 6 3 2 7 | 5 | 6 6 4 5 3 > 0.9994 || = 0.48 499 516 493 466 478 | 500 < 0.0007 9 2 8 13 7 | 5 | 3 2 5 4 4 > 0.9993 || = 0.47 529 500 478 518 509 | 500 < 0.0008 4 2 9 2 7 | 5 | 6 3 6 4 4 > 0.9992 || = 0.46 475 497 514 500 507 | 500 < 0.0009 6 4 8 6 4 | 5 | 7 5 6 3 2 > 0.9991 || = 0.45 547 451 505 513 488 | 500 < 0.001 4 8 8 5 3 | 5 | 1 3 5 8 2 > 0.999 || = 0.44 475 518 520 545 507 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 502 509 500 525 487 | 500 < 0.001 49 39 56 58 54 | 50 | 39 38 53 40 42 > 0.999 || = 0.42 538 539 516 530 466 | 500 < 0.002 42 36 40 63 52 | 50 | 57 49 44 50 50 > 0.998 || = 0.41 477 493 479 478 508 | 500 < 0.003 52 50 40 31 57 | 50 | 56 54 42 52 59 > 0.997 || = 0.40 523 456 492 470 479 | 500 < 0.004 66 49 58 46 56 | 50 | 60 50 52 48 55 > 0.996 || = 0.39 499 476 513 499 477 | 500 < 0.005 54 54 52 50 56 | 50 | 57 51 54 47 42 > 0.995 || = 0.38 536 488 539 526 495 | 500 < 0.006 39 52 49 37 51 | 50 | 52 56 45 53 37 > 0.994 || = 0.37 537 497 469 500 499 | 500 < 0.007 45 44 47 53 59 | 50 | 53 52 65 48 35 > 0.993 || = 0.36 510 478 471 496 492 | 500 < 0.008 63 52 69 46 44 | 50 | 52 48 58 43 50 > 0.992 || = 0.35 481 519 506 485 516 | 500 < 0.009 58 53 45 55 51 | 50 | 56 45 52 59 45 > 0.991 || = 0.34 468 482 463 513 499 | 500 < 0.01 47 42 51 48 43 | 50 | 50 53 58 45 57 > 0.99 || = 0.33 504 491 521 513 468 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 503 527 508 459 508 | 500 < 0.01 515 471 507 487 523 | 497.5 | 532 496 523 485 472 > 0.99 || = 0.31 504 495 496 473 476 | 500 = 0.01 275 249 247 235 252 | 252.5 | 253 283 255 261 235 = 0.99 || = 0.30 493 477 502 507 467 | 500 = 0.02 512 483 489 508 485 | 500 | 482 530 489 480 501 = 0.98 || = 0.29 463 474 494 454 501 | 500 =================================================================| 500 | 539 453 470 511 545 = 0.97 || = 0.28 475 499 482 468 498 | 500 sstring_HammingWeight2 test: | 500 | 503 518 479 473 501 = 0.96 || = 0.27 491 507 499 474 472 | 500 ----------------------------------------------- | 500 | 490 508 492 498 502 = 0.95 || = 0.26 480 462 495 528 527 | 500 N = 10, n = 1000000000, r = 0, s = 3, L = 1000000 | 500 | 507 501 520 515 518 = 0.94 || = 0.25 491 495 490 503 519 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 448 470 512 513 512 = 0.93 || = 0.24 498 512 498 495 500 | 500 | 500 | 504 538 502 509 476 = 0.92 || = 0.23 504 484 553 490 492 | 500 =================================================================| 500 | 474 502 515 478 521 = 0.91 || = 0.22 479 497 508 493 526 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 498 501 488 477 504 = 0.90 || = 0.21 464 501 537 476 552 | 500 -----------------------------------------------------------------| 500 | 559 497 516 499 504 = 0.89 || = 0.20 507 519 508 499 522 | 500 SD Bern.: d 1.01403 1.20807 0.90376 | 500 | 507 496 506 521 485 = 0.88 || = 0.19 463 508 504 526 498 | 500 s 0.89754 0.95020 0.69315 | 500 | 533 488 499 531 513 = 0.87 || = 0.18 520 515 523 492 495 | 500 t 0.88448 1.18464 1.01143 | 500 | 536 514 509 504 494 = 0.86 || = 0.17 498 517 486 473 522 | 500 m 0.99895 1.29137 0.75534 | 500 | 493 527 505 533 517 = 0.85 || = 0.16 468 486 496 505 505 | 500 x 0.94858 0.78651 1.18549 | 500 | 515 497 476 453 520 = 0.84 || = 0.15 483 468 509 512 445 | 500 | 500 | 496 494 499 514 527 = 0.83 || = 0.14 524 501 489 468 524 | 500 Changes: d 49 4 2 | 500 | 496 510 505 528 496 = 0.82 || = 0.13 483 510 497 485 529 | 500 s 48 4 5 | 500 | 481 515 506 490 538 = 0.81 || = 0.12 494 495 466 504 477 | 500 t 48 6 4 | 500 | 495 526 514 536 494 = 0.80 || = 0.11 499 515 488 487 471 | 500 m 44 5 6 | 500 | 492 509 482 520 538 = 0.79 || = 0.10 521 530 537 498 486 | 500 x 53 3 3 | 500 | 474 497 483 546 520 = 0.78 || = 0.09 526 504 492 489 473 | 500 -----------------------------------------------------------------| 500 | 495 511 449 523 498 = 0.77 || = 0.08 481 453 524 492 529 | 500 Aver./ d 0.50001 498 > 500: 7 3 2 6 6 6 4 0 5 6 | 500 | 484 484 505 491 536 = 0.76 || = 0.07 527 505 491 508 510 | 500 median s 0.50160 501 ----- 5 7 4 2 5 4 7 6 5 7 | 500 | 497 469 522 516 482 = 0.75 || = 0.06 485 517 509 515 498 | 500 t 0.49896 500 5 4 4 6 5 5 6 3 6 6 | 500 | 490 517 479 459 526 = 0.74 || = 0.05 478 489 536 504 468 | 500 m 0.50075 500 6 4 2 4 6 9 2 6 6 5 | 500 | 472 518 492 509 483 = 0.73 || = 0.04 521 510 522 519 500 | 500 x 0.50094 499 4 4 6 2 5 3 3 4 7 7 | 500 | 462 502 500 478 497 = 0.72 || = 0.03 530 520 469 543 525 | 500 -----------------------------------------------------------------| 500 | 487 494 487 438 495 = 0.71 || = 0.02 512 483 489 508 485 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 526 520 506 483 499 = 0.70 || = 0.01 275 249 247 235 252 | 252.5 d 0 0 1 18 61 19 2 0 0 | 500 | 498 502 502 476 496 = 0.69 || < 0.01 515 471 507 487 523 | 497.5 s 0 0 4 9 77 11 0 0 0 | 500 | 525 515 495 498 505 = 0.68 ||========================================================================= t 0 0 1 10 78 10 2 0 0 | 500 | 481 486 468 484 478 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 16 67 12 3 0 0 | 500 | 477 510 457 476 452 = 0.66 ||========================================================================= x 0 0 2 16 67 13 3 0 0 | 500 | 487 504 510 492 505 = 0.65 || sstring_HammingWeight2 test: no 208 test no 209 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingWeight2 test: test no 209 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 0 0 0 | 0.5 | 1 1 1 0 0 > 0.99999 || = 0.64 455 509 472 469 488 | 500 < 0.00002 0 1 0 1 1 | 0.5 | 0 0 2 0 0 > 0.99998 || = 0.63 474 499 479 498 503 | 500 < 0.00003 1 0 1 0 0 | 0.5 | 0 1 0 0 1 > 0.99997 || = 0.62 476 453 523 479 501 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99996 || = 0.61 522 517 507 503 490 | 500 < 0.00005 1 0 0 1 1 | 0.5 | 0 0 0 1 1 > 0.99995 || = 0.60 519 492 475 471 498 | 500 < 0.00006 1 0 0 0 1 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 490 493 508 440 497 | 500 < 0.00007 0 1 0 0 0 | 0.5 | 1 1 0 0 1 > 0.99993 || = 0.58 483 498 516 500 465 | 500 < 0.00008 1 1 0 0 0 | 0.5 | 0 0 0 0 3 > 0.99992 || = 0.57 486 502 525 467 511 | 500 < 0.00009 1 0 1 0 0 | 0.5 | 1 1 0 1 2 > 0.99991 || = 0.56 506 479 511 514 506 | 500 < 0.0001 0 0 1 0 0 | 0.5 | 0 0 1 0 1 > 0.9999 || = 0.55 492 450 521 508 505 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 445 531 493 498 472 | 500 < 0.0001 7 3 3 2 3 | 5 | 3 4 5 3 10 > 0.9999 || = 0.53 481 506 498 487 468 | 500 < 0.0002 7 5 6 9 6 | 5 | 1 2 3 3 5 > 0.9998 || = 0.52 506 495 496 504 484 | 500 < 0.0003 3 8 7 10 7 | 5 | 5 3 2 3 7 > 0.9997 || = 0.51 499 514 491 524 507 | 500 < 0.0004 7 7 6 7 8 | 5 | 3 2 8 4 6 > 0.9996 || = 0.50 535 472 502 507 479 | 500 < 0.0005 4 1 6 6 6 | 5 | 6 3 2 6 7 > 0.9995 || = 0.49 502 507 520 462 495 | 500 < 0.0006 5 6 5 4 5 | 5 | 3 6 3 7 8 > 0.9994 || = 0.48 500 469 519 529 513 | 500 < 0.0007 4 11 4 8 6 | 5 | 4 6 9 4 3 > 0.9993 || = 0.47 503 489 509 491 529 | 500 < 0.0008 5 4 7 8 7 | 5 | 5 8 5 9 1 > 0.9992 || = 0.46 491 500 493 470 506 | 500 < 0.0009 7 4 2 7 7 | 5 | 6 3 4 8 4 > 0.9991 || = 0.45 509 472 513 490 500 | 500 < 0.001 4 3 5 4 4 | 5 | 6 5 2 5 7 > 0.999 || = 0.44 484 481 496 498 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 478 494 510 492 488 | 500 < 0.001 53 52 51 65 59 | 50 | 42 42 43 52 58 > 0.999 || = 0.42 554 490 492 482 516 | 500 < 0.002 48 57 46 36 52 | 50 | 57 48 41 42 45 > 0.998 || = 0.41 512 511 505 498 499 | 500 < 0.003 40 51 64 54 40 | 50 | 46 41 57 54 52 > 0.997 || = 0.40 495 504 515 479 483 | 500 < 0.004 60 58 49 49 42 | 50 | 42 42 47 54 61 > 0.996 || = 0.39 531 487 508 498 519 | 500 < 0.005 59 47 65 52 42 | 50 | 52 60 48 52 53 > 0.995 || = 0.38 511 523 561 465 492 | 500 < 0.006 51 51 63 39 42 | 50 | 54 49 50 48 40 > 0.994 || = 0.37 508 532 467 502 515 | 500 < 0.007 57 49 58 51 52 | 50 | 49 54 43 38 49 > 0.993 || = 0.36 458 470 524 495 508 | 500 < 0.008 43 44 56 52 37 | 50 | 41 42 50 45 50 > 0.992 || = 0.35 493 506 480 524 482 | 500 < 0.009 51 49 44 65 63 | 50 | 52 57 55 45 65 > 0.991 || = 0.34 508 488 534 511 523 | 500 < 0.01 49 55 48 38 48 | 50 | 47 48 43 61 57 > 0.99 || = 0.33 482 483 476 517 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 529 529 524 503 497 | 500 < 0.01 511 513 544 501 477 | 497.5 | 482 483 477 491 530 > 0.99 || = 0.31 487 497 511 536 514 | 500 = 0.01 243 259 242 273 253 | 252.5 | 287 244 271 255 248 = 0.99 || = 0.30 523 512 515 521 473 | 500 = 0.02 509 495 451 492 484 | 500 | 527 500 498 524 493 = 0.98 || = 0.29 496 464 510 478 517 | 500 =================================================================| 500 | 477 473 505 511 504 = 0.97 || = 0.28 520 457 517 502 487 | 500 sstring_HammingWeight2 test: | 500 | 513 521 510 502 535 = 0.96 || = 0.27 487 508 475 547 500 | 500 ----------------------------------------------- | 500 | 510 493 491 475 501 = 0.95 || = 0.26 479 532 489 516 518 | 500 N = 10, n = 1000000000, r = 0, s = 3, L = 1000000 | 500 | 491 479 470 506 479 = 0.94 || = 0.25 502 508 477 476 492 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 490 470 518 486 478 = 0.93 || = 0.24 458 510 493 510 513 | 500 | 500 | 467 532 482 490 507 = 0.92 || = 0.23 526 534 474 525 537 | 500 =================================================================| 500 | 527 496 516 503 486 = 0.91 || = 0.22 491 507 473 500 506 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 501 499 509 494 485 = 0.90 || = 0.21 489 504 516 485 499 | 500 -----------------------------------------------------------------| 500 | 528 481 468 492 518 = 0.89 || = 0.20 479 480 510 470 512 | 500 SD Bern.: d 0.96098 0.88925 0.78523 | 500 | 487 498 500 504 504 = 0.88 || = 0.19 513 507 463 535 508 | 500 s 0.93662 0.61836 0.94597 | 500 | 499 515 507 523 486 = 0.87 || = 0.18 495 510 500 531 534 | 500 t 0.94202 1.22371 0.79411 | 500 | 509 479 504 538 494 = 0.86 || = 0.17 555 479 453 493 505 | 500 m 0.94158 1.36962 0.92023 | 500 | 496 488 481 485 464 = 0.85 || = 0.16 523 478 476 498 501 | 500 x 0.81526 1.20309 1.09415 | 500 | 490 486 507 490 529 = 0.84 || = 0.15 508 562 476 504 453 | 500 | 500 | 517 544 481 479 489 = 0.83 || = 0.14 503 543 495 531 499 | 500 Changes: d 57 5 6 | 500 | 474 482 492 498 500 = 0.82 || = 0.13 504 529 498 521 492 | 500 s 51 4 6 | 500 | 497 484 483 500 489 = 0.81 || = 0.12 536 511 533 509 480 | 500 t 49 5 4 | 500 | 491 535 500 539 528 = 0.80 || = 0.11 487 516 510 486 534 | 500 m 43 7 4 | 500 | 494 500 502 503 507 = 0.79 || = 0.10 507 489 496 518 495 | 500 x 59 5 4 | 500 | 459 499 517 525 496 = 0.78 || = 0.09 482 497 507 506 556 | 500 -----------------------------------------------------------------| 500 | 487 526 531 499 477 = 0.77 || = 0.08 492 508 463 459 475 | 500 Aver./ d 0.49891 499 > 500: 4 8 3 6 5 3 5 4 4 5 | 500 | 508 509 500 514 506 = 0.76 || = 0.07 487 509 511 536 485 | 500 median s 0.49803 499 ----- 6 7 7 5 3 4 5 6 2 2 | 500 | 492 504 504 498 517 = 0.75 || = 0.06 523 534 518 486 506 | 500 t 0.50053 502 5 2 4 7 7 5 6 6 4 5 | 500 | 506 515 495 474 488 = 0.74 || = 0.05 484 485 532 501 475 | 500 m 0.49928 500 5 7 5 7 1 4 3 6 3 6 | 500 | 509 497 472 499 505 = 0.73 || = 0.04 492 524 476 479 480 | 500 x 0.49980 500 4 5 6 5 5 4 6 5 3 5 | 500 | 523 517 503 504 482 = 0.72 || = 0.03 542 473 489 487 524 | 500 -----------------------------------------------------------------| 500 | 465 482 519 534 487 = 0.71 || = 0.02 509 495 451 492 484 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 470 506 533 493 514 = 0.70 || = 0.01 243 259 242 273 253 | 252.5 d 0 0 2 10 72 14 3 0 0 | 500 | 528 481 519 482 494 = 0.69 || < 0.01 511 513 544 501 477 | 497.5 s 0 0 2 9 75 14 1 0 0 | 500 | 521 513 471 480 515 = 0.68 ||========================================================================= t 0 0 2 18 68 11 2 0 0 | 500 | 500 522 533 531 523 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 12 69 18 1 0 0 | 500 | 518 487 466 536 487 = 0.66 ||========================================================================= x 0 0 1 8 80 11 1 0 0 | 500 | 510 481 509 456 515 = 0.65 || sstring_HammingWeight2 test: no 209 test no 210 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingWeight2 test: test no 210 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 525 538 478 491 542 | 500 < 0.00002 1 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 543 458 518 494 475 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 500 468 481 486 482 | 500 < 0.00004 2 0 0 1 1 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 489 513 539 502 490 | 500 < 0.00005 0 2 1 0 2 | 0.5 | 0 0 0 1 1 > 0.99995 || = 0.60 489 474 553 509 480 | 500 < 0.00006 0 0 0 1 0 | 0.5 | 0 0 1 0 2 > 0.99994 || = 0.59 516 516 530 491 481 | 500 < 0.00007 2 0 0 0 0 | 0.5 | 1 1 0 0 0 > 0.99993 || = 0.58 491 485 484 469 512 | 500 < 0.00008 0 0 3 0 1 | 0.5 | 0 0 0 1 0 > 0.99992 || = 0.57 487 488 483 489 531 | 500 < 0.00009 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 463 513 502 474 495 | 500 < 0.0001 0 0 0 1 1 | 0.5 | 0 0 2 0 0 > 0.9999 || = 0.55 482 526 534 488 537 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 560 494 501 478 489 | 500 < 0.0001 5 3 4 4 6 | 5 | 2 1 3 2 3 > 0.9999 || = 0.53 480 444 536 482 494 | 500 < 0.0002 8 7 4 4 4 | 5 | 2 0 0 1 2 > 0.9998 || = 0.52 452 481 470 465 479 | 500 < 0.0003 3 5 3 8 8 | 5 | 4 1 1 4 3 > 0.9997 || = 0.51 516 465 472 548 495 | 500 < 0.0004 6 8 6 9 6 | 5 | 4 6 1 4 2 > 0.9996 || = 0.50 521 495 438 503 514 | 500 < 0.0005 6 7 4 7 4 | 5 | 3 2 4 2 6 > 0.9995 || = 0.49 502 511 502 499 491 | 500 < 0.0006 11 5 2 7 4 | 5 | 4 2 4 7 4 > 0.9994 || = 0.48 531 532 463 521 534 | 500 < 0.0007 7 6 8 5 4 | 5 | 4 2 3 2 0 > 0.9993 || = 0.47 506 509 475 463 479 | 500 < 0.0008 12 3 5 4 5 | 5 | 4 2 6 6 8 > 0.9992 || = 0.46 466 476 488 505 536 | 500 < 0.0009 2 2 4 12 5 | 5 | 2 3 3 2 4 > 0.9991 || = 0.45 494 500 529 503 493 | 500 < 0.001 1 5 6 6 4 | 5 | 3 3 3 3 3 > 0.999 || = 0.44 535 489 483 493 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 493 487 538 559 524 | 500 < 0.001 61 51 46 66 50 | 50 | 32 22 28 33 35 > 0.999 || = 0.42 521 550 446 504 492 | 500 < 0.002 67 37 56 68 52 | 50 | 41 42 42 49 55 > 0.998 || = 0.41 513 507 479 471 489 | 500 < 0.003 50 49 50 43 50 | 50 | 43 47 44 36 49 > 0.997 || = 0.40 498 528 471 462 527 | 500 < 0.004 48 39 62 48 60 | 50 | 49 55 50 46 45 > 0.996 || = 0.39 461 514 467 501 505 | 500 < 0.005 58 43 47 55 56 | 50 | 49 55 49 51 57 > 0.995 || = 0.38 504 515 480 471 466 | 500 < 0.006 37 44 49 50 62 | 50 | 37 54 57 54 43 > 0.994 || = 0.37 515 510 559 500 517 | 500 < 0.007 57 45 55 48 58 | 50 | 43 49 47 37 60 > 0.993 || = 0.36 503 481 488 518 507 | 500 < 0.008 50 46 40 53 55 | 50 | 48 49 39 45 36 > 0.992 || = 0.35 457 476 522 517 523 | 500 < 0.009 52 50 62 51 45 | 50 | 41 51 47 58 47 > 0.991 || = 0.34 484 536 542 516 478 | 500 < 0.01 49 66 60 44 68 | 50 | 52 51 52 43 52 > 0.99 || = 0.33 533 511 493 522 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 452 493 533 528 491 | 500 < 0.01 529 470 527 526 556 | 497.5 | 435 475 455 452 479 > 0.99 || = 0.31 527 505 486 452 533 | 500 = 0.01 244 260 271 251 262 | 252.5 | 248 213 273 263 236 = 0.99 || = 0.30 504 495 489 528 508 | 500 = 0.02 560 507 504 499 470 | 500 | 520 549 512 519 494 = 0.98 || = 0.29 510 578 519 510 483 | 500 =================================================================| 500 | 481 531 540 513 557 = 0.97 || = 0.28 509 500 502 468 473 | 500 sstring_HammingWeight2 test: | 500 | 529 531 468 554 480 = 0.96 || = 0.27 493 501 495 451 492 | 500 ----------------------------------------------- | 500 | 501 466 496 474 502 = 0.95 || = 0.26 479 550 477 490 501 | 500 N = 10, n = 1000000000, r = 0, s = 3, L = 1000000 | 500 | 472 519 499 517 472 = 0.94 || = 0.25 495 507 499 526 498 | 500 Anderson-Darling statistic = A2 | 500 | 481 466 502 480 515 = 0.93 || = 0.24 499 497 492 507 506 | 500 | 500 | 511 549 519 527 501 = 0.92 || = 0.23 486 498 509 501 510 | 500 =================================================================| 500 | 481 500 524 504 501 = 0.91 || = 0.22 516 528 511 489 470 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 477 479 488 501 491 = 0.90 || = 0.21 503 499 494 504 525 | 500 -----------------------------------------------------------------| 500 | 519 466 537 493 512 = 0.89 || = 0.20 494 519 504 491 492 | 500 SD Bern.: d 1.11280 1.18465 1.23592 | 500 | 567 513 534 520 484 = 0.88 || = 0.19 492 464 494 488 502 | 500 s 1.25991 1.16161 1.36228 | 500 | 527 525 491 517 494 = 0.87 || = 0.18 509 506 498 523 494 | 500 t 1.12657 1.07291 1.24721 | 500 | 514 479 474 463 500 = 0.86 || = 0.17 474 494 501 486 498 | 500 m 1.06218 1.19054 1.28593 | 500 | 471 453 443 495 482 = 0.85 || = 0.16 517 513 512 554 484 | 500 x 0.89761 1.20226 1.16933 | 500 | 497 515 507 504 508 = 0.84 || = 0.15 512 552 549 530 515 | 500 | 500 | 477 501 552 493 499 = 0.83 || = 0.14 535 452 524 490 498 | 500 Changes: d 45 7 1 | 500 | 485 545 511 503 496 = 0.82 || = 0.13 492 498 470 524 499 | 500 s 52 2 3 | 500 | 480 494 503 551 500 = 0.81 || = 0.12 514 515 501 490 532 | 500 t 47 7 3 | 500 | 530 502 489 468 485 = 0.80 || = 0.11 535 486 494 492 510 | 500 m 57 5 4 | 500 | 516 546 499 513 476 = 0.79 || = 0.10 488 516 523 518 520 | 500 x 49 5 7 | 500 | 513 519 523 491 472 = 0.78 || = 0.09 499 487 490 500 494 | 500 -----------------------------------------------------------------| 500 | 500 521 501 450 495 = 0.77 || = 0.08 533 479 456 468 499 | 500 Aver./ d 0.49851 499 > 500: 4 6 4 6 6 3 2 7 4 4 | 500 | 522 428 528 487 493 = 0.76 || = 0.07 508 513 483 511 516 | 500 median s 0.49888 501 ----- 5 5 6 6 6 3 5 5 5 5 | 500 | 499 502 491 524 486 = 0.75 || = 0.06 498 520 479 488 459 | 500 t 0.50082 499 3 6 5 4 3 6 4 5 6 6 | 500 | 463 463 514 533 509 = 0.74 || = 0.05 493 485 474 522 483 | 500 m 0.49960 500 4 5 5 7 5 2 3 4 6 7 | 500 | 505 454 510 467 526 = 0.73 || = 0.04 481 440 494 475 464 | 500 x 0.49947 498 4 5 4 6 5 3 5 4 2 5 | 500 | 505 464 481 494 502 = 0.72 || = 0.03 464 539 495 519 502 | 500 -----------------------------------------------------------------| 500 | 538 465 495 523 504 = 0.71 || = 0.02 560 507 504 499 470 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 482 505 473 500 532 = 0.70 || = 0.01 244 260 271 251 262 | 252.5 d 0 0 4 12 68 14 2 1 0 | 500 | 443 491 479 494 523 = 0.69 || < 0.01 529 470 527 526 556 | 497.5 s 0 1 6 15 60 11 7 1 0 | 500 | 492 499 514 540 502 = 0.68 ||========================================================================= t 0 0 3 14 61 19 4 0 0 | 500 | 474 490 489 492 528 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 14 66 12 5 0 0 | 500 | 479 523 486 505 477 = 0.66 ||========================================================================= x 0 0 0 12 72 15 2 0 0 | 500 | 492 503 507 483 490 = 0.65 || sstring_HammingWeight2 test: no 210 test no 211 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingWeight2 test: test no 211 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 507 497 496 495 455 | 500 < 0.00002 2 1 0 1 1 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 485 516 472 493 511 | 500 < 0.00003 1 1 1 1 0 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 552 496 484 497 517 | 500 < 0.00004 2 0 1 0 1 | 0.5 | 0 0 0 1 1 > 0.99996 || = 0.61 511 473 523 525 483 | 500 < 0.00005 0 0 1 0 1 | 0.5 | 1 0 0 0 1 > 0.99995 || = 0.60 506 502 499 495 502 | 500 < 0.00006 0 0 1 0 1 | 0.5 | 0 0 2 1 0 > 0.99994 || = 0.59 480 507 487 502 464 | 500 < 0.00007 2 0 0 0 0 | 0.5 | 0 0 0 1 0 > 0.99993 || = 0.58 543 501 477 517 503 | 500 < 0.00008 1 1 1 1 1 | 0.5 | 0 1 0 1 0 > 0.99992 || = 0.57 523 497 527 458 481 | 500 < 0.00009 0 2 0 1 0 | 0.5 | 1 0 1 3 2 > 0.99991 || = 0.56 486 505 525 498 497 | 500 < 0.0001 0 2 3 1 0 | 0.5 | 1 1 0 1 2 > 0.9999 || = 0.55 473 488 494 471 531 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 475 506 530 521 470 | 500 < 0.0001 9 7 8 5 5 | 5 | 4 3 3 8 7 > 0.9999 || = 0.53 491 510 512 487 504 | 500 < 0.0002 8 6 2 8 4 | 5 | 2 3 1 2 2 > 0.9998 || = 0.52 479 483 486 539 494 | 500 < 0.0003 3 6 5 7 10 | 5 | 5 5 3 6 11 > 0.9997 || = 0.51 479 466 532 488 510 | 500 < 0.0004 8 6 5 8 5 | 5 | 3 4 6 6 7 > 0.9996 || = 0.50 504 523 518 506 487 | 500 < 0.0005 7 4 5 5 4 | 5 | 9 5 4 4 2 > 0.9995 || = 0.49 490 501 516 530 481 | 500 < 0.0006 4 3 11 1 6 | 5 | 10 0 5 5 8 > 0.9994 || = 0.48 479 500 506 537 515 | 500 < 0.0007 3 2 6 6 4 | 5 | 4 8 3 1 3 > 0.9993 || = 0.47 530 505 528 477 498 | 500 < 0.0008 7 4 7 7 2 | 5 | 4 5 3 5 4 > 0.9992 || = 0.46 489 502 476 512 517 | 500 < 0.0009 7 6 6 5 7 | 5 | 3 4 4 3 10 > 0.9991 || = 0.45 501 492 500 505 546 | 500 < 0.001 2 2 2 3 3 | 5 | 8 7 7 6 5 > 0.999 || = 0.44 506 493 528 517 463 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 438 560 465 452 501 | 500 < 0.001 58 46 57 55 50 | 50 | 52 44 39 46 59 > 0.999 || = 0.42 511 474 485 496 484 | 500 < 0.002 58 46 42 56 45 | 50 | 55 42 61 71 53 > 0.998 || = 0.41 550 476 495 524 492 | 500 < 0.003 44 49 53 42 51 | 50 | 57 35 53 45 56 > 0.997 || = 0.40 499 488 477 478 474 | 500 < 0.004 70 45 60 42 61 | 50 | 40 51 56 56 60 > 0.996 || = 0.39 495 558 532 498 498 | 500 < 0.005 42 53 58 65 56 | 50 | 57 58 57 53 50 > 0.995 || = 0.38 496 522 497 509 488 | 500 < 0.006 46 53 60 53 47 | 50 | 51 46 53 50 61 > 0.994 || = 0.37 493 461 476 516 566 | 500 < 0.007 59 52 58 48 45 | 50 | 52 43 51 43 57 > 0.993 || = 0.36 500 467 488 484 476 | 500 < 0.008 56 56 57 47 56 | 50 | 52 51 50 53 52 > 0.992 || = 0.35 456 520 504 474 497 | 500 < 0.009 55 56 34 52 61 | 50 | 57 57 49 48 58 > 0.991 || = 0.34 489 454 507 509 523 | 500 < 0.01 43 40 55 53 42 | 50 | 55 53 44 52 70 > 0.99 || = 0.33 472 526 520 528 509 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 547 494 483 487 529 | 500 < 0.01 531 496 534 513 514 | 497.5 | 528 480 513 517 576 > 0.99 || = 0.31 528 493 538 501 490 | 500 = 0.01 226 254 249 249 230 | 252.5 | 256 228 249 237 240 = 0.99 || = 0.30 472 486 482 499 502 | 500 = 0.02 508 483 479 502 471 | 500 | 486 519 536 501 465 = 0.98 || = 0.29 528 489 482 476 480 | 500 =================================================================| 500 | 511 494 459 497 491 = 0.97 || = 0.28 501 500 534 509 508 | 500 sstring_HammingWeight2 test: | 500 | 479 521 483 520 512 = 0.96 || = 0.27 487 495 507 504 483 | 500 ----------------------------------------------- | 500 | 524 457 489 496 514 = 0.95 || = 0.26 476 496 467 538 483 | 500 N = 10, n = 1000000000, r = 0, s = 3, L = 1000000 | 500 | 492 539 499 512 487 = 0.94 || = 0.25 513 522 478 536 533 | 500 Test on the sum of all N observations | 500 | 469 496 503 496 477 = 0.93 || = 0.24 503 469 525 530 487 | 500 | 500 | 502 483 440 506 516 = 0.92 || = 0.23 515 493 511 537 492 | 500 =================================================================| 500 | 513 525 494 515 497 = 0.91 || = 0.22 522 545 516 485 525 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 502 486 497 520 510 = 0.90 || = 0.21 476 473 484 503 490 | 500 -----------------------------------------------------------------| 500 | 495 536 507 514 519 = 0.89 || = 0.20 460 517 501 515 500 | 500 SD Bern.: d 1.09091 1.29292 0.78778 | 500 | 492 509 496 475 522 = 0.88 || = 0.19 488 518 467 508 470 | 500 s 1.06967 0.71027 1.01440 | 500 | 526 480 517 489 497 = 0.87 || = 0.18 489 519 484 484 536 | 500 t 0.98447 1.24961 0.87564 | 500 | 507 541 503 527 482 = 0.86 || = 0.17 483 468 501 495 525 | 500 m 0.94643 0.94809 1.08957 | 500 | 462 470 507 505 520 = 0.85 || = 0.16 499 511 467 499 513 | 500 x 1.05516 0.93640 1.31518 | 500 | 528 479 521 433 494 = 0.84 || = 0.15 458 515 474 537 503 | 500 | 500 | 514 495 480 467 465 = 0.83 || = 0.14 548 498 514 534 515 | 500 Changes: d 50 5 2 | 500 | 505 510 523 480 456 = 0.82 || = 0.13 489 493 527 486 509 | 500 s 58 2 3 | 500 | 493 453 478 491 520 = 0.81 || = 0.12 492 545 537 500 502 | 500 t 50 4 2 | 500 | 537 497 486 532 508 = 0.80 || = 0.11 485 546 475 512 508 | 500 m 54 4 7 | 500 | 464 468 549 501 490 = 0.79 || = 0.10 530 542 490 499 552 | 500 x 54 4 2 | 500 | 522 499 507 471 502 = 0.78 || = 0.09 528 531 525 459 546 | 500 -----------------------------------------------------------------| 500 | 477 529 530 513 482 = 0.77 || = 0.08 515 493 513 504 484 | 500 Aver./ d 0.50016 499 > 500: 7 2 6 2 5 3 6 5 6 6 | 500 | 475 464 501 500 478 = 0.76 || = 0.07 499 536 466 457 494 | 500 median s 0.49790 499 ----- 4 7 3 4 4 6 3 4 4 4 | 500 | 524 448 495 483 487 = 0.75 || = 0.06 505 500 450 485 513 | 500 t 0.50049 500 6 4 6 5 4 5 5 5 6 3 | 500 | 497 500 498 473 528 = 0.74 || = 0.05 479 500 502 495 453 | 500 m 0.49886 500 4 4 8 5 6 4 2 4 4 6 | 500 | 489 504 498 490 509 = 0.73 || = 0.04 526 473 504 526 510 | 500 x 0.49976 500 4 9 3 5 4 5 5 6 5 4 | 500 | 507 520 501 525 504 = 0.72 || = 0.03 521 518 501 497 453 | 500 -----------------------------------------------------------------| 500 | 537 514 478 500 524 = 0.71 || = 0.02 508 483 479 502 471 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 543 481 518 505 506 = 0.70 || = 0.01 226 254 249 249 230 | 252.5 d 0 1 1 15 63 17 4 0 0 | 500 | 490 500 493 495 515 = 0.69 || < 0.01 531 496 534 513 514 | 497.5 s 0 0 3 16 66 11 5 0 0 | 500 | 479 504 517 493 484 = 0.68 ||========================================================================= t 0 0 2 14 66 18 1 0 0 | 500 | 521 477 522 471 489 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 1 13 70 16 0 0 0 | 500 | 433 529 522 473 520 = 0.66 ||========================================================================= x 0 0 3 13 71 9 4 1 0 | 500 | 506 485 462 478 474 = 0.65 || sstring_HammingWeight2 test: no 211 test no 212 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingWeight2 test: test no 212 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 1 2 | 0.5 | 0 1 2 0 0 > 0.99999 || = 0.64 523 504 500 513 543 | 500 < 0.00002 2 0 0 1 2 | 0.5 | 0 0 0 1 0 > 0.99998 || = 0.63 522 517 474 499 509 | 500 < 0.00003 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 469 466 530 485 481 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 0 1 1 1 0 > 0.99996 || = 0.61 511 470 506 505 493 | 500 < 0.00005 0 1 3 1 0 | 0.5 | 1 1 1 0 1 > 0.99995 || = 0.60 507 463 473 473 491 | 500 < 0.00006 1 1 1 0 0 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 503 485 489 494 460 | 500 < 0.00007 1 0 2 0 0 | 0.5 | 0 0 0 0 1 > 0.99993 || = 0.58 516 473 479 483 498 | 500 < 0.00008 1 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 456 499 494 527 506 | 500 < 0.00009 0 0 1 0 1 | 0.5 | 1 0 0 3 1 > 0.99991 || = 0.56 511 516 469 511 490 | 500 < 0.0001 1 1 0 1 2 | 0.5 | 0 2 0 0 0 > 0.9999 || = 0.55 485 511 477 476 474 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 490 487 521 478 533 | 500 < 0.0001 7 4 8 4 8 | 5 | 3 5 4 5 4 > 0.9999 || = 0.53 496 458 527 500 484 | 500 < 0.0002 2 7 3 5 9 | 5 | 3 3 2 1 1 > 0.9998 || = 0.52 546 481 515 504 503 | 500 < 0.0003 7 6 3 4 7 | 5 | 6 6 4 5 2 > 0.9997 || = 0.51 529 509 479 484 431 | 500 < 0.0004 4 4 7 5 5 | 5 | 7 6 4 2 2 > 0.9996 || = 0.50 484 486 499 474 503 | 500 < 0.0005 4 7 3 1 8 | 5 | 5 6 6 3 4 > 0.9995 || = 0.49 493 487 516 509 494 | 500 < 0.0006 5 4 7 5 4 | 5 | 4 7 5 4 2 > 0.9994 || = 0.48 456 472 499 519 458 | 500 < 0.0007 8 4 6 7 5 | 5 | 4 4 8 6 6 > 0.9993 || = 0.47 515 492 499 481 529 | 500 < 0.0008 6 4 2 4 10 | 5 | 4 4 4 4 6 > 0.9992 || = 0.46 507 508 515 503 493 | 500 < 0.0009 3 7 5 8 1 | 5 | 5 3 3 6 7 > 0.9991 || = 0.45 520 511 508 491 513 | 500 < 0.001 3 5 3 4 3 | 5 | 11 6 3 5 5 > 0.999 || = 0.44 540 492 536 507 509 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 469 494 500 512 508 | 500 < 0.001 49 52 47 47 60 | 50 | 52 50 43 41 39 > 0.999 || = 0.42 469 464 499 477 523 | 500 < 0.002 49 48 49 58 36 | 50 | 40 53 48 39 40 > 0.998 || = 0.41 501 571 519 529 490 | 500 < 0.003 49 52 48 36 64 | 50 | 47 43 54 44 51 > 0.997 || = 0.40 502 539 473 516 493 | 500 < 0.004 48 54 47 48 47 | 50 | 44 55 49 59 55 > 0.996 || = 0.39 504 539 525 490 484 | 500 < 0.005 47 44 56 54 59 | 50 | 46 59 48 43 51 > 0.995 || = 0.38 513 479 500 506 491 | 500 < 0.006 56 59 53 44 62 | 50 | 43 53 45 42 65 > 0.994 || = 0.37 488 496 494 551 523 | 500 < 0.007 49 56 55 62 47 | 50 | 49 61 47 42 45 > 0.993 || = 0.36 517 500 481 497 512 | 500 < 0.008 51 48 38 60 40 | 50 | 49 51 44 51 60 > 0.992 || = 0.35 482 512 498 514 504 | 500 < 0.009 49 49 61 47 40 | 50 | 57 44 50 53 49 > 0.991 || = 0.34 496 538 544 513 511 | 500 < 0.01 54 53 47 53 45 | 50 | 52 40 48 47 34 > 0.99 || = 0.33 508 518 505 496 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 488 508 508 510 579 | 500 < 0.01 501 515 501 509 500 | 497.5 | 479 509 476 461 489 > 0.99 || = 0.31 498 496 507 483 515 | 500 = 0.01 258 238 252 238 263 | 252.5 | 233 239 251 241 274 = 0.99 || = 0.30 527 453 483 487 505 | 500 = 0.02 498 493 514 524 476 | 500 | 498 479 477 446 516 = 0.98 || = 0.29 496 519 484 536 494 | 500 =================================================================| 500 | 502 527 479 480 507 = 0.97 || = 0.28 485 527 491 486 509 | 500 sstring_HammingWeight2 test: | 500 | 506 484 496 486 516 = 0.96 || = 0.27 479 538 503 509 516 | 500 ----------------------------------------------- | 500 | 489 497 525 493 473 = 0.95 || = 0.26 470 509 496 535 471 | 500 N = 10, n = 1000000000, r = 27, s = 3, L = 1000000 | 500 | 461 514 512 527 481 = 0.94 || = 0.25 492 495 488 478 530 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 518 487 501 526 484 = 0.93 || = 0.24 519 539 501 492 516 | 500 | 500 | 532 523 498 511 499 = 0.92 || = 0.23 476 478 511 532 474 | 500 =================================================================| 500 | 524 519 510 514 485 = 0.91 || = 0.22 507 524 481 467 465 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 493 483 506 490 500 = 0.90 || = 0.21 511 490 517 495 524 | 500 -----------------------------------------------------------------| 500 | 488 483 484 528 507 = 0.89 || = 0.20 508 540 476 462 510 | 500 SD Bern.: d 0.98031 0.37700 0.73383 | 500 | 508 494 473 490 488 = 0.88 || = 0.19 492 526 514 544 507 | 500 s 1.03109 0.62480 0.92889 | 500 | 482 502 517 513 490 = 0.87 || = 0.18 481 518 499 515 487 | 500 t 0.77985 0.85716 0.54431 | 500 | 478 490 495 481 498 = 0.86 || = 0.17 502 494 489 514 493 | 500 m 0.96831 1.08405 1.01538 | 500 | 515 461 505 465 520 = 0.85 || = 0.16 494 512 505 526 494 | 500 x 0.97499 1.38632 1.30831 | 500 | 511 486 507 532 532 = 0.84 || = 0.15 506 487 502 467 503 | 500 | 500 | 488 522 476 481 515 = 0.83 || = 0.14 502 486 527 471 489 | 500 Changes: d 45 5 2 | 500 | 473 479 500 505 495 = 0.82 || = 0.13 492 503 464 462 523 | 500 s 50 6 4 | 500 | 522 535 506 495 458 = 0.81 || = 0.12 505 475 531 518 496 | 500 t 51 4 2 | 500 | 515 477 517 486 536 = 0.80 || = 0.11 490 531 502 510 497 | 500 m 53 7 4 | 500 | 539 505 503 490 506 = 0.79 || = 0.10 455 509 520 525 523 | 500 x 49 5 4 | 500 | 522 482 470 494 491 = 0.78 || = 0.09 467 488 490 517 495 | 500 -----------------------------------------------------------------| 500 | 539 459 512 516 543 = 0.77 || = 0.08 458 474 515 457 505 | 500 Aver./ d 0.50279 502 > 500: 4 4 4 5 6 6 8 8 4 5 | 500 | 505 530 481 485 498 = 0.76 || = 0.07 488 467 528 514 492 | 500 median s 0.49795 496 ----- 4 6 7 5 4 3 4 5 3 5 | 500 | 511 486 481 490 454 = 0.75 || = 0.06 511 524 477 514 532 | 500 t 0.49890 500 5 7 4 5 5 3 5 6 5 4 | 500 | 487 483 488 493 499 = 0.74 || = 0.05 502 506 513 507 456 | 500 m 0.49818 499 7 7 4 5 7 3 6 2 4 4 | 500 | 513 510 531 479 495 = 0.73 || = 0.04 466 497 493 479 501 | 500 x 0.49975 499 5 4 6 7 5 3 6 3 4 4 | 500 | 480 537 503 489 484 = 0.72 || = 0.03 470 542 483 536 484 | 500 -----------------------------------------------------------------| 500 | 559 517 506 520 472 = 0.71 || = 0.02 498 493 514 524 476 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 512 502 530 519 527 = 0.70 || = 0.01 258 238 252 238 263 | 252.5 d 0 0 1 14 74 9 3 0 0 | 500 | 533 522 475 523 515 = 0.69 || < 0.01 501 515 501 509 500 | 497.5 s 0 0 1 13 69 17 0 1 0 | 500 | 503 491 507 493 509 = 0.68 ||========================================================================= t 0 0 0 13 77 11 0 0 0 | 500 | 481 484 482 531 495 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 13 70 16 1 0 0 | 500 | 519 486 519 469 486 = 0.66 ||========================================================================= x 0 1 1 11 72 15 0 1 0 | 500 | 560 478 493 522 509 = 0.65 || sstring_HammingWeight2 test: no 212 test no 213 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingWeight2 test: test no 213 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 1 0 | 0.5 | 0 1 0 0 0 > 0.99999 || = 0.64 496 500 478 500 553 | 500 < 0.00002 0 0 0 0 1 | 0.5 | 0 0 1 1 0 > 0.99998 || = 0.63 508 504 479 474 499 | 500 < 0.00003 0 1 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 475 546 512 527 459 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 501 512 478 501 503 | 500 < 0.00005 1 0 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99995 || = 0.60 518 510 486 479 498 | 500 < 0.00006 2 2 1 3 3 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 497 527 451 488 469 | 500 < 0.00007 0 0 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 512 506 484 476 531 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99992 || = 0.57 538 506 485 531 545 | 500 < 0.00009 0 0 1 0 0 | 0.5 | 0 1 1 0 0 > 0.99991 || = 0.56 522 513 501 448 486 | 500 < 0.0001 0 2 0 0 2 | 0.5 | 0 0 2 0 1 > 0.9999 || = 0.55 505 461 533 512 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 511 522 462 505 502 | 500 < 0.0001 4 6 4 7 7 | 5 | 2 2 5 2 2 > 0.9999 || = 0.53 503 492 493 485 466 | 500 < 0.0002 9 5 8 8 3 | 5 | 4 1 1 1 1 > 0.9998 || = 0.52 517 502 513 463 504 | 500 < 0.0003 4 5 4 5 4 | 5 | 7 5 5 3 3 > 0.9997 || = 0.51 556 479 522 511 528 | 500 < 0.0004 8 5 10 5 5 | 5 | 5 1 7 8 6 > 0.9996 || = 0.50 512 477 489 512 476 | 500 < 0.0005 6 9 6 6 5 | 5 | 6 4 5 1 2 > 0.9995 || = 0.49 507 476 477 502 469 | 500 < 0.0006 7 5 4 5 2 | 5 | 7 5 8 3 5 > 0.9994 || = 0.48 529 525 542 526 517 | 500 < 0.0007 4 4 5 8 1 | 5 | 4 2 6 9 7 > 0.9993 || = 0.47 516 504 483 511 510 | 500 < 0.0008 3 5 7 6 5 | 5 | 3 4 3 3 4 > 0.9992 || = 0.46 511 513 480 500 474 | 500 < 0.0009 5 6 7 6 2 | 5 | 4 7 3 10 5 > 0.9991 || = 0.45 472 487 519 481 499 | 500 < 0.001 5 5 6 4 6 | 5 | 2 5 4 6 2 > 0.999 || = 0.44 473 483 490 505 452 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 501 523 510 538 471 | 500 < 0.001 55 55 61 60 40 | 50 | 44 36 47 46 37 > 0.999 || = 0.42 523 495 503 518 471 | 500 < 0.002 49 46 51 53 51 | 50 | 43 55 46 59 53 > 0.998 || = 0.41 477 458 547 484 475 | 500 < 0.003 46 54 50 50 48 | 50 | 46 52 60 53 45 > 0.997 || = 0.40 514 504 573 517 464 | 500 < 0.004 57 58 51 36 38 | 50 | 44 45 49 57 54 > 0.996 || = 0.39 508 511 517 487 500 | 500 < 0.005 52 43 52 40 58 | 50 | 46 57 42 45 46 > 0.995 || = 0.38 503 494 511 513 525 | 500 < 0.006 51 50 52 51 58 | 50 | 55 46 63 61 56 > 0.994 || = 0.37 485 527 514 525 478 | 500 < 0.007 56 51 44 41 51 | 50 | 41 49 41 45 53 > 0.993 || = 0.36 467 500 513 511 509 | 500 < 0.008 54 52 43 62 47 | 50 | 54 46 51 56 52 > 0.992 || = 0.35 471 451 519 513 507 | 500 < 0.009 41 37 46 61 66 | 50 | 41 49 47 39 45 > 0.991 || = 0.34 475 531 528 502 512 | 500 < 0.01 46 48 51 53 51 | 50 | 50 46 50 69 55 > 0.99 || = 0.33 504 511 490 497 514 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 489 549 468 518 500 | 500 < 0.01 507 494 501 507 508 | 497.5 | 464 481 496 530 496 > 0.99 || = 0.31 524 536 486 453 529 | 500 = 0.01 236 246 234 255 265 | 252.5 | 252 260 272 253 248 = 0.99 || = 0.30 503 503 500 482 463 | 500 = 0.02 499 519 474 484 510 | 500 | 473 487 527 503 521 = 0.98 || = 0.29 529 503 520 463 486 | 500 =================================================================| 500 | 469 507 521 503 489 = 0.97 || = 0.28 476 515 502 509 494 | 500 sstring_HammingWeight2 test: | 500 | 557 510 505 478 534 = 0.96 || = 0.27 515 464 525 500 559 | 500 ----------------------------------------------- | 500 | 484 492 528 515 501 = 0.95 || = 0.26 497 503 466 500 495 | 500 N = 10, n = 1000000000, r = 27, s = 3, L = 1000000 | 500 | 477 532 507 506 497 = 0.94 || = 0.25 522 471 501 501 509 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 503 500 515 473 513 = 0.93 || = 0.24 480 520 540 487 515 | 500 | 500 | 486 489 507 481 549 = 0.92 || = 0.23 452 493 505 488 497 | 500 =================================================================| 500 | 506 497 457 491 481 = 0.91 || = 0.22 502 474 500 503 514 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 510 490 502 465 495 = 0.90 || = 0.21 504 521 511 465 488 | 500 -----------------------------------------------------------------| 500 | 494 516 507 509 465 = 0.89 || = 0.20 456 459 523 503 536 | 500 SD Bern.: d 0.94904 0.70034 0.84420 | 500 | 499 501 508 481 538 = 0.88 || = 0.19 547 485 493 507 490 | 500 s 0.89302 0.83467 0.83587 | 500 | 443 525 510 503 472 = 0.87 || = 0.18 512 527 489 491 458 | 500 t 1.01060 0.68297 0.94914 | 500 | 504 507 494 507 504 = 0.86 || = 0.17 528 510 485 529 488 | 500 m 0.99798 1.23430 1.29987 | 500 | 470 504 491 557 494 = 0.85 || = 0.16 488 492 485 527 499 | 500 x 1.11763 1.13546 0.81771 | 500 | 497 513 454 483 500 = 0.84 || = 0.15 529 496 520 481 492 | 500 | 500 | 475 498 492 520 473 = 0.83 || = 0.14 484 481 476 467 503 | 500 Changes: d 51 3 4 | 500 | 508 499 541 517 500 = 0.82 || = 0.13 485 502 513 497 473 | 500 s 56 5 4 | 500 | 495 520 485 475 509 = 0.81 || = 0.12 502 497 476 502 476 | 500 t 41 4 6 | 500 | 510 475 477 467 501 = 0.80 || = 0.11 496 506 521 512 535 | 500 m 50 4 7 | 500 | 488 506 509 489 524 = 0.79 || = 0.10 528 481 469 474 467 | 500 x 49 5 7 | 500 | 521 478 476 481 491 = 0.78 || = 0.09 502 510 499 498 470 | 500 -----------------------------------------------------------------| 500 | 526 505 516 523 458 = 0.77 || = 0.08 515 485 500 513 527 | 500 Aver./ d 0.49835 502 > 500: 6 6 5 5 7 9 5 5 3 3 | 500 | 505 505 515 492 510 = 0.76 || = 0.07 520 513 513 517 507 | 500 median s 0.50173 502 ----- 3 4 5 7 5 7 6 6 7 4 | 500 | 479 508 532 519 508 = 0.75 || = 0.06 516 500 503 506 516 | 500 t 0.50134 501 3 3 8 6 6 4 3 5 5 8 | 500 | 506 524 508 474 467 = 0.74 || = 0.05 492 482 481 471 535 | 500 m 0.50085 502 5 5 4 6 7 4 7 5 6 6 | 500 | 479 468 486 512 515 = 0.73 || = 0.04 502 443 456 495 486 | 500 x 0.50007 500 8 2 5 6 2 5 6 7 3 5 | 500 | 481 502 475 530 534 = 0.72 || = 0.03 491 466 462 488 536 | 500 -----------------------------------------------------------------| 500 | 483 489 484 571 510 = 0.71 || = 0.02 499 519 474 484 510 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 497 484 493 457 504 = 0.70 || = 0.01 236 246 234 255 265 | 252.5 d 0 0 2 16 70 10 3 0 0 | 500 | 492 529 530 518 512 = 0.69 || < 0.01 507 494 501 507 508 | 497.5 s 0 0 2 11 75 11 2 0 0 | 500 | 526 493 500 503 565 = 0.68 ||========================================================================= t 0 0 2 15 69 13 1 1 0 | 500 | 480 509 485 505 526 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 14 72 10 2 1 0 | 500 | 522 489 528 512 449 = 0.66 ||========================================================================= x 0 0 2 22 58 14 5 0 0 | 500 | 504 512 488 562 470 = 0.65 || sstring_HammingWeight2 test: no 213 test no 214 TestU01 250000 runs BigCrush Test smarsa_S string_HammingWeight2 test: test no 214 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 498 516 498 488 509 | 500 < 0.00002 2 0 2 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 536 518 519 547 529 | 500 < 0.00003 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 498 513 510 495 510 | 500 < 0.00004 1 0 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 509 512 515 502 493 | 500 < 0.00005 0 0 1 1 1 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 475 523 503 500 499 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 503 522 508 499 511 | 500 < 0.00007 0 1 1 1 1 | 0.5 | 0 1 0 0 1 > 0.99993 || = 0.58 501 562 548 514 532 | 500 < 0.00008 1 0 0 2 0 | 0.5 | 0 0 1 0 0 > 0.99992 || = 0.57 474 483 459 501 502 | 500 < 0.00009 0 1 1 1 1 | 0.5 | 1 0 1 0 0 > 0.99991 || = 0.56 470 499 537 520 463 | 500 < 0.0001 1 0 1 1 1 | 0.5 | 0 0 0 0 1 > 0.9999 || = 0.55 502 513 491 444 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 513 460 503 435 509 | 500 < 0.0001 7 2 6 8 6 | 5 | 1 1 3 0 2 > 0.9999 || = 0.53 510 517 541 498 475 | 500 < 0.0002 3 5 5 9 7 | 5 | 1 1 2 2 0 > 0.9998 || = 0.52 466 474 490 508 514 | 500 < 0.0003 5 4 3 9 5 | 5 | 1 2 3 6 2 > 0.9997 || = 0.51 518 468 516 502 510 | 500 < 0.0004 2 6 6 7 3 | 5 | 3 7 1 3 3 > 0.9996 || = 0.50 480 503 466 505 470 | 500 < 0.0005 5 4 7 5 9 | 5 | 2 2 2 2 3 > 0.9995 || = 0.49 483 502 492 506 506 | 500 < 0.0006 3 7 8 1 5 | 5 | 5 7 3 2 6 > 0.9994 || = 0.48 488 487 475 514 499 | 500 < 0.0007 4 7 5 0 3 | 5 | 3 4 3 6 8 > 0.9993 || = 0.47 488 494 530 487 476 | 500 < 0.0008 2 4 6 8 3 | 5 | 2 4 2 5 4 > 0.9992 || = 0.46 506 513 534 520 519 | 500 < 0.0009 6 7 6 5 7 | 5 | 0 4 2 4 8 > 0.9991 || = 0.45 478 564 491 529 497 | 500 < 0.001 5 8 7 4 9 | 5 | 7 4 5 6 6 > 0.999 || = 0.44 502 507 447 512 484 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 566 495 508 477 521 | 500 < 0.001 42 54 59 56 57 | 50 | 25 36 26 36 42 > 0.999 || = 0.42 516 490 506 484 554 | 500 < 0.002 58 52 55 55 36 | 50 | 37 39 39 39 52 > 0.998 || = 0.41 523 510 493 502 484 | 500 < 0.003 53 60 59 65 57 | 50 | 49 45 45 43 50 > 0.997 || = 0.40 466 470 516 493 473 | 500 < 0.004 61 54 51 42 47 | 50 | 38 43 55 46 39 > 0.996 || = 0.39 476 499 483 493 471 | 500 < 0.005 40 57 40 35 59 | 50 | 35 40 52 42 53 > 0.995 || = 0.38 491 490 499 526 486 | 500 < 0.006 52 39 49 44 61 | 50 | 43 41 41 39 41 > 0.994 || = 0.37 503 523 488 532 525 | 500 < 0.007 42 56 47 54 46 | 50 | 43 42 63 42 53 > 0.993 || = 0.36 500 521 471 445 508 | 500 < 0.008 36 52 45 46 43 | 50 | 50 55 40 56 56 > 0.992 || = 0.35 536 499 520 502 528 | 500 < 0.009 55 54 42 53 45 | 50 | 54 58 40 59 62 > 0.991 || = 0.34 491 467 567 514 481 | 500 < 0.01 47 40 53 47 54 | 50 | 61 53 49 47 57 > 0.99 || = 0.33 483 491 485 505 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 507 512 520 526 477 | 500 < 0.01 486 518 500 497 505 | 497.5 | 435 452 450 449 505 > 0.99 || = 0.31 483 487 500 509 503 | 500 = 0.01 254 251 266 275 272 | 252.5 | 286 234 278 253 240 = 0.99 || = 0.30 512 517 510 495 526 | 500 = 0.02 497 497 503 503 488 | 500 | 577 514 447 536 543 = 0.98 || = 0.29 481 517 523 502 505 | 500 =================================================================| 500 | 533 507 497 510 518 = 0.97 || = 0.28 529 503 490 471 518 | 500 string_HammingWeight2 test: | 500 | 491 508 528 530 470 = 0.96 || = 0.27 484 489 508 477 506 | 500 ----------------------------------------------- | 500 | 487 479 471 515 456 = 0.95 || = 0.26 526 476 502 480 510 | 500 N = 10, n = 1000000000, r = 27, s = 3, L = 1000000 | 500 | 494 508 489 497 473 = 0.94 || = 0.25 477 507 489 476 463 | 500 Anderson-Darling statistic = A2 | 500 | 585 517 477 493 487 = 0.93 || = 0.24 467 491 471 467 495 | 500 | 500 | 515 507 525 502 496 = 0.92 || = 0.23 506 505 470 506 516 | 500 =================================================================| 500 | 500 518 519 491 499 = 0.91 || = 0.22 491 479 518 519 541 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 518 507 511 533 480 = 0.90 || = 0.21 505 485 502 535 475 | 500 -----------------------------------------------------------------| 500 | 477 530 493 485 495 = 0.89 || = 0.20 489 498 525 541 511 | 500 SD Bern.: d 1.18204 1.14599 1.67355 | 500 | 472 488 491 505 539 = 0.88 || = 0.19 482 481 487 508 491 | 500 s 1.02375 0.96172 1.21220 | 500 | 529 494 533 506 532 = 0.87 || = 0.18 470 472 483 530 495 | 500 t 0.99126 0.89038 1.55125 | 500 | 472 489 510 540 477 = 0.86 || = 0.17 465 460 473 466 507 | 500 m 1.03681 1.15035 1.23105 | 500 | 507 462 486 488 451 = 0.85 || = 0.16 540 504 514 499 481 | 500 x 0.92479 1.10598 1.01735 | 500 | 494 493 491 488 517 = 0.84 || = 0.15 483 497 474 495 506 | 500 | 500 | 490 533 489 513 518 = 0.83 || = 0.14 495 517 482 528 527 | 500 Changes: d 66 6 1 | 500 | 505 483 523 494 503 = 0.82 || = 0.13 516 468 477 528 496 | 500 s 49 3 1 | 500 | 475 490 471 490 475 = 0.81 || = 0.12 491 467 536 481 505 | 500 t 49 2 4 | 500 | 493 539 496 510 481 = 0.80 || = 0.11 477 533 494 485 506 | 500 m 49 5 2 | 500 | 578 498 469 487 492 = 0.79 || = 0.10 474 498 500 497 520 | 500 x 48 6 5 | 500 | 524 466 516 483 480 = 0.78 || = 0.09 504 512 491 519 501 | 500 -----------------------------------------------------------------| 500 | 496 464 503 484 527 = 0.77 || = 0.08 491 462 476 503 495 | 500 Aver./ d 0.50251 497 > 500: 5 2 4 4 5 6 3 5 4 5 | 500 | 508 515 536 559 512 = 0.76 || = 0.07 509 492 534 513 537 | 500 median s 0.50146 499 ----- 5 3 4 4 5 5 8 4 3 7 | 500 | 469 484 509 489 484 = 0.75 || = 0.06 497 452 490 447 507 | 500 t 0.49997 500 5 2 6 4 5 7 5 7 4 4 | 500 | 536 525 501 492 477 = 0.74 || = 0.05 534 511 491 522 515 | 500 m 0.50008 502 7 4 5 7 6 5 4 4 5 6 | 500 | 479 566 485 506 490 = 0.73 || = 0.04 460 515 488 506 500 | 500 x 0.49807 502 6 6 7 6 4 7 5 3 5 3 | 500 | 556 484 507 503 508 = 0.72 || = 0.03 519 515 507 464 476 | 500 -----------------------------------------------------------------| 500 | 497 498 509 487 472 = 0.71 || = 0.02 497 497 503 503 488 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 492 534 485 474 507 = 0.70 || = 0.01 254 251 266 275 272 | 252.5 d 0 0 1 19 63 12 3 3 0 | 500 | 499 510 497 503 490 = 0.69 || < 0.01 486 518 500 497 505 | 497.5 s 0 0 2 15 72 9 3 0 0 | 500 | 457 478 517 462 497 = 0.68 ||========================================================================= t 0 0 3 14 68 14 1 1 0 | 500 | 498 533 493 518 502 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 5 10 70 14 2 0 0 | 500 | 495 494 491 456 498 = 0.66 ||========================================================================= x 0 0 1 18 68 13 1 0 0 | 500 | 531 506 504 500 472 = 0.65 || string_HammingWeight2 test: no 214 test no 215 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingWeight2 test: test no 215 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 0 0 | 0.5 | 1 0 0 1 1 > 0.99999 || = 0.64 488 485 484 523 467 | 500 < 0.00002 0 0 0 1 1 | 0.5 | 1 0 0 1 0 > 0.99998 || = 0.63 471 497 485 534 474 | 500 < 0.00003 1 0 0 1 0 | 0.5 | 0 1 2 0 0 > 0.99997 || = 0.62 512 529 476 514 504 | 500 < 0.00004 3 0 2 0 0 | 0.5 | 0 1 2 0 0 > 0.99996 || = 0.61 464 492 542 502 481 | 500 < 0.00005 0 1 0 2 1 | 0.5 | 0 1 2 2 1 > 0.99995 || = 0.60 490 448 517 520 478 | 500 < 0.00006 0 1 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99994 || = 0.59 452 495 534 482 525 | 500 < 0.00007 2 0 1 1 1 | 0.5 | 1 0 0 2 1 > 0.99993 || = 0.58 518 517 464 507 523 | 500 < 0.00008 1 1 0 0 1 | 0.5 | 0 1 1 0 0 > 0.99992 || = 0.57 502 487 507 509 483 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 0 1 1 1 0 > 0.99991 || = 0.56 470 459 483 542 520 | 500 < 0.0001 0 1 0 1 2 | 0.5 | 0 1 0 0 0 > 0.9999 || = 0.55 536 545 523 503 482 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 568 518 524 465 527 | 500 < 0.0001 8 4 4 8 6 | 5 | 3 6 8 7 4 > 0.9999 || = 0.53 507 498 542 490 453 | 500 < 0.0002 5 6 5 5 6 | 5 | 1 0 2 1 5 > 0.9998 || = 0.52 502 511 473 524 504 | 500 < 0.0003 2 4 7 5 3 | 5 | 4 2 7 1 5 > 0.9997 || = 0.51 516 518 495 490 526 | 500 < 0.0004 3 7 5 4 6 | 5 | 8 4 3 6 5 > 0.9996 || = 0.50 502 468 496 494 485 | 500 < 0.0005 2 6 9 6 5 | 5 | 10 5 4 7 5 > 0.9995 || = 0.49 528 485 489 528 463 | 500 < 0.0006 7 4 5 9 4 | 5 | 5 8 8 6 5 > 0.9994 || = 0.48 495 497 514 497 471 | 500 < 0.0007 4 1 4 7 3 | 5 | 3 12 7 3 3 > 0.9993 || = 0.47 511 520 463 485 486 | 500 < 0.0008 3 5 3 7 5 | 5 | 2 4 1 6 3 > 0.9992 || = 0.46 516 522 523 491 494 | 500 < 0.0009 4 3 5 6 1 | 5 | 4 6 4 8 8 > 0.9991 || = 0.45 515 512 460 503 474 | 500 < 0.001 6 5 8 8 5 | 5 | 10 4 3 6 4 > 0.999 || = 0.44 479 494 465 503 501 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 544 495 501 493 503 | 500 < 0.001 44 45 55 65 44 | 50 | 50 51 47 51 47 > 0.999 || = 0.42 511 493 475 473 533 | 500 < 0.002 51 50 47 41 42 | 50 | 49 57 53 51 62 > 0.998 || = 0.41 495 520 474 472 507 | 500 < 0.003 42 62 56 51 63 | 50 | 44 49 40 57 41 > 0.997 || = 0.40 495 517 460 489 500 | 500 < 0.004 46 54 43 53 46 | 50 | 57 49 62 45 56 > 0.996 || = 0.39 492 495 495 507 506 | 500 < 0.005 43 60 54 51 48 | 50 | 46 57 44 58 50 > 0.995 || = 0.38 491 493 506 506 519 | 500 < 0.006 53 44 54 41 46 | 50 | 59 50 66 51 54 > 0.994 || = 0.37 477 525 509 501 502 | 500 < 0.007 53 48 54 37 50 | 50 | 43 57 44 53 66 > 0.993 || = 0.36 482 496 510 536 521 | 500 < 0.008 33 37 41 41 51 | 50 | 46 48 58 47 50 > 0.992 || = 0.35 480 529 534 519 461 | 500 < 0.009 46 40 52 52 60 | 50 | 49 49 51 58 48 > 0.991 || = 0.34 511 502 482 476 500 | 500 < 0.01 58 51 41 53 54 | 50 | 51 49 46 52 44 > 0.99 || = 0.33 531 512 524 506 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 524 517 514 517 492 | 500 < 0.01 469 491 497 485 504 | 497.5 | 494 516 511 523 518 > 0.99 || = 0.31 488 519 491 508 497 | 500 = 0.01 259 266 241 262 250 | 252.5 | 259 261 252 241 239 = 0.99 || = 0.30 469 502 506 475 488 | 500 = 0.02 532 520 513 472 514 | 500 | 480 461 537 534 474 = 0.98 || = 0.29 517 466 481 496 462 | 500 =================================================================| 500 | 458 482 493 494 528 = 0.97 || = 0.28 499 507 491 480 493 | 500 sstring_HammingWeight2 test: | 500 | 483 522 496 500 511 = 0.96 || = 0.27 536 508 526 517 518 | 500 ----------------------------------------------- | 500 | 485 525 517 503 502 = 0.95 || = 0.26 491 518 510 452 486 | 500 N = 10, n = 1000000000, r = 27, s = 3, L = 1000000 | 500 | 497 472 509 507 504 = 0.94 || = 0.25 547 481 550 476 539 | 500 Test on the sum of all N observations | 500 | 510 498 477 494 473 = 0.93 || = 0.24 534 495 490 489 450 | 500 | 500 | 492 519 552 479 512 = 0.92 || = 0.23 487 500 506 520 479 | 500 =================================================================| 500 | 464 484 487 461 510 = 0.91 || = 0.22 518 460 475 490 547 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 494 522 530 516 542 = 0.90 || = 0.21 488 482 504 484 469 | 500 -----------------------------------------------------------------| 500 | 475 502 479 483 510 = 0.89 || = 0.20 520 502 479 513 558 | 500 SD Bern.: d 1.09423 1.05218 0.70744 | 500 | 513 495 511 497 498 = 0.88 || = 0.19 510 492 473 481 501 | 500 s 0.96885 1.09141 0.55883 | 500 | 501 465 523 491 484 = 0.87 || = 0.18 501 529 505 507 464 | 500 t 1.07974 0.81649 1.15901 | 500 | 469 546 457 508 525 = 0.86 || = 0.17 498 484 494 507 479 | 500 m 0.83612 1.15035 0.67412 | 500 | 529 489 494 492 460 = 0.85 || = 0.16 520 535 519 526 474 | 500 x 1.04007 0.91915 1.07942 | 500 | 505 513 531 487 537 = 0.84 || = 0.15 506 464 533 503 499 | 500 | 500 | 502 483 498 503 500 = 0.83 || = 0.14 442 510 505 496 517 | 500 Changes: d 46 5 5 | 500 | 514 502 476 514 520 = 0.82 || = 0.13 513 500 490 503 513 | 500 s 53 3 5 | 500 | 554 461 496 501 480 = 0.81 || = 0.12 480 475 493 466 503 | 500 t 55 7 8 | 500 | 489 503 504 512 504 = 0.80 || = 0.11 479 514 489 498 529 | 500 m 45 4 4 | 500 | 493 526 501 518 501 = 0.79 || = 0.10 542 475 509 512 543 | 500 x 48 3 6 | 500 | 457 516 470 510 497 = 0.78 || = 0.09 506 499 461 495 505 | 500 -----------------------------------------------------------------| 500 | 473 511 481 477 468 = 0.77 || = 0.08 523 453 450 485 485 | 500 Aver./ d 0.49754 501 > 500: 8 6 6 3 6 7 4 3 7 2 | 500 | 505 522 539 482 477 = 0.76 || = 0.07 503 504 552 529 514 | 500 median s 0.50140 502 ----- 4 4 4 7 5 5 5 8 5 5 | 500 | 574 529 479 519 499 = 0.75 || = 0.06 470 458 531 510 534 | 500 t 0.50136 498 3 5 5 7 3 6 5 3 4 5 | 500 | 466 513 486 520 490 = 0.74 || = 0.05 517 507 449 484 504 | 500 m 0.50142 501 3 6 3 8 3 6 8 6 5 4 | 500 | 457 448 480 498 475 = 0.73 || = 0.04 501 479 500 493 486 | 500 x 0.49969 501 6 6 4 5 4 6 5 3 5 7 | 500 | 507 518 499 474 467 = 0.72 || = 0.03 505 475 484 476 480 | 500 -----------------------------------------------------------------| 500 | 468 495 494 516 524 = 0.71 || = 0.02 532 520 513 472 514 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 483 493 554 491 507 = 0.70 || = 0.01 259 266 241 262 250 | 252.5 d 0 0 2 16 68 11 2 2 0 | 500 | 510 502 538 477 500 = 0.69 || < 0.01 469 491 497 485 504 | 497.5 s 0 0 3 13 74 9 2 0 0 | 500 | 488 515 502 532 537 = 0.68 ||========================================================================= t 0 0 2 16 62 17 4 0 0 | 500 | 495 515 487 505 520 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 13 75 12 0 0 0 | 500 | 509 525 521 507 533 = 0.66 ||========================================================================= x 0 0 2 17 63 17 2 0 0 | 500 | 503 490 499 543 497 = 0.65 || sstring_HammingWeight2 test: no 215 test no 216 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingCorr test: test no 216 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 1 2 | 0.5 | 2 0 3 2 0 > 0.99999 || = 0.64 489 476 525 503 485 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 2 0 0 0 1 > 0.99998 || = 0.63 454 487 509 527 486 | 500 < 0.00003 0 1 2 0 1 | 0.5 | 1 0 1 0 0 > 0.99997 || = 0.62 508 487 519 507 500 | 500 < 0.00004 1 0 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99996 || = 0.61 481 486 489 485 489 | 500 < 0.00005 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 516 477 476 510 524 | 500 < 0.00006 0 0 0 0 2 | 0.5 | 3 0 0 0 0 > 0.99994 || = 0.59 539 532 473 505 497 | 500 < 0.00007 0 0 1 0 1 | 0.5 | 1 1 1 0 2 > 0.99993 || = 0.58 460 507 486 497 508 | 500 < 0.00008 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 478 474 516 525 474 | 500 < 0.00009 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 524 487 510 505 504 | 500 < 0.0001 0 0 1 0 1 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 498 479 468 520 516 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 522 497 453 522 504 | 500 < 0.0001 2 3 5 1 7 | 5 | 9 1 7 2 4 > 0.9999 || = 0.53 497 510 498 535 534 | 500 < 0.0002 5 5 2 3 7 | 5 | 1 5 1 3 3 > 0.9998 || = 0.52 492 532 473 517 482 | 500 < 0.0003 7 8 4 3 9 | 5 | 3 7 3 4 8 > 0.9997 || = 0.51 493 511 502 497 511 | 500 < 0.0004 6 7 5 3 11 | 5 | 6 7 6 2 3 > 0.9996 || = 0.50 472 496 512 471 506 | 500 < 0.0005 4 4 6 2 3 | 5 | 4 4 2 4 11 > 0.9995 || = 0.49 502 513 482 485 510 | 500 < 0.0006 4 8 7 8 4 | 5 | 5 9 5 5 3 > 0.9994 || = 0.48 508 531 503 530 533 | 500 < 0.0007 4 4 1 7 7 | 5 | 1 7 7 5 6 > 0.9993 || = 0.47 486 500 465 493 515 | 500 < 0.0008 8 7 5 8 3 | 5 | 9 4 7 10 8 > 0.9992 || = 0.46 480 549 498 488 495 | 500 < 0.0009 3 4 6 3 5 | 5 | 4 9 4 3 3 > 0.9991 || = 0.45 470 504 510 488 526 | 500 < 0.001 4 8 4 4 4 | 5 | 5 4 4 7 4 > 0.999 || = 0.44 494 503 505 535 462 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 536 527 506 475 491 | 500 < 0.001 47 58 45 42 60 | 50 | 47 57 46 45 53 > 0.999 || = 0.42 460 549 490 484 491 | 500 < 0.002 59 52 51 49 46 | 50 | 54 47 71 53 55 > 0.998 || = 0.41 534 529 476 491 502 | 500 < 0.003 54 47 48 48 43 | 50 | 58 44 50 51 39 > 0.997 || = 0.40 495 487 513 528 475 | 500 < 0.004 47 45 43 56 48 | 50 | 49 53 55 50 39 > 0.996 || = 0.39 512 484 483 498 515 | 500 < 0.005 55 58 39 49 43 | 50 | 47 50 57 48 58 > 0.995 || = 0.38 487 517 496 524 478 | 500 < 0.006 48 49 49 45 52 | 50 | 50 43 48 39 54 > 0.994 || = 0.37 507 515 539 479 522 | 500 < 0.007 32 54 54 43 40 | 50 | 54 53 46 54 47 > 0.993 || = 0.36 485 492 455 513 482 | 500 < 0.008 55 52 45 55 35 | 50 | 49 61 52 56 50 > 0.992 || = 0.35 537 535 515 472 502 | 500 < 0.009 52 48 51 42 44 | 50 | 54 64 53 43 67 > 0.991 || = 0.34 490 487 473 521 468 | 500 < 0.01 45 52 39 47 39 | 50 | 51 56 51 37 39 > 0.99 || = 0.33 502 517 521 469 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 516 441 507 512 521 | 500 < 0.01 494 515 464 476 450 | 497.5 | 513 528 529 476 501 > 0.99 || = 0.31 515 453 493 494 513 | 500 = 0.01 231 264 268 242 252 | 252.5 | 255 255 257 263 251 = 0.99 || = 0.30 534 482 506 522 516 | 500 = 0.02 513 509 507 498 548 | 500 | 504 526 480 472 507 = 0.98 || = 0.29 492 532 524 504 501 | 500 =================================================================| 500 | 497 492 495 493 524 = 0.97 || = 0.28 493 514 473 500 489 | 500 sstring_HammingCorr test: | 500 | 473 497 496 459 499 = 0.96 || = 0.27 487 445 481 523 500 | 500 ----------------------------------------------- | 500 | 527 494 498 526 479 = 0.95 || = 0.26 496 471 506 471 509 | 500 N = 1, n = 1000000000, r = 10, s = 10, L = 30 | 500 | 524 518 464 456 454 = 0.94 || = 0.25 497 488 473 504 483 | 500 Normal statistic | 500 | 512 474 518 491 502 = 0.93 || = 0.24 494 489 514 500 481 | 500 | 500 | 487 511 494 520 543 = 0.92 || = 0.23 526 511 522 487 487 | 500 =================================================================| 500 | 508 513 494 523 493 = 0.91 || = 0.22 508 506 506 511 507 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 475 520 536 490 536 = 0.90 || = 0.21 465 515 484 487 537 | 500 -----------------------------------------------------------------| 500 | 478 503 521 501 496 = 0.89 || = 0.20 493 499 499 489 512 | 500 SD Bern.: d 0.93812 1.02227 0.51599 | 500 | 478 505 527 496 539 = 0.88 || = 0.19 477 509 550 535 470 | 500 s 0.94770 0.62480 1.01440 | 500 | 525 476 526 491 512 = 0.87 || = 0.18 504 488 492 531 470 | 500 t 0.96945 0.85364 1.06354 | 500 | 532 484 520 450 495 = 0.86 || = 0.17 523 500 505 471 529 | 500 m 0.91937 0.74601 0.92781 | 500 | 522 483 472 500 491 = 0.85 || = 0.16 455 490 489 489 536 | 500 x 0.90029 1.18717 1.24560 | 500 | 497 482 486 482 499 = 0.84 || = 0.15 540 496 504 515 504 | 500 | 500 | 505 493 462 547 508 = 0.83 || = 0.14 526 477 541 510 472 | 500 Changes: d 53 6 5 | 500 | 488 528 537 476 509 = 0.82 || = 0.13 546 464 511 520 494 | 500 s 40 6 4 | 500 | 455 477 485 513 489 = 0.81 || = 0.12 513 483 539 515 512 | 500 t 53 6 5 | 500 | 509 509 517 505 497 = 0.80 || = 0.11 519 510 521 484 507 | 500 m 54 4 4 | 500 | 478 482 485 489 496 = 0.79 || = 0.10 495 501 493 521 498 | 500 x 53 3 5 | 500 | 484 474 537 511 492 = 0.78 || = 0.09 518 531 499 503 509 | 500 -----------------------------------------------------------------| 500 | 493 509 493 493 505 = 0.77 || = 0.08 509 525 522 496 447 | 500 Aver./ d 0.49907 499 > 500: 6 7 2 7 4 4 5 4 4 7 | 500 | 503 517 484 449 508 = 0.76 || = 0.07 506 503 492 488 494 | 500 median s 0.50053 501 ----- 7 3 5 4 8 5 2 7 4 6 | 500 | 490 506 513 477 473 = 0.75 || = 0.06 506 506 474 493 515 | 500 t 0.49970 502 5 7 5 5 5 3 7 4 6 3 | 500 | 512 503 488 520 479 = 0.74 || = 0.05 503 479 508 530 482 | 500 m 0.49890 497 2 7 4 5 3 8 6 3 3 4 | 500 | 524 476 486 494 504 = 0.73 || = 0.04 472 471 477 487 476 | 500 x 0.50120 500 3 5 5 6 5 7 4 4 5 5 | 500 | 456 543 504 496 531 = 0.72 || = 0.03 499 491 518 486 490 | 500 -----------------------------------------------------------------| 500 | 497 510 491 489 470 = 0.71 || = 0.02 513 509 507 498 548 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 509 488 464 539 511 = 0.70 || = 0.01 231 264 268 242 252 | 252.5 d 0 0 3 11 70 16 1 0 0 | 500 | 487 497 510 520 502 = 0.69 || < 0.01 494 515 464 476 450 | 497.5 s 0 0 3 13 70 13 2 0 0 | 500 | 509 518 531 489 492 = 0.68 ||========================================================================= t 0 0 2 17 69 12 1 0 0 | 500 | 491 477 516 489 489 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 11 72 15 1 0 0 | 500 | 526 489 522 494 515 = 0.66 ||========================================================================= x 0 0 3 10 75 12 1 0 0 | 500 | 504 508 461 528 520 = 0.65 || sstring_HammingCorr test: no 216 test no 217 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingCorr test: test no 217 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 1 0 0 0 | 0.5 | 0 1 2 0 0 > 0.99999 || = 0.64 477 485 469 498 482 | 500 < 0.00002 1 0 1 0 1 | 0.5 | 0 0 0 0 2 > 0.99998 || = 0.63 502 500 527 534 495 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 1 0 0 2 0 > 0.99997 || = 0.62 502 482 511 515 490 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 513 482 517 521 473 | 500 < 0.00005 0 1 0 1 1 | 0.5 | 0 0 0 1 0 > 0.99995 || = 0.60 517 514 513 483 467 | 500 < 0.00006 1 1 0 0 0 | 0.5 | 1 1 0 0 1 > 0.99994 || = 0.59 495 508 510 502 463 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 1 0 1 0 1 > 0.99993 || = 0.58 481 502 506 517 492 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 0 3 0 2 5 > 0.99992 || = 0.57 471 505 543 483 542 | 500 < 0.00009 0 0 1 1 0 | 0.5 | 0 1 1 1 1 > 0.99991 || = 0.56 496 443 511 475 468 | 500 < 0.0001 0 0 2 1 1 | 0.5 | 1 1 1 0 1 > 0.9999 || = 0.55 487 529 469 521 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 456 545 479 496 512 | 500 < 0.0001 4 4 4 5 3 | 5 | 4 7 6 6 11 > 0.9999 || = 0.53 531 503 460 463 544 | 500 < 0.0002 3 3 7 3 2 | 5 | 1 2 4 2 3 > 0.9998 || = 0.52 517 462 478 497 514 | 500 < 0.0003 8 6 7 3 4 | 5 | 9 6 5 6 8 > 0.9997 || = 0.51 519 502 510 491 562 | 500 < 0.0004 3 8 6 5 3 | 5 | 2 4 6 6 5 > 0.9996 || = 0.50 483 475 493 525 495 | 500 < 0.0005 6 8 4 6 6 | 5 | 5 3 6 2 4 > 0.9995 || = 0.49 522 483 472 523 484 | 500 < 0.0006 7 8 4 3 3 | 5 | 7 3 8 7 7 > 0.9994 || = 0.48 526 561 518 512 502 | 500 < 0.0007 6 7 4 2 9 | 5 | 6 10 6 7 7 > 0.9993 || = 0.47 526 482 484 485 503 | 500 < 0.0008 4 3 4 9 6 | 5 | 3 5 5 3 3 > 0.9992 || = 0.46 486 500 557 527 509 | 500 < 0.0009 7 4 2 5 5 | 5 | 7 5 5 4 4 > 0.9991 || = 0.45 493 493 485 473 491 | 500 < 0.001 7 7 3 3 7 | 5 | 5 4 5 3 4 > 0.999 || = 0.44 523 490 494 518 491 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 505 493 549 520 482 | 500 < 0.001 55 58 45 44 48 | 50 | 49 49 56 46 56 > 0.999 || = 0.42 487 534 497 524 468 | 500 < 0.002 49 53 38 58 47 | 50 | 48 43 42 59 45 > 0.998 || = 0.41 504 474 493 476 509 | 500 < 0.003 51 47 62 57 48 | 50 | 61 35 45 43 46 > 0.997 || = 0.40 510 492 481 512 549 | 500 < 0.004 51 51 57 58 60 | 50 | 39 45 63 48 48 > 0.996 || = 0.39 495 496 499 518 505 | 500 < 0.005 55 48 49 57 52 | 50 | 58 63 56 54 56 > 0.995 || = 0.38 499 484 533 482 495 | 500 < 0.006 52 52 38 44 44 | 50 | 49 42 46 51 61 > 0.994 || = 0.37 479 507 463 479 485 | 500 < 0.007 44 35 52 56 60 | 50 | 52 50 48 54 59 > 0.993 || = 0.36 491 472 526 498 476 | 500 < 0.008 50 45 53 33 41 | 50 | 57 53 51 48 53 > 0.992 || = 0.35 479 466 452 541 491 | 500 < 0.009 36 43 58 50 56 | 50 | 48 44 50 58 49 > 0.991 || = 0.34 493 509 543 446 483 | 500 < 0.01 45 52 48 55 58 | 50 | 42 42 50 47 44 > 0.99 || = 0.33 519 506 512 440 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 513 457 523 488 499 | 500 < 0.01 488 484 500 512 514 | 497.5 | 503 466 507 508 517 > 0.99 || = 0.31 486 488 495 542 518 | 500 = 0.01 249 261 256 277 261 | 252.5 | 261 255 279 246 256 = 0.99 || = 0.30 522 506 497 494 485 | 500 = 0.02 504 515 474 514 513 | 500 | 561 489 471 493 491 = 0.98 || = 0.29 508 476 495 499 531 | 500 =================================================================| 500 | 474 526 517 504 497 = 0.97 || = 0.28 494 560 494 532 492 | 500 sstring_HammingCorr test: | 500 | 541 520 509 526 499 = 0.96 || = 0.27 490 542 510 456 517 | 500 ----------------------------------------------- | 500 | 519 505 491 502 490 = 0.95 || = 0.26 448 476 501 490 494 | 500 N = 1, n = 100000000, r = 10, s = 10, L = 300 | 500 | 506 469 477 498 502 = 0.94 || = 0.25 460 496 506 487 489 | 500 Normal statistic | 500 | 511 504 495 502 496 = 0.93 || = 0.24 509 499 491 472 502 | 500 | 500 | 525 492 506 473 513 = 0.92 || = 0.23 508 535 509 519 500 | 500 =================================================================| 500 | 490 475 497 497 500 = 0.91 || = 0.22 483 542 545 489 516 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 454 509 488 484 499 = 0.90 || = 0.21 482 447 466 477 503 | 500 -----------------------------------------------------------------| 500 | 518 502 497 473 531 = 0.89 || = 0.20 560 510 518 479 507 | 500 SD Bern.: d 1.10683 0.79285 0.93104 | 500 | 463 547 499 522 476 = 0.88 || = 0.19 494 498 511 451 482 | 500 s 1.08305 0.88813 1.13369 | 500 | 526 502 475 521 506 = 0.87 || = 0.18 503 523 481 497 507 | 500 t 1.00398 1.08497 0.83826 | 500 | 504 534 506 505 473 = 0.86 || = 0.17 486 516 517 511 532 | 500 m 1.06442 1.13898 0.72145 | 500 | 473 503 473 508 511 = 0.85 || = 0.16 493 491 462 533 489 | 500 x 0.91895 0.93640 0.85481 | 500 | 504 520 532 509 550 = 0.84 || = 0.15 516 507 494 470 509 | 500 | 500 | 527 454 485 497 515 = 0.83 || = 0.14 484 488 489 505 476 | 500 Changes: d 49 3 6 | 500 | 564 501 515 533 512 = 0.82 || = 0.13 530 472 461 541 510 | 500 s 50 6 4 | 500 | 483 471 518 516 512 = 0.81 || = 0.12 528 483 502 457 445 | 500 t 46 4 5 | 500 | 448 491 504 548 470 = 0.80 || = 0.11 486 489 541 524 493 | 500 m 48 5 6 | 500 | 486 542 506 483 510 = 0.79 || = 0.10 534 508 504 469 497 | 500 x 44 5 3 | 500 | 459 523 488 480 501 = 0.78 || = 0.09 482 472 495 553 518 | 500 -----------------------------------------------------------------| 500 | 493 497 461 509 502 = 0.77 || = 0.08 482 532 484 460 465 | 500 Aver./ d 0.50139 498 > 500: 2 5 4 3 7 4 7 3 6 8 | 500 | 516 489 478 454 497 = 0.76 || = 0.07 525 506 467 494 496 | 500 median s 0.50054 500 ----- 6 4 5 4 2 8 2 5 8 5 | 500 | 560 549 540 518 473 = 0.75 || = 0.06 492 501 491 473 481 | 500 t 0.50069 501 3 5 6 5 3 6 8 6 4 5 | 500 | 498 484 505 502 510 = 0.74 || = 0.05 498 506 500 484 487 | 500 m 0.50087 498 6 5 2 3 7 3 5 5 7 5 | 500 | 524 515 505 494 502 = 0.73 || = 0.04 481 496 488 520 502 | 500 x 0.50071 500 6 4 6 2 5 6 3 6 7 4 | 500 | 475 543 492 505 526 = 0.72 || = 0.03 462 486 509 527 510 | 500 -----------------------------------------------------------------| 500 | 471 483 526 492 461 = 0.71 || = 0.02 504 515 474 514 513 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 526 486 506 488 495 = 0.70 || = 0.01 249 261 256 277 261 | 252.5 d 0 0 4 12 66 15 4 0 0 | 500 | 453 466 501 493 549 = 0.69 || < 0.01 488 484 500 512 514 | 497.5 s 0 0 3 15 64 14 5 0 0 | 500 | 516 528 510 494 501 = 0.68 ||========================================================================= t 0 0 1 16 69 12 3 0 0 | 500 | 462 524 507 511 518 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 14 65 16 2 0 0 | 500 | 519 499 461 528 478 = 0.66 ||========================================================================= x 0 0 1 13 77 6 4 0 0 | 500 | 523 490 543 493 495 = 0.65 || sstring_HammingCorr test: no 217 test no 218 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingCorr test: test no 218 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99999 || = 0.64 498 534 532 472 514 | 500 < 0.00002 0 0 1 0 1 | 0.5 | 1 0 0 0 1 > 0.99998 || = 0.63 502 455 519 498 492 | 500 < 0.00003 0 0 0 2 0 | 0.5 | 0 1 1 0 1 > 0.99997 || = 0.62 466 502 485 513 521 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 1 3 0 1 0 > 0.99996 || = 0.61 502 489 494 474 479 | 500 < 0.00005 0 2 0 0 0 | 0.5 | 0 0 1 1 2 > 0.99995 || = 0.60 498 494 532 501 486 | 500 < 0.00006 0 1 2 0 0 | 0.5 | 0 1 0 1 2 > 0.99994 || = 0.59 492 502 470 520 510 | 500 < 0.00007 0 0 0 0 1 | 0.5 | 0 0 2 0 0 > 0.99993 || = 0.58 522 524 450 531 497 | 500 < 0.00008 1 1 0 0 2 | 0.5 | 1 0 1 1 0 > 0.99992 || = 0.57 472 512 497 486 488 | 500 < 0.00009 1 1 0 1 0 | 0.5 | 2 0 2 2 1 > 0.99991 || = 0.56 521 534 489 503 485 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 1 0 1 0 > 0.9999 || = 0.55 457 494 475 496 522 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 480 491 505 471 501 | 500 < 0.0001 2 5 3 5 4 | 5 | 5 6 7 7 8 > 0.9999 || = 0.53 498 458 497 478 491 | 500 < 0.0002 5 2 3 4 6 | 5 | 1 4 3 3 3 > 0.9998 || = 0.52 487 535 504 512 517 | 500 < 0.0003 6 10 10 2 2 | 5 | 2 3 5 4 9 > 0.9997 || = 0.51 481 513 504 498 521 | 500 < 0.0004 4 4 2 1 7 | 5 | 5 5 2 4 4 > 0.9996 || = 0.50 452 503 508 491 545 | 500 < 0.0005 6 6 5 4 10 | 5 | 7 4 6 3 4 > 0.9995 || = 0.49 503 466 492 533 523 | 500 < 0.0006 4 7 11 7 5 | 5 | 8 8 3 6 3 > 0.9994 || = 0.48 486 483 496 489 461 | 500 < 0.0007 9 1 3 6 4 | 5 | 2 5 2 2 7 > 0.9993 || = 0.47 479 529 519 520 467 | 500 < 0.0008 10 3 3 4 6 | 5 | 6 6 4 5 5 > 0.9992 || = 0.46 478 458 519 485 526 | 500 < 0.0009 5 7 8 8 5 | 5 | 3 4 7 9 5 > 0.9991 || = 0.45 483 532 511 493 507 | 500 < 0.001 3 6 9 10 5 | 5 | 5 5 2 7 8 > 0.999 || = 0.44 454 507 481 504 536 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 494 503 477 498 512 | 500 < 0.001 54 51 57 51 54 | 50 | 44 50 41 50 56 > 0.999 || = 0.42 526 531 517 503 519 | 500 < 0.002 43 48 47 55 45 | 50 | 47 50 42 49 40 > 0.998 || = 0.41 482 493 475 475 519 | 500 < 0.003 52 52 56 58 47 | 50 | 67 54 54 27 57 > 0.997 || = 0.40 503 540 555 549 537 | 500 < 0.004 46 49 46 42 39 | 50 | 51 43 51 54 54 > 0.996 || = 0.39 531 504 485 489 510 | 500 < 0.005 51 60 44 50 53 | 50 | 62 57 36 54 45 > 0.995 || = 0.38 501 521 469 482 520 | 500 < 0.006 58 49 55 47 45 | 50 | 48 59 44 36 50 > 0.994 || = 0.37 516 511 472 513 482 | 500 < 0.007 50 49 47 39 47 | 50 | 50 44 47 54 47 > 0.993 || = 0.36 505 490 483 484 470 | 500 < 0.008 43 46 43 43 45 | 50 | 33 51 42 51 65 > 0.992 || = 0.35 515 500 482 476 524 | 500 < 0.009 52 60 47 59 41 | 50 | 52 58 53 75 55 > 0.991 || = 0.34 475 509 490 481 511 | 500 < 0.01 53 32 56 44 55 | 50 | 46 50 70 47 47 > 0.99 || = 0.33 520 537 528 520 520 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 512 501 527 424 497 | 500 < 0.01 502 496 498 488 471 | 497.5 | 500 516 480 497 516 > 0.99 || = 0.31 473 513 512 532 489 | 500 = 0.01 262 249 240 229 252 | 252.5 | 255 254 237 243 236 = 0.99 || = 0.30 565 493 512 497 542 | 500 = 0.02 510 486 490 455 440 | 500 | 502 521 547 487 512 = 0.98 || = 0.29 518 538 521 476 481 | 500 =================================================================| 500 | 467 526 473 499 500 = 0.97 || = 0.28 525 478 477 494 488 | 500 sstring_HammingCorr test: | 500 | 532 495 493 550 470 = 0.96 || = 0.27 524 509 536 519 479 | 500 ----------------------------------------------- | 500 | 486 483 516 487 498 = 0.95 || = 0.26 505 474 526 507 483 | 500 N = 1, n = 100000000, r = 10, s = 10, L = 1200 | 500 | 477 495 474 512 501 = 0.94 || = 0.25 525 483 469 510 457 | 500 Normal statistic | 500 | 510 487 479 515 522 = 0.93 || = 0.24 537 515 517 518 477 | 500 | 500 | 486 555 558 464 509 = 0.92 || = 0.23 511 464 472 469 517 | 500 =================================================================| 500 | 493 510 501 515 468 = 0.91 || = 0.22 476 490 504 513 476 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 534 493 506 522 486 = 0.90 || = 0.21 536 519 468 497 484 | 500 -----------------------------------------------------------------| 500 | 525 529 495 533 490 = 0.89 || = 0.20 496 487 466 507 520 | 500 SD Bern.: d 0.91624 0.65146 1.25919 | 500 | 513 453 578 507 493 = 0.88 || = 0.19 518 486 491 520 484 | 500 s 1.04286 1.05123 0.76979 | 500 | 508 510 525 513 526 = 0.87 || = 0.18 514 522 507 512 500 | 500 t 1.12578 0.74063 1.32428 | 500 | 502 498 519 483 503 = 0.86 || = 0.17 515 477 514 466 516 | 500 m 1.02452 0.94915 1.67952 | 500 | 504 479 481 498 535 = 0.85 || = 0.16 475 507 494 506 486 | 500 x 0.96488 0.83107 0.99446 | 500 | 497 475 509 557 537 = 0.84 || = 0.15 492 503 535 474 506 | 500 | 500 | 518 525 474 498 502 = 0.83 || = 0.14 488 481 488 500 498 | 500 Changes: d 46 6 4 | 500 | 483 455 533 500 504 = 0.82 || = 0.13 492 468 474 456 466 | 500 s 51 7 6 | 500 | 498 519 491 509 527 = 0.81 || = 0.12 522 512 462 509 530 | 500 t 53 6 3 | 500 | 487 524 506 540 536 = 0.80 || = 0.11 499 465 491 513 505 | 500 m 52 3 4 | 500 | 484 485 482 532 498 = 0.79 || = 0.10 487 529 536 502 525 | 500 x 39 4 5 | 500 | 491 473 467 483 523 = 0.78 || = 0.09 516 517 503 541 514 | 500 -----------------------------------------------------------------| 500 | 528 509 538 489 505 = 0.77 || = 0.08 460 472 450 536 507 | 500 Aver./ d 0.49945 501 > 500: 5 4 8 8 3 2 4 5 7 5 | 500 | 510 511 511 485 515 = 0.76 || = 0.07 509 556 501 513 503 | 500 median s 0.49965 501 ----- 5 5 4 7 6 6 3 4 4 6 | 500 | 549 461 482 503 496 = 0.75 || = 0.06 498 529 511 502 494 | 500 t 0.50218 497 4 4 5 4 5 4 5 5 6 4 | 500 | 476 511 529 514 492 = 0.74 || = 0.05 500 521 488 485 495 | 500 m 0.50192 499 4 6 6 3 5 5 4 5 6 4 | 500 | 502 495 497 458 471 = 0.73 || = 0.04 472 512 498 487 490 | 500 x 0.50133 500 3 5 2 6 8 5 4 4 7 5 | 500 | 498 473 464 532 486 = 0.72 || = 0.03 492 461 485 493 483 | 500 -----------------------------------------------------------------| 500 | 505 478 562 482 486 = 0.71 || = 0.02 510 486 490 455 440 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 510 487 520 464 447 = 0.70 || = 0.01 262 249 240 229 252 | 252.5 d 0 0 2 12 74 11 2 0 0 | 500 | 493 487 532 537 482 = 0.69 || < 0.01 502 496 498 488 471 | 497.5 s 0 0 3 15 65 16 2 0 0 | 500 | 492 508 472 505 505 = 0.68 ||========================================================================= t 0 0 2 19 62 13 4 1 0 | 500 | 504 479 520 492 483 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 1 14 72 10 3 0 0 | 500 | 493 476 478 508 503 = 0.66 ||========================================================================= x 0 0 2 13 71 14 1 0 0 | 500 | 483 498 496 499 469 = 0.65 || sstring_HammingCorr test: no 218 test no 219 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 219 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 0 0 | 0.5 | 0 0 3 1 0 > 0.99999 || = 0.64 457 536 522 488 459 | 500 < 0.00002 0 0 1 0 0 | 0.5 | 1 1 0 0 1 > 0.99998 || = 0.63 485 466 478 509 510 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 1 1 0 3 0 > 0.99997 || = 0.62 503 512 488 496 465 | 500 < 0.00004 0 0 1 0 0 | 0.5 | 0 0 1 0 2 > 0.99996 || = 0.61 513 470 426 490 519 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 1 1 0 0 0 > 0.99995 || = 0.60 500 524 477 508 478 | 500 < 0.00006 0 1 0 0 0 | 0.5 | 0 2 0 1 2 > 0.99994 || = 0.59 544 533 494 528 481 | 500 < 0.00007 1 0 0 0 0 | 0.5 | 1 2 2 0 0 > 0.99993 || = 0.58 531 482 513 496 523 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 0 1 0 0 1 > 0.99992 || = 0.57 507 512 501 533 492 | 500 < 0.00009 0 1 0 1 3 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 529 511 525 423 519 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.9999 || = 0.55 463 530 534 508 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 505 453 496 504 504 | 500 < 0.0001 2 2 3 4 3 | 5 | 4 9 6 5 6 > 0.9999 || = 0.53 513 515 498 492 486 | 500 < 0.0002 5 3 2 3 7 | 5 | 2 3 2 4 5 > 0.9998 || = 0.52 463 498 536 524 458 | 500 < 0.0003 9 7 5 3 3 | 5 | 3 3 7 1 9 > 0.9997 || = 0.51 536 530 500 466 488 | 500 < 0.0004 2 2 7 4 1 | 5 | 2 5 2 7 3 > 0.9996 || = 0.50 504 520 507 499 515 | 500 < 0.0005 11 8 3 2 4 | 5 | 6 4 7 9 4 > 0.9995 || = 0.49 504 526 536 522 497 | 500 < 0.0006 4 8 6 4 9 | 5 | 9 5 4 4 2 > 0.9994 || = 0.48 513 488 462 496 510 | 500 < 0.0007 5 5 2 5 5 | 5 | 5 5 3 6 6 > 0.9993 || = 0.47 484 493 520 532 528 | 500 < 0.0008 4 7 9 7 5 | 5 | 1 6 4 2 2 > 0.9992 || = 0.46 510 507 482 514 481 | 500 < 0.0009 6 2 3 4 2 | 5 | 5 5 5 3 7 > 0.9991 || = 0.45 445 484 523 497 508 | 500 < 0.001 5 4 6 9 4 | 5 | 4 4 5 6 4 > 0.999 || = 0.44 525 465 488 465 544 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 495 526 502 487 529 | 500 < 0.001 53 48 46 45 43 | 50 | 41 49 45 47 48 > 0.999 || = 0.42 543 496 455 458 488 | 500 < 0.002 59 44 50 37 38 | 50 | 47 63 39 50 63 > 0.998 || = 0.41 513 513 515 510 548 | 500 < 0.003 44 45 53 64 54 | 50 | 48 60 64 55 50 > 0.997 || = 0.40 471 509 529 496 457 | 500 < 0.004 58 48 46 50 40 | 50 | 54 44 52 46 43 > 0.996 || = 0.39 472 503 506 520 495 | 500 < 0.005 50 42 47 52 46 | 50 | 46 46 47 46 44 > 0.995 || = 0.38 486 524 506 561 491 | 500 < 0.006 41 56 53 52 57 | 50 | 50 52 51 47 53 > 0.994 || = 0.37 469 486 494 513 484 | 500 < 0.007 43 53 60 40 53 | 50 | 45 46 44 62 50 > 0.993 || = 0.36 526 464 495 491 506 | 500 < 0.008 76 43 56 48 66 | 50 | 54 53 44 54 54 > 0.992 || = 0.35 490 490 457 532 526 | 500 < 0.009 42 54 50 65 62 | 50 | 57 46 52 51 50 > 0.991 || = 0.34 494 508 539 505 533 | 500 < 0.01 54 46 48 47 51 | 50 | 41 51 52 48 42 > 0.99 || = 0.33 480 489 466 482 535 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 533 488 511 513 503 | 500 < 0.01 520 479 509 500 510 | 497.5 | 483 510 490 506 497 > 0.99 || = 0.31 430 497 560 490 502 | 500 = 0.01 225 232 256 245 240 | 252.5 | 256 284 260 266 282 = 0.99 || = 0.30 528 444 471 485 479 | 500 = 0.02 506 493 517 468 495 | 500 | 539 534 527 500 512 = 0.98 || = 0.29 518 492 470 474 479 | 500 =================================================================| 500 | 533 508 481 476 523 = 0.97 || = 0.28 515 498 506 492 465 | 500 sstring_HammingIndep test: | 500 | 494 488 487 509 490 = 0.96 || = 0.27 538 537 518 482 543 | 500 ----------------------------------------------- | 500 | 494 504 519 511 468 = 0.95 || = 0.26 495 518 513 530 460 | 500 N = 10, n = 30000000, r = 0, s = 3, L = 30, d = 0 | 500 | 462 511 467 451 498 = 0.94 || = 0.25 508 517 481 520 519 | 500 Counters with expected numbers >= 10 | 500 | 487 495 487 530 483 = 0.93 || = 0.24 506 455 494 492 487 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 489 502 489 523 510 = 0.92 || = 0.23 533 526 516 505 484 | 500 =================================================================| 500 | 517 489 485 510 539 = 0.91 || = 0.22 488 490 497 503 522 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 510 514 523 469 496 = 0.90 || = 0.21 552 525 499 531 475 | 500 -----------------------------------------------------------------| 500 | 486 534 502 509 521 = 0.89 || = 0.20 478 497 526 482 493 | 500 SD Bern.: d 1.10661 1.46770 0.77109 | 500 | 495 485 475 474 472 = 0.88 || = 0.19 481 494 501 519 467 | 500 s 1.00986 0.72007 0.85832 | 500 | 469 509 502 542 495 = 0.87 || = 0.18 518 511 491 516 476 | 500 t 1.08485 0.63118 0.93426 | 500 | 505 476 506 494 520 = 0.86 || = 0.17 515 464 479 489 537 | 500 m 0.97863 1.21386 0.69315 | 500 | 484 513 477 491 526 = 0.85 || = 0.16 502 522 501 502 495 | 500 x 1.04800 1.25282 0.83347 | 500 | 490 517 477 504 519 = 0.84 || = 0.15 524 496 479 492 458 | 500 | 500 | 423 509 507 518 482 = 0.83 || = 0.14 469 476 522 480 541 | 500 Changes: d 47 6 4 | 500 | 493 502 517 511 473 = 0.82 || = 0.13 523 457 486 477 532 | 500 s 57 4 7 | 500 | 482 503 513 501 522 = 0.81 || = 0.12 528 466 510 514 516 | 500 t 53 4 5 | 500 | 525 485 500 471 497 = 0.80 || = 0.11 483 468 476 537 482 | 500 m 58 6 4 | 500 | 505 516 522 489 501 = 0.79 || = 0.10 510 520 475 509 475 | 500 x 49 3 6 | 500 | 511 538 471 501 504 = 0.78 || = 0.09 479 467 494 477 455 | 500 -----------------------------------------------------------------| 500 | 523 486 547 507 512 = 0.77 || = 0.08 491 512 444 507 509 | 500 Aver./ d 0.49879 502 > 500: 4 7 7 3 6 7 4 6 2 4 | 500 | 535 534 494 466 522 = 0.76 || = 0.07 466 474 474 491 513 | 500 median s 0.50279 502 ----- 4 3 5 3 5 7 4 5 8 7 | 500 | 526 513 492 497 466 = 0.75 || = 0.06 513 505 516 523 490 | 500 t 0.49998 501 7 4 5 5 6 5 4 4 7 3 | 500 | 491 462 485 520 504 = 0.74 || = 0.05 531 486 531 507 532 | 500 m 0.49988 501 4 6 5 6 4 6 3 5 6 7 | 500 | 487 473 502 524 480 = 0.73 || = 0.04 500 542 502 498 510 | 500 x 0.50064 499 5 4 3 6 6 4 6 5 5 5 | 500 | 495 485 543 489 472 = 0.72 || = 0.03 488 508 519 490 488 | 500 -----------------------------------------------------------------| 500 | 494 501 487 510 480 = 0.71 || = 0.02 506 493 517 468 495 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 491 491 486 464 511 = 0.70 || = 0.01 225 232 256 245 240 | 252.5 d 0 2 1 12 63 22 1 0 0 | 500 | 491 493 562 524 520 = 0.69 || < 0.01 520 479 509 500 510 | 497.5 s 0 0 3 15 65 18 0 0 0 | 500 | 481 532 513 469 520 = 0.68 ||========================================================================= t 0 1 3 14 67 13 3 0 0 | 500 | 514 491 453 527 518 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 1 15 68 15 1 0 0 | 500 | 467 484 543 487 472 = 0.66 ||========================================================================= x 0 0 1 17 66 16 1 0 0 | 500 | 506 510 495 475 494 = 0.65 || sstring_HammingIndep test: no 219 test no 220 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 220 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 1 0 1 | 0.5 | 0 0 1 0 0 > 0.99999 || = 0.64 486 504 520 525 491 | 500 < 0.00002 1 1 1 0 0 | 0.5 | 0 2 1 0 0 > 0.99998 || = 0.63 494 510 486 536 522 | 500 < 0.00003 0 1 1 0 0 | 0.5 | 1 0 1 0 0 > 0.99997 || = 0.62 504 477 496 483 485 | 500 < 0.00004 1 0 1 1 0 | 0.5 | 0 2 0 0 0 > 0.99996 || = 0.61 487 481 528 488 508 | 500 < 0.00005 2 0 2 0 0 | 0.5 | 0 2 1 2 1 > 0.99995 || = 0.60 508 507 447 520 550 | 500 < 0.00006 0 1 3 1 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 490 509 534 512 517 | 500 < 0.00007 0 1 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99993 || = 0.58 529 476 515 504 479 | 500 < 0.00008 1 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 492 497 549 537 516 | 500 < 0.00009 1 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 515 459 490 483 533 | 500 < 0.0001 0 0 0 1 1 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 493 525 511 480 481 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 494 460 533 496 502 | 500 < 0.0001 7 7 9 4 2 | 5 | 2 6 4 2 2 > 0.9999 || = 0.53 496 512 511 528 477 | 500 < 0.0002 3 6 7 10 7 | 5 | 4 2 4 3 0 > 0.9998 || = 0.52 499 521 469 487 491 | 500 < 0.0003 6 6 4 9 3 | 5 | 4 8 5 4 6 > 0.9997 || = 0.51 495 492 501 524 508 | 500 < 0.0004 6 8 3 3 4 | 5 | 1 11 3 3 7 > 0.9996 || = 0.50 517 529 535 505 497 | 500 < 0.0005 7 5 11 11 9 | 5 | 6 8 3 8 3 > 0.9995 || = 0.49 503 518 513 542 516 | 500 < 0.0006 3 3 6 8 2 | 5 | 2 3 2 4 4 > 0.9994 || = 0.48 526 479 503 520 477 | 500 < 0.0007 7 6 7 9 3 | 5 | 6 5 5 5 5 > 0.9993 || = 0.47 502 464 467 489 503 | 500 < 0.0008 7 7 8 3 2 | 5 | 6 4 7 3 4 > 0.9992 || = 0.46 550 499 498 483 523 | 500 < 0.0009 5 4 6 6 5 | 5 | 6 10 5 3 5 > 0.9991 || = 0.45 531 500 526 510 500 | 500 < 0.001 14 2 0 4 4 | 5 | 4 2 5 2 2 > 0.999 || = 0.44 480 515 484 509 533 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 532 460 505 537 496 | 500 < 0.001 65 54 61 67 41 | 50 | 41 59 43 37 38 > 0.999 || = 0.42 497 524 487 514 474 | 500 < 0.002 39 43 47 50 37 | 50 | 40 39 47 57 72 > 0.998 || = 0.41 505 519 518 529 525 | 500 < 0.003 54 48 53 49 38 | 50 | 42 69 32 55 43 > 0.997 || = 0.40 472 511 531 471 492 | 500 < 0.004 48 59 44 50 60 | 50 | 49 49 50 48 51 > 0.996 || = 0.39 524 455 497 501 495 | 500 < 0.005 47 35 58 59 39 | 50 | 44 60 48 54 59 > 0.995 || = 0.38 452 504 466 485 489 | 500 < 0.006 50 58 54 33 55 | 50 | 53 50 53 47 58 > 0.994 || = 0.37 468 481 432 478 515 | 500 < 0.007 43 45 51 45 52 | 50 | 58 53 57 48 53 > 0.993 || = 0.36 463 520 508 481 513 | 500 < 0.008 44 46 54 48 47 | 50 | 40 49 39 44 40 > 0.992 || = 0.35 501 517 503 476 502 | 500 < 0.009 45 55 42 34 57 | 50 | 48 48 58 52 60 > 0.991 || = 0.34 502 505 494 491 495 | 500 < 0.01 46 67 49 45 53 | 50 | 56 42 54 44 66 > 0.99 || = 0.33 490 486 535 523 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 479 496 540 471 502 | 500 < 0.01 481 510 513 480 479 | 497.5 | 471 518 481 486 540 > 0.99 || = 0.31 511 499 491 523 452 | 500 = 0.01 254 255 237 264 244 | 252.5 | 224 268 264 250 250 = 0.99 || = 0.30 506 511 517 508 476 | 500 = 0.02 483 486 536 487 488 | 500 | 511 531 488 505 505 = 0.98 || = 0.29 484 467 521 481 521 | 500 =================================================================| 500 | 461 506 535 496 496 = 0.97 || = 0.28 504 484 487 521 536 | 500 sstring_HammingIndep test: | 500 | 487 485 483 504 469 = 0.96 || = 0.27 514 506 531 441 454 | 500 ----------------------------------------------- | 500 | 506 532 478 468 486 = 0.95 || = 0.26 511 550 496 511 472 | 500 N = 10, n = 30000000, r = 0, s = 3, L = 30, d = 0 | 500 | 483 497 530 515 534 = 0.94 || = 0.25 521 516 486 530 463 | 500 Counters with expected numbers >= 10 | 500 | 534 482 517 503 478 = 0.93 || = 0.24 494 466 484 451 520 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 494 506 502 503 473 = 0.92 || = 0.23 488 506 494 518 512 | 500 =================================================================| 500 | 470 468 522 498 479 = 0.91 || = 0.22 520 490 467 494 547 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 521 481 484 508 489 = 0.90 || = 0.21 496 518 488 483 494 | 500 -----------------------------------------------------------------| 500 | 495 445 522 486 458 = 0.89 || = 0.20 487 490 507 522 470 | 500 SD Bern.: d 0.92032 1.00149 0.99547 | 500 | 501 522 482 474 509 = 0.88 || = 0.19 520 533 507 509 492 | 500 s 1.00405 1.26078 1.21879 | 500 | 499 461 478 510 525 = 0.87 || = 0.18 485 486 501 515 467 | 500 t 0.98153 0.82138 1.13634 | 500 | 506 476 473 507 503 = 0.86 || = 0.17 517 489 522 490 568 | 500 m 0.90901 1.39353 0.83945 | 500 | 513 472 486 459 498 = 0.85 || = 0.16 481 537 494 489 530 | 500 x 1.03703 1.19306 1.60578 | 500 | 489 519 497 499 489 = 0.84 || = 0.15 506 499 501 509 494 | 500 | 500 | 498 532 483 481 506 = 0.83 || = 0.14 512 509 505 515 493 | 500 Changes: d 58 3 3 | 500 | 487 533 514 502 482 = 0.82 || = 0.13 473 522 537 520 539 | 500 s 54 6 7 | 500 | 539 515 469 478 510 = 0.81 || = 0.12 519 491 479 482 498 | 500 t 53 5 3 | 500 | 524 519 517 494 523 = 0.80 || = 0.11 509 501 507 487 487 | 500 m 50 3 6 | 500 | 532 489 502 504 477 = 0.79 || = 0.10 494 473 506 472 473 | 500 x 53 5 5 | 500 | 495 511 509 496 498 = 0.78 || = 0.09 480 480 519 490 500 | 500 -----------------------------------------------------------------| 500 | 511 509 477 491 474 = 0.77 || = 0.08 489 528 503 499 498 | 500 Aver./ d 0.50134 499 > 500: 2 6 5 5 7 3 3 8 5 3 | 500 | 546 505 479 538 487 = 0.76 || = 0.07 496 504 469 503 497 | 500 median s 0.49837 504 ----- 8 5 5 5 5 5 3 6 5 6 | 500 | 516 473 485 535 485 = 0.75 || = 0.06 481 525 505 504 515 | 500 t 0.49921 501 5 8 3 5 6 7 5 4 2 6 | 500 | 478 526 489 488 517 = 0.74 || = 0.05 533 518 480 491 525 | 500 m 0.49997 499 4 5 5 4 7 6 5 4 4 5 | 500 | 503 479 491 530 469 = 0.73 || = 0.04 476 530 488 528 476 | 500 x 0.49922 498 3 3 5 5 5 6 6 3 5 3 | 500 | 521 508 494 465 480 = 0.72 || = 0.03 444 539 489 495 551 | 500 -----------------------------------------------------------------| 500 | 524 496 510 482 511 = 0.71 || = 0.02 483 486 536 487 488 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 470 497 480 483 508 = 0.70 || = 0.01 254 255 237 264 244 | 252.5 d 0 0 2 10 75 12 2 0 0 | 500 | 514 494 522 489 543 = 0.69 || < 0.01 481 510 513 480 479 | 497.5 s 0 0 2 16 68 14 1 0 0 | 500 | 497 508 467 491 470 = 0.68 ||========================================================================= t 0 1 1 10 75 13 1 0 0 | 500 | 498 484 520 520 512 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 8 76 15 0 0 0 | 500 | 500 462 464 510 499 = 0.66 ||========================================================================= x 0 0 2 17 64 14 3 1 0 | 500 | 537 461 507 522 524 = 0.65 || sstring_HammingIndep test: no 220 test no 221 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 221 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 488 472 515 497 516 | 500 < 0.00002 1 0 1 3 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 508 497 474 509 508 | 500 < 0.00003 0 1 2 0 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 499 488 522 521 512 | 500 < 0.00004 0 0 0 1 1 | 0.5 | 0 1 0 1 0 > 0.99996 || = 0.61 510 499 489 496 510 | 500 < 0.00005 1 0 1 0 1 | 0.5 | 1 0 0 0 1 > 0.99995 || = 0.60 516 505 486 458 494 | 500 < 0.00006 0 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 516 535 532 503 467 | 500 < 0.00007 0 1 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99993 || = 0.58 524 485 529 474 479 | 500 < 0.00008 1 0 1 0 1 | 0.5 | 0 0 1 0 0 > 0.99992 || = 0.57 478 485 483 493 484 | 500 < 0.00009 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 473 526 476 487 519 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 511 519 510 513 513 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 527 497 466 506 523 | 500 < 0.0001 3 4 5 5 6 | 5 | 2 1 1 1 1 > 0.9999 || = 0.53 517 539 483 486 522 | 500 < 0.0002 5 2 7 5 1 | 5 | 4 2 2 4 1 > 0.9998 || = 0.52 482 457 504 523 515 | 500 < 0.0003 5 3 4 2 5 | 5 | 1 4 2 3 4 > 0.9997 || = 0.51 521 488 510 510 474 | 500 < 0.0004 7 6 6 4 8 | 5 | 0 0 5 2 5 > 0.9996 || = 0.50 487 467 493 522 569 | 500 < 0.0005 9 5 3 8 4 | 5 | 5 4 7 5 2 > 0.9995 || = 0.49 511 502 515 479 506 | 500 < 0.0006 2 5 6 5 2 | 5 | 1 5 2 4 6 > 0.9994 || = 0.48 492 473 478 499 512 | 500 < 0.0007 2 5 5 3 7 | 5 | 2 6 3 4 8 > 0.9993 || = 0.47 488 524 501 463 474 | 500 < 0.0008 7 6 2 7 4 | 5 | 6 4 1 1 7 > 0.9992 || = 0.46 516 499 521 498 521 | 500 < 0.0009 6 4 3 2 4 | 5 | 3 3 4 2 1 > 0.9991 || = 0.45 537 523 507 473 473 | 500 < 0.001 3 4 2 6 5 | 5 | 3 9 6 2 5 > 0.999 || = 0.44 531 511 500 524 486 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 481 461 491 467 510 | 500 < 0.001 49 44 43 47 46 | 50 | 27 38 33 28 40 > 0.999 || = 0.42 485 524 478 507 504 | 500 < 0.002 46 55 57 47 39 | 50 | 33 49 40 47 42 > 0.998 || = 0.41 511 479 501 481 489 | 500 < 0.003 58 53 50 62 46 | 50 | 58 42 40 37 50 > 0.997 || = 0.40 461 480 501 508 478 | 500 < 0.004 47 54 59 56 57 | 50 | 38 43 45 43 48 > 0.996 || = 0.39 527 481 509 498 521 | 500 < 0.005 42 52 44 46 38 | 50 | 49 51 55 49 43 > 0.995 || = 0.38 497 472 527 506 448 | 500 < 0.006 45 35 57 68 45 | 50 | 45 49 57 62 49 > 0.994 || = 0.37 490 492 482 487 471 | 500 < 0.007 57 41 42 53 41 | 50 | 52 43 55 50 37 > 0.993 || = 0.36 508 486 525 510 515 | 500 < 0.008 51 60 51 58 54 | 50 | 58 42 50 55 48 > 0.992 || = 0.35 458 509 536 485 487 | 500 < 0.009 57 49 45 53 49 | 50 | 64 47 43 49 50 > 0.991 || = 0.34 472 493 490 538 472 | 500 < 0.01 40 49 58 51 51 | 50 | 65 60 50 63 48 > 0.99 || = 0.33 513 484 525 558 530 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 497 516 484 502 524 | 500 < 0.01 492 492 506 541 466 | 497.5 | 489 464 468 483 455 > 0.99 || = 0.31 494 536 528 498 468 | 500 = 0.01 245 244 250 252 260 | 252.5 | 264 249 267 250 269 = 0.99 || = 0.30 510 490 472 476 520 | 500 = 0.02 518 489 502 504 486 | 500 | 513 538 553 552 519 = 0.98 || = 0.29 494 506 502 497 494 | 500 =================================================================| 500 | 530 540 484 486 529 = 0.97 || = 0.28 513 515 498 515 500 | 500 sstring_HammingIndep test: | 500 | 533 514 512 490 489 = 0.96 || = 0.27 516 437 500 529 499 | 500 ----------------------------------------------- | 500 | 514 503 457 498 476 = 0.95 || = 0.26 526 469 489 505 462 | 500 N = 10, n = 30000000, r = 0, s = 3, L = 30, d = 0 | 500 | 495 503 530 473 488 = 0.94 || = 0.25 531 501 482 496 524 | 500 Counters with expected numbers >= 10 | 500 | 512 493 519 510 539 = 0.93 || = 0.24 557 514 534 458 515 | 500 Anderson-Darling statistic = A2 | 500 | 516 487 487 467 467 = 0.92 || = 0.23 488 504 468 535 486 | 500 =================================================================| 500 | 482 471 483 498 472 = 0.91 || = 0.22 512 509 501 530 471 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 467 502 488 551 484 = 0.90 || = 0.21 511 519 479 470 491 | 500 -----------------------------------------------------------------| 500 | 517 493 502 541 516 = 0.89 || = 0.20 496 506 512 486 538 | 500 SD Bern.: d 1.04364 0.86991 1.75643 | 500 | 522 476 474 502 477 = 0.88 || = 0.19 494 477 483 487 486 | 500 s 1.03871 0.99848 0.98231 | 500 | 497 490 482 493 529 = 0.87 || = 0.18 464 472 509 517 515 | 500 t 0.92960 0.91478 1.15122 | 500 | 475 501 501 504 493 = 0.86 || = 0.17 545 477 507 518 475 | 500 m 0.95404 1.11500 1.45054 | 500 | 502 486 474 487 495 = 0.85 || = 0.16 502 510 506 498 508 | 500 x 1.00363 0.97001 0.88925 | 500 | 499 526 507 495 509 = 0.84 || = 0.15 483 529 508 503 514 | 500 | 500 | 460 524 513 517 519 = 0.83 || = 0.14 488 527 519 525 481 | 500 Changes: d 52 4 3 | 500 | 464 474 511 490 492 = 0.82 || = 0.13 469 524 501 489 516 | 500 s 44 4 3 | 500 | 553 501 475 491 509 = 0.81 || = 0.12 508 514 503 520 539 | 500 t 65 9 2 | 500 | 538 530 464 507 486 = 0.80 || = 0.11 494 537 499 444 465 | 500 m 57 3 5 | 500 | 530 512 519 519 527 = 0.79 || = 0.10 457 477 469 506 497 | 500 x 52 5 0 | 500 | 516 508 461 509 510 = 0.78 || = 0.09 515 516 548 482 520 | 500 -----------------------------------------------------------------| 500 | 482 515 527 521 509 = 0.77 || = 0.08 466 546 488 504 502 | 500 Aver./ d 0.50178 499 > 500: 4 3 7 4 5 7 3 5 4 7 | 500 | 492 498 476 520 539 = 0.76 || = 0.07 505 490 510 487 523 | 500 median s 0.49890 499 ----- 5 6 8 3 5 5 3 5 5 5 | 500 | 466 529 511 486 464 = 0.75 || = 0.06 513 475 488 506 528 | 500 t 0.49873 501 7 7 4 6 6 5 5 5 5 5 | 500 | 512 499 499 530 487 = 0.74 || = 0.05 468 532 513 483 482 | 500 m 0.50030 498 4 6 5 5 3 5 3 8 5 2 | 500 | 485 486 513 504 483 = 0.73 || = 0.04 458 535 501 499 516 | 500 x 0.49977 502 7 5 3 5 5 5 7 4 5 4 | 500 | 544 456 469 491 491 = 0.72 || = 0.03 465 533 519 473 509 | 500 -----------------------------------------------------------------| 500 | 488 476 542 505 496 = 0.71 || = 0.02 518 489 502 504 486 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 471 519 492 490 491 = 0.70 || = 0.01 245 244 250 252 260 | 252.5 d 0 0 1 17 67 13 3 0 0 | 500 | 490 512 506 480 515 = 0.69 || < 0.01 492 492 506 541 466 | 497.5 s 0 0 2 19 58 21 1 0 0 | 500 | 485 476 469 485 526 = 0.68 ||========================================================================= t 0 0 0 16 71 12 2 0 0 | 500 | 525 453 507 484 483 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 12 75 10 3 0 0 | 500 | 453 484 539 516 506 = 0.66 ||========================================================================= x 0 0 1 18 66 15 0 1 0 | 500 | 490 542 482 461 479 = 0.65 || sstring_HammingIndep test: no 221 test no 222 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 222 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 3 2 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 513 497 503 505 482 | 500 < 0.00002 1 0 0 0 0 | 0.5 | 0 1 0 1 1 > 0.99998 || = 0.63 514 533 468 560 481 | 500 < 0.00003 1 2 1 0 1 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 503 513 509 524 500 | 500 < 0.00004 1 1 1 1 0 | 0.5 | 0 0 2 0 1 > 0.99996 || = 0.61 495 524 496 531 513 | 500 < 0.00005 0 0 0 0 1 | 0.5 | 0 0 0 0 2 > 0.99995 || = 0.60 498 472 533 529 506 | 500 < 0.00006 0 0 2 0 0 | 0.5 | 0 0 1 1 0 > 0.99994 || = 0.59 523 492 509 514 464 | 500 < 0.00007 0 1 1 0 0 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 488 482 490 533 478 | 500 < 0.00008 0 1 1 0 1 | 0.5 | 0 0 0 2 0 > 0.99992 || = 0.57 517 479 481 461 525 | 500 < 0.00009 0 0 0 0 2 | 0.5 | 2 1 0 2 0 > 0.99991 || = 0.56 489 487 530 509 519 | 500 < 0.0001 0 1 0 0 1 | 0.5 | 0 0 0 0 1 > 0.9999 || = 0.55 520 473 497 511 481 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 476 524 537 506 486 | 500 < 0.0001 4 6 7 4 8 | 5 | 2 3 3 7 5 > 0.9999 || = 0.53 521 473 541 497 489 | 500 < 0.0002 9 7 8 3 4 | 5 | 1 3 2 3 2 > 0.9998 || = 0.52 500 535 484 506 477 | 500 < 0.0003 4 4 5 10 3 | 5 | 8 3 1 3 6 > 0.9997 || = 0.51 474 536 493 503 472 | 500 < 0.0004 3 2 3 4 8 | 5 | 4 4 3 3 3 > 0.9996 || = 0.50 517 499 490 482 526 | 500 < 0.0005 4 5 5 4 4 | 5 | 4 5 5 2 4 > 0.9995 || = 0.49 478 513 455 529 486 | 500 < 0.0006 6 5 12 6 2 | 5 | 3 7 4 8 2 > 0.9994 || = 0.48 524 504 527 514 476 | 500 < 0.0007 4 7 4 3 5 | 5 | 4 11 4 7 10 > 0.9993 || = 0.47 506 535 526 510 488 | 500 < 0.0008 5 7 3 4 5 | 5 | 5 4 4 4 3 > 0.9992 || = 0.46 523 501 493 494 496 | 500 < 0.0009 7 7 6 6 6 | 5 | 5 4 3 2 5 > 0.9991 || = 0.45 471 480 497 490 470 | 500 < 0.001 6 3 2 7 4 | 5 | 4 4 10 8 3 > 0.999 || = 0.44 521 470 467 503 533 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 515 490 494 497 528 | 500 < 0.001 52 53 55 51 49 | 50 | 40 48 39 47 43 > 0.999 || = 0.42 472 452 495 490 457 | 500 < 0.002 50 53 51 45 53 | 50 | 57 49 53 55 38 > 0.998 || = 0.41 534 511 484 514 506 | 500 < 0.003 41 41 52 51 47 | 50 | 45 47 47 62 45 > 0.997 || = 0.40 491 458 494 486 525 | 500 < 0.004 39 46 57 67 42 | 50 | 41 54 46 38 47 > 0.996 || = 0.39 476 511 474 505 514 | 500 < 0.005 53 62 57 36 54 | 50 | 48 60 56 55 51 > 0.995 || = 0.38 505 531 501 526 472 | 500 < 0.006 54 35 59 48 51 | 50 | 45 62 66 46 49 > 0.994 || = 0.37 526 469 493 530 507 | 500 < 0.007 47 64 46 60 46 | 50 | 48 47 37 58 67 > 0.993 || = 0.36 527 464 508 515 507 | 500 < 0.008 43 56 51 56 52 | 50 | 51 46 54 51 62 > 0.992 || = 0.35 507 520 508 478 520 | 500 < 0.009 48 46 45 44 44 | 50 | 47 54 61 56 41 > 0.991 || = 0.34 506 485 507 493 477 | 500 < 0.01 41 54 55 45 49 | 50 | 50 61 53 62 49 > 0.99 || = 0.33 456 539 528 460 494 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 516 508 521 530 518 | 500 < 0.01 468 510 528 503 487 | 497.5 | 472 528 512 530 492 > 0.99 || = 0.31 498 534 533 483 492 | 500 = 0.01 258 271 237 249 268 | 252.5 | 244 217 248 258 278 = 0.99 || = 0.30 515 468 502 481 514 | 500 = 0.02 484 529 480 526 488 | 500 | 511 500 531 504 490 = 0.98 || = 0.29 490 516 474 509 533 | 500 =================================================================| 500 | 467 483 524 446 517 = 0.97 || = 0.28 475 532 430 531 494 | 500 sstring_HammingIndep test: | 500 | 476 497 474 509 523 = 0.96 || = 0.27 485 483 493 537 518 | 500 ----------------------------------------------- | 500 | 485 545 484 487 506 = 0.95 || = 0.26 498 500 512 514 546 | 500 N = 10, n = 30000000, r = 0, s = 3, L = 30, d = 0 | 500 | 490 506 486 504 489 = 0.94 || = 0.25 473 523 544 531 540 | 500 Counters with expected numbers >= 10 | 500 | 506 502 523 486 484 = 0.93 || = 0.24 518 498 478 468 468 | 500 Test on the sum of all N observations | 500 | 472 486 511 453 487 = 0.92 || = 0.23 481 443 491 488 525 | 500 =================================================================| 500 | 541 499 498 507 545 = 0.91 || = 0.22 485 531 533 458 505 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 541 491 455 513 502 = 0.90 || = 0.21 484 542 552 472 504 | 500 -----------------------------------------------------------------| 500 | 493 524 489 525 489 = 0.89 || = 0.20 513 505 488 507 490 | 500 SD Bern.: d 0.87988 0.86529 0.77238 | 500 | 507 482 493 523 479 = 0.88 || = 0.19 510 430 489 484 559 | 500 s 1.16271 1.22371 0.93426 | 500 | 522 486 482 494 476 = 0.87 || = 0.18 485 491 502 502 519 | 500 t 1.06483 0.74333 1.23511 | 500 | 497 459 484 484 481 = 0.86 || = 0.17 501 480 501 504 471 | 500 m 1.03850 1.19474 1.10326 | 500 | 491 503 527 487 523 = 0.85 || = 0.16 527 508 523 513 476 | 500 x 0.98599 0.56062 1.22043 | 500 | 488 504 457 524 473 = 0.84 || = 0.15 478 446 482 475 464 | 500 | 500 | 519 485 467 492 490 = 0.83 || = 0.14 494 513 504 480 480 | 500 Changes: d 54 3 4 | 500 | 508 541 541 500 509 = 0.82 || = 0.13 518 529 505 506 491 | 500 s 46 6 3 | 500 | 496 498 511 462 490 = 0.81 || = 0.12 473 511 453 501 501 | 500 t 50 4 5 | 500 | 494 492 497 470 464 = 0.80 || = 0.11 509 519 490 500 522 | 500 m 46 5 5 | 500 | 502 476 543 485 515 = 0.79 || = 0.10 528 547 516 491 490 | 500 x 52 6 4 | 500 | 508 500 471 508 485 = 0.78 || = 0.09 511 484 476 491 476 | 500 -----------------------------------------------------------------| 500 | 500 471 476 485 534 = 0.77 || = 0.08 505 500 508 507 514 | 500 Aver./ d 0.50095 498 > 500: 3 6 2 7 6 4 6 4 5 3 | 500 | 530 487 488 493 479 = 0.76 || = 0.07 457 553 551 524 520 | 500 median s 0.49760 500 ----- 6 6 6 6 5 3 6 2 4 4 | 500 | 525 503 517 458 521 = 0.75 || = 0.06 493 491 470 490 498 | 500 t 0.49928 499 5 6 4 8 2 5 5 5 3 5 | 500 | 491 463 501 485 531 = 0.74 || = 0.05 499 556 500 509 504 | 500 m 0.49976 504 5 5 6 5 5 8 9 2 4 6 | 500 | 486 477 501 523 480 = 0.73 || = 0.04 494 506 530 491 498 | 500 x 0.49960 494 4 4 7 6 4 3 3 6 3 5 | 500 | 469 498 452 468 516 = 0.72 || = 0.03 497 497 504 457 493 | 500 -----------------------------------------------------------------| 500 | 485 501 507 441 540 = 0.71 || = 0.02 484 529 480 526 488 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 498 527 499 515 484 = 0.70 || = 0.01 258 271 237 249 268 | 252.5 d 0 0 0 16 71 14 0 0 0 | 500 | 541 501 513 520 494 = 0.69 || < 0.01 468 510 528 503 487 | 497.5 s 0 1 4 14 58 20 4 0 0 | 500 | 483 496 504 516 534 = 0.68 ||========================================================================= t 0 1 4 11 63 20 2 0 0 | 500 | 540 473 500 458 481 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 12 66 18 2 0 0 | 500 | 519 515 526 519 489 = 0.66 ||========================================================================= x 0 0 0 16 67 15 3 0 0 | 500 | 497 478 496 551 509 = 0.65 || sstring_HammingIndep test: no 222 test no 223 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 223 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 0 0 | 0.5 | 0 2 1 0 0 > 0.99999 || = 0.64 503 484 508 470 532 | 500 < 0.00002 0 0 1 0 2 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 540 470 503 480 493 | 500 < 0.00003 0 0 1 0 1 | 0.5 | 1 0 0 0 1 > 0.99997 || = 0.62 499 463 502 524 526 | 500 < 0.00004 0 0 0 0 2 | 0.5 | 0 2 1 0 1 > 0.99996 || = 0.61 549 512 536 511 504 | 500 < 0.00005 0 1 1 0 1 | 0.5 | 0 0 0 0 2 > 0.99995 || = 0.60 491 491 516 463 447 | 500 < 0.00006 0 1 0 0 0 | 0.5 | 1 1 1 2 0 > 0.99994 || = 0.59 543 489 495 529 489 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 1 2 0 0 0 > 0.99993 || = 0.58 479 489 526 506 488 | 500 < 0.00008 0 0 0 0 1 | 0.5 | 0 0 0 1 1 > 0.99992 || = 0.57 519 483 503 494 466 | 500 < 0.00009 0 1 1 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 503 502 470 472 501 | 500 < 0.0001 0 0 0 1 1 | 0.5 | 0 2 0 0 1 > 0.9999 || = 0.55 535 470 520 516 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 526 510 506 498 497 | 500 < 0.0001 1 3 4 2 8 | 5 | 3 9 3 3 7 > 0.9999 || = 0.53 503 507 477 462 470 | 500 < 0.0002 6 7 9 2 6 | 5 | 1 4 3 5 6 > 0.9998 || = 0.52 538 520 519 492 501 | 500 < 0.0003 2 1 5 5 4 | 5 | 10 4 6 5 5 > 0.9997 || = 0.51 517 477 474 516 527 | 500 < 0.0004 6 8 5 5 9 | 5 | 6 1 5 4 5 > 0.9996 || = 0.50 473 496 541 519 548 | 500 < 0.0005 7 6 5 2 4 | 5 | 2 4 6 6 5 > 0.9995 || = 0.49 507 507 502 476 509 | 500 < 0.0006 2 5 3 5 6 | 5 | 3 8 10 8 4 > 0.9994 || = 0.48 479 512 510 525 480 | 500 < 0.0007 7 5 2 7 1 | 5 | 6 5 7 1 7 > 0.9993 || = 0.47 512 472 480 490 469 | 500 < 0.0008 3 4 3 5 8 | 5 | 6 1 3 4 5 > 0.9992 || = 0.46 481 501 480 505 499 | 500 < 0.0009 8 5 6 1 7 | 5 | 6 5 1 9 3 > 0.9991 || = 0.45 436 471 478 501 464 | 500 < 0.001 6 6 2 6 4 | 5 | 9 5 7 6 5 > 0.999 || = 0.44 496 516 534 519 502 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 543 488 520 484 498 | 500 < 0.001 48 50 44 40 57 | 50 | 52 46 51 51 52 > 0.999 || = 0.42 492 506 492 472 503 | 500 < 0.002 41 40 54 49 57 | 50 | 40 50 57 55 43 > 0.998 || = 0.41 489 534 496 445 479 | 500 < 0.003 46 54 42 46 56 | 50 | 52 50 70 49 56 > 0.997 || = 0.40 527 516 522 483 519 | 500 < 0.004 59 53 33 60 50 | 50 | 54 50 49 42 57 > 0.996 || = 0.39 492 483 493 518 483 | 500 < 0.005 53 39 51 39 54 | 50 | 37 56 45 48 49 > 0.995 || = 0.38 498 485 491 505 492 | 500 < 0.006 55 46 53 57 54 | 50 | 49 42 51 47 47 > 0.994 || = 0.37 485 520 494 510 497 | 500 < 0.007 58 49 50 48 52 | 50 | 42 60 31 54 44 > 0.993 || = 0.36 507 502 505 478 518 | 500 < 0.008 49 44 42 71 55 | 50 | 65 63 46 52 46 > 0.992 || = 0.35 493 519 489 507 499 | 500 < 0.009 43 60 48 42 56 | 50 | 66 44 53 59 50 > 0.991 || = 0.34 504 525 514 523 512 | 500 < 0.01 47 44 51 64 58 | 50 | 50 47 48 46 54 > 0.99 || = 0.33 503 499 511 526 493 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 495 536 509 510 489 | 500 < 0.01 499 479 468 516 549 | 497.5 | 507 508 501 503 498 > 0.99 || = 0.31 511 499 554 519 554 | 500 = 0.01 263 274 274 263 265 | 252.5 | 260 268 252 238 258 = 0.99 || = 0.30 478 479 496 466 490 | 500 = 0.02 523 505 527 507 479 | 500 | 474 522 496 499 513 = 0.98 || = 0.29 517 483 483 511 532 | 500 =================================================================| 500 | 502 480 522 522 530 = 0.97 || = 0.28 511 442 480 476 475 | 500 sstring_HammingIndep test: | 500 | 494 501 475 476 489 = 0.96 || = 0.27 517 474 526 525 483 | 500 ----------------------------------------------- | 500 | 518 549 521 516 495 = 0.95 || = 0.26 491 508 503 466 505 | 500 N = 10, n = 30000000, r = 27, s = 3, L = 30, d = 0 | 500 | 502 514 485 484 473 = 0.94 || = 0.25 478 523 515 485 503 | 500 Counters with expected numbers >= 10 | 500 | 543 506 526 495 484 = 0.93 || = 0.24 492 468 493 516 519 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 484 501 488 501 491 = 0.92 || = 0.23 448 522 504 479 500 | 500 =================================================================| 500 | 503 517 500 535 495 = 0.91 || = 0.22 437 478 511 491 494 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 506 478 471 493 465 = 0.90 || = 0.21 512 503 497 545 505 | 500 -----------------------------------------------------------------| 500 | 523 516 469 539 477 = 0.89 || = 0.20 489 517 521 485 500 | 500 SD Bern.: d 1.00116 0.82381 1.29601 | 500 | 515 509 491 490 486 = 0.88 || = 0.19 493 514 496 478 467 | 500 s 0.90429 0.93319 0.92782 | 500 | 490 479 485 511 487 = 0.87 || = 0.18 500 498 512 489 495 | 500 t 0.96359 0.98435 1.31746 | 500 | 447 482 515 524 520 = 0.86 || = 0.17 511 498 505 535 505 | 500 m 0.92722 1.47857 0.66514 | 500 | 501 522 473 482 499 = 0.85 || = 0.16 460 523 469 470 482 | 500 x 0.90435 0.76849 0.65758 | 500 | 512 489 516 506 494 = 0.84 || = 0.15 488 487 507 522 487 | 500 | 500 | 471 533 500 484 535 = 0.83 || = 0.14 536 494 458 475 496 | 500 Changes: d 50 2 5 | 500 | 518 541 481 517 488 = 0.82 || = 0.13 474 477 502 486 502 | 500 s 49 4 4 | 500 | 507 469 482 531 527 = 0.81 || = 0.12 483 498 457 502 490 | 500 t 55 5 5 | 500 | 512 470 477 504 525 = 0.80 || = 0.11 508 520 501 518 500 | 500 m 58 7 3 | 500 | 462 508 462 520 497 = 0.79 || = 0.10 518 531 492 502 516 | 500 x 55 2 4 | 500 | 499 505 535 505 535 = 0.78 || = 0.09 486 518 508 493 499 | 500 -----------------------------------------------------------------| 500 | 496 494 510 468 490 = 0.77 || = 0.08 478 491 495 485 498 | 500 Aver./ d 0.50163 502 > 500: 6 4 4 4 4 8 7 4 7 7 | 500 | 490 487 472 520 520 = 0.76 || = 0.07 471 509 545 502 502 | 500 median s 0.50051 501 ----- 6 4 5 5 7 4 2 6 5 9 | 500 | 486 523 466 502 531 = 0.75 || = 0.06 504 503 498 476 511 | 500 t 0.49805 500 7 5 6 5 5 6 5 3 2 4 | 500 | 502 481 500 507 511 = 0.74 || = 0.05 507 495 536 492 489 | 500 m 0.50104 502 5 5 4 8 4 4 5 7 6 5 | 500 | 520 507 492 477 487 = 0.73 || = 0.04 509 471 506 506 492 | 500 x 0.49962 498 5 3 5 3 4 3 6 6 3 4 | 500 | 510 518 547 524 531 = 0.72 || = 0.03 482 512 520 499 535 | 500 -----------------------------------------------------------------| 500 | 492 528 496 480 490 = 0.71 || = 0.02 523 505 527 507 479 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 526 482 499 484 501 = 0.70 || = 0.01 263 274 274 263 265 | 252.5 d 0 0 4 9 74 13 1 0 0 | 500 | 501 519 535 532 480 = 0.69 || < 0.01 499 479 468 516 549 | 497.5 s 0 0 1 13 75 11 1 0 0 | 500 | 515 498 467 530 522 = 0.68 ||========================================================================= t 0 0 0 18 69 11 3 0 0 | 500 | 469 494 464 480 472 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 15 70 14 1 0 0 | 500 | 477 469 472 491 491 = 0.66 ||========================================================================= x 0 0 1 10 75 12 3 0 0 | 500 | 535 485 482 521 517 = 0.65 || sstring_HammingIndep test: no 223 test no 224 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 224 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 1 1 1 0 | 0.5 | 1 0 1 0 0 > 0.99999 || = 0.64 474 497 515 477 531 | 500 < 0.00002 0 1 2 1 0 | 0.5 | 1 0 1 1 0 > 0.99998 || = 0.63 480 510 475 502 497 | 500 < 0.00003 0 1 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 497 488 527 480 483 | 500 < 0.00004 0 0 0 3 1 | 0.5 | 1 1 1 0 0 > 0.99996 || = 0.61 533 465 517 523 499 | 500 < 0.00005 0 1 0 0 0 | 0.5 | 1 2 0 1 1 > 0.99995 || = 0.60 479 507 487 540 515 | 500 < 0.00006 2 0 0 0 3 | 0.5 | 2 0 1 0 0 > 0.99994 || = 0.59 491 493 538 497 517 | 500 < 0.00007 0 1 0 0 0 | 0.5 | 1 1 1 0 0 > 0.99993 || = 0.58 485 499 506 511 536 | 500 < 0.00008 0 1 1 0 0 | 0.5 | 0 1 0 0 1 > 0.99992 || = 0.57 506 534 495 524 538 | 500 < 0.00009 0 2 0 1 2 | 0.5 | 0 2 0 1 0 > 0.99991 || = 0.56 504 509 487 472 463 | 500 < 0.0001 0 0 0 3 1 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 476 514 513 520 538 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 511 500 518 479 515 | 500 < 0.0001 4 8 4 10 7 | 5 | 7 7 6 3 2 > 0.9999 || = 0.53 503 469 511 471 503 | 500 < 0.0002 2 7 6 4 2 | 5 | 1 0 1 2 3 > 0.9998 || = 0.52 514 475 491 488 500 | 500 < 0.0003 9 8 6 8 7 | 5 | 5 5 4 2 0 > 0.9997 || = 0.51 553 501 517 518 503 | 500 < 0.0004 5 5 3 4 3 | 5 | 8 6 9 4 8 > 0.9996 || = 0.50 483 480 525 522 496 | 500 < 0.0005 11 5 8 8 3 | 5 | 7 7 3 5 3 > 0.9995 || = 0.49 525 479 534 502 466 | 500 < 0.0006 6 4 9 7 10 | 5 | 2 3 5 9 4 > 0.9994 || = 0.48 526 466 502 492 546 | 500 < 0.0007 5 10 6 5 3 | 5 | 3 6 10 6 3 > 0.9993 || = 0.47 502 529 483 511 517 | 500 < 0.0008 4 8 2 5 7 | 5 | 4 5 5 6 5 > 0.9992 || = 0.46 486 500 526 458 510 | 500 < 0.0009 9 4 6 5 3 | 5 | 6 5 4 5 5 > 0.9991 || = 0.45 479 513 499 490 502 | 500 < 0.001 11 5 4 5 3 | 5 | 4 3 8 4 4 > 0.999 || = 0.44 515 476 526 519 500 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 460 518 447 476 521 | 500 < 0.001 66 64 54 61 48 | 50 | 47 47 55 46 37 > 0.999 || = 0.42 538 476 488 523 504 | 500 < 0.002 49 58 46 59 52 | 50 | 51 44 50 35 38 > 0.998 || = 0.41 449 483 481 518 539 | 500 < 0.003 45 40 56 51 50 | 50 | 40 50 47 44 62 > 0.997 || = 0.40 453 471 501 469 511 | 500 < 0.004 52 34 50 60 54 | 50 | 49 39 44 62 57 > 0.996 || = 0.39 490 506 510 487 500 | 500 < 0.005 41 61 66 59 52 | 50 | 47 53 49 39 43 > 0.995 || = 0.38 493 507 467 522 505 | 500 < 0.006 48 60 60 46 53 | 50 | 51 42 49 45 52 > 0.994 || = 0.37 506 516 466 489 502 | 500 < 0.007 49 53 61 59 51 | 50 | 50 54 49 45 45 > 0.993 || = 0.36 483 510 481 484 496 | 500 < 0.008 47 56 43 48 59 | 50 | 45 53 56 53 55 > 0.992 || = 0.35 462 486 474 499 514 | 500 < 0.009 38 56 39 42 55 | 50 | 53 56 42 43 40 > 0.991 || = 0.34 505 512 498 504 492 | 500 < 0.01 42 54 62 50 48 | 50 | 60 39 56 47 56 > 0.99 || = 0.33 484 493 528 541 508 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 505 506 518 522 503 | 500 < 0.01 477 536 537 535 522 | 497.5 | 493 477 497 459 485 > 0.99 || = 0.31 522 491 485 524 462 | 500 = 0.01 266 224 215 259 278 | 252.5 | 253 266 225 234 261 = 0.99 || = 0.30 487 497 538 460 494 | 500 = 0.02 497 496 478 514 481 | 500 | 522 543 518 478 485 = 0.98 || = 0.29 504 536 505 457 502 | 500 =================================================================| 500 | 504 451 523 514 507 = 0.97 || = 0.28 502 514 483 518 468 | 500 sstring_HammingIndep test: | 500 | 512 453 520 477 522 = 0.96 || = 0.27 537 521 512 518 494 | 500 ----------------------------------------------- | 500 | 475 495 514 513 505 = 0.95 || = 0.26 511 511 508 479 514 | 500 N = 10, n = 30000000, r = 27, s = 3, L = 30, d = 0 | 500 | 477 486 490 539 518 = 0.94 || = 0.25 530 476 500 500 466 | 500 Counters with expected numbers >= 10 | 500 | 508 497 483 503 501 = 0.93 || = 0.24 480 466 508 486 498 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 504 497 482 494 511 = 0.92 || = 0.23 510 490 514 493 504 | 500 =================================================================| 500 | 506 480 509 500 513 = 0.91 || = 0.22 503 505 518 511 506 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 481 522 491 507 474 = 0.90 || = 0.21 504 534 509 514 540 | 500 -----------------------------------------------------------------| 500 | 490 509 517 489 491 = 0.89 || = 0.20 497 514 527 511 522 | 500 SD Bern.: d 0.91497 1.08589 0.71449 | 500 | 506 487 503 510 505 = 0.88 || = 0.19 512 460 514 513 472 | 500 s 0.97413 1.36742 0.91805 | 500 | 473 510 493 500 484 = 0.87 || = 0.18 489 460 469 476 493 | 500 t 0.93871 1.31137 0.64683 | 500 | 489 494 508 468 483 = 0.86 || = 0.17 511 512 498 485 509 | 500 m 0.96049 1.04837 1.14860 | 500 | 505 487 488 515 466 = 0.85 || = 0.16 475 506 475 499 483 | 500 x 0.98732 0.54432 1.22125 | 500 | 471 530 528 487 486 = 0.84 || = 0.15 473 502 458 496 490 | 500 | 500 | 535 522 492 488 549 = 0.83 || = 0.14 492 493 481 491 482 | 500 Changes: d 51 3 5 | 500 | 497 497 484 510 464 = 0.82 || = 0.13 489 529 497 453 540 | 500 s 51 2 4 | 500 | 511 483 487 522 498 = 0.81 || = 0.12 512 516 470 544 526 | 500 t 47 6 4 | 500 | 509 480 509 545 460 = 0.80 || = 0.11 508 529 501 526 503 | 500 m 49 3 4 | 500 | 515 504 517 527 516 = 0.79 || = 0.10 537 484 514 497 468 | 500 x 45 4 7 | 500 | 508 486 531 469 532 = 0.78 || = 0.09 511 510 488 495 479 | 500 -----------------------------------------------------------------| 500 | 523 525 533 506 496 = 0.77 || = 0.08 486 515 454 496 497 | 500 Aver./ d 0.50015 503 > 500: 4 5 8 4 5 6 6 6 4 7 | 500 | 522 504 495 488 462 = 0.76 || = 0.07 526 503 508 461 474 | 500 median s 0.49889 502 ----- 6 6 7 6 3 5 6 6 5 2 | 500 | 474 510 491 527 493 = 0.75 || = 0.06 477 490 482 509 467 | 500 t 0.50178 500 3 3 8 4 5 6 6 5 4 5 | 500 | 471 510 516 473 539 = 0.74 || = 0.05 518 527 495 479 491 | 500 m 0.49935 500 6 3 5 5 5 5 4 5 5 4 | 500 | 497 457 474 492 514 = 0.73 || = 0.04 499 495 525 519 493 | 500 x 0.50048 501 2 4 6 5 8 8 3 5 2 8 | 500 | 493 463 489 481 479 = 0.72 || = 0.03 480 502 482 523 477 | 500 -----------------------------------------------------------------| 500 | 505 528 499 526 520 = 0.71 || = 0.02 497 496 478 514 481 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 523 554 482 504 493 = 0.70 || = 0.01 266 224 215 259 278 | 252.5 d 0 0 2 13 73 11 2 0 0 | 500 | 504 482 531 497 474 = 0.69 || < 0.01 477 536 537 535 522 | 497.5 s 0 0 2 14 71 13 1 0 0 | 500 | 514 532 505 497 501 = 0.68 ||========================================================================= t 0 0 3 10 72 16 0 0 0 | 500 | 557 518 505 512 469 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 16 69 14 1 0 0 | 500 | 497 518 478 480 458 = 0.66 ||========================================================================= x 0 0 0 18 69 12 2 0 0 | 500 | 504 511 494 498 521 = 0.65 || sstring_HammingIndep test: no 224 test no 225 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 225 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 1 1 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 486 524 499 478 492 | 500 < 0.00002 0 1 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 510 519 533 491 507 | 500 < 0.00003 0 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 502 516 518 466 501 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 467 528 508 485 509 | 500 < 0.00005 1 1 0 0 1 | 0.5 | 1 1 0 0 0 > 0.99995 || = 0.60 515 543 488 516 567 | 500 < 0.00006 1 1 0 1 1 | 0.5 | 0 0 1 0 0 > 0.99994 || = 0.59 505 499 512 523 503 | 500 < 0.00007 0 1 0 2 1 | 0.5 | 0 1 1 0 1 > 0.99993 || = 0.58 538 480 506 550 476 | 500 < 0.00008 0 0 0 2 0 | 0.5 | 1 1 1 1 0 > 0.99992 || = 0.57 504 522 515 485 524 | 500 < 0.00009 0 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 484 455 498 471 494 | 500 < 0.0001 0 1 1 0 1 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 497 518 484 488 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 499 492 512 541 525 | 500 < 0.0001 3 6 3 7 8 | 5 | 2 3 3 1 2 > 0.9999 || = 0.53 547 482 454 509 505 | 500 < 0.0002 8 9 7 14 4 | 5 | 1 1 2 2 3 > 0.9998 || = 0.52 495 489 485 497 467 | 500 < 0.0003 7 7 6 8 6 | 5 | 3 1 4 2 1 > 0.9997 || = 0.51 531 540 494 486 476 | 500 < 0.0004 7 7 7 8 3 | 5 | 4 2 1 6 5 > 0.9996 || = 0.50 468 457 520 533 487 | 500 < 0.0005 8 10 5 5 4 | 5 | 6 8 4 3 3 > 0.9995 || = 0.49 568 509 532 505 483 | 500 < 0.0006 5 2 6 8 6 | 5 | 3 6 5 5 4 > 0.9994 || = 0.48 512 510 492 457 471 | 500 < 0.0007 7 0 4 3 6 | 5 | 4 2 7 3 5 > 0.9993 || = 0.47 506 489 508 496 495 | 500 < 0.0008 6 8 4 5 6 | 5 | 2 5 6 9 5 > 0.9992 || = 0.46 524 521 507 513 485 | 500 < 0.0009 6 6 5 5 7 | 5 | 5 5 5 6 5 > 0.9991 || = 0.45 503 491 471 491 484 | 500 < 0.001 5 5 4 1 6 | 5 | 7 2 4 3 2 > 0.999 || = 0.44 462 489 533 489 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 456 490 494 522 492 | 500 < 0.001 62 60 51 64 56 | 50 | 37 35 41 40 35 > 0.999 || = 0.42 483 470 449 470 546 | 500 < 0.002 47 48 46 48 51 | 50 | 42 43 49 42 41 > 0.998 || = 0.41 485 493 498 476 491 | 500 < 0.003 68 60 55 54 63 | 50 | 37 48 51 39 45 > 0.997 || = 0.40 511 498 523 501 477 | 500 < 0.004 45 61 52 49 55 | 50 | 45 48 46 47 38 > 0.996 || = 0.39 455 470 531 471 478 | 500 < 0.005 52 48 54 53 49 | 50 | 58 41 47 49 57 > 0.995 || = 0.38 473 524 521 510 489 | 500 < 0.006 38 48 68 47 52 | 50 | 53 46 52 46 42 > 0.994 || = 0.37 542 486 487 473 471 | 500 < 0.007 48 43 59 53 56 | 50 | 57 55 59 69 61 > 0.993 || = 0.36 500 558 484 485 520 | 500 < 0.008 51 52 38 61 65 | 50 | 58 48 64 54 49 > 0.992 || = 0.35 502 460 465 503 513 | 500 < 0.009 39 51 69 52 54 | 50 | 54 55 50 51 38 > 0.991 || = 0.34 524 496 504 514 535 | 500 < 0.01 36 32 54 47 46 | 50 | 47 38 57 59 58 > 0.99 || = 0.33 471 513 481 457 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 493 486 497 480 488 | 500 < 0.01 486 503 546 528 547 | 497.5 | 488 457 516 496 464 > 0.99 || = 0.31 487 539 516 492 523 | 500 = 0.01 243 238 254 231 290 | 252.5 | 271 292 264 267 251 = 0.99 || = 0.30 494 471 494 492 493 | 500 = 0.02 525 524 477 525 525 | 500 | 533 528 514 519 524 = 0.98 || = 0.29 489 483 494 483 470 | 500 =================================================================| 500 | 513 509 501 454 498 = 0.97 || = 0.28 525 521 491 487 509 | 500 sstring_HammingIndep test: | 500 | 530 499 478 493 531 = 0.96 || = 0.27 493 523 499 520 487 | 500 ----------------------------------------------- | 500 | 508 519 474 574 511 = 0.95 || = 0.26 488 497 514 487 490 | 500 N = 10, n = 30000000, r = 27, s = 3, L = 30, d = 0 | 500 | 500 426 487 491 511 = 0.94 || = 0.25 498 503 488 507 474 | 500 Counters with expected numbers >= 10 | 500 | 513 480 515 482 503 = 0.93 || = 0.24 467 514 515 481 501 | 500 Anderson-Darling statistic = A2 | 500 | 528 503 470 522 506 = 0.92 || = 0.23 565 530 537 504 515 | 500 =================================================================| 500 | 516 508 479 501 499 = 0.91 || = 0.22 499 521 479 503 531 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 481 483 503 495 515 = 0.90 || = 0.21 481 481 503 494 502 | 500 -----------------------------------------------------------------| 500 | 496 515 473 513 490 = 0.89 || = 0.20 512 515 445 478 508 | 500 SD Bern.: d 1.06642 1.39496 1.13015 | 500 | 531 512 518 508 524 = 0.88 || = 0.19 471 526 508 516 467 | 500 s 1.12024 1.19306 1.07477 | 500 | 476 490 517 505 474 = 0.87 || = 0.18 466 508 488 498 485 | 500 t 1.01334 1.40640 0.93640 | 500 | 493 443 499 510 509 = 0.86 || = 0.17 489 517 513 479 518 | 500 m 0.99237 0.86991 1.24157 | 500 | 472 561 515 482 502 = 0.85 || = 0.16 511 516 541 491 458 | 500 x 0.97213 1.02910 1.35566 | 500 | 536 489 468 487 478 = 0.84 || = 0.15 503 455 518 484 542 | 500 | 500 | 523 470 518 500 497 = 0.83 || = 0.14 497 514 500 535 470 | 500 Changes: d 46 7 2 | 500 | 487 514 511 518 507 = 0.82 || = 0.13 476 503 479 517 508 | 500 s 47 5 4 | 500 | 502 464 484 508 491 = 0.81 || = 0.12 519 511 509 543 506 | 500 t 56 4 5 | 500 | 452 521 427 480 511 = 0.80 || = 0.11 512 533 489 512 496 | 500 m 43 7 1 | 500 | 502 507 486 480 506 = 0.79 || = 0.10 495 521 512 539 489 | 500 x 45 3 5 | 500 | 476 484 522 452 498 = 0.78 || = 0.09 472 480 486 499 481 | 500 -----------------------------------------------------------------| 500 | 530 490 500 487 485 = 0.77 || = 0.08 522 493 452 487 488 | 500 Aver./ d 0.50106 499 > 500: 6 4 3 3 6 6 2 5 4 8 | 500 | 520 469 521 483 497 = 0.76 || = 0.07 516 503 533 498 504 | 500 median s 0.49830 499 ----- 4 9 7 4 3 4 6 2 4 6 | 500 | 485 477 495 492 501 = 0.75 || = 0.06 515 503 495 493 480 | 500 t 0.50028 502 4 6 4 4 5 4 7 6 6 5 | 500 | 491 484 533 536 539 = 0.74 || = 0.05 506 490 473 490 548 | 500 m 0.49959 498 4 6 4 3 4 5 5 3 6 5 | 500 | 499 481 505 512 474 = 0.73 || = 0.04 521 498 478 523 503 | 500 x 0.50020 498 6 4 6 4 1 5 6 4 5 6 | 500 | 523 491 517 494 496 = 0.72 || = 0.03 477 481 506 536 460 | 500 -----------------------------------------------------------------| 500 | 537 482 512 506 471 = 0.71 || = 0.02 525 524 477 525 525 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 496 500 539 512 497 = 0.70 || = 0.01 243 238 254 231 290 | 252.5 d 0 0 2 19 60 17 2 1 0 | 500 | 473 477 519 501 531 = 0.69 || < 0.01 486 503 546 528 547 | 497.5 s 0 1 3 11 70 12 4 0 0 | 500 | 469 480 522 527 516 = 0.68 ||========================================================================= t 0 1 4 9 76 10 1 0 0 | 500 | 470 499 487 518 508 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 9 75 13 1 1 0 | 500 | 482 506 458 532 499 = 0.66 ||========================================================================= x 0 0 0 16 68 12 4 1 0 | 500 | 460 558 518 479 489 = 0.65 || sstring_HammingIndep test: no 225 test no 226 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 226 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 1 1 0 1 | 0.5 | 0 1 0 2 2 > 0.99999 || = 0.64 474 509 525 485 467 | 500 < 0.00002 1 2 0 2 1 | 0.5 | 2 1 1 1 1 > 0.99998 || = 0.63 484 473 466 522 493 | 500 < 0.00003 1 1 0 1 0 | 0.5 | 0 0 1 1 2 > 0.99997 || = 0.62 526 467 553 512 498 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 1 2 0 2 > 0.99996 || = 0.61 499 480 492 484 544 | 500 < 0.00005 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 495 484 510 534 564 | 500 < 0.00006 0 0 1 1 1 | 0.5 | 1 0 0 1 0 > 0.99994 || = 0.59 509 511 527 494 507 | 500 < 0.00007 1 1 0 1 1 | 0.5 | 1 0 1 2 0 > 0.99993 || = 0.58 499 509 504 532 484 | 500 < 0.00008 1 1 1 1 0 | 0.5 | 0 0 1 1 1 > 0.99992 || = 0.57 495 509 496 525 538 | 500 < 0.00009 0 1 1 1 0 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 504 464 514 492 479 | 500 < 0.0001 0 0 0 2 2 | 0.5 | 0 2 2 2 1 > 0.9999 || = 0.55 517 480 496 493 423 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 504 484 476 480 492 | 500 < 0.0001 6 8 4 9 6 | 5 | 4 6 8 10 9 > 0.9999 || = 0.53 529 549 487 514 486 | 500 < 0.0002 7 10 5 9 6 | 5 | 2 1 4 2 0 > 0.9998 || = 0.52 527 506 544 501 543 | 500 < 0.0003 11 3 5 5 6 | 5 | 5 6 4 6 6 > 0.9997 || = 0.51 480 479 545 531 481 | 500 < 0.0004 5 4 4 6 2 | 5 | 4 4 5 3 7 > 0.9996 || = 0.50 506 530 482 499 510 | 500 < 0.0005 7 13 4 5 4 | 5 | 5 7 7 3 7 > 0.9995 || = 0.49 510 515 492 495 513 | 500 < 0.0006 3 7 4 3 6 | 5 | 2 3 4 4 4 > 0.9994 || = 0.48 503 470 485 484 456 | 500 < 0.0007 9 3 8 7 6 | 5 | 5 5 4 5 5 > 0.9993 || = 0.47 489 518 515 515 478 | 500 < 0.0008 10 5 2 5 8 | 5 | 2 4 5 4 3 > 0.9992 || = 0.46 529 495 503 491 508 | 500 < 0.0009 4 4 5 5 8 | 5 | 8 6 3 2 6 > 0.9991 || = 0.45 515 486 537 495 511 | 500 < 0.001 7 8 5 9 14 | 5 | 6 6 5 5 3 > 0.999 || = 0.44 459 519 530 497 523 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 510 501 520 486 489 | 500 < 0.001 69 65 46 63 66 | 50 | 43 48 49 44 50 > 0.999 || = 0.42 469 522 471 477 513 | 500 < 0.002 39 51 54 54 52 | 50 | 55 42 44 53 50 > 0.998 || = 0.41 533 480 475 514 480 | 500 < 0.003 54 42 68 44 48 | 50 | 51 46 58 45 61 > 0.997 || = 0.40 490 493 489 496 506 | 500 < 0.004 51 57 53 58 52 | 50 | 46 51 44 41 56 > 0.996 || = 0.39 518 487 515 503 500 | 500 < 0.005 35 40 56 71 56 | 50 | 49 45 35 37 52 > 0.995 || = 0.38 486 504 464 527 514 | 500 < 0.006 41 43 53 45 44 | 50 | 57 61 65 51 36 > 0.994 || = 0.37 478 509 506 486 499 | 500 < 0.007 57 39 53 51 57 | 50 | 45 50 58 54 44 > 0.993 || = 0.36 511 480 543 501 507 | 500 < 0.008 49 45 42 53 61 | 50 | 46 45 56 51 52 > 0.992 || = 0.35 495 472 445 473 477 | 500 < 0.009 42 57 52 48 49 | 50 | 62 48 47 49 46 > 0.991 || = 0.34 475 509 503 494 488 | 500 < 0.01 57 48 48 51 62 | 50 | 39 44 40 53 44 > 0.99 || = 0.33 484 519 529 482 535 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 502 459 517 534 508 | 500 < 0.01 494 487 525 538 547 | 497.5 | 493 480 496 478 491 > 0.99 || = 0.31 502 509 501 544 502 | 500 = 0.01 233 294 243 260 253 | 252.5 | 255 261 241 257 250 = 0.99 || = 0.30 504 477 509 504 536 | 500 = 0.02 549 453 509 482 483 | 500 | 521 502 481 498 510 = 0.98 || = 0.29 497 518 496 518 500 | 500 =================================================================| 500 | 487 484 494 463 542 = 0.97 || = 0.28 515 497 532 487 527 | 500 sstring_HammingIndep test: | 500 | 526 519 516 531 501 = 0.96 || = 0.27 529 505 486 496 494 | 500 ----------------------------------------------- | 500 | 486 478 515 465 486 = 0.95 || = 0.26 515 514 462 505 514 | 500 N = 10, n = 30000000, r = 27, s = 3, L = 30, d = 0 | 500 | 505 494 550 540 547 = 0.94 || = 0.25 483 460 498 462 507 | 500 Counters with expected numbers >= 10 | 500 | 495 511 483 491 483 = 0.93 || = 0.24 499 472 500 492 510 | 500 Test on the sum of all N observations | 500 | 554 454 540 501 491 = 0.92 || = 0.23 505 513 466 487 493 | 500 =================================================================| 500 | 485 499 490 494 501 = 0.91 || = 0.22 534 498 506 483 471 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 469 523 513 522 514 = 0.90 || = 0.21 520 489 524 509 526 | 500 -----------------------------------------------------------------| 500 | 551 445 514 470 511 = 0.89 || = 0.20 487 470 525 496 475 | 500 SD Bern.: d 0.95252 1.39209 0.94598 | 500 | 463 486 455 506 469 = 0.88 || = 0.19 527 554 486 483 504 | 500 s 1.08160 1.17275 0.76979 | 500 | 486 555 490 506 482 = 0.87 || = 0.18 505 491 467 491 474 | 500 t 1.06300 0.99145 1.26237 | 500 | 475 477 487 527 525 = 0.86 || = 0.17 476 517 499 515 515 | 500 m 0.92759 1.23835 0.83467 | 500 | 536 525 506 523 551 = 0.85 || = 0.16 514 507 498 490 499 | 500 x 1.07703 1.14512 0.94809 | 500 | 499 475 459 496 519 = 0.84 || = 0.15 484 520 493 496 479 | 500 | 500 | 460 503 528 489 512 = 0.83 || = 0.14 482 512 495 458 473 | 500 Changes: d 58 6 6 | 500 | 470 496 511 503 489 = 0.82 || = 0.13 520 534 508 535 496 | 500 s 58 5 4 | 500 | 481 523 520 528 501 = 0.81 || = 0.12 484 556 500 512 478 | 500 t 43 4 4 | 500 | 465 506 539 492 488 = 0.80 || = 0.11 505 488 493 503 504 | 500 m 53 6 5 | 500 | 510 509 509 499 492 = 0.79 || = 0.10 510 521 478 494 496 | 500 x 52 6 4 | 500 | 467 500 492 466 500 = 0.78 || = 0.09 508 497 512 556 473 | 500 -----------------------------------------------------------------| 500 | 540 511 496 466 461 = 0.77 || = 0.08 529 485 503 499 527 | 500 Aver./ d 0.49921 501 > 500: 4 6 6 5 6 6 6 4 2 5 | 500 | 474 493 526 509 541 = 0.76 || = 0.07 473 536 492 505 478 | 500 median s 0.49821 501 ----- 4 8 4 5 5 5 4 6 5 4 | 500 | 474 472 500 523 520 = 0.75 || = 0.06 490 492 466 474 477 | 500 t 0.50125 498 4 1 4 8 5 6 3 4 6 4 | 500 | 495 520 531 469 472 = 0.74 || = 0.05 470 511 472 527 466 | 500 m 0.49869 498 7 4 3 6 2 6 4 3 7 4 | 500 | 508 477 498 482 484 = 0.73 || = 0.04 501 546 481 513 547 | 500 x 0.50066 499 5 3 5 6 6 4 3 2 7 5 | 500 | 508 513 459 499 487 = 0.72 || = 0.03 495 489 494 527 509 | 500 -----------------------------------------------------------------| 500 | 471 533 492 509 484 = 0.71 || = 0.02 549 453 509 482 483 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 503 502 465 463 462 = 0.70 || = 0.01 233 294 243 260 253 | 252.5 d 0 0 0 18 67 13 3 0 0 | 500 | 502 527 441 485 510 = 0.69 || < 0.01 494 487 525 538 547 | 497.5 s 0 0 4 14 68 9 6 0 0 | 500 | 512 455 468 508 520 = 0.68 ||========================================================================= t 0 0 3 14 64 17 3 0 0 | 500 | 497 484 499 504 489 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 14 69 17 1 0 0 | 500 | 528 493 497 475 483 = 0.66 ||========================================================================= x 0 1 0 14 69 12 5 0 0 | 500 | 506 531 524 474 485 = 0.65 || sstring_HammingIndep test: no 226 test no 227 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 227 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 0 0 1 | 0.5 | 0 1 0 2 0 > 0.99999 || = 0.64 505 500 454 523 475 | 500 < 0.00002 0 1 1 0 2 | 0.5 | 2 0 0 0 2 > 0.99998 || = 0.63 469 527 519 544 464 | 500 < 0.00003 0 1 1 0 0 | 0.5 | 2 2 0 1 1 > 0.99997 || = 0.62 477 524 533 489 500 | 500 < 0.00004 0 0 2 0 0 | 0.5 | 0 1 0 2 1 > 0.99996 || = 0.61 508 493 502 495 453 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 1 0 0 1 1 > 0.99995 || = 0.60 515 506 503 539 461 | 500 < 0.00006 0 0 0 1 0 | 0.5 | 1 0 0 1 1 > 0.99994 || = 0.59 530 497 533 497 496 | 500 < 0.00007 1 0 1 0 1 | 0.5 | 0 2 1 1 1 > 0.99993 || = 0.58 491 521 511 496 498 | 500 < 0.00008 0 0 0 0 1 | 0.5 | 1 1 0 1 1 > 0.99992 || = 0.57 512 510 473 495 502 | 500 < 0.00009 1 1 0 1 1 | 0.5 | 1 1 0 1 1 > 0.99991 || = 0.56 486 503 503 464 513 | 500 < 0.0001 1 0 0 0 1 | 0.5 | 0 0 2 1 1 > 0.9999 || = 0.55 540 447 468 475 508 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 491 489 523 521 536 | 500 < 0.0001 5 3 5 3 7 | 5 | 8 8 3 11 10 > 0.9999 || = 0.53 470 473 479 518 483 | 500 < 0.0002 2 4 3 4 8 | 5 | 2 2 1 2 0 > 0.9998 || = 0.52 496 502 522 493 494 | 500 < 0.0003 5 6 6 5 3 | 5 | 6 3 3 6 6 > 0.9997 || = 0.51 502 507 506 453 474 | 500 < 0.0004 5 3 7 2 6 | 5 | 6 3 6 7 4 > 0.9996 || = 0.50 480 502 533 508 520 | 500 < 0.0005 6 4 6 5 10 | 5 | 6 5 4 6 5 > 0.9995 || = 0.49 501 515 470 488 464 | 500 < 0.0006 3 3 8 4 5 | 5 | 4 7 6 6 3 > 0.9994 || = 0.48 483 496 510 513 504 | 500 < 0.0007 6 6 10 4 3 | 5 | 13 1 6 7 3 > 0.9993 || = 0.47 503 511 480 516 558 | 500 < 0.0008 4 4 5 5 6 | 5 | 4 6 4 9 6 > 0.9992 || = 0.46 516 489 475 486 472 | 500 < 0.0009 6 2 2 3 2 | 5 | 4 7 3 3 7 > 0.9991 || = 0.45 469 486 514 476 494 | 500 < 0.001 7 2 3 2 3 | 5 | 4 5 3 4 5 > 0.999 || = 0.44 511 538 470 489 515 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 510 513 505 530 516 | 500 < 0.001 49 37 55 37 53 | 50 | 57 47 39 61 49 > 0.999 || = 0.42 476 497 522 520 516 | 500 < 0.002 53 47 55 42 42 | 50 | 45 59 49 59 36 > 0.998 || = 0.41 478 487 433 466 476 | 500 < 0.003 47 49 59 45 43 | 50 | 64 53 52 51 48 > 0.997 || = 0.40 491 517 493 484 518 | 500 < 0.004 52 52 52 53 54 | 50 | 56 54 51 51 50 > 0.996 || = 0.39 551 475 473 508 479 | 500 < 0.005 44 52 46 41 75 | 50 | 65 46 47 47 44 > 0.995 || = 0.38 503 469 506 473 527 | 500 < 0.006 46 59 56 64 48 | 50 | 52 44 62 50 43 > 0.994 || = 0.37 467 514 505 529 493 | 500 < 0.007 44 54 58 59 41 | 50 | 47 45 52 46 53 > 0.993 || = 0.36 557 497 529 481 508 | 500 < 0.008 41 59 47 58 42 | 50 | 56 49 50 45 60 > 0.992 || = 0.35 504 535 490 472 490 | 500 < 0.009 45 53 46 58 56 | 50 | 55 42 56 56 47 > 0.991 || = 0.34 460 544 505 534 499 | 500 < 0.01 48 40 56 63 53 | 50 | 55 55 52 58 53 > 0.99 || = 0.33 518 500 494 508 496 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 498 492 477 530 517 | 500 < 0.01 469 502 530 520 507 | 497.5 | 552 494 510 524 483 > 0.99 || = 0.31 507 469 482 519 508 | 500 = 0.01 242 260 292 256 262 | 252.5 | 264 251 257 283 275 = 0.99 || = 0.30 510 557 519 507 500 | 500 = 0.02 464 522 502 511 483 | 500 | 508 520 479 485 512 = 0.98 || = 0.29 464 517 502 510 504 | 500 =================================================================| 500 | 553 488 502 525 490 = 0.97 || = 0.28 502 487 489 468 500 | 500 sstring_HammingIndep test: | 500 | 492 470 516 522 486 = 0.96 || = 0.27 509 522 517 494 502 | 500 ----------------------------------------------- | 500 | 468 459 485 491 472 = 0.95 || = 0.26 497 482 543 484 487 | 500 N = 1, n = 30000000, r = 0, s = 4, L = 300, d = 0 | 500 | 480 516 490 524 501 = 0.94 || = 0.25 504 529 469 492 500 | 500 Counters with expected numbers >= 10 | 500 | 519 505 499 507 501 = 0.93 || = 0.24 475 491 512 490 484 | 500 Number of degrees of freedom : 4117 | 500 | 560 485 482 531 526 = 0.92 || = 0.23 440 496 537 510 485 | 500 =================================================================| 500 | 501 526 490 528 489 = 0.91 || = 0.22 487 489 484 523 505 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 476 476 500 486 509 = 0.90 || = 0.21 464 477 505 491 501 | 500 -----------------------------------------------------------------| 500 | 481 504 479 423 498 = 0.89 || = 0.20 493 491 497 490 475 | 500 SD Bern.: d 1.06983 0.66515 1.12304 | 500 | 537 473 495 513 498 = 0.88 || = 0.19 494 499 530 476 499 | 500 s 0.89918 0.97413 0.75136 | 500 | 487 489 515 511 489 = 0.87 || = 0.18 474 500 467 537 504 | 500 t 1.05159 0.79032 0.80537 | 500 | 472 506 509 493 509 = 0.86 || = 0.17 503 466 518 505 468 | 500 m 0.97813 1.35861 0.84183 | 500 | 518 510 518 470 536 = 0.85 || = 0.16 478 472 547 477 502 | 500 x 0.88575 1.38416 0.90929 | 500 | 526 499 505 497 476 = 0.84 || = 0.15 505 503 514 489 513 | 500 | 500 | 505 492 485 479 507 = 0.83 || = 0.14 468 521 472 494 486 | 500 Changes: d 51 4 4 | 500 | 550 522 466 471 478 = 0.82 || = 0.13 495 515 518 468 512 | 500 s 49 2 3 | 500 | 514 489 491 514 504 = 0.81 || = 0.12 486 515 502 505 484 | 500 t 50 4 5 | 500 | 540 511 537 510 536 = 0.80 || = 0.11 505 491 482 489 487 | 500 m 46 3 2 | 500 | 471 509 494 496 477 = 0.79 || = 0.10 509 468 494 527 528 | 500 x 53 4 3 | 500 | 531 512 467 492 490 = 0.78 || = 0.09 528 509 531 499 517 | 500 -----------------------------------------------------------------| 500 | 497 496 498 504 506 = 0.77 || = 0.08 489 508 482 526 512 | 500 Aver./ d 0.50348 500 > 500: 3 4 3 7 5 5 4 6 6 7 | 500 | 513 507 505 462 512 = 0.76 || = 0.07 524 462 538 508 509 | 500 median s 0.49866 500 ----- 8 4 3 4 5 6 3 6 4 4 | 500 | 506 505 483 479 510 = 0.75 || = 0.06 497 563 498 518 495 | 500 t 0.49706 502 8 6 6 5 4 7 5 5 4 4 | 500 | 483 503 465 489 492 = 0.74 || = 0.05 500 518 523 508 476 | 500 m 0.49981 497 7 4 3 7 4 3 4 4 3 8 | 500 | 499 491 512 507 471 = 0.73 || = 0.04 537 497 524 493 518 | 500 x 0.49966 501 7 5 4 4 6 4 5 5 5 5 | 500 | 531 469 516 482 503 = 0.72 || = 0.03 496 503 510 495 533 | 500 -----------------------------------------------------------------| 500 | 505 498 510 538 485 = 0.71 || = 0.02 464 522 502 511 483 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 500 497 526 486 530 = 0.70 || = 0.01 242 260 292 256 262 | 252.5 d 0 0 1 19 65 10 6 0 0 | 500 | 474 500 497 483 509 = 0.69 || < 0.01 469 502 530 520 507 | 497.5 s 0 0 1 15 76 7 2 0 0 | 500 | 497 492 446 507 491 = 0.68 ||========================================================================= t 0 1 3 13 67 15 2 0 0 | 500 | 494 466 446 519 519 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 1 13 67 19 0 0 0 | 500 | 506 491 502 487 562 = 0.66 ||========================================================================= x 0 0 1 14 75 9 2 0 0 | 500 | 507 502 480 490 503 = 0.65 || sstring_HammingIndep test: no 227 test no 228 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 228 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 1 1 | 0.5 | 0 1 0 1 0 > 0.99999 || = 0.64 497 533 498 521 477 | 500 < 0.00002 1 1 1 0 1 | 0.5 | 0 1 0 0 0 > 0.99998 || = 0.63 508 489 545 496 506 | 500 < 0.00003 1 1 0 0 1 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 502 508 508 505 495 | 500 < 0.00004 0 1 0 0 0 | 0.5 | 1 0 1 1 0 > 0.99996 || = 0.61 541 483 530 501 488 | 500 < 0.00005 2 1 1 1 1 | 0.5 | 0 0 1 0 1 > 0.99995 || = 0.60 493 513 503 500 522 | 500 < 0.00006 0 1 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99994 || = 0.59 503 505 517 502 490 | 500 < 0.00007 1 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 527 515 486 456 491 | 500 < 0.00008 0 0 2 0 0 | 0.5 | 0 0 2 0 1 > 0.99992 || = 0.57 492 507 523 525 463 | 500 < 0.00009 1 0 0 0 2 | 0.5 | 0 1 0 1 1 > 0.99991 || = 0.56 493 507 503 485 522 | 500 < 0.0001 1 2 2 0 0 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 484 506 529 495 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 515 546 526 500 479 | 500 < 0.0001 7 7 8 3 7 | 5 | 2 4 5 3 3 > 0.9999 || = 0.53 506 492 481 534 523 | 500 < 0.0002 7 5 4 4 4 | 5 | 0 2 5 4 3 > 0.9998 || = 0.52 474 515 506 540 483 | 500 < 0.0003 6 8 4 9 3 | 5 | 8 6 4 2 4 > 0.9997 || = 0.51 485 483 506 515 469 | 500 < 0.0004 5 2 11 5 9 | 5 | 10 12 0 3 2 > 0.9996 || = 0.50 508 508 470 510 471 | 500 < 0.0005 4 5 8 5 3 | 5 | 3 1 4 6 2 > 0.9995 || = 0.49 481 484 515 517 525 | 500 < 0.0006 12 3 5 1 5 | 5 | 4 5 7 3 7 > 0.9994 || = 0.48 519 504 535 521 517 | 500 < 0.0007 11 4 7 9 5 | 5 | 7 2 2 5 2 > 0.9993 || = 0.47 511 480 478 494 495 | 500 < 0.0008 5 9 2 5 5 | 5 | 3 7 2 5 5 > 0.9992 || = 0.46 524 499 516 484 494 | 500 < 0.0009 11 4 4 3 5 | 5 | 5 3 4 6 10 > 0.9991 || = 0.45 526 496 469 537 495 | 500 < 0.001 4 4 10 1 3 | 5 | 5 6 6 3 8 > 0.999 || = 0.44 479 494 547 490 489 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 469 479 478 496 496 | 500 < 0.001 72 51 63 45 49 | 50 | 47 48 39 40 46 > 0.999 || = 0.42 491 497 492 516 508 | 500 < 0.002 39 47 45 55 57 | 50 | 48 41 52 52 50 > 0.998 || = 0.41 473 534 507 448 509 | 500 < 0.003 43 39 49 38 54 | 50 | 65 45 63 46 41 > 0.997 || = 0.40 477 462 463 461 502 | 500 < 0.004 42 55 47 57 48 | 50 | 47 38 49 44 57 > 0.996 || = 0.39 475 519 477 524 530 | 500 < 0.005 59 54 49 51 55 | 50 | 50 50 51 51 45 > 0.995 || = 0.38 513 514 487 493 477 | 500 < 0.006 47 41 59 38 56 | 50 | 61 58 44 56 65 > 0.994 || = 0.37 533 477 516 527 536 | 500 < 0.007 49 55 46 49 39 | 50 | 49 54 56 45 50 > 0.993 || = 0.36 482 479 487 512 496 | 500 < 0.008 62 55 50 64 57 | 50 | 44 52 44 49 55 > 0.992 || = 0.35 487 481 479 487 497 | 500 < 0.009 46 47 47 48 49 | 50 | 63 50 54 51 53 > 0.991 || = 0.34 498 525 495 471 474 | 500 < 0.01 46 58 61 48 52 | 50 | 60 55 51 46 49 > 0.99 || = 0.33 495 460 478 495 526 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 509 494 546 507 515 | 500 < 0.01 505 502 516 493 516 | 497.5 | 534 491 503 480 511 > 0.99 || = 0.31 492 501 504 468 512 | 500 = 0.01 270 243 276 253 272 | 252.5 | 254 255 262 267 251 = 0.99 || = 0.30 491 468 510 482 486 | 500 = 0.02 473 475 480 501 527 | 500 | 498 542 468 534 493 = 0.98 || = 0.29 530 493 511 483 470 | 500 =================================================================| 500 | 495 496 509 522 478 = 0.97 || = 0.28 526 561 542 515 482 | 500 sstring_HammingIndep test: | 500 | 497 512 481 481 480 = 0.96 || = 0.27 488 465 520 519 510 | 500 ----------------------------------------------- | 500 | 481 493 478 478 517 = 0.95 || = 0.26 506 486 485 480 536 | 500 N = 1, n = 30000000, r = 26, s = 4, L = 300, d = 0 | 500 | 492 521 506 495 495 = 0.94 || = 0.25 529 531 493 488 512 | 500 Counters with expected numbers >= 10 | 500 | 525 529 527 484 508 = 0.93 || = 0.24 486 490 454 469 500 | 500 Number of degrees of freedom : 4117 | 500 | 494 536 528 535 498 = 0.92 || = 0.23 480 531 499 468 505 | 500 =================================================================| 500 | 510 512 508 502 462 = 0.91 || = 0.22 494 482 560 531 540 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 493 472 487 513 487 = 0.90 || = 0.21 498 470 455 478 496 | 500 -----------------------------------------------------------------| 500 | 506 511 493 496 509 = 0.89 || = 0.20 500 478 505 517 492 | 500 SD Bern.: d 0.89547 1.40426 1.16160 | 500 | 483 561 499 505 511 = 0.88 || = 0.19 527 502 505 488 512 | 500 s 1.06764 0.86760 0.85247 | 500 | 527 475 466 452 523 = 0.87 || = 0.18 490 502 469 494 478 | 500 t 1.04923 0.92997 0.91805 | 500 | 483 513 512 490 511 = 0.86 || = 0.17 473 477 509 508 531 | 500 m 0.96893 1.08957 0.68735 | 500 | 495 439 472 502 493 = 0.85 || = 0.16 493 485 476 446 516 | 500 x 0.89084 0.78268 0.92889 | 500 | 522 520 457 516 506 = 0.84 || = 0.15 537 515 522 528 506 | 500 | 500 | 473 520 477 526 519 = 0.83 || = 0.14 542 525 500 493 551 | 500 Changes: d 48 5 5 | 500 | 471 495 526 513 488 = 0.82 || = 0.13 483 510 476 515 492 | 500 s 57 6 3 | 500 | 504 517 461 513 515 = 0.81 || = 0.12 503 515 509 494 486 | 500 t 50 4 7 | 500 | 524 493 480 536 488 = 0.80 || = 0.11 483 516 503 495 513 | 500 m 53 6 6 | 500 | 475 516 520 510 511 = 0.79 || = 0.10 514 534 523 464 487 | 500 x 46 7 6 | 500 | 519 517 479 469 505 = 0.78 || = 0.09 502 473 481 493 496 | 500 -----------------------------------------------------------------| 500 | 477 493 499 519 496 = 0.77 || = 0.08 529 457 526 490 488 | 500 Aver./ d 0.50079 497 > 500: 4 5 4 3 4 4 6 3 4 4 | 500 | 561 493 464 502 529 = 0.76 || = 0.07 500 450 512 508 465 | 500 median s 0.50227 501 ----- 3 8 3 4 2 8 4 5 6 7 | 500 | 481 513 479 498 521 = 0.75 || = 0.06 461 501 485 489 536 | 500 t 0.49861 503 6 6 5 4 5 8 6 4 2 7 | 500 | 497 462 492 502 503 = 0.74 || = 0.05 467 500 501 557 451 | 500 m 0.50180 500 4 3 4 4 4 5 7 6 7 5 | 500 | 489 479 508 479 521 = 0.73 || = 0.04 485 499 535 499 494 | 500 x 0.49895 497 4 6 5 5 5 3 2 6 7 3 | 500 | 499 530 517 520 474 = 0.72 || = 0.03 485 524 492 469 483 | 500 -----------------------------------------------------------------| 500 | 492 501 524 498 480 = 0.71 || = 0.02 473 475 480 501 527 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 534 525 517 482 490 = 0.70 || = 0.01 270 243 276 253 272 | 252.5 d 0 0 0 13 69 18 1 0 0 | 500 | 493 483 494 478 463 = 0.69 || < 0.01 505 502 516 493 516 | 497.5 s 0 0 2 16 66 14 3 0 0 | 500 | 511 470 525 512 495 = 0.68 ||========================================================================= t 0 0 3 14 65 15 4 0 0 | 500 | 521 459 449 532 504 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 9 75 13 1 0 0 | 500 | 490 537 511 513 500 = 0.66 ||========================================================================= x 0 0 1 12 74 13 1 0 0 | 500 | 488 470 492 506 465 = 0.65 || sstring_HammingIndep test: no 228 test no 229 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 229 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 0 | 0.5 | 0 1 0 0 3 > 0.99999 || = 0.64 494 491 502 529 516 | 500 < 0.00002 0 1 1 0 1 | 0.5 | 1 1 0 0 0 > 0.99998 || = 0.63 477 473 504 504 486 | 500 < 0.00003 0 0 1 3 0 | 0.5 | 1 1 1 0 0 > 0.99997 || = 0.62 500 482 534 484 519 | 500 < 0.00004 0 0 2 2 1 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 551 495 540 432 510 | 500 < 0.00005 2 0 2 0 0 | 0.5 | 0 0 1 0 1 > 0.99995 || = 0.60 471 515 465 523 504 | 500 < 0.00006 0 1 0 2 0 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 500 483 490 478 485 | 500 < 0.00007 1 2 1 0 1 | 0.5 | 0 0 1 1 2 > 0.99993 || = 0.58 476 501 510 516 513 | 500 < 0.00008 0 0 0 0 2 | 0.5 | 1 1 1 0 0 > 0.99992 || = 0.57 489 509 496 492 551 | 500 < 0.00009 0 1 1 0 0 | 0.5 | 2 0 1 0 1 > 0.99991 || = 0.56 458 491 505 470 521 | 500 < 0.0001 0 3 1 0 2 | 0.5 | 1 0 0 0 1 > 0.9999 || = 0.55 474 469 500 511 472 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 520 509 512 504 496 | 500 < 0.0001 4 9 9 7 7 | 5 | 7 4 5 2 8 > 0.9999 || = 0.53 512 492 496 506 497 | 500 < 0.0002 5 7 8 4 2 | 5 | 1 3 2 2 4 > 0.9998 || = 0.52 501 524 449 470 546 | 500 < 0.0003 7 7 6 8 5 | 5 | 5 5 7 6 7 > 0.9997 || = 0.51 507 523 479 500 518 | 500 < 0.0004 8 3 7 5 2 | 5 | 2 7 6 2 2 > 0.9996 || = 0.50 525 494 477 506 525 | 500 < 0.0005 11 0 5 3 5 | 5 | 8 4 7 7 5 > 0.9995 || = 0.49 519 486 485 498 518 | 500 < 0.0006 9 4 5 5 6 | 5 | 4 9 5 10 10 > 0.9994 || = 0.48 525 492 497 490 511 | 500 < 0.0007 8 4 3 5 7 | 5 | 3 6 7 6 12 > 0.9993 || = 0.47 516 495 483 475 494 | 500 < 0.0008 7 9 4 3 2 | 5 | 9 3 5 4 10 > 0.9992 || = 0.46 507 523 471 522 504 | 500 < 0.0009 2 3 6 2 7 | 5 | 3 8 6 3 1 > 0.9991 || = 0.45 467 487 464 509 469 | 500 < 0.001 5 11 9 7 3 | 5 | 6 6 3 2 6 > 0.999 || = 0.44 509 513 494 522 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 481 521 532 473 480 | 500 < 0.001 66 57 62 49 46 | 50 | 48 55 53 44 65 > 0.999 || = 0.42 492 467 450 508 466 | 500 < 0.002 48 39 49 48 51 | 50 | 59 46 46 62 39 > 0.998 || = 0.41 473 504 508 505 447 | 500 < 0.003 48 47 48 41 52 | 50 | 51 48 46 50 55 > 0.997 || = 0.40 494 505 498 522 508 | 500 < 0.004 59 58 48 55 58 | 50 | 52 51 57 42 49 > 0.996 || = 0.39 485 497 496 490 493 | 500 < 0.005 48 54 56 59 46 | 50 | 57 56 47 49 34 > 0.995 || = 0.38 484 503 527 537 500 | 500 < 0.006 50 49 58 57 59 | 50 | 64 47 55 35 44 > 0.994 || = 0.37 530 526 471 495 475 | 500 < 0.007 60 50 43 54 48 | 50 | 58 77 51 52 69 > 0.993 || = 0.36 489 495 474 481 526 | 500 < 0.008 59 50 46 47 61 | 50 | 62 58 60 50 44 > 0.992 || = 0.35 511 484 491 460 521 | 500 < 0.009 48 63 55 56 42 | 50 | 40 48 51 63 49 > 0.991 || = 0.34 504 476 448 531 477 | 500 < 0.01 54 49 52 55 46 | 50 | 51 42 48 58 47 > 0.99 || = 0.33 512 464 454 481 454 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 472 494 519 503 509 | 500 < 0.01 540 516 517 521 509 | 497.5 | 542 528 514 505 495 > 0.99 || = 0.31 512 506 501 489 471 | 500 = 0.01 251 246 274 236 251 | 252.5 | 249 252 278 224 229 = 0.99 || = 0.30 494 505 555 501 485 | 500 = 0.02 550 459 527 512 511 | 500 | 517 502 509 491 496 = 0.98 || = 0.29 519 497 479 479 522 | 500 =================================================================| 500 | 501 530 475 508 500 = 0.97 || = 0.28 483 470 510 484 461 | 500 sstring_HammingIndep test: | 500 | 509 515 513 484 486 = 0.96 || = 0.27 522 499 549 473 486 | 500 ----------------------------------------------- | 500 | 500 489 504 499 486 = 0.95 || = 0.26 510 486 451 513 454 | 500 N = 1, n = 10000000, r = 0, s = 5, L = 1200, d = 0 | 500 | 498 496 465 486 487 = 0.94 || = 0.25 524 493 511 475 503 | 500 Counters with expected numbers >= 10 | 500 | 498 490 480 536 498 = 0.93 || = 0.24 490 479 512 461 508 | 500 Counters with expected numbers >= 10 | 500 | 521 541 492 489 531 = 0.92 || = 0.23 547 527 506 497 499 | 500 =================================================================| 500 | 493 492 481 522 494 = 0.91 || = 0.22 514 503 480 461 511 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 469 524 534 480 494 = 0.90 || = 0.21 513 509 489 542 489 | 500 -----------------------------------------------------------------| 500 | 475 526 499 534 497 = 0.89 || = 0.20 498 541 519 494 502 | 500 SD Bern.: d 1.00220 1.04932 1.13546 | 500 | 514 482 548 501 485 = 0.88 || = 0.19 503 489 451 480 469 | 500 s 0.94533 0.92782 1.38053 | 500 | 490 476 524 528 522 = 0.87 || = 0.18 511 488 507 557 520 | 500 t 1.13372 0.83347 0.67856 | 500 | 497 509 505 493 509 = 0.86 || = 0.17 512 490 481 479 483 | 500 m 0.99716 0.80909 1.18970 | 500 | 486 488 497 536 483 = 0.85 || = 0.16 494 461 518 504 499 | 500 x 1.06715 0.88021 1.46428 | 500 | 510 512 504 486 487 = 0.84 || = 0.15 513 524 528 481 535 | 500 | 500 | 468 465 539 480 578 = 0.83 || = 0.14 536 468 501 531 528 | 500 Changes: d 48 6 3 | 500 | 474 503 511 505 495 = 0.82 || = 0.13 491 485 549 485 542 | 500 s 50 5 5 | 500 | 454 492 485 541 481 = 0.81 || = 0.12 542 537 502 501 525 | 500 t 48 4 5 | 500 | 488 519 470 477 506 = 0.80 || = 0.11 428 481 493 523 508 | 500 m 66 3 5 | 500 | 524 477 533 498 483 = 0.79 || = 0.10 495 510 527 483 487 | 500 x 49 6 5 | 500 | 505 502 496 505 571 = 0.78 || = 0.09 528 454 471 538 529 | 500 -----------------------------------------------------------------| 500 | 500 530 509 513 511 = 0.77 || = 0.08 518 477 485 488 489 | 500 Aver./ d 0.49725 500 > 500: 6 6 7 5 5 4 3 4 2 5 | 500 | 507 483 516 495 516 = 0.76 || = 0.07 469 515 468 512 494 | 500 median s 0.50076 498 ----- 6 3 4 4 5 6 4 7 5 5 | 500 | 489 485 484 517 473 = 0.75 || = 0.06 490 533 485 493 481 | 500 t 0.50142 501 4 7 6 4 2 3 9 5 7 5 | 500 | 495 501 486 500 519 = 0.74 || = 0.05 521 515 482 538 486 | 500 m 0.50026 500 6 5 2 4 6 5 4 6 6 4 | 500 | 481 516 504 513 468 = 0.73 || = 0.04 515 558 507 524 491 | 500 x 0.50070 497 3 6 5 3 4 6 6 6 3 1 | 500 | 488 521 497 508 470 = 0.72 || = 0.03 493 529 483 466 472 | 500 -----------------------------------------------------------------| 500 | 512 518 525 524 548 = 0.71 || = 0.02 550 459 527 512 511 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 470 478 523 477 510 = 0.70 || = 0.01 251 246 274 236 251 | 252.5 d 0 1 2 14 71 9 4 0 0 | 500 | 484 505 514 494 497 = 0.69 || < 0.01 540 516 517 521 509 | 497.5 s 0 0 1 14 68 17 1 0 0 | 500 | 445 544 557 501 494 = 0.68 ||========================================================================= t 0 0 7 11 62 16 5 0 0 | 500 | 486 501 524 498 528 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 0 14 68 17 1 0 0 | 500 | 509 508 513 515 468 = 0.66 ||========================================================================= x 0 0 3 14 70 9 3 2 0 | 500 | 501 467 453 489 506 = 0.65 || sstring_HammingIndep test: no 229 test no 230 TestU01 250000 runs BigCrush Test smarsa_S sstring_HammingIndep test: test no 230 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 1 0 0 1 | 0.5 | 0 0 1 0 0 > 0.99999 || = 0.64 554 523 491 479 480 | 500 < 0.00002 4 0 0 1 1 | 0.5 | 0 0 2 1 0 > 0.99998 || = 0.63 478 472 501 510 520 | 500 < 0.00003 1 1 0 1 0 | 0.5 | 1 1 0 1 1 > 0.99997 || = 0.62 510 540 467 487 521 | 500 < 0.00004 0 2 1 0 2 | 0.5 | 0 1 0 1 0 > 0.99996 || = 0.61 502 483 519 546 509 | 500 < 0.00005 1 0 0 0 0 | 0.5 | 0 0 1 2 0 > 0.99995 || = 0.60 507 500 498 506 494 | 500 < 0.00006 0 0 1 1 2 | 0.5 | 0 0 0 1 1 > 0.99994 || = 0.59 453 519 498 517 516 | 500 < 0.00007 0 1 0 1 1 | 0.5 | 1 0 0 0 0 > 0.99993 || = 0.58 496 488 518 513 495 | 500 < 0.00008 0 0 2 1 2 | 0.5 | 2 2 0 1 1 > 0.99992 || = 0.57 553 534 526 519 521 | 500 < 0.00009 2 0 0 0 1 | 0.5 | 0 0 3 0 0 > 0.99991 || = 0.56 500 483 476 496 512 | 500 < 0.0001 0 3 0 0 0 | 0.5 | 1 0 0 1 1 > 0.9999 || = 0.55 522 513 460 468 483 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 509 512 496 505 488 | 500 < 0.0001 10 8 4 5 10 | 5 | 5 4 7 8 4 > 0.9999 || = 0.53 500 506 514 483 477 | 500 < 0.0002 6 7 2 3 6 | 5 | 4 2 3 1 5 > 0.9998 || = 0.52 472 497 506 525 498 | 500 < 0.0003 8 10 5 5 4 | 5 | 9 6 5 6 5 > 0.9997 || = 0.51 458 501 481 516 487 | 500 < 0.0004 5 4 7 4 6 | 5 | 4 3 3 7 6 > 0.9996 || = 0.50 486 517 507 480 463 | 500 < 0.0005 7 5 9 4 5 | 5 | 2 2 1 9 5 > 0.9995 || = 0.49 531 497 499 486 478 | 500 < 0.0006 6 2 2 4 2 | 5 | 7 0 6 5 6 > 0.9994 || = 0.48 526 498 538 504 513 | 500 < 0.0007 8 7 4 5 2 | 5 | 3 5 5 1 6 > 0.9993 || = 0.47 503 472 477 525 541 | 500 < 0.0008 3 5 4 3 3 | 5 | 1 4 6 7 0 > 0.9992 || = 0.46 476 523 556 507 500 | 500 < 0.0009 10 6 5 5 6 | 5 | 4 5 9 6 5 > 0.9991 || = 0.45 516 480 464 488 469 | 500 < 0.001 3 5 8 4 12 | 5 | 4 8 5 6 4 > 0.999 || = 0.44 481 516 554 477 502 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 512 504 482 506 479 | 500 < 0.001 66 59 50 42 56 | 50 | 43 39 50 56 46 > 0.999 || = 0.42 518 485 496 501 478 | 500 < 0.002 43 64 49 53 45 | 50 | 50 49 60 50 45 > 0.998 || = 0.41 478 502 504 468 523 | 500 < 0.003 53 49 49 45 60 | 50 | 52 45 50 50 41 > 0.997 || = 0.40 483 548 523 502 530 | 500 < 0.004 51 65 48 60 52 | 50 | 62 39 45 52 47 > 0.996 || = 0.39 507 517 535 449 515 | 500 < 0.005 50 49 63 47 42 | 50 | 46 62 47 48 58 > 0.995 || = 0.38 508 506 510 484 495 | 500 < 0.006 46 44 56 53 42 | 50 | 47 47 64 57 62 > 0.994 || = 0.37 515 521 500 512 497 | 500 < 0.007 54 62 66 62 45 | 50 | 45 54 59 59 56 > 0.993 || = 0.36 473 483 523 508 482 | 500 < 0.008 51 49 47 41 47 | 50 | 44 47 47 60 46 > 0.992 || = 0.35 469 508 474 509 500 | 500 < 0.009 53 44 57 52 58 | 50 | 41 45 47 48 58 > 0.991 || = 0.34 481 497 503 471 502 | 500 < 0.01 54 39 56 43 51 | 50 | 69 55 51 56 52 > 0.99 || = 0.33 492 485 465 495 467 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 486 489 432 469 478 | 500 < 0.01 521 524 541 498 498 | 497.5 | 499 482 520 536 511 > 0.99 || = 0.31 473 483 503 538 537 | 500 = 0.01 272 246 232 240 263 | 252.5 | 262 258 266 255 255 = 0.99 || = 0.30 514 489 511 502 501 | 500 = 0.02 540 524 476 475 507 | 500 | 499 501 479 498 503 = 0.98 || = 0.29 467 512 496 509 505 | 500 =================================================================| 500 | 521 475 484 519 456 = 0.97 || = 0.28 484 515 513 515 485 | 500 sstring_HammingIndep test: | 500 | 503 510 467 479 516 = 0.96 || = 0.27 517 515 484 541 493 | 500 ----------------------------------------------- | 500 | 524 492 514 520 473 = 0.95 || = 0.26 534 499 477 545 508 | 500 N = 1, n = 10000000, r = 25, s = 5, L = 1200, d = 0 | 500 | 542 496 538 473 489 = 0.94 || = 0.25 471 517 519 482 491 | 500 Counters with expected numbers >= 10 | 500 | 474 504 498 504 497 = 0.93 || = 0.24 523 500 524 481 536 | 500 Number of degrees of freedom : 11825 | 500 | 481 485 490 539 480 = 0.92 || = 0.23 539 473 491 486 498 | 500 =================================================================| 500 | 476 508 501 533 494 = 0.91 || = 0.22 504 512 503 527 478 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 488 495 548 489 479 = 0.90 || = 0.21 458 484 519 516 521 | 500 -----------------------------------------------------------------| 500 | 527 463 497 479 512 = 0.89 || = 0.20 468 489 525 472 525 | 500 SD Bern.: d 1.08276 0.86414 1.20475 | 500 | 505 522 496 504 485 = 0.88 || = 0.19 464 514 479 536 471 | 500 s 0.87113 1.29833 0.99648 | 500 | 550 481 488 515 475 = 0.87 || = 0.18 507 521 494 516 482 | 500 t 1.05708 1.05976 0.92781 | 500 | 510 506 528 498 525 = 0.86 || = 0.17 484 475 487 501 456 | 500 m 0.97721 0.99447 0.79284 | 500 | 486 482 490 474 534 = 0.85 || = 0.16 506 476 476 516 466 | 500 x 0.94800 0.88587 0.95859 | 500 | 500 474 512 496 492 = 0.84 || = 0.15 506 492 506 487 484 | 500 | 500 | 480 492 487 508 529 = 0.83 || = 0.14 472 513 522 467 506 | 500 Changes: d 48 4 3 | 500 | 501 529 500 495 509 = 0.82 || = 0.13 477 479 498 493 488 | 500 s 59 5 5 | 500 | 534 492 465 497 517 = 0.81 || = 0.12 481 525 490 518 513 | 500 t 56 3 5 | 500 | 510 494 466 528 505 = 0.80 || = 0.11 528 487 504 524 514 | 500 m 52 8 6 | 500 | 458 480 460 479 514 = 0.79 || = 0.10 513 489 469 468 460 | 500 x 43 4 3 | 500 | 550 510 492 494 512 = 0.78 || = 0.09 497 489 494 490 504 | 500 -----------------------------------------------------------------| 500 | 509 503 486 525 467 = 0.77 || = 0.08 494 511 460 513 501 | 500 Aver./ d 0.50120 502 > 500: 6 5 5 4 6 4 6 6 6 6 | 500 | 513 494 515 439 523 = 0.76 || = 0.07 457 493 539 476 555 | 500 median s 0.49785 498 ----- 6 4 5 4 5 6 4 3 3 5 | 500 | 473 489 505 486 494 = 0.75 || = 0.06 503 542 497 521 506 | 500 t 0.49977 500 5 3 6 6 5 4 6 5 3 5 | 500 | 501 498 515 528 490 = 0.74 || = 0.05 512 490 513 499 541 | 500 m 0.50062 500 4 6 6 5 6 7 3 4 3 7 | 500 | 499 525 510 500 494 = 0.73 || = 0.04 495 514 535 476 550 | 500 x 0.49875 500 10 3 5 4 5 3 5 5 6 4 | 500 | 519 494 443 501 512 = 0.72 || = 0.03 527 547 501 514 529 | 500 -----------------------------------------------------------------| 500 | 474 467 511 486 491 = 0.71 || = 0.02 540 524 476 475 507 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 516 471 514 472 463 = 0.70 || = 0.01 272 246 232 240 263 | 252.5 d 0 0 2 20 60 15 4 0 0 | 500 | 474 532 497 477 498 = 0.69 || < 0.01 521 524 541 498 498 | 497.5 s 0 0 1 11 75 12 2 0 0 | 500 | 504 494 516 485 517 = 0.68 ||========================================================================= t 0 1 1 17 65 14 3 0 0 | 500 | 532 445 511 500 519 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 68 14 2 0 0 | 500 | 452 475 487 541 494 = 0.66 ||========================================================================= x 0 0 0 13 74 12 2 0 0 | 500 | 491 524 533 495 491 = 0.65 || sstring_HammingIndep test: no 230 test no 231 TestU01 250000 runs BigCrush Test smarsa_S sstring_Run test: test no 231 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 2 2 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 446 409 488 438 455 | 500 < 0.00002 3 2 1 1 2 | 0.5 | 1 0 1 0 0 > 0.99998 || = 0.63 462 470 494 440 435 | 500 < 0.00003 0 2 3 1 2 | 0.5 | 0 0 2 0 1 > 0.99997 || = 0.62 435 467 458 455 467 | 500 < 0.00004 1 3 1 2 2 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 443 489 462 477 471 | 500 < 0.00005 0 2 1 0 4 | 0.5 | 1 0 0 0 0 > 0.99995 || = 0.60 466 462 479 490 458 | 500 < 0.00006 1 3 3 0 3 | 0.5 | 0 1 1 0 1 > 0.99994 || = 0.59 442 440 473 447 436 | 500 < 0.00007 1 1 0 0 0 | 0.5 | 1 1 0 0 0 > 0.99993 || = 0.58 465 460 487 449 459 | 500 < 0.00008 0 1 0 4 2 | 0.5 | 0 0 0 1 0 > 0.99992 || = 0.57 440 489 434 476 454 | 500 < 0.00009 1 1 2 0 3 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 440 492 462 465 497 | 500 < 0.0001 1 5 1 2 3 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 474 474 472 486 484 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 496 447 491 450 480 | 500 < 0.0001 9 20 12 12 23 | 5 | 4 3 4 1 2 > 0.9999 || = 0.53 470 471 485 447 474 | 500 < 0.0002 11 12 18 13 11 | 5 | 2 0 1 1 1 > 0.9998 || = 0.52 475 470 484 451 473 | 500 < 0.0003 14 15 7 14 14 | 5 | 3 1 3 3 4 > 0.9997 || = 0.51 519 485 492 477 516 | 500 < 0.0004 12 14 12 16 9 | 5 | 1 1 4 2 3 > 0.9996 || = 0.50 479 502 527 498 474 | 500 < 0.0005 14 13 13 13 24 | 5 | 3 5 5 4 2 > 0.9995 || = 0.49 506 536 467 470 473 | 500 < 0.0006 8 13 5 14 9 | 5 | 5 2 4 2 2 > 0.9994 || = 0.48 469 513 474 475 464 | 500 < 0.0007 10 17 14 11 21 | 5 | 5 3 2 7 4 > 0.9993 || = 0.47 481 449 512 484 507 | 500 < 0.0008 8 8 12 13 9 | 5 | 5 0 1 3 2 > 0.9992 || = 0.46 477 492 467 489 516 | 500 < 0.0009 10 10 10 13 11 | 5 | 1 6 4 4 2 > 0.9991 || = 0.45 493 491 457 469 489 | 500 < 0.001 12 7 11 13 12 | 5 | 5 2 2 1 2 > 0.999 || = 0.44 513 493 491 483 484 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 514 515 532 514 471 | 500 < 0.001 108 129 114 132 143 | 50 | 34 23 30 28 24 > 0.999 || = 0.42 498 491 492 528 526 | 500 < 0.002 82 99 105 92 106 | 50 | 30 26 30 26 31 > 0.998 || = 0.41 538 467 458 496 512 | 500 < 0.003 99 107 111 91 97 | 50 | 39 31 34 43 31 > 0.997 || = 0.40 512 483 474 498 527 | 500 < 0.004 101 84 87 98 94 | 50 | 41 28 33 34 38 > 0.996 || = 0.39 554 504 525 502 518 | 500 < 0.005 82 83 93 95 107 | 50 | 37 32 23 42 35 > 0.995 || = 0.38 506 509 509 512 499 | 500 < 0.006 101 74 82 83 86 | 50 | 39 38 30 40 34 > 0.994 || = 0.37 555 484 480 495 501 | 500 < 0.007 86 86 77 75 92 | 50 | 40 36 42 25 34 > 0.993 || = 0.36 486 531 547 536 539 | 500 < 0.008 67 82 102 106 80 | 50 | 30 33 27 42 43 > 0.992 || = 0.35 496 516 515 513 530 | 500 < 0.009 84 87 74 86 71 | 50 | 34 42 37 39 40 > 0.991 || = 0.34 488 543 533 524 564 | 500 < 0.01 76 97 82 92 90 | 50 | 27 29 43 26 35 > 0.99 || = 0.33 531 521 527 527 522 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 560 522 517 543 490 | 500 < 0.01 886 928 927 950 966 | 497.5 | 351 318 329 345 345 > 0.99 || = 0.31 527 541 480 520 535 | 500 = 0.01 425 387 410 423 391 | 252.5 | 155 182 176 176 149 = 0.99 || = 0.30 569 584 523 547 530 | 500 = 0.02 791 795 755 789 768 | 500 | 404 357 357 370 366 = 0.98 || = 0.29 548 506 515 517 513 | 500 =================================================================| 500 | 373 374 377 358 360 = 0.97 || = 0.28 543 547 586 583 521 | 500 sstring_Run test: | 500 | 402 400 374 384 395 = 0.96 || = 0.27 548 515 519 535 551 | 500 ----------------------------------------------- | 500 | 397 400 371 377 350 = 0.95 || = 0.26 493 556 566 555 528 | 500 N = 1, n = 2000000000, r = 0, s = 3 | 500 | 350 364 354 363 376 = 0.94 || = 0.25 585 541 564 537 560 | 500 Chi2 statistic for number of runs | 500 | 385 379 374 370 366 = 0.93 || = 0.24 544 543 519 544 544 | 500 | 500 | 385 380 368 420 457 = 0.92 || = 0.23 602 534 556 565 596 | 500 =================================================================| 500 | 388 392 385 399 387 = 0.91 || = 0.22 576 516 588 552 542 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 423 414 407 418 374 = 0.90 || = 0.21 562 545 567 509 583 | 500 -----------------------------------------------------------------| 500 | 431 410 424 381 424 = 0.89 || = 0.20 585 567 586 577 588 | 500 SD Bern.: d 4.37103 5.73558 2.20699 | 500 | 383 380 401 417 382 = 0.88 || = 0.19 570 622 559 601 585 | 500 s 4.49482 6.42349 2.68759 | 500 | 399 435 406 410 373 = 0.87 || = 0.18 562 562 559 599 599 | 500 t 4.33839 6.34620 2.56447 | 500 | 393 411 421 403 384 = 0.86 || = 0.17 562 572 570 602 593 | 500 m 4.60156 6.69782 2.41574 | 500 | 388 402 401 401 424 = 0.85 || = 0.16 593 602 552 584 630 | 500 x 4.52540 7.10002 2.30462 | 500 | 415 426 439 416 441 = 0.84 || = 0.15 605 622 566 588 582 | 500 | 500 | 394 406 419 412 402 = 0.83 || = 0.14 592 585 591 562 581 | 500 Changes: d 11 0 0 | 500 | 413 400 418 387 419 = 0.82 || = 0.13 623 647 608 573 601 | 500 s 7 0 0 | 500 | 381 400 416 460 425 = 0.81 || = 0.12 638 629 583 632 613 | 500 t 11 0 0 | 500 | 403 444 427 424 422 = 0.80 || = 0.11 581 596 626 637 601 | 500 m 5 0 0 | 500 | 406 414 464 413 408 = 0.79 || = 0.10 582 612 613 631 641 | 500 x 9 0 0 | 500 | 439 426 455 420 439 = 0.78 || = 0.09 592 658 631 618 645 | 500 -----------------------------------------------------------------| 500 | 441 412 426 451 392 = 0.77 || = 0.08 659 656 630 630 600 | 500 Aver./ d 0.44873 481 > 500:10 10 9 7 5 1 0 0 0 0 | 500 | 434 437 421 400 446 = 0.76 || = 0.07 617 644 642 687 620 | 500 median s 0.44779 485 ----- 10 10 10 9 3 0 0 0 0 0 | 500 | 437 419 436 448 408 = 0.75 || = 0.06 650 645 679 606 687 | 500 t 0.44996 480 10 10 10 8 2 0 0 0 0 0 | 500 | 429 457 419 447 445 = 0.74 || = 0.05 652 650 636 689 669 | 500 m 0.44695 477 10 10 10 9 2 0 0 0 0 0 | 500 | 403 441 449 422 409 = 0.73 || = 0.04 697 702 677 708 673 | 500 x 0.44725 480 10 10 10 8 5 1 0 0 0 0 | 500 | 449 426 442 435 437 = 0.72 || = 0.03 684 731 744 763 686 | 500 -----------------------------------------------------------------| 500 | 488 436 442 432 470 = 0.71 || = 0.02 791 795 755 789 768 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 422 452 438 432 440 = 0.70 || = 0.01 425 387 410 423 391 | 252.5 d 19 7 12 11 16 5 8 7 16 | 500 | 451 439 455 445 421 = 0.69 || < 0.01 886 928 927 950 966 | 497.5 s 19 7 12 10 21 7 4 4 17 | 500 | 423 445 455 437 415 = 0.68 ||========================================================================= t 14 9 11 14 19 6 8 6 14 | 500 | 467 464 456 422 456 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 15 13 14 9 16 8 5 5 16 | 500 | 461 396 471 460 455 = 0.66 ||========================================================================= x 18 7 12 13 16 9 3 5 18 | 500 | 465 435 435 428 451 = 0.65 || sstring_Run test: no 231 test no 232 TestU01 250000 runs BigCrush Test smarsa_S sstring_Run test: test no 232 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 665 709 672 650 637 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 648 712 645 673 634 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 663 680 678 664 695 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 661 731 688 677 705 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 745 639 669 666 672 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 689 712 651 680 703 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 663 694 727 753 670 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 703 664 694 700 658 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 679 697 720 674 772 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 711 688 687 692 641 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 680 713 698 671 691 | 500 < 0.0001 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9999 || = 0.53 720 654 699 725 698 | 500 < 0.0002 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 742 715 727 725 735 | 500 < 0.0003 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9997 || = 0.51 721 741 722 703 722 | 500 < 0.0004 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9996 || = 0.50 701 714 687 629 748 | 500 < 0.0005 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9995 || = 0.49 749 733 703 718 703 | 500 < 0.0006 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9994 || = 0.48 697 724 682 763 714 | 500 < 0.0007 0 0 0 1 0 | 5 | 0 0 0 0 0 > 0.9993 || = 0.47 691 743 691 720 703 | 500 < 0.0008 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9992 || = 0.46 750 712 746 680 712 | 500 < 0.0009 0 0 0 0 1 | 5 | 0 0 0 0 0 > 0.9991 || = 0.45 701 730 717 719 642 | 500 < 0.001 0 0 0 0 0 | 5 | 1 0 0 0 0 > 0.999 || = 0.44 688 710 685 720 702 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 699 741 689 691 677 | 500 < 0.001 0 0 0 1 1 | 50 | 1 0 0 0 0 > 0.999 || = 0.42 727 727 724 698 674 | 500 < 0.002 2 0 0 0 1 | 50 | 5 1 0 2 1 > 0.998 || = 0.41 671 669 618 722 683 | 500 < 0.003 1 2 0 3 0 | 50 | 2 0 1 1 0 > 0.997 || = 0.40 679 702 741 707 685 | 500 < 0.004 3 3 3 2 1 | 50 | 2 3 2 1 1 > 0.996 || = 0.39 663 665 679 640 666 | 500 < 0.005 5 2 4 4 2 | 50 | 1 4 5 5 1 > 0.995 || = 0.38 657 636 696 678 689 | 500 < 0.006 2 3 5 1 2 | 50 | 2 3 1 5 5 > 0.994 || = 0.37 649 647 652 685 715 | 500 < 0.007 3 2 4 2 2 | 50 | 3 0 3 4 2 > 0.993 || = 0.36 672 666 708 657 708 | 500 < 0.008 3 3 4 3 4 | 50 | 1 4 3 4 10 > 0.992 || = 0.35 689 657 659 642 651 | 500 < 0.009 6 4 7 3 5 | 50 | 4 4 7 6 6 > 0.991 || = 0.34 670 637 687 653 652 | 500 < 0.01 8 8 4 7 4 | 50 | 2 3 2 5 6 > 0.99 || = 0.33 659 646 667 667 633 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 669 657 638 613 622 | 500 < 0.01 33 27 31 26 22 | 497.5 | 23 22 24 33 32 > 0.99 || = 0.31 584 627 624 620 647 | 500 = 0.01 23 28 30 36 33 | 252.5 | 24 22 30 35 28 = 0.99 || = 0.30 654 623 587 622 618 | 500 = 0.02 87 75 77 74 92 | 500 | 68 97 79 68 97 = 0.98 || = 0.29 590 596 577 615 576 | 500 =================================================================| 500 | 114 119 126 121 114 = 0.97 || = 0.28 618 584 551 602 597 | 500 sstring_Run test: | 500 | 132 127 174 138 162 = 0.96 || = 0.27 576 566 607 615 574 | 500 ----------------------------------------------- | 500 | 166 181 146 204 168 = 0.95 || = 0.26 559 561 527 574 566 | 500 N = 1, n = 2000000000, r = 0, s = 3 | 500 | 212 205 214 201 217 = 0.94 || = 0.25 542 565 580 553 538 | 500 Normal statistic for number of bits | 500 | 231 238 229 214 246 = 0.93 || = 0.24 561 549 562 565 538 | 500 | 500 | 268 278 261 257 268 = 0.92 || = 0.23 550 549 543 524 594 | 500 =================================================================| 500 | 308 308 321 281 293 = 0.91 || = 0.22 528 524 482 538 562 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 301 319 337 338 335 = 0.90 || = 0.21 538 521 537 522 496 | 500 -----------------------------------------------------------------| 500 | 325 342 312 335 352 = 0.89 || = 0.20 479 466 452 517 541 | 500 SD Bern.: d 8.88970 6.61556 6.75155 | 500 | 368 328 379 339 350 = 0.88 || = 0.19 503 453 472 462 470 | 500 s 8.97140 6.69946 6.76739 | 500 | 398 378 384 379 397 = 0.87 || = 0.18 473 464 448 462 469 | 500 t 8.87958 6.64365 6.74161 | 500 | 386 387 388 415 404 = 0.86 || = 0.17 450 413 484 431 429 | 500 m 8.87132 6.71185 6.61374 | 500 | 417 394 430 403 429 = 0.85 || = 0.16 432 441 427 457 426 | 500 x 8.81436 6.76681 6.63716 | 500 | 442 419 413 434 470 = 0.84 || = 0.15 447 444 427 423 437 | 500 | 500 | 469 442 412 460 439 = 0.83 || = 0.14 380 376 368 400 406 | 500 Changes: d 4 0 0 | 500 | 416 462 456 440 494 = 0.82 || = 0.13 376 359 371 383 366 | 500 s 2 0 0 | 500 | 470 475 447 506 453 = 0.81 || = 0.12 354 376 332 341 330 | 500 t 4 0 0 | 500 | 478 500 521 451 508 = 0.80 || = 0.11 319 350 353 347 315 | 500 m 6 0 0 | 500 | 512 512 533 527 504 = 0.79 || = 0.10 311 308 293 318 274 | 500 x 4 0 0 | 500 | 548 513 512 488 524 = 0.78 || = 0.09 314 296 264 265 291 | 500 -----------------------------------------------------------------| 500 | 506 508 523 541 514 = 0.77 || = 0.08 276 239 263 252 246 | 500 Aver./ d 0.49793 554 > 500: 0 1 9 10 10 10 10 9 0 0 | 500 | 526 559 539 554 549 = 0.76 || = 0.07 246 222 267 255 238 | 500 median s 0.50045 559 ----- 0 0 9 10 10 10 10 9 0 0 | 500 | 559 557 571 578 587 = 0.75 || = 0.06 227 192 210 202 215 | 500 t 0.50064 551 0 0 8 10 10 10 10 10 0 0 | 500 | 575 576 577 557 556 = 0.74 || = 0.05 194 180 196 178 166 | 500 m 0.49902 554 0 0 10 10 10 10 10 8 1 0 | 500 | 554 585 598 551 589 = 0.73 || = 0.04 127 156 162 157 126 | 500 x 0.50128 562 0 0 9 10 10 10 10 10 0 0 | 500 | 591 611 624 598 593 = 0.72 || = 0.03 110 124 111 120 133 | 500 -----------------------------------------------------------------| 500 | 570 599 611 621 621 = 0.71 || = 0.02 87 75 77 74 92 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 633 617 605 598 607 = 0.70 || = 0.01 23 28 30 36 33 | 252.5 d 30 3 3 3 5 4 6 4 43 | 500 | 611 632 609 611 631 = 0.69 || < 0.01 33 27 31 26 22 | 497.5 s 31 2 4 4 5 1 7 3 44 | 500 | 649 601 655 642 591 = 0.68 ||========================================================================= t 30 5 3 2 4 6 2 5 44 | 500 | 640 679 665 659 612 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 30 3 3 4 4 4 5 2 46 | 500 | 615 639 639 660 650 = 0.66 ||========================================================================= x 30 3 3 3 5 4 4 3 46 | 500 | 663 650 695 652 673 = 0.65 || sstring_Run test: no 232 test no 233 TestU01 250000 runs BigCrush Test smarsa_S sstring_Run test: test no 233 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 6 6 2 3 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 456 468 436 497 407 | 500 < 0.00002 6 2 3 1 3 | 0.5 | 0 2 0 1 0 > 0.99998 || = 0.63 450 495 478 477 450 | 500 < 0.00003 3 3 3 3 1 | 0.5 | 1 0 0 1 0 > 0.99997 || = 0.62 467 421 463 450 436 | 500 < 0.00004 3 4 2 1 2 | 0.5 | 0 0 1 0 0 > 0.99996 || = 0.61 412 472 456 440 467 | 500 < 0.00005 0 0 2 0 1 | 0.5 | 2 0 0 0 0 > 0.99995 || = 0.60 450 427 431 472 477 | 500 < 0.00006 1 2 2 1 1 | 0.5 | 0 0 1 1 0 > 0.99994 || = 0.59 463 444 436 427 476 | 500 < 0.00007 0 0 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 471 441 442 466 488 | 500 < 0.00008 0 1 1 1 3 | 0.5 | 0 1 1 0 1 > 0.99992 || = 0.57 436 478 487 473 454 | 500 < 0.00009 2 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 476 476 419 450 450 | 500 < 0.0001 0 1 2 4 2 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 477 479 502 455 482 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 521 489 452 441 446 | 500 < 0.0001 21 20 17 15 14 | 5 | 4 4 3 3 1 > 0.9999 || = 0.53 451 445 493 463 506 | 500 < 0.0002 7 10 9 9 14 | 5 | 0 2 1 2 0 > 0.9998 || = 0.52 505 479 485 470 463 | 500 < 0.0003 18 16 13 10 10 | 5 | 5 5 2 4 4 > 0.9997 || = 0.51 494 475 449 479 487 | 500 < 0.0004 10 14 13 15 11 | 5 | 1 4 3 1 3 > 0.9996 || = 0.50 467 484 470 473 467 | 500 < 0.0005 15 13 12 12 13 | 5 | 4 6 5 3 5 > 0.9995 || = 0.49 485 482 494 502 461 | 500 < 0.0006 13 16 8 10 11 | 5 | 3 4 4 2 3 > 0.9994 || = 0.48 469 471 484 480 471 | 500 < 0.0007 11 7 12 9 10 | 5 | 6 4 6 1 1 > 0.9993 || = 0.47 496 502 503 513 464 | 500 < 0.0008 12 8 11 12 9 | 5 | 3 3 5 3 5 > 0.9992 || = 0.46 475 487 486 489 499 | 500 < 0.0009 5 6 9 7 6 | 5 | 4 3 1 2 5 > 0.9991 || = 0.45 486 495 498 504 509 | 500 < 0.001 6 11 14 7 15 | 5 | 4 3 6 5 2 > 0.999 || = 0.44 446 497 517 488 522 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 488 489 496 493 479 | 500 < 0.001 118 121 118 106 113 | 50 | 34 38 36 26 29 > 0.999 || = 0.42 496 471 483 490 498 | 500 < 0.002 90 115 104 93 92 | 50 | 27 25 34 32 30 > 0.998 || = 0.41 496 468 561 544 496 | 500 < 0.003 91 103 105 108 85 | 50 | 36 39 26 29 37 > 0.997 || = 0.40 500 504 521 497 485 | 500 < 0.004 104 95 92 79 86 | 50 | 31 47 34 30 37 > 0.996 || = 0.39 529 508 508 487 489 | 500 < 0.005 101 115 101 99 87 | 50 | 37 36 32 27 47 > 0.995 || = 0.38 520 533 489 518 512 | 500 < 0.006 85 85 83 89 82 | 50 | 33 30 45 31 27 > 0.994 || = 0.37 530 512 540 511 492 | 500 < 0.007 86 90 76 75 88 | 50 | 23 35 29 36 47 > 0.993 || = 0.36 488 531 482 498 522 | 500 < 0.008 89 75 64 87 68 | 50 | 21 29 38 33 34 > 0.992 || = 0.35 506 585 544 519 504 | 500 < 0.009 82 93 68 65 79 | 50 | 36 44 23 28 38 > 0.991 || = 0.34 533 506 535 527 554 | 500 < 0.01 86 72 76 92 90 | 50 | 33 38 31 33 40 > 0.99 || = 0.33 524 523 559 506 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 498 524 559 540 533 | 500 < 0.01 932 964 887 893 870 | 497.5 | 311 361 328 305 366 > 0.99 || = 0.31 547 538 516 537 561 | 500 = 0.01 439 423 378 398 371 | 252.5 | 190 172 168 169 163 = 0.99 || = 0.30 529 550 525 519 540 | 500 = 0.02 778 779 769 742 764 | 500 | 371 365 380 361 378 = 0.98 || = 0.29 543 529 553 545 495 | 500 =================================================================| 500 | 359 420 338 364 377 = 0.97 || = 0.28 497 502 534 537 528 | 500 sstring_Run test: | 500 | 392 358 391 365 406 = 0.96 || = 0.27 541 559 522 566 510 | 500 ----------------------------------------------- | 500 | 366 391 376 404 362 = 0.95 || = 0.26 531 605 563 548 547 | 500 N = 1, n = 2000000000, r = 27, s = 3 | 500 | 373 364 365 389 389 = 0.94 || = 0.25 561 496 543 555 552 | 500 Chi2 statistic for number of runs | 500 | 398 379 429 356 379 = 0.93 || = 0.24 512 556 518 552 534 | 500 | 500 | 362 386 413 375 381 = 0.92 || = 0.23 562 549 545 552 562 | 500 =================================================================| 500 | 385 420 377 408 396 = 0.91 || = 0.22 501 522 540 523 591 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 375 410 397 407 391 = 0.90 || = 0.21 567 550 568 586 565 | 500 -----------------------------------------------------------------| 500 | 393 417 407 377 420 = 0.89 || = 0.20 571 581 617 580 531 | 500 SD Bern.: d 4.62414 6.29345 2.77806 | 500 | 400 401 365 428 434 = 0.88 || = 0.19 550 594 585 588 536 | 500 s 4.53102 6.94724 2.16486 | 500 | 415 445 421 402 375 = 0.87 || = 0.18 573 606 529 529 609 | 500 t 4.38086 5.98479 2.57343 | 500 | 402 419 410 394 403 = 0.86 || = 0.17 574 565 586 581 537 | 500 m 4.40148 5.85014 2.79029 | 500 | 451 416 415 403 418 = 0.85 || = 0.16 590 567 593 564 609 | 500 x 4.21241 5.45359 2.11102 | 500 | 432 420 449 454 438 = 0.84 || = 0.15 579 626 621 568 579 | 500 | 500 | 394 398 422 421 434 = 0.83 || = 0.14 665 585 586 617 581 | 500 Changes: d 11 0 0 | 500 | 432 408 386 393 425 = 0.82 || = 0.13 620 590 592 609 605 | 500 s 5 0 0 | 500 | 396 405 453 407 417 = 0.81 || = 0.12 624 648 547 627 586 | 500 t 11 0 0 | 500 | 422 431 402 387 436 = 0.80 || = 0.11 612 594 610 598 652 | 500 m 11 0 0 | 500 | 393 388 429 451 425 = 0.79 || = 0.10 646 565 639 617 612 | 500 x 11 0 0 | 500 | 478 395 413 446 443 = 0.78 || = 0.09 648 590 660 645 643 | 500 -----------------------------------------------------------------| 500 | 440 424 440 426 448 = 0.77 || = 0.08 655 622 656 619 660 | 500 Aver./ d 0.44706 478 > 500:10 10 9 8 0 2 0 0 0 0 | 500 | 413 406 403 423 394 = 0.76 || = 0.07 620 691 663 664 646 | 500 median s 0.44853 479 ----- 10 10 9 10 2 0 0 0 0 0 | 500 | 450 437 443 426 466 = 0.75 || = 0.06 630 654 612 692 695 | 500 t 0.44879 486 10 10 10 8 4 1 0 0 0 0 | 500 | 443 420 444 443 420 = 0.74 || = 0.05 705 649 677 690 639 | 500 m 0.44827 487 10 10 10 8 4 0 0 0 0 0 | 500 | 404 432 412 419 415 = 0.73 || = 0.04 729 701 720 701 695 | 500 x 0.45103 485 10 10 9 8 2 1 1 0 0 0 | 500 | 434 450 471 481 460 = 0.72 || = 0.03 751 740 719 742 730 | 500 -----------------------------------------------------------------| 500 | 469 461 438 462 434 = 0.71 || = 0.02 778 779 769 742 764 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 429 460 448 459 473 = 0.70 || = 0.01 439 423 378 398 371 | 252.5 d 17 8 12 13 18 8 4 5 16 | 500 | 456 448 437 449 503 = 0.69 || < 0.01 932 964 887 893 870 | 497.5 s 16 14 9 9 19 6 7 4 17 | 500 | 459 424 437 433 464 = 0.68 ||========================================================================= t 16 10 14 5 21 8 7 4 16 | 500 | 469 444 458 455 436 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 18 8 12 9 20 7 7 5 15 | 500 | 447 424 497 487 490 = 0.66 ||========================================================================= x 15 7 13 13 21 7 6 3 16 | 500 | 454 450 407 448 456 = 0.65 || sstring_Run test: no 233 test no 234 TestU01 250000 runs BigCrush Test smarsa_S sstring_Run test: test no 234 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 687 690 630 640 626 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 684 650 664 659 641 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 710 644 667 698 650 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 679 634 683 681 662 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 652 656 705 738 695 | 500 < 0.00006 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 675 711 699 691 715 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 701 668 720 692 634 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 663 675 693 690 663 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 679 701 759 723 730 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 708 710 712 711 694 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 706 712 657 717 716 | 500 < 0.0001 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9999 || = 0.53 687 667 676 752 723 | 500 < 0.0002 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9998 || = 0.52 704 716 696 749 715 | 500 < 0.0003 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9997 || = 0.51 702 732 718 705 723 | 500 < 0.0004 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9996 || = 0.50 718 707 696 762 753 | 500 < 0.0005 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9995 || = 0.49 733 732 667 743 666 | 500 < 0.0006 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9994 || = 0.48 732 738 692 660 684 | 500 < 0.0007 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9993 || = 0.47 751 698 705 711 721 | 500 < 0.0008 0 0 0 0 0 | 5 | 0 0 0 0 1 > 0.9992 || = 0.46 690 700 713 705 707 | 500 < 0.0009 0 0 0 0 0 | 5 | 0 0 0 0 0 > 0.9991 || = 0.45 663 638 726 700 688 | 500 < 0.001 0 0 0 0 0 | 5 | 1 0 0 0 0 > 0.999 || = 0.44 720 667 705 675 712 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 757 746 703 680 659 | 500 < 0.001 0 0 0 0 0 | 50 | 1 0 0 0 1 > 0.999 || = 0.42 695 706 715 656 698 | 500 < 0.002 1 1 0 1 0 | 50 | 0 3 3 1 1 > 0.998 || = 0.41 701 682 695 700 625 | 500 < 0.003 2 0 2 1 3 | 50 | 2 0 0 1 0 > 0.997 || = 0.40 684 719 702 675 691 | 500 < 0.004 2 3 4 1 3 | 50 | 2 6 1 1 3 > 0.996 || = 0.39 704 663 701 717 698 | 500 < 0.005 3 0 2 1 6 | 50 | 3 1 2 2 1 > 0.995 || = 0.38 669 656 673 668 700 | 500 < 0.006 4 6 1 3 3 | 50 | 1 2 2 1 5 > 0.994 || = 0.37 634 672 672 715 675 | 500 < 0.007 5 2 1 9 6 | 50 | 1 2 1 2 5 > 0.993 || = 0.36 672 683 723 654 658 | 500 < 0.008 2 1 7 4 5 | 50 | 2 7 2 5 2 > 0.992 || = 0.35 658 651 669 702 622 | 500 < 0.009 5 2 5 1 1 | 50 | 2 5 1 3 5 > 0.991 || = 0.34 665 684 636 671 665 | 500 < 0.01 2 0 4 4 4 | 50 | 6 2 6 10 3 > 0.99 || = 0.33 656 657 650 631 640 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 611 678 667 643 665 | 500 < 0.01 26 15 26 25 31 | 497.5 | 20 28 18 26 26 > 0.99 || = 0.31 589 642 598 643 617 | 500 = 0.01 28 29 32 27 31 | 252.5 | 22 34 30 29 28 = 0.99 || = 0.30 600 601 651 628 608 | 500 = 0.02 89 82 78 85 101 | 500 | 95 70 87 83 82 = 0.98 || = 0.29 603 605 617 605 663 | 500 =================================================================| 500 | 123 112 126 111 114 = 0.97 || = 0.28 579 611 584 571 578 | 500 sstring_Run test: | 500 | 160 161 157 153 133 = 0.96 || = 0.27 607 584 580 564 623 | 500 ----------------------------------------------- | 500 | 166 169 182 191 190 = 0.95 || = 0.26 587 584 552 572 569 | 500 N = 1, n = 2000000000, r = 27, s = 3 | 500 | 225 200 199 191 206 = 0.94 || = 0.25 563 534 534 510 586 | 500 Normal statistic for number of bits | 500 | 255 268 219 216 251 = 0.93 || = 0.24 572 538 531 561 596 | 500 | 500 | 284 275 268 255 262 = 0.92 || = 0.23 495 567 545 575 531 | 500 =================================================================| 500 | 266 296 303 324 283 = 0.91 || = 0.22 498 509 499 538 498 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 304 300 328 275 332 = 0.90 || = 0.21 468 522 534 509 484 | 500 -----------------------------------------------------------------| 500 | 340 332 314 372 331 = 0.89 || = 0.20 505 502 506 468 498 | 500 SD Bern.: d 8.80041 6.71036 6.79515 | 500 | 392 331 345 341 321 = 0.88 || = 0.19 490 480 460 486 478 | 500 s 8.83812 6.86710 6.68645 | 500 | 349 382 373 388 391 = 0.87 || = 0.18 432 493 464 458 478 | 500 t 8.89470 6.71394 6.82396 | 500 | 433 383 418 428 408 = 0.86 || = 0.17 435 451 430 403 425 | 500 m 9.00902 6.73047 6.71841 | 500 | 416 403 412 401 399 = 0.85 || = 0.16 439 448 430 424 436 | 500 x 8.88993 6.64274 6.71155 | 500 | 455 405 429 455 455 = 0.84 || = 0.15 442 392 425 384 400 | 500 | 500 | 423 462 422 459 454 = 0.83 || = 0.14 368 403 383 350 383 | 500 Changes: d 8 0 0 | 500 | 503 474 465 439 488 = 0.82 || = 0.13 388 378 391 396 368 | 500 s 4 0 0 | 500 | 490 516 456 520 516 = 0.81 || = 0.12 363 354 328 386 347 | 500 t 4 0 0 | 500 | 516 455 494 508 489 = 0.80 || = 0.11 324 336 330 320 311 | 500 m 4 0 0 | 500 | 490 491 521 529 506 = 0.79 || = 0.10 321 329 311 314 318 | 500 x 4 0 0 | 500 | 504 520 528 500 531 = 0.78 || = 0.09 258 279 279 276 289 | 500 -----------------------------------------------------------------| 500 | 533 526 599 537 549 = 0.77 || = 0.08 265 291 254 240 278 | 500 Aver./ d 0.50074 563 > 500: 0 0 7 10 10 10 10 9 1 0 | 500 | 563 557 538 535 525 = 0.76 || = 0.07 251 249 227 217 227 | 500 median s 0.49838 557 ----- 0 0 10 10 10 10 10 8 1 0 | 500 | 562 561 613 537 557 = 0.75 || = 0.06 194 219 214 219 207 | 500 t 0.50022 552 0 0 9 10 10 10 10 9 0 0 | 500 | 558 544 553 543 617 = 0.74 || = 0.05 191 169 194 174 159 | 500 m 0.50119 543 0 0 9 10 10 10 10 9 1 0 | 500 | 612 590 588 581 573 = 0.73 || = 0.04 169 156 157 143 126 | 500 x 0.50097 569 0 0 7 10 10 10 10 9 1 0 | 500 | 590 579 598 565 641 = 0.72 || = 0.03 136 117 121 111 110 | 500 -----------------------------------------------------------------| 500 | 565 626 622 607 588 = 0.71 || = 0.02 89 82 78 85 101 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 594 664 585 656 625 = 0.70 || = 0.01 28 29 32 27 31 | 252.5 d 29 4 4 1 9 1 5 4 44 | 500 | 587 597 650 623 656 = 0.69 || < 0.01 26 15 26 25 31 | 497.5 s 33 0 3 2 8 4 2 4 45 | 500 | 611 688 630 604 643 = 0.68 ||========================================================================= t 29 7 0 4 4 5 3 4 45 | 500 | 621 638 654 660 626 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 32 2 2 3 6 6 3 4 43 | 500 | 639 621 598 603 682 = 0.66 ||========================================================================= x 32 1 3 0 9 3 2 5 46 | 500 | 709 630 624 659 654 = 0.65 || sstring_Run test: no 234 test no 235 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 235 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 2 0 0 | 0.5 | 0 0 0 0 1 > 0.99999 || = 0.64 511 504 505 464 525 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 1 1 3 0 > 0.99998 || = 0.63 472 510 525 513 510 | 500 < 0.00003 1 0 0 1 1 | 0.5 | 0 1 0 1 0 > 0.99997 || = 0.62 529 472 531 526 507 | 500 < 0.00004 1 0 1 1 0 | 0.5 | 0 0 0 1 0 > 0.99996 || = 0.61 508 530 518 501 524 | 500 < 0.00005 1 0 1 1 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 474 477 483 513 501 | 500 < 0.00006 1 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99994 || = 0.59 488 494 480 536 495 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 0 2 0 0 0 > 0.99993 || = 0.58 472 552 500 507 500 | 500 < 0.00008 1 1 3 1 2 | 0.5 | 0 0 1 0 1 > 0.99992 || = 0.57 509 496 477 488 500 | 500 < 0.00009 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 498 496 509 516 507 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 0 0 1 0 1 > 0.9999 || = 0.55 491 497 505 521 498 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 498 503 495 481 533 | 500 < 0.0001 6 4 7 5 3 | 5 | 0 5 3 5 3 > 0.9999 || = 0.53 520 474 489 445 497 | 500 < 0.0002 5 11 3 4 4 | 5 | 8 1 3 2 2 > 0.9998 || = 0.52 480 532 490 476 460 | 500 < 0.0003 8 3 5 1 2 | 5 | 6 4 3 3 4 > 0.9997 || = 0.51 484 482 509 496 462 | 500 < 0.0004 3 7 7 3 6 | 5 | 9 3 4 1 5 > 0.9996 || = 0.50 520 463 459 493 497 | 500 < 0.0005 9 2 8 6 6 | 5 | 2 5 11 5 7 > 0.9995 || = 0.49 501 485 494 525 518 | 500 < 0.0006 3 2 4 13 2 | 5 | 6 0 8 5 4 > 0.9994 || = 0.48 487 505 486 537 522 | 500 < 0.0007 7 13 4 4 4 | 5 | 7 5 4 3 7 > 0.9993 || = 0.47 503 512 522 470 528 | 500 < 0.0008 4 7 3 8 3 | 5 | 3 6 3 5 4 > 0.9992 || = 0.46 491 509 515 479 499 | 500 < 0.0009 7 6 6 4 2 | 5 | 5 2 0 7 4 > 0.9991 || = 0.45 523 521 462 526 484 | 500 < 0.001 6 7 6 10 7 | 5 | 10 9 6 7 7 > 0.999 || = 0.44 472 551 497 539 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 476 469 521 504 525 | 500 < 0.001 58 62 53 58 39 | 50 | 56 40 45 43 47 > 0.999 || = 0.42 492 489 480 518 481 | 500 < 0.002 60 52 59 46 40 | 50 | 58 52 48 48 57 > 0.998 || = 0.41 497 507 472 493 518 | 500 < 0.003 47 48 43 43 44 | 50 | 39 51 49 45 50 > 0.997 || = 0.40 483 488 507 488 473 | 500 < 0.004 56 51 55 55 51 | 50 | 52 54 48 59 46 > 0.996 || = 0.39 487 474 497 523 466 | 500 < 0.005 43 56 46 54 49 | 50 | 55 31 56 45 44 > 0.995 || = 0.38 547 517 506 504 495 | 500 < 0.006 42 42 51 54 44 | 50 | 50 61 63 39 41 > 0.994 || = 0.37 462 536 504 524 502 | 500 < 0.007 53 37 42 50 67 | 50 | 47 51 54 51 56 > 0.993 || = 0.36 522 518 533 517 521 | 500 < 0.008 59 41 36 51 54 | 50 | 42 53 49 40 38 > 0.992 || = 0.35 489 471 523 484 503 | 500 < 0.009 42 35 44 58 47 | 50 | 51 49 57 53 51 > 0.991 || = 0.34 518 492 555 528 485 | 500 < 0.01 61 52 51 55 36 | 50 | 60 66 46 49 43 > 0.99 || = 0.33 519 513 486 476 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 485 547 506 499 529 | 500 < 0.01 521 476 480 524 471 | 497.5 | 510 508 515 472 473 > 0.99 || = 0.31 481 537 525 469 477 | 500 = 0.01 264 255 251 237 212 | 252.5 | 229 248 269 256 260 = 0.99 || = 0.30 541 465 497 511 476 | 500 = 0.02 489 522 556 498 468 | 500 | 479 499 516 494 500 = 0.98 || = 0.29 481 500 493 489 497 | 500 =================================================================| 500 | 522 465 457 500 468 = 0.97 || = 0.28 497 489 489 529 478 | 500 sstring_AutoCor test: | 500 | 543 486 479 486 512 = 0.96 || = 0.27 507 487 492 477 489 | 500 ----------------------------------------------- | 500 | 488 455 500 490 504 = 0.95 || = 0.26 478 513 474 537 523 | 500 N = 10, n = 1000000030, r = 0, s = 3, d = 1 | 500 | 452 493 504 484 470 = 0.94 || = 0.25 529 524 490 474 494 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 499 486 480 479 502 = 0.93 || = 0.24 451 494 467 493 523 | 500 | 500 | 503 469 530 498 498 = 0.92 || = 0.23 529 487 513 513 469 | 500 =================================================================| 500 | 552 492 490 472 546 = 0.91 || = 0.22 506 502 489 497 520 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 530 483 462 524 486 = 0.90 || = 0.21 515 482 519 507 499 | 500 -----------------------------------------------------------------| 500 | 491 498 476 510 504 = 0.89 || = 0.20 540 527 492 514 506 | 500 SD Bern.: d 1.02891 1.09324 0.92131 | 500 | 505 547 510 478 446 = 0.88 || = 0.19 479 463 534 528 488 | 500 s 0.98842 1.21056 1.31974 | 500 | 511 516 491 528 485 = 0.87 || = 0.18 520 508 484 539 494 | 500 t 0.97362 0.97823 0.80164 | 500 | 499 499 489 509 502 = 0.86 || = 0.17 508 505 460 463 505 | 500 m 0.99492 0.74333 0.91258 | 500 | 458 477 500 552 528 = 0.85 || = 0.16 526 539 522 495 487 | 500 x 0.98183 1.26948 0.91805 | 500 | 474 482 522 510 512 = 0.84 || = 0.15 509 476 466 509 542 | 500 | 500 | 480 507 539 502 540 = 0.83 || = 0.14 463 500 474 486 515 | 500 Changes: d 54 6 4 | 500 | 513 516 505 499 528 = 0.82 || = 0.13 469 511 506 464 458 | 500 s 45 4 5 | 500 | 533 473 462 503 506 = 0.81 || = 0.12 510 465 497 459 510 | 500 t 45 6 4 | 500 | 527 484 486 505 511 = 0.80 || = 0.11 487 474 484 501 503 | 500 m 45 4 6 | 500 | 497 526 538 476 515 = 0.79 || = 0.10 505 495 494 498 502 | 500 x 52 4 6 | 500 | 488 490 492 495 504 = 0.78 || = 0.09 457 504 486 474 455 | 500 -----------------------------------------------------------------| 500 | 536 470 483 464 524 = 0.77 || = 0.08 501 526 498 485 518 | 500 Aver./ d 0.49959 501 > 500: 7 6 6 5 3 2 6 5 5 5 | 500 | 517 506 492 462 490 = 0.76 || = 0.07 536 545 483 462 484 | 500 median s 0.49831 499 ----- 8 4 4 6 6 3 7 5 4 1 | 500 | 476 492 491 510 511 = 0.75 || = 0.06 520 470 499 474 524 | 500 t 0.50037 497 3 3 2 7 4 3 7 4 4 5 | 500 | 454 498 531 482 502 = 0.74 || = 0.05 476 509 496 543 466 | 500 m 0.49996 500 4 4 5 6 6 5 7 4 8 1 | 500 | 499 504 540 519 527 = 0.73 || = 0.04 512 507 530 509 497 | 500 x 0.50247 502 2 6 4 5 5 3 7 8 7 5 | 500 | 521 522 511 536 500 = 0.72 || = 0.03 518 516 507 517 475 | 500 -----------------------------------------------------------------| 500 | 513 502 484 488 507 = 0.71 || = 0.02 489 522 556 498 468 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 477 476 489 506 484 = 0.70 || = 0.01 264 255 251 237 212 | 252.5 d 0 0 3 15 67 14 2 0 0 | 500 | 503 523 548 498 473 = 0.69 || < 0.01 521 476 480 524 471 | 497.5 s 0 0 1 19 66 10 5 0 0 | 500 | 512 516 495 509 517 = 0.68 ||========================================================================= t 0 0 0 13 71 14 3 0 0 | 500 | 504 494 520 514 536 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 18 63 18 1 0 0 | 500 | 480 521 493 511 536 = 0.66 ||========================================================================= x 0 0 3 16 64 17 1 0 0 | 500 | 492 518 523 494 499 = 0.65 || sstring_AutoCor test: no 235 test no 236 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 236 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 1 0 | 0.5 | 0 0 2 1 2 > 0.99999 || = 0.64 481 500 488 526 485 | 500 < 0.00002 2 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 503 521 509 503 523 | 500 < 0.00003 0 0 0 0 0 | 0.5 | 0 0 0 1 2 > 0.99997 || = 0.62 515 475 486 477 476 | 500 < 0.00004 0 0 0 0 0 | 0.5 | 0 1 0 0 0 > 0.99996 || = 0.61 512 487 486 487 533 | 500 < 0.00005 1 1 1 0 0 | 0.5 | 1 2 1 1 1 > 0.99995 || = 0.60 473 494 501 538 457 | 500 < 0.00006 0 0 0 1 1 | 0.5 | 2 0 0 0 0 > 0.99994 || = 0.59 458 517 524 448 525 | 500 < 0.00007 1 3 0 0 2 | 0.5 | 1 0 1 0 0 > 0.99993 || = 0.58 470 553 515 520 530 | 500 < 0.00008 0 2 0 0 0 | 0.5 | 0 1 0 1 0 > 0.99992 || = 0.57 498 535 477 501 465 | 500 < 0.00009 1 0 2 0 1 | 0.5 | 0 0 1 0 0 > 0.99991 || = 0.56 505 473 497 491 537 | 500 < 0.0001 0 1 1 0 0 | 0.5 | 1 0 1 0 1 > 0.9999 || = 0.55 534 456 517 490 502 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 523 474 459 532 501 | 500 < 0.0001 6 7 4 2 4 | 5 | 5 4 6 4 6 > 0.9999 || = 0.53 512 485 495 479 513 | 500 < 0.0002 2 3 2 5 5 | 5 | 2 4 1 3 2 > 0.9998 || = 0.52 480 544 506 510 501 | 500 < 0.0003 4 4 8 8 6 | 5 | 6 6 5 5 2 > 0.9997 || = 0.51 496 478 477 491 495 | 500 < 0.0004 4 8 3 5 4 | 5 | 2 1 6 1 2 > 0.9996 || = 0.50 515 511 512 522 484 | 500 < 0.0005 5 3 6 4 6 | 5 | 4 0 3 3 1 > 0.9995 || = 0.49 488 473 493 481 504 | 500 < 0.0006 6 6 3 2 5 | 5 | 2 4 3 8 7 > 0.9994 || = 0.48 475 459 529 473 513 | 500 < 0.0007 6 3 7 5 5 | 5 | 5 2 7 5 3 > 0.9993 || = 0.47 524 460 501 509 514 | 500 < 0.0008 8 3 4 8 4 | 5 | 2 9 6 4 2 > 0.9992 || = 0.46 507 543 499 495 524 | 500 < 0.0009 9 1 4 5 8 | 5 | 3 5 6 7 1 > 0.9991 || = 0.45 515 531 508 492 502 | 500 < 0.001 3 7 5 2 8 | 5 | 3 7 4 4 6 > 0.999 || = 0.44 479 520 513 498 528 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 489 466 493 508 482 | 500 < 0.001 53 45 46 46 55 | 50 | 34 42 47 44 32 > 0.999 || = 0.42 505 468 490 482 498 | 500 < 0.002 53 41 43 39 53 | 50 | 45 59 61 60 62 > 0.998 || = 0.41 502 510 472 500 519 | 500 < 0.003 56 51 54 46 55 | 50 | 51 51 50 50 53 > 0.997 || = 0.40 526 499 501 536 529 | 500 < 0.004 47 50 53 63 46 | 50 | 47 43 50 44 48 > 0.996 || = 0.39 482 476 443 485 514 | 500 < 0.005 61 49 56 40 51 | 50 | 52 66 49 54 39 > 0.995 || = 0.38 502 527 539 490 517 | 500 < 0.006 55 44 48 38 36 | 50 | 55 44 51 48 47 > 0.994 || = 0.37 474 500 458 481 518 | 500 < 0.007 51 44 52 56 51 | 50 | 40 54 56 48 44 > 0.993 || = 0.36 517 502 496 481 503 | 500 < 0.008 34 44 46 55 55 | 50 | 63 44 49 48 47 > 0.992 || = 0.35 503 520 494 457 484 | 500 < 0.009 47 52 54 49 44 | 50 | 44 62 44 51 39 > 0.991 || = 0.34 489 504 495 492 507 | 500 < 0.01 56 57 66 55 43 | 50 | 50 58 53 55 42 > 0.99 || = 0.33 497 497 510 498 540 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 493 504 523 519 525 | 500 < 0.01 513 477 518 487 489 | 497.5 | 481 523 510 502 453 > 0.99 || = 0.31 539 509 481 484 493 | 500 = 0.01 241 244 271 260 272 | 252.5 | 249 246 238 262 236 = 0.99 || = 0.30 508 491 481 519 485 | 500 = 0.02 521 470 501 488 473 | 500 | 508 516 514 494 471 = 0.98 || = 0.29 485 484 494 505 451 | 500 =================================================================| 500 | 469 531 493 446 502 = 0.97 || = 0.28 461 482 489 474 522 | 500 sstring_AutoCor test: | 500 | 521 479 520 486 518 = 0.96 || = 0.27 460 521 495 479 546 | 500 ----------------------------------------------- | 500 | 503 498 496 509 498 = 0.95 || = 0.26 503 511 494 488 518 | 500 N = 10, n = 1000000030, r = 0, s = 3, d = 1 | 500 | 487 510 495 505 454 = 0.94 || = 0.25 547 544 486 500 496 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 528 520 492 485 483 = 0.93 || = 0.24 523 480 492 484 509 | 500 | 500 | 519 499 484 516 463 = 0.92 || = 0.23 471 491 507 495 519 | 500 =================================================================| 500 | 516 503 513 510 485 = 0.91 || = 0.22 508 530 489 542 517 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 494 481 513 499 509 = 0.90 || = 0.21 540 475 506 455 489 | 500 -----------------------------------------------------------------| 500 | 486 475 484 505 503 = 0.89 || = 0.20 519 424 489 487 492 | 500 SD Bern.: d 1.06029 1.01143 1.11858 | 500 | 527 505 520 492 493 = 0.88 || = 0.19 522 490 500 534 471 | 500 s 1.12070 0.73384 1.22289 | 500 | 483 527 505 509 535 = 0.87 || = 0.18 499 482 460 487 533 | 500 t 0.88616 0.91914 0.65453 | 500 | 481 538 527 482 467 = 0.86 || = 0.17 473 498 505 499 524 | 500 m 0.92302 1.14337 0.67263 | 500 | 514 521 487 511 493 = 0.85 || = 0.16 491 526 497 511 483 | 500 x 1.06519 0.87564 1.29755 | 500 | 504 560 478 509 476 = 0.84 || = 0.15 525 509 454 523 506 | 500 | 500 | 507 497 512 516 498 = 0.83 || = 0.14 492 494 518 502 486 | 500 Changes: d 51 4 6 | 500 | 456 496 553 499 463 = 0.82 || = 0.13 488 483 510 506 504 | 500 s 47 3 7 | 500 | 511 560 496 514 514 = 0.81 || = 0.12 464 525 495 521 476 | 500 t 54 5 5 | 500 | 511 518 497 512 553 = 0.80 || = 0.11 503 527 493 509 534 | 500 m 53 5 5 | 500 | 472 491 501 487 475 = 0.79 || = 0.10 545 494 537 540 476 | 500 x 48 5 2 | 500 | 516 480 498 514 549 = 0.78 || = 0.09 487 516 489 440 499 | 500 -----------------------------------------------------------------| 500 | 472 512 475 513 550 = 0.77 || = 0.08 500 466 493 494 492 | 500 Aver./ d 0.49924 502 > 500: 5 4 6 5 6 4 5 5 5 6 | 500 | 525 493 518 506 467 = 0.76 || = 0.07 519 502 501 533 503 | 500 median s 0.50318 498 ----- 2 4 4 6 4 4 4 2 6 6 | 500 | 542 461 487 496 490 = 0.75 || = 0.06 516 498 519 505 512 | 500 t 0.50077 497 7 4 2 3 5 5 4 5 6 4 | 500 | 480 494 517 502 470 = 0.74 || = 0.05 480 461 502 476 461 | 500 m 0.50015 500 5 8 2 2 3 5 6 6 6 6 | 500 | 479 487 501 489 512 = 0.73 || = 0.04 516 482 495 509 505 | 500 x 0.49791 502 5 5 6 7 8 7 5 4 4 2 | 500 | 487 476 539 483 489 = 0.72 || = 0.03 481 478 530 531 506 | 500 -----------------------------------------------------------------| 500 | 525 499 465 505 472 = 0.71 || = 0.02 521 470 501 488 473 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 487 522 488 519 519 = 0.70 || = 0.01 241 244 271 260 272 | 252.5 d 0 1 0 15 69 13 2 1 0 | 500 | 493 548 511 539 510 = 0.69 || < 0.01 513 477 518 487 489 | 497.5 s 0 1 0 17 64 15 4 0 0 | 500 | 510 497 498 467 479 = 0.68 ||========================================================================= t 0 0 2 8 80 9 2 0 0 | 500 | 578 526 519 499 467 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 6 78 13 0 0 0 | 500 | 421 487 562 530 487 = 0.66 ||========================================================================= x 0 0 3 19 60 15 4 0 0 | 500 | 476 498 497 529 507 = 0.65 || sstring_AutoCor test: no 236 test no 237 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 237 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 499 492 518 476 491 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 487 498 489 492 516 | 500 < 0.00003 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 471 527 455 464 507 | 500 < 0.00004 0 0 0 0 2 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 516 501 504 511 512 | 500 < 0.00005 1 4 0 0 1 | 0.5 | 0 1 1 1 0 > 0.99995 || = 0.60 466 474 486 523 512 | 500 < 0.00006 1 0 1 0 1 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 485 527 492 488 490 | 500 < 0.00007 1 1 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99993 || = 0.58 513 483 506 528 508 | 500 < 0.00008 0 0 1 1 2 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 487 521 508 522 458 | 500 < 0.00009 0 2 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 509 519 484 495 523 | 500 < 0.0001 0 2 1 0 0 | 0.5 | 0 0 0 0 0 > 0.9999 || = 0.55 486 519 475 489 498 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 524 496 526 471 483 | 500 < 0.0001 4 11 3 3 7 | 5 | 1 1 1 2 1 > 0.9999 || = 0.53 471 501 488 485 490 | 500 < 0.0002 5 2 9 5 3 | 5 | 1 4 2 0 0 > 0.9998 || = 0.52 473 492 495 503 497 | 500 < 0.0003 10 10 2 4 5 | 5 | 2 5 3 2 2 > 0.9997 || = 0.51 550 544 473 498 501 | 500 < 0.0004 9 7 2 4 3 | 5 | 3 3 7 7 3 > 0.9996 || = 0.50 512 470 467 481 511 | 500 < 0.0005 2 4 3 9 11 | 5 | 8 1 1 8 5 > 0.9995 || = 0.49 501 511 489 507 481 | 500 < 0.0006 3 3 6 2 6 | 5 | 3 5 2 2 5 > 0.9994 || = 0.48 510 493 521 513 509 | 500 < 0.0007 4 4 6 2 4 | 5 | 6 3 6 7 6 > 0.9993 || = 0.47 502 508 481 507 522 | 500 < 0.0008 6 6 4 3 8 | 5 | 2 6 3 6 6 > 0.9992 || = 0.46 534 491 505 516 545 | 500 < 0.0009 6 1 5 6 3 | 5 | 4 3 4 7 2 > 0.9991 || = 0.45 513 534 481 487 568 | 500 < 0.001 7 3 5 1 1 | 5 | 4 2 3 6 3 > 0.999 || = 0.44 503 484 505 513 534 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 488 513 487 485 514 | 500 < 0.001 56 51 45 39 51 | 50 | 34 33 32 47 33 > 0.999 || = 0.42 474 484 505 486 520 | 500 < 0.002 39 41 62 46 38 | 50 | 51 34 39 35 44 > 0.998 || = 0.41 486 472 473 503 514 | 500 < 0.003 50 45 38 43 51 | 50 | 46 51 49 52 56 > 0.997 || = 0.40 536 492 512 515 522 | 500 < 0.004 48 53 54 61 54 | 50 | 53 49 45 40 40 > 0.996 || = 0.39 487 477 453 484 488 | 500 < 0.005 43 43 60 50 50 | 50 | 48 55 44 50 52 > 0.995 || = 0.38 534 467 512 460 511 | 500 < 0.006 54 58 53 44 49 | 50 | 51 50 38 48 51 > 0.994 || = 0.37 517 470 534 462 530 | 500 < 0.007 53 50 61 43 40 | 50 | 52 44 52 49 47 > 0.993 || = 0.36 543 525 482 527 489 | 500 < 0.008 56 57 63 54 51 | 50 | 36 63 57 57 64 > 0.992 || = 0.35 487 515 533 539 499 | 500 < 0.009 57 44 32 54 55 | 50 | 38 53 54 41 46 > 0.991 || = 0.34 495 521 495 479 521 | 500 < 0.01 64 51 51 64 54 | 50 | 46 69 45 53 65 > 0.99 || = 0.33 502 465 478 465 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 483 527 543 501 496 | 500 < 0.01 520 493 519 498 493 | 497.5 | 455 501 455 472 498 > 0.99 || = 0.31 479 510 497 507 520 | 500 = 0.01 239 240 276 236 253 | 252.5 | 237 270 276 244 278 = 0.99 || = 0.30 475 518 491 513 494 | 500 = 0.02 521 538 574 504 473 | 500 | 504 494 518 530 540 = 0.98 || = 0.29 476 480 520 511 489 | 500 =================================================================| 500 | 518 545 527 535 508 = 0.97 || = 0.28 538 479 497 483 474 | 500 sstring_AutoCor test: | 500 | 519 478 538 480 481 = 0.96 || = 0.27 494 479 491 527 478 | 500 ----------------------------------------------- | 500 | 486 530 501 494 484 = 0.95 || = 0.26 494 459 458 501 495 | 500 N = 10, n = 1000000030, r = 0, s = 3, d = 1 | 500 | 477 498 519 510 490 = 0.94 || = 0.25 526 520 538 529 520 | 500 Anderson-Darling statistic = A2 | 500 | 506 494 527 487 510 = 0.93 || = 0.24 496 520 492 476 461 | 500 | 500 | 485 494 524 520 475 = 0.92 || = 0.23 521 502 545 495 484 | 500 =================================================================| 500 | 457 503 472 489 517 = 0.91 || = 0.22 531 497 476 529 496 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 492 454 489 501 526 = 0.90 || = 0.21 510 524 480 497 508 | 500 -----------------------------------------------------------------| 500 | 531 499 509 521 479 = 0.89 || = 0.20 498 515 495 477 515 | 500 SD Bern.: d 0.95263 1.01637 1.13809 | 500 | 498 508 481 539 511 = 0.88 || = 0.19 504 439 473 488 517 | 500 s 0.97313 0.79411 1.51534 | 500 | 477 471 489 514 528 = 0.87 || = 0.18 478 484 508 513 456 | 500 t 1.05955 1.45192 1.22125 | 500 | 488 525 492 472 495 = 0.86 || = 0.17 504 517 504 488 485 | 500 m 0.97853 1.11410 0.98231 | 500 | 534 522 526 453 505 = 0.85 || = 0.16 476 501 506 508 475 | 500 x 0.95647 0.78140 1.35122 | 500 | 527 491 533 539 501 = 0.84 || = 0.15 481 498 469 520 492 | 500 | 500 | 481 523 502 505 479 = 0.83 || = 0.14 525 488 502 545 473 | 500 Changes: d 51 2 6 | 500 | 495 516 489 461 515 = 0.82 || = 0.13 483 497 536 502 462 | 500 s 49 8 5 | 500 | 495 538 466 489 536 = 0.81 || = 0.12 538 485 473 495 520 | 500 t 53 5 2 | 500 | 488 506 487 473 466 = 0.80 || = 0.11 471 530 510 503 521 | 500 m 51 3 5 | 500 | 500 466 497 486 482 = 0.79 || = 0.10 540 494 489 512 486 | 500 x 48 4 7 | 500 | 503 488 509 483 542 = 0.78 || = 0.09 521 488 503 511 455 | 500 -----------------------------------------------------------------| 500 | 521 485 483 473 502 = 0.77 || = 0.08 474 464 497 554 484 | 500 Aver./ d 0.49828 498 > 500: 6 5 5 4 7 4 2 6 3 4 | 500 | 522 467 508 538 468 = 0.76 || = 0.07 513 478 466 514 505 | 500 median s 0.50231 498 ----- 1 3 5 6 4 6 7 5 6 5 | 500 | 493 539 534 486 511 = 0.75 || = 0.06 492 496 491 477 485 | 500 t 0.50036 497 5 6 3 4 5 3 6 6 4 8 | 500 | 501 513 509 515 492 = 0.74 || = 0.05 484 491 512 495 498 | 500 m 0.49894 500 6 7 5 5 7 4 3 4 6 4 | 500 | 533 511 528 464 505 = 0.73 || = 0.04 509 483 492 526 473 | 500 x 0.50263 500 2 3 3 5 9 4 5 5 7 6 | 500 | 513 518 520 532 516 = 0.72 || = 0.03 506 475 491 473 483 | 500 -----------------------------------------------------------------| 500 | 464 499 470 507 496 = 0.71 || = 0.02 521 538 574 504 473 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 514 491 469 490 524 = 0.70 || = 0.01 239 240 276 236 253 | 252.5 d 0 0 0 15 69 16 1 0 0 | 500 | 484 513 516 489 487 = 0.69 || < 0.01 520 493 519 498 493 | 497.5 s 0 0 2 13 69 16 1 0 0 | 500 | 486 523 509 513 500 = 0.68 ||========================================================================= t 0 0 3 15 64 17 1 1 0 | 500 | 480 509 513 500 469 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 17 66 15 2 0 0 | 500 | 495 522 536 481 487 = 0.66 ||========================================================================= x 0 0 1 13 75 10 1 1 0 | 500 | 480 501 453 533 504 = 0.65 || sstring_AutoCor test: no 237 test no 238 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 238 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 1 0 1 | 0.5 | 0 1 0 1 0 > 0.99999 || = 0.64 482 523 526 495 530 | 500 < 0.00002 0 1 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99998 || = 0.63 495 467 493 504 478 | 500 < 0.00003 0 0 0 0 1 | 0.5 | 1 0 3 0 1 > 0.99997 || = 0.62 499 539 453 493 522 | 500 < 0.00004 1 1 1 1 0 | 0.5 | 2 0 1 0 0 > 0.99996 || = 0.61 475 497 504 454 495 | 500 < 0.00005 0 0 0 2 0 | 0.5 | 0 1 1 0 1 > 0.99995 || = 0.60 459 487 485 504 539 | 500 < 0.00006 0 2 1 0 1 | 0.5 | 0 2 0 0 1 > 0.99994 || = 0.59 469 469 480 475 470 | 500 < 0.00007 0 1 0 0 1 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 493 501 472 515 441 | 500 < 0.00008 0 1 0 1 0 | 0.5 | 0 1 0 0 0 > 0.99992 || = 0.57 499 530 500 494 514 | 500 < 0.00009 1 1 0 0 0 | 0.5 | 3 0 1 0 0 > 0.99991 || = 0.56 519 536 485 526 522 | 500 < 0.0001 0 1 0 0 0 | 0.5 | 0 0 1 0 0 > 0.9999 || = 0.55 512 537 454 498 532 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 484 480 505 510 502 | 500 < 0.0001 3 9 3 5 4 | 5 | 7 6 7 1 3 > 0.9999 || = 0.53 496 501 508 488 521 | 500 < 0.0002 6 6 6 4 8 | 5 | 3 3 1 1 7 > 0.9998 || = 0.52 508 505 522 487 533 | 500 < 0.0003 4 3 3 3 9 | 5 | 3 5 4 6 3 > 0.9997 || = 0.51 515 534 497 526 516 | 500 < 0.0004 3 2 5 3 2 | 5 | 8 6 5 6 5 > 0.9996 || = 0.50 498 504 497 506 515 | 500 < 0.0005 6 5 1 4 1 | 5 | 6 5 10 8 5 > 0.9995 || = 0.49 520 506 529 511 524 | 500 < 0.0006 3 3 9 2 5 | 5 | 4 3 5 4 3 > 0.9994 || = 0.48 524 485 471 492 498 | 500 < 0.0007 7 5 4 1 4 | 5 | 6 6 2 7 6 > 0.9993 || = 0.47 496 498 531 478 492 | 500 < 0.0008 3 3 5 4 5 | 5 | 3 6 11 7 3 > 0.9992 || = 0.46 523 474 494 473 488 | 500 < 0.0009 3 2 3 3 7 | 5 | 6 4 7 7 5 > 0.9991 || = 0.45 476 539 481 557 467 | 500 < 0.001 4 4 6 6 3 | 5 | 5 2 7 2 3 > 0.999 || = 0.44 486 507 517 530 529 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 498 491 467 491 510 | 500 < 0.001 42 42 45 35 48 | 50 | 51 46 59 49 43 > 0.999 || = 0.42 490 517 525 496 530 | 500 < 0.002 43 46 50 45 54 | 50 | 43 48 47 50 46 > 0.998 || = 0.41 483 516 500 478 500 | 500 < 0.003 61 48 53 50 52 | 50 | 51 53 49 51 37 > 0.997 || = 0.40 502 500 509 487 477 | 500 < 0.004 46 54 49 45 52 | 50 | 50 50 52 60 48 > 0.996 || = 0.39 470 490 525 486 513 | 500 < 0.005 56 57 43 47 56 | 50 | 37 58 50 39 51 > 0.995 || = 0.38 499 487 522 511 506 | 500 < 0.006 53 49 67 55 54 | 50 | 47 44 53 56 50 > 0.994 || = 0.37 524 502 520 522 491 | 500 < 0.007 57 48 53 62 67 | 50 | 41 39 56 50 40 > 0.993 || = 0.36 517 500 521 454 507 | 500 < 0.008 49 50 48 43 41 | 50 | 58 58 51 40 46 > 0.992 || = 0.35 516 517 483 435 497 | 500 < 0.009 59 43 69 39 43 | 50 | 53 56 54 43 53 > 0.991 || = 0.34 488 480 513 498 513 | 500 < 0.01 44 38 58 55 42 | 50 | 54 43 55 50 50 > 0.99 || = 0.33 497 492 504 498 514 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 507 488 467 509 491 | 500 < 0.01 510 475 535 476 509 | 497.5 | 485 495 526 488 464 > 0.99 || = 0.31 475 496 523 503 493 | 500 = 0.01 236 254 291 237 239 | 252.5 | 265 261 264 247 254 = 0.99 || = 0.30 475 508 504 521 521 | 500 = 0.02 484 492 507 495 461 | 500 | 525 511 498 484 439 = 0.98 || = 0.29 498 524 520 458 499 | 500 =================================================================| 500 | 485 497 470 509 517 = 0.97 || = 0.28 511 540 497 508 480 | 500 sstring_AutoCor test: | 500 | 488 562 507 521 496 = 0.96 || = 0.27 486 497 513 500 546 | 500 ----------------------------------------------- | 500 | 477 509 469 504 495 = 0.95 || = 0.26 504 497 526 494 523 | 500 N = 10, n = 1000000030, r = 0, s = 3, d = 1 | 500 | 474 500 547 503 469 = 0.94 || = 0.25 508 497 473 529 495 | 500 Tests on the sum of all N observations | 500 | 537 497 478 523 488 = 0.93 || = 0.24 500 482 473 513 499 | 500 | 500 | 546 504 495 499 480 = 0.92 || = 0.23 507 478 484 504 490 | 500 =================================================================| 500 | 518 506 486 493 485 = 0.91 || = 0.22 533 522 505 537 495 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 466 499 506 531 484 = 0.90 || = 0.21 497 524 515 490 523 | 500 -----------------------------------------------------------------| 500 | 510 468 511 489 473 = 0.89 || = 0.20 517 510 470 478 538 | 500 SD Bern.: d 0.80230 0.96172 0.89374 | 500 | 513 523 526 507 476 = 0.88 || = 0.19 497 486 476 492 530 | 500 s 1.02297 0.83348 0.89374 | 500 | 532 510 509 463 478 = 0.87 || = 0.18 502 504 475 467 515 | 500 t 1.03087 1.27421 0.60361 | 500 | 497 453 477 502 475 = 0.86 || = 0.17 493 498 468 523 518 | 500 m 0.88739 1.13898 0.90376 | 500 | 502 519 457 489 500 = 0.85 || = 0.16 465 488 561 515 481 | 500 x 1.03906 1.06165 0.85364 | 500 | 495 463 479 479 546 = 0.84 || = 0.15 478 513 501 483 504 | 500 | 500 | 507 533 533 494 492 = 0.83 || = 0.14 526 516 511 515 506 | 500 Changes: d 55 6 4 | 500 | 498 510 506 510 508 = 0.82 || = 0.13 487 454 485 508 516 | 500 s 52 2 6 | 500 | 496 486 506 528 531 = 0.81 || = 0.12 546 504 517 485 561 | 500 t 44 5 4 | 500 | 505 525 509 506 490 = 0.80 || = 0.11 489 477 515 515 501 | 500 m 44 3 4 | 500 | 487 473 528 500 492 = 0.79 || = 0.10 488 493 500 502 478 | 500 x 43 2 4 | 500 | 513 513 503 499 506 = 0.78 || = 0.09 500 467 522 519 499 | 500 -----------------------------------------------------------------| 500 | 492 499 489 495 521 = 0.77 || = 0.08 529 511 487 525 453 | 500 Aver./ d 0.49969 498 > 500: 5 3 6 4 4 4 3 5 5 5 | 500 | 491 485 468 491 476 = 0.76 || = 0.07 509 486 488 505 499 | 500 median s 0.50278 499 ----- 3 4 5 3 5 7 5 3 5 6 | 500 | 503 477 497 497 495 = 0.75 || = 0.06 490 445 475 487 507 | 500 t 0.49945 501 5 5 5 8 5 3 3 6 7 4 | 500 | 479 487 526 534 482 = 0.74 || = 0.05 527 431 472 496 476 | 500 m 0.50026 499 4 6 5 5 3 5 4 5 5 5 | 500 | 502 493 496 510 496 = 0.73 || = 0.04 529 503 476 495 510 | 500 x 0.49721 499 4 8 4 6 4 8 4 3 3 2 | 500 | 521 537 521 507 508 = 0.72 || = 0.03 493 487 519 526 513 | 500 -----------------------------------------------------------------| 500 | 488 479 535 514 479 = 0.71 || = 0.02 484 492 507 495 461 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 500 562 464 526 520 = 0.70 || = 0.01 236 254 291 237 239 | 252.5 d 0 0 0 12 76 11 2 0 0 | 500 | 486 525 476 476 530 = 0.69 || < 0.01 510 475 535 476 509 | 497.5 s 0 1 3 10 70 15 2 0 0 | 500 | 507 489 478 525 471 = 0.68 ||========================================================================= t 0 0 2 20 61 15 3 0 0 | 500 | 504 484 495 508 487 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 7 76 14 1 0 0 | 500 | 496 489 496 474 498 = 0.66 ||========================================================================= x 0 0 4 12 69 13 3 0 0 | 500 | 502 519 525 493 444 = 0.65 || sstring_AutoCor test: no 238 test no 239 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 239 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 0 | 0.5 | 1 1 0 0 1 > 0.99999 || = 0.64 498 496 518 502 503 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 2 0 0 > 0.99998 || = 0.63 481 503 532 473 487 | 500 < 0.00003 0 0 2 2 0 | 0.5 | 0 1 0 1 0 > 0.99997 || = 0.62 530 509 465 509 508 | 500 < 0.00004 0 2 0 0 1 | 0.5 | 1 0 0 0 1 > 0.99996 || = 0.61 464 501 467 488 501 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 1 0 1 0 0 > 0.99995 || = 0.60 507 504 529 464 459 | 500 < 0.00006 1 0 0 2 0 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 482 496 494 505 488 | 500 < 0.00007 2 2 1 0 0 | 0.5 | 0 1 0 0 0 > 0.99993 || = 0.58 481 522 473 491 501 | 500 < 0.00008 2 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 534 495 508 500 503 | 500 < 0.00009 1 0 0 3 0 | 0.5 | 0 0 0 2 0 > 0.99991 || = 0.56 534 509 537 506 486 | 500 < 0.0001 1 0 0 1 0 | 0.5 | 2 0 2 0 0 > 0.9999 || = 0.55 490 472 519 523 553 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 538 530 448 465 498 | 500 < 0.0001 7 5 3 9 2 | 5 | 6 3 5 3 3 > 0.9999 || = 0.53 522 476 485 524 510 | 500 < 0.0002 3 8 6 3 4 | 5 | 0 1 0 6 5 > 0.9998 || = 0.52 492 494 501 458 512 | 500 < 0.0003 11 9 4 4 7 | 5 | 7 4 1 5 8 > 0.9997 || = 0.51 476 492 522 476 478 | 500 < 0.0004 1 4 7 4 6 | 5 | 4 4 3 2 4 > 0.9996 || = 0.50 485 478 486 443 489 | 500 < 0.0005 5 6 3 3 3 | 5 | 9 7 5 4 5 > 0.9995 || = 0.49 490 473 509 511 488 | 500 < 0.0006 5 0 6 1 7 | 5 | 6 5 4 7 4 > 0.9994 || = 0.48 527 535 495 514 482 | 500 < 0.0007 2 3 9 4 4 | 5 | 6 6 5 3 6 > 0.9993 || = 0.47 455 488 495 548 502 | 500 < 0.0008 4 8 4 5 4 | 5 | 5 4 3 5 5 > 0.9992 || = 0.46 471 523 523 511 496 | 500 < 0.0009 4 6 3 5 5 | 5 | 6 10 5 7 5 > 0.9991 || = 0.45 497 489 501 505 521 | 500 < 0.001 2 5 4 5 2 | 5 | 5 9 5 6 3 > 0.999 || = 0.44 534 500 529 514 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 522 503 512 494 473 | 500 < 0.001 44 54 49 43 44 | 50 | 54 53 36 48 48 > 0.999 || = 0.42 544 552 450 489 483 | 500 < 0.002 40 53 47 39 48 | 50 | 52 52 42 49 43 > 0.998 || = 0.41 537 498 495 495 544 | 500 < 0.003 51 59 54 47 58 | 50 | 50 38 46 56 34 > 0.997 || = 0.40 485 510 533 503 488 | 500 < 0.004 66 51 46 50 55 | 50 | 48 48 50 49 67 > 0.996 || = 0.39 505 484 518 521 488 | 500 < 0.005 52 53 51 52 41 | 50 | 44 46 47 57 45 > 0.995 || = 0.38 500 505 521 543 523 | 500 < 0.006 52 46 46 62 42 | 50 | 33 60 54 50 43 > 0.994 || = 0.37 441 505 502 493 485 | 500 < 0.007 48 43 51 64 45 | 50 | 46 53 51 50 60 > 0.993 || = 0.36 476 504 534 506 508 | 500 < 0.008 59 56 60 52 71 | 50 | 50 50 45 42 42 > 0.992 || = 0.35 470 492 451 492 470 | 500 < 0.009 50 43 38 59 68 | 50 | 51 69 48 51 33 > 0.991 || = 0.34 542 518 474 520 510 | 500 < 0.01 45 47 35 61 50 | 50 | 46 45 53 57 59 > 0.99 || = 0.33 507 499 496 523 485 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 512 526 512 470 514 | 500 < 0.01 507 505 477 529 522 | 497.5 | 474 514 472 509 474 > 0.99 || = 0.31 514 509 494 504 489 | 500 = 0.01 226 260 237 272 210 | 252.5 | 288 236 242 263 250 = 0.99 || = 0.30 483 520 517 517 491 | 500 = 0.02 481 492 464 509 545 | 500 | 530 505 534 496 515 = 0.98 || = 0.29 503 519 482 495 520 | 500 =================================================================| 500 | 510 472 470 478 492 = 0.97 || = 0.28 520 500 493 499 501 | 500 sstring_AutoCor test: | 500 | 529 479 507 487 529 = 0.96 || = 0.27 475 488 515 504 508 | 500 ----------------------------------------------- | 500 | 470 492 490 509 467 = 0.95 || = 0.26 484 463 490 485 475 | 500 N = 10, n = 1000000030, r = 0, s = 3, d = 1 | 500 | 494 486 516 526 532 = 0.94 || = 0.25 544 501 489 501 472 | 500 Sample variance | 500 | 516 482 485 505 524 = 0.93 || = 0.24 475 526 508 464 517 | 500 | 500 | 508 468 517 523 479 = 0.92 || = 0.23 497 486 515 484 489 | 500 =================================================================| 500 | 519 478 492 484 511 = 0.91 || = 0.22 498 546 505 442 504 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 521 483 519 489 506 = 0.90 || = 0.21 512 542 537 479 510 | 500 -----------------------------------------------------------------| 500 | 452 529 503 471 471 = 0.89 || = 0.20 500 489 451 498 509 | 500 SD Bern.: d 1.13771 1.01143 0.87449 | 500 | 492 475 486 521 504 = 0.88 || = 0.19 561 515 492 492 504 | 500 s 0.85376 0.74198 1.15988 | 500 | 508 509 528 486 495 = 0.87 || = 0.18 453 492 512 503 476 | 500 t 1.05350 1.02910 0.82502 | 500 | 529 491 476 501 494 = 0.86 || = 0.17 495 483 495 484 536 | 500 m 0.93309 1.20807 0.64062 | 500 | 509 508 498 490 496 = 0.85 || = 0.16 465 502 542 483 503 | 500 x 0.98891 1.45949 1.55383 | 500 | 492 490 533 497 516 = 0.84 || = 0.15 503 520 408 492 525 | 500 | 500 | 511 485 492 526 506 = 0.83 || = 0.14 493 506 536 492 509 | 500 Changes: d 51 4 3 | 500 | 516 503 527 481 492 = 0.82 || = 0.13 522 523 469 479 504 | 500 s 54 3 5 | 500 | 463 518 500 521 493 = 0.81 || = 0.12 491 494 520 495 464 | 500 t 60 6 3 | 500 | 524 498 521 507 517 = 0.80 || = 0.11 480 510 480 498 552 | 500 m 46 1 5 | 500 | 547 517 492 498 499 = 0.79 || = 0.10 497 506 509 493 500 | 500 x 57 4 5 | 500 | 493 474 517 535 546 = 0.78 || = 0.09 475 487 515 515 492 | 500 -----------------------------------------------------------------| 500 | 522 533 511 508 523 = 0.77 || = 0.08 479 493 511 476 451 | 500 Aver./ d 0.50113 498 > 500: 5 3 4 5 5 5 2 6 6 7 | 500 | 521 507 481 520 479 = 0.76 || = 0.07 532 525 508 502 512 | 500 median s 0.49658 499 ----- 6 7 5 7 5 4 4 3 5 2 | 500 | 493 497 503 520 446 = 0.75 || = 0.06 538 494 541 549 514 | 500 t 0.50040 500 5 5 5 6 6 6 3 5 5 4 | 500 | 504 497 489 491 495 = 0.74 || = 0.05 467 523 499 528 493 | 500 m 0.49999 502 9 1 2 7 7 4 5 8 4 6 | 500 | 483 493 489 518 512 = 0.73 || = 0.04 521 520 500 525 508 | 500 x 0.49963 501 6 7 7 4 3 5 5 6 4 5 | 500 | 459 474 510 506 512 = 0.72 || = 0.03 507 517 503 510 501 | 500 -----------------------------------------------------------------| 500 | 504 495 475 514 542 = 0.71 || = 0.02 481 492 464 509 545 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 470 479 499 498 457 = 0.70 || = 0.01 226 260 237 272 210 | 252.5 d 0 0 4 18 60 16 3 0 0 | 500 | 502 512 493 503 493 = 0.69 || < 0.01 507 505 477 529 522 | 497.5 s 0 0 1 12 75 11 2 0 0 | 500 | 471 449 521 511 481 = 0.68 ||========================================================================= t 1 0 4 11 70 15 0 0 0 | 500 | 479 468 500 445 486 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 9 75 12 2 0 0 | 500 | 495 494 473 482 508 = 0.66 ||========================================================================= x 0 0 3 11 72 11 4 0 0 | 500 | 475 473 491 504 528 = 0.65 || sstring_AutoCor test: no 239 test no 240 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 240 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 0 2 | 0.5 | 1 1 0 1 1 > 0.99999 || = 0.64 494 504 506 510 492 | 500 < 0.00002 0 0 1 0 0 | 0.5 | 0 1 0 2 0 > 0.99998 || = 0.63 500 529 501 508 501 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 1 0 1 1 1 > 0.99997 || = 0.62 509 481 465 489 516 | 500 < 0.00004 1 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99996 || = 0.61 462 467 503 504 531 | 500 < 0.00005 1 0 1 1 1 | 0.5 | 0 1 0 0 1 > 0.99995 || = 0.60 478 482 523 480 506 | 500 < 0.00006 2 0 1 1 0 | 0.5 | 0 1 2 0 0 > 0.99994 || = 0.59 496 500 486 536 494 | 500 < 0.00007 0 2 0 0 2 | 0.5 | 0 0 2 1 1 > 0.99993 || = 0.58 511 506 525 462 508 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 1 0 2 1 1 > 0.99992 || = 0.57 505 511 517 499 481 | 500 < 0.00009 0 0 0 1 1 | 0.5 | 0 0 0 1 1 > 0.99991 || = 0.56 467 464 527 542 473 | 500 < 0.0001 0 0 0 0 2 | 0.5 | 1 0 0 0 1 > 0.9999 || = 0.55 507 491 460 486 495 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 470 488 468 482 469 | 500 < 0.0001 4 3 3 4 9 | 5 | 4 4 7 7 8 > 0.9999 || = 0.53 489 480 467 454 482 | 500 < 0.0002 4 11 3 6 6 | 5 | 4 3 2 1 2 > 0.9998 || = 0.52 495 521 534 514 506 | 500 < 0.0003 11 3 7 11 2 | 5 | 7 3 7 2 6 > 0.9997 || = 0.51 535 517 503 464 531 | 500 < 0.0004 8 5 6 7 6 | 5 | 6 5 5 4 2 > 0.9996 || = 0.50 485 500 451 510 504 | 500 < 0.0005 7 4 10 7 8 | 5 | 8 9 4 11 7 > 0.9995 || = 0.49 496 489 522 503 475 | 500 < 0.0006 5 4 11 3 6 | 5 | 2 5 4 4 4 > 0.9994 || = 0.48 506 435 491 530 496 | 500 < 0.0007 5 4 8 4 4 | 5 | 7 6 6 9 3 > 0.9993 || = 0.47 496 543 493 515 487 | 500 < 0.0008 3 7 3 13 4 | 5 | 4 2 3 7 9 > 0.9992 || = 0.46 484 550 504 509 492 | 500 < 0.0009 5 3 6 4 4 | 5 | 8 3 3 7 7 > 0.9991 || = 0.45 480 525 534 492 511 | 500 < 0.001 3 7 5 6 3 | 5 | 5 3 6 3 6 > 0.999 || = 0.44 497 506 498 498 536 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 521 517 520 521 489 | 500 < 0.001 55 51 62 65 52 | 50 | 55 43 47 55 54 > 0.999 || = 0.42 507 503 503 523 472 | 500 < 0.002 50 40 46 48 49 | 50 | 50 47 54 46 47 > 0.998 || = 0.41 486 512 552 455 516 | 500 < 0.003 45 52 44 43 58 | 50 | 58 52 55 48 45 > 0.997 || = 0.40 490 477 510 454 489 | 500 < 0.004 51 54 46 53 57 | 50 | 61 48 44 42 52 > 0.996 || = 0.39 493 476 520 499 492 | 500 < 0.005 55 53 43 50 55 | 50 | 39 53 51 45 53 > 0.995 || = 0.38 508 519 483 475 507 | 500 < 0.006 62 47 65 56 43 | 50 | 49 50 60 52 54 > 0.994 || = 0.37 473 516 489 501 528 | 500 < 0.007 47 40 46 65 55 | 50 | 43 62 46 45 34 > 0.993 || = 0.36 501 498 501 511 507 | 500 < 0.008 62 45 32 63 44 | 50 | 53 48 48 50 44 > 0.992 || = 0.35 492 523 513 487 486 | 500 < 0.009 51 60 54 60 55 | 50 | 42 54 61 50 40 > 0.991 || = 0.34 524 515 499 536 528 | 500 < 0.01 44 43 47 44 54 | 50 | 39 60 42 45 59 > 0.99 || = 0.33 496 511 537 512 511 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 498 501 491 514 464 | 500 < 0.01 522 485 485 547 522 | 497.5 | 489 517 508 478 482 > 0.99 || = 0.31 480 519 485 530 506 | 500 = 0.01 269 217 239 239 250 | 252.5 | 244 232 250 255 257 = 0.99 || = 0.30 489 513 499 494 496 | 500 = 0.02 511 508 501 519 502 | 500 | 488 453 473 508 478 = 0.98 || = 0.29 538 520 447 530 490 | 500 =================================================================| 500 | 512 502 515 497 497 = 0.97 || = 0.28 532 495 518 489 482 | 500 sstring_AutoCor test: | 500 | 499 512 545 486 509 = 0.96 || = 0.27 510 467 504 467 501 | 500 ----------------------------------------------- | 500 | 499 511 443 547 518 = 0.95 || = 0.26 514 517 539 492 480 | 500 N = 10, n = 1000000029, r = 0, s = 3, d = 3 | 500 | 509 454 528 487 514 = 0.94 || = 0.25 475 500 483 464 472 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 493 454 531 536 544 = 0.93 || = 0.24 521 449 494 501 475 | 500 | 500 | 470 484 475 462 530 = 0.92 || = 0.23 499 546 538 516 495 | 500 =================================================================| 500 | 512 508 512 447 502 = 0.91 || = 0.22 517 527 497 522 506 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 512 491 483 495 469 = 0.90 || = 0.21 550 504 470 486 523 | 500 -----------------------------------------------------------------| 500 | 488 537 499 517 525 = 0.89 || = 0.20 519 536 474 538 522 | 500 SD Bern.: d 0.92382 0.90598 1.07290 | 500 | 487 525 454 493 481 = 0.88 || = 0.19 519 545 463 500 519 | 500 s 1.17075 0.90929 0.82380 | 500 | 472 485 467 487 481 = 0.87 || = 0.18 477 492 495 560 535 | 500 t 1.06491 1.30525 0.88587 | 500 | 504 498 520 502 477 = 0.86 || = 0.17 525 500 544 490 474 | 500 m 1.10125 1.30678 0.61348 | 500 | 500 483 518 490 499 = 0.85 || = 0.16 475 561 502 525 506 | 500 x 0.92994 0.76718 1.05123 | 500 | 502 495 528 523 489 = 0.84 || = 0.15 517 481 520 529 462 | 500 | 500 | 493 529 482 509 517 = 0.83 || = 0.14 552 482 524 502 489 | 500 Changes: d 53 5 5 | 500 | 498 507 476 519 473 = 0.82 || = 0.13 522 501 504 498 472 | 500 s 41 5 7 | 500 | 511 533 500 498 518 = 0.81 || = 0.12 528 468 496 484 508 | 500 t 45 5 6 | 500 | 487 529 506 496 490 = 0.80 || = 0.11 486 465 512 504 516 | 500 m 53 5 3 | 500 | 503 514 501 517 523 = 0.79 || = 0.10 556 520 456 500 457 | 500 x 49 6 4 | 500 | 509 497 502 478 497 = 0.78 || = 0.09 468 489 482 496 462 | 500 -----------------------------------------------------------------| 500 | 493 485 523 471 506 = 0.77 || = 0.08 457 538 494 489 517 | 500 Aver./ d 0.49766 499 > 500: 5 7 8 3 3 4 3 6 4 3 | 500 | 509 492 500 485 496 = 0.76 || = 0.07 469 470 497 543 529 | 500 median s 0.49937 500 ----- 3 4 6 8 7 4 4 4 5 5 | 500 | 489 493 478 505 531 = 0.75 || = 0.06 471 446 486 514 482 | 500 t 0.49934 501 4 6 4 4 7 6 5 7 3 6 | 500 | 484 487 521 535 559 = 0.74 || = 0.05 509 525 537 479 479 | 500 m 0.49877 499 4 5 5 6 6 3 4 4 5 4 | 500 | 516 519 512 545 475 = 0.73 || = 0.04 530 492 518 426 507 | 500 x 0.50121 499 6 5 4 6 3 4 5 5 3 7 | 500 | 545 459 459 496 492 = 0.72 || = 0.03 491 492 528 491 513 | 500 -----------------------------------------------------------------| 500 | 505 565 514 482 516 = 0.71 || = 0.02 511 508 501 519 502 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 453 512 514 459 538 = 0.70 || = 0.01 269 217 239 239 250 | 252.5 d 0 0 1 14 73 9 4 0 0 | 500 | 500 506 475 497 500 = 0.69 || < 0.01 522 485 485 547 522 | 497.5 s 0 0 7 12 64 13 5 0 0 | 500 | 515 494 486 487 499 = 0.68 ||========================================================================= t 0 0 4 15 64 16 2 0 0 | 500 | 504 478 505 499 479 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 4 9 69 14 4 0 0 | 500 | 476 464 472 506 524 = 0.66 ||========================================================================= x 0 0 0 16 68 16 1 0 0 | 500 | 481 469 498 467 491 = 0.65 || sstring_AutoCor test: no 240 test no 241 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 241 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 1 0 0 | 0.5 | 0 0 3 1 0 > 0.99999 || = 0.64 499 481 488 511 469 | 500 < 0.00002 0 1 0 1 2 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 490 517 548 493 471 | 500 < 0.00003 0 0 0 0 1 | 0.5 | 0 1 2 0 0 > 0.99997 || = 0.62 509 489 542 492 524 | 500 < 0.00004 1 0 0 0 0 | 0.5 | 0 0 1 3 0 > 0.99996 || = 0.61 506 480 500 480 512 | 500 < 0.00005 0 0 0 2 1 | 0.5 | 1 0 0 1 0 > 0.99995 || = 0.60 475 542 487 493 508 | 500 < 0.00006 2 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 485 496 511 508 497 | 500 < 0.00007 0 0 0 0 0 | 0.5 | 1 1 0 0 2 > 0.99993 || = 0.58 488 514 490 556 492 | 500 < 0.00008 0 0 1 0 1 | 0.5 | 1 0 1 2 2 > 0.99992 || = 0.57 477 505 524 542 505 | 500 < 0.00009 1 0 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 513 526 498 513 508 | 500 < 0.0001 1 2 1 0 0 | 0.5 | 0 1 0 1 0 > 0.9999 || = 0.55 517 515 461 476 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 489 501 476 499 474 | 500 < 0.0001 5 3 3 3 6 | 5 | 4 3 7 8 4 > 0.9999 || = 0.53 473 488 520 530 502 | 500 < 0.0002 7 4 7 9 3 | 5 | 3 3 2 0 7 > 0.9998 || = 0.52 510 521 490 521 528 | 500 < 0.0003 3 6 3 6 1 | 5 | 7 5 5 4 5 > 0.9997 || = 0.51 525 505 456 474 477 | 500 < 0.0004 0 4 3 7 4 | 5 | 3 7 5 7 9 > 0.9996 || = 0.50 472 485 455 489 542 | 500 < 0.0005 7 7 6 6 7 | 5 | 5 3 4 5 5 > 0.9995 || = 0.49 486 522 515 491 504 | 500 < 0.0006 7 5 4 5 5 | 5 | 8 5 5 5 6 > 0.9994 || = 0.48 502 499 501 490 499 | 500 < 0.0007 4 4 5 3 6 | 5 | 2 6 6 2 2 > 0.9993 || = 0.47 504 546 490 484 515 | 500 < 0.0008 3 3 1 2 7 | 5 | 3 2 2 4 3 > 0.9992 || = 0.46 478 520 486 524 465 | 500 < 0.0009 5 10 6 9 6 | 5 | 6 6 4 6 9 > 0.9991 || = 0.45 489 544 474 517 525 | 500 < 0.001 8 4 14 3 7 | 5 | 5 10 7 3 4 > 0.999 || = 0.44 471 540 500 536 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 445 534 536 489 490 | 500 < 0.001 49 50 52 53 52 | 50 | 46 50 47 44 54 > 0.999 || = 0.42 488 522 507 529 529 | 500 < 0.002 47 40 44 43 51 | 50 | 47 43 40 51 48 > 0.998 || = 0.41 506 536 526 506 501 | 500 < 0.003 45 52 40 44 40 | 50 | 48 57 52 55 48 > 0.997 || = 0.40 498 502 512 549 501 | 500 < 0.004 53 56 47 52 49 | 50 | 54 57 55 47 47 > 0.996 || = 0.39 527 484 497 490 493 | 500 < 0.005 55 51 53 56 48 | 50 | 54 55 49 68 34 > 0.995 || = 0.38 480 503 491 502 508 | 500 < 0.006 49 55 52 51 54 | 50 | 72 39 56 56 42 > 0.994 || = 0.37 533 516 514 509 475 | 500 < 0.007 52 49 57 46 54 | 50 | 42 47 58 47 39 > 0.993 || = 0.36 506 490 514 490 515 | 500 < 0.008 58 53 45 63 44 | 50 | 56 41 38 44 56 > 0.992 || = 0.35 489 532 500 470 481 | 500 < 0.009 43 50 51 47 42 | 50 | 47 51 41 43 61 > 0.991 || = 0.34 483 499 483 483 507 | 500 < 0.01 53 56 44 49 60 | 50 | 50 51 50 53 45 > 0.99 || = 0.33 496 470 516 532 499 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 475 488 464 498 480 | 500 < 0.01 504 512 485 504 494 | 497.5 | 516 491 486 508 474 > 0.99 || = 0.31 459 471 499 487 497 | 500 = 0.01 270 245 261 246 240 | 252.5 | 247 265 296 249 260 = 0.99 || = 0.30 462 505 508 511 530 | 500 = 0.02 533 484 509 484 517 | 500 | 487 483 504 554 492 = 0.98 || = 0.29 509 496 532 525 498 | 500 =================================================================| 500 | 505 489 491 485 509 = 0.97 || = 0.28 459 481 479 500 490 | 500 sstring_AutoCor test: | 500 | 507 485 523 508 483 = 0.96 || = 0.27 533 516 514 510 524 | 500 ----------------------------------------------- | 500 | 495 512 493 533 497 = 0.95 || = 0.26 553 490 459 490 524 | 500 N = 10, n = 1000000029, r = 0, s = 3, d = 3 | 500 | 507 512 473 474 517 = 0.94 || = 0.25 516 503 499 520 487 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 519 531 440 537 511 = 0.93 || = 0.24 486 482 523 502 454 | 500 | 500 | 517 516 505 502 465 = 0.92 || = 0.23 472 501 506 496 441 | 500 =================================================================| 500 | 514 502 542 520 501 = 0.91 || = 0.22 479 494 514 486 499 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 487 514 489 456 490 = 0.90 || = 0.21 474 495 484 505 490 | 500 -----------------------------------------------------------------| 500 | 506 506 512 492 490 = 0.89 || = 0.20 461 477 499 496 493 | 500 SD Bern.: d 0.97263 0.62640 1.14424 | 500 | 491 502 500 510 516 = 0.88 || = 0.19 530 468 471 482 492 | 500 s 0.88653 0.65146 0.87792 | 500 | 558 510 500 494 522 = 0.87 || = 0.18 522 473 474 491 508 | 500 t 1.00444 0.73927 0.96379 | 500 | 490 478 486 481 514 = 0.86 || = 0.17 484 485 517 531 513 | 500 m 0.91633 0.81280 1.03394 | 500 | 534 475 524 502 504 = 0.85 || = 0.16 521 508 515 478 466 | 500 x 0.89404 0.82744 1.14599 | 500 | 489 496 477 498 510 = 0.84 || = 0.15 504 491 507 498 500 | 500 | 500 | 525 487 519 489 515 = 0.83 || = 0.14 477 507 522 490 499 | 500 Changes: d 52 5 4 | 500 | 495 504 485 481 531 = 0.82 || = 0.13 512 474 494 497 453 | 500 s 47 5 3 | 500 | 494 503 452 466 488 = 0.81 || = 0.12 524 516 548 487 508 | 500 t 52 5 4 | 500 | 525 507 515 488 475 = 0.80 || = 0.11 513 489 510 481 535 | 500 m 50 5 5 | 500 | 483 481 501 490 506 = 0.79 || = 0.10 524 462 514 494 477 | 500 x 48 4 3 | 500 | 511 462 502 487 534 = 0.78 || = 0.09 535 487 498 509 517 | 500 -----------------------------------------------------------------| 500 | 484 513 468 473 535 = 0.77 || = 0.08 503 482 515 496 517 | 500 Aver./ d 0.50094 502 > 500: 7 8 4 3 3 4 6 7 4 7 | 500 | 504 532 473 515 504 = 0.76 || = 0.07 470 515 511 511 510 | 500 median s 0.50186 501 ----- 4 3 3 4 9 8 6 4 6 6 | 500 | 517 479 486 499 535 = 0.75 || = 0.06 520 501 455 454 494 | 500 t 0.49924 500 5 7 5 4 6 3 4 5 3 5 | 500 | 506 486 521 513 490 = 0.74 || = 0.05 485 516 491 524 480 | 500 m 0.49995 496 6 1 5 4 6 6 3 3 2 7 | 500 | 536 536 498 489 480 = 0.73 || = 0.04 501 469 522 514 519 | 500 x 0.50054 501 6 4 2 4 7 6 4 5 7 5 | 500 | 515 486 518 482 478 = 0.72 || = 0.03 476 460 491 513 527 | 500 -----------------------------------------------------------------| 500 | 471 477 500 501 480 = 0.71 || = 0.02 533 484 509 484 517 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 524 507 484 465 519 = 0.70 || = 0.01 270 245 261 246 240 | 252.5 d 0 0 1 17 66 15 2 0 0 | 500 | 491 475 499 509 498 = 0.69 || < 0.01 504 512 485 504 494 | 497.5 s 0 0 0 13 77 10 1 0 0 | 500 | 475 509 486 491 488 = 0.68 ||========================================================================= t 0 0 4 12 71 11 3 0 0 | 500 | 508 503 530 478 516 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 9 76 12 3 0 0 | 500 | 501 517 524 469 491 = 0.66 ||========================================================================= x 0 0 3 11 73 14 0 0 0 | 500 | 511 502 500 534 481 = 0.65 || sstring_AutoCor test: no 241 test no 242 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 242 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 2 0 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 497 531 488 479 526 | 500 < 0.00002 1 2 0 1 1 | 0.5 | 0 0 0 0 0 > 0.99998 || = 0.63 500 506 537 490 496 | 500 < 0.00003 0 0 0 2 1 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 501 493 480 534 447 | 500 < 0.00004 1 1 0 1 0 | 0.5 | 0 1 0 0 2 > 0.99996 || = 0.61 523 508 507 501 482 | 500 < 0.00005 1 0 1 1 0 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 498 486 487 489 524 | 500 < 0.00006 0 1 0 1 0 | 0.5 | 0 0 1 0 1 > 0.99994 || = 0.59 539 514 470 458 505 | 500 < 0.00007 1 0 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99993 || = 0.58 511 518 542 499 515 | 500 < 0.00008 0 0 1 0 0 | 0.5 | 0 0 1 0 1 > 0.99992 || = 0.57 515 496 507 488 485 | 500 < 0.00009 0 0 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99991 || = 0.56 496 460 499 542 518 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 549 530 490 482 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 463 549 516 497 493 | 500 < 0.0001 4 4 2 9 3 | 5 | 1 1 3 0 6 > 0.9999 || = 0.53 505 505 509 520 500 | 500 < 0.0002 9 4 4 2 5 | 5 | 4 0 3 1 0 > 0.9998 || = 0.52 482 505 487 512 468 | 500 < 0.0003 6 2 1 1 3 | 5 | 3 1 2 2 3 > 0.9997 || = 0.51 473 516 539 521 524 | 500 < 0.0004 4 0 6 9 3 | 5 | 2 4 3 2 1 > 0.9996 || = 0.50 518 502 482 502 475 | 500 < 0.0005 2 4 4 6 11 | 5 | 1 3 2 2 1 > 0.9995 || = 0.49 463 523 481 505 492 | 500 < 0.0006 2 2 4 1 4 | 5 | 0 4 3 8 4 > 0.9994 || = 0.48 475 499 505 508 553 | 500 < 0.0007 5 4 2 4 10 | 5 | 1 2 1 5 5 > 0.9993 || = 0.47 494 477 490 506 451 | 500 < 0.0008 9 5 4 7 5 | 5 | 5 4 3 4 4 > 0.9992 || = 0.46 485 479 482 468 513 | 500 < 0.0009 6 6 7 6 6 | 5 | 5 3 5 2 5 > 0.9991 || = 0.45 493 485 525 476 517 | 500 < 0.001 3 5 5 6 6 | 5 | 2 4 3 2 7 > 0.999 || = 0.44 506 510 478 470 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 472 467 500 516 490 | 500 < 0.001 50 36 39 51 56 | 50 | 24 26 28 28 36 > 0.999 || = 0.42 533 493 476 484 485 | 500 < 0.002 52 46 49 49 41 | 50 | 46 34 46 41 34 > 0.998 || = 0.41 557 516 536 497 527 | 500 < 0.003 56 56 47 48 55 | 50 | 50 50 60 41 54 > 0.997 || = 0.40 540 488 531 503 504 | 500 < 0.004 46 41 50 62 64 | 50 | 43 47 48 54 49 > 0.996 || = 0.39 495 460 482 498 503 | 500 < 0.005 57 55 53 51 44 | 50 | 57 42 59 41 47 > 0.995 || = 0.38 521 490 517 512 479 | 500 < 0.006 52 44 47 52 48 | 50 | 63 51 48 40 46 > 0.994 || = 0.37 512 479 483 507 486 | 500 < 0.007 54 48 47 54 52 | 50 | 47 55 51 43 48 > 0.993 || = 0.36 471 486 492 517 483 | 500 < 0.008 58 42 45 62 41 | 50 | 48 51 42 39 47 > 0.992 || = 0.35 482 509 531 516 468 | 500 < 0.009 52 33 63 52 52 | 50 | 47 48 33 51 58 > 0.991 || = 0.34 533 519 504 484 497 | 500 < 0.01 51 53 56 50 71 | 50 | 57 50 60 56 56 > 0.99 || = 0.33 469 516 511 495 492 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 440 510 503 502 478 | 500 < 0.01 528 454 496 531 524 | 497.5 | 482 454 475 434 475 > 0.99 || = 0.31 487 533 517 479 504 | 500 = 0.01 273 263 228 265 245 | 252.5 | 278 243 254 267 276 = 0.99 || = 0.30 515 481 494 483 481 | 500 = 0.02 493 493 547 480 510 | 500 | 511 507 520 459 528 = 0.98 || = 0.29 503 512 474 497 504 | 500 =================================================================| 500 | 504 496 501 508 513 = 0.97 || = 0.28 494 501 548 480 485 | 500 sstring_AutoCor test: | 500 | 458 529 530 540 537 = 0.96 || = 0.27 491 516 518 525 500 | 500 ----------------------------------------------- | 500 | 471 496 485 483 539 = 0.95 || = 0.26 538 500 490 479 510 | 500 N = 10, n = 1000000029, r = 0, s = 3, d = 3 | 500 | 494 508 477 479 545 = 0.94 || = 0.25 463 471 513 498 510 | 500 Anderson-Darling statistic = A2 | 500 | 492 526 493 515 502 = 0.93 || = 0.24 520 496 553 510 511 | 500 | 500 | 476 494 517 487 475 = 0.92 || = 0.23 515 476 462 533 466 | 500 =================================================================| 500 | 522 528 475 500 536 = 0.91 || = 0.22 489 506 495 482 522 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 512 471 522 504 493 = 0.90 || = 0.21 544 512 475 483 485 | 500 -----------------------------------------------------------------| 500 | 486 521 527 507 553 = 0.89 || = 0.20 529 474 491 522 513 | 500 SD Bern.: d 1.03645 0.62320 1.43598 | 500 | 512 508 501 546 485 = 0.88 || = 0.19 495 495 497 493 501 | 500 s 0.96799 1.23024 1.36889 | 500 | 481 506 496 521 522 = 0.87 || = 0.18 500 513 499 504 496 | 500 t 0.96607 0.88134 1.51269 | 500 | 507 506 465 507 490 = 0.86 || = 0.17 482 530 437 513 486 | 500 m 0.96823 0.79914 1.44985 | 500 | 469 514 518 537 436 = 0.85 || = 0.16 511 502 523 472 498 | 500 x 1.02238 1.34825 1.10235 | 500 | 477 515 504 510 518 = 0.84 || = 0.15 505 499 495 496 504 | 500 | 500 | 554 546 495 508 487 = 0.83 || = 0.14 473 526 513 523 513 | 500 Changes: d 53 3 3 | 500 | 469 494 510 461 467 = 0.82 || = 0.13 510 495 497 489 492 | 500 s 46 5 2 | 500 | 495 545 473 516 501 = 0.81 || = 0.12 521 465 516 462 500 | 500 t 50 3 7 | 500 | 473 509 477 533 460 = 0.80 || = 0.11 488 464 516 520 465 | 500 m 45 3 3 | 500 | 502 524 526 496 495 = 0.79 || = 0.10 487 533 524 514 521 | 500 x 49 6 3 | 500 | 503 509 504 478 487 = 0.78 || = 0.09 506 496 510 481 476 | 500 -----------------------------------------------------------------| 500 | 494 480 499 547 506 = 0.77 || = 0.08 494 491 523 499 515 | 500 Aver./ d 0.49785 498 > 500: 6 4 6 4 4 5 5 4 4 4 | 500 | 504 492 483 476 498 = 0.76 || = 0.07 495 450 488 511 515 | 500 median s 0.50227 502 ----- 3 5 5 5 3 7 5 6 8 5 | 500 | 471 452 496 463 473 = 0.75 || = 0.06 535 505 475 502 510 | 500 t 0.49910 498 4 5 4 6 4 5 4 3 6 5 | 500 | 481 494 482 528 479 = 0.74 || = 0.05 504 479 489 509 484 | 500 m 0.49960 501 6 5 4 5 5 4 5 3 9 4 | 500 | 499 503 506 491 536 = 0.73 || = 0.04 529 487 488 532 506 | 500 x 0.50107 501 7 4 6 2 6 6 6 2 4 8 | 500 | 498 501 487 500 496 = 0.72 || = 0.03 492 505 509 494 504 | 500 -----------------------------------------------------------------| 500 | 522 505 479 478 468 = 0.71 || = 0.02 493 493 547 480 510 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 521 491 522 461 485 = 0.70 || = 0.01 273 263 228 265 245 | 252.5 d 0 0 1 19 65 13 3 0 0 | 500 | 472 478 469 490 507 = 0.69 || < 0.01 528 454 496 531 524 | 497.5 s 0 0 2 13 70 13 3 0 0 | 500 | 474 484 485 506 556 = 0.68 ||========================================================================= t 0 0 1 15 69 13 3 0 0 | 500 | 490 535 522 520 506 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 11 76 11 2 0 0 | 500 | 520 526 481 510 513 = 0.66 ||========================================================================= x 0 0 3 12 71 11 4 0 0 | 500 | 506 462 477 495 504 = 0.65 || sstring_AutoCor test: no 242 test no 243 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 243 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 1 0 | 0.5 | 1 0 1 4 0 > 0.99999 || = 0.64 532 498 501 473 520 | 500 < 0.00002 0 1 0 0 0 | 0.5 | 0 1 0 2 1 > 0.99998 || = 0.63 492 538 481 504 493 | 500 < 0.00003 1 0 0 1 0 | 0.5 | 0 0 0 1 0 > 0.99997 || = 0.62 492 489 518 506 498 | 500 < 0.00004 1 1 1 0 0 | 0.5 | 1 0 0 0 1 > 0.99996 || = 0.61 469 465 540 497 515 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 1 0 0 > 0.99995 || = 0.60 514 488 514 514 491 | 500 < 0.00006 0 1 0 0 0 | 0.5 | 0 0 0 0 2 > 0.99994 || = 0.59 485 466 502 520 540 | 500 < 0.00007 0 0 0 0 2 | 0.5 | 0 0 0 0 1 > 0.99993 || = 0.58 507 512 494 533 510 | 500 < 0.00008 0 0 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99992 || = 0.57 489 510 478 529 479 | 500 < 0.00009 2 1 1 0 0 | 0.5 | 0 0 1 0 0 > 0.99991 || = 0.56 495 540 484 516 507 | 500 < 0.0001 1 0 0 1 1 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 517 507 512 474 494 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 497 495 515 494 527 | 500 < 0.0001 5 4 2 3 3 | 5 | 4 1 4 7 5 > 0.9999 || = 0.53 501 508 514 501 504 | 500 < 0.0002 3 4 2 2 2 | 5 | 5 0 4 3 4 > 0.9998 || = 0.52 525 503 497 505 508 | 500 < 0.0003 8 1 5 2 4 | 5 | 9 4 6 6 10 > 0.9997 || = 0.51 479 488 484 497 494 | 500 < 0.0004 4 8 2 3 4 | 5 | 6 5 3 7 6 > 0.9996 || = 0.50 545 494 480 463 504 | 500 < 0.0005 5 4 3 1 5 | 5 | 2 8 5 8 9 > 0.9995 || = 0.49 482 500 521 513 466 | 500 < 0.0006 7 1 5 7 6 | 5 | 5 2 7 5 10 > 0.9994 || = 0.48 462 510 518 490 507 | 500 < 0.0007 3 6 6 5 6 | 5 | 4 9 1 3 2 > 0.9993 || = 0.47 519 520 495 468 432 | 500 < 0.0008 4 3 7 5 10 | 5 | 3 6 6 3 5 > 0.9992 || = 0.46 489 501 510 531 519 | 500 < 0.0009 6 9 3 9 3 | 5 | 1 4 5 5 5 > 0.9991 || = 0.45 499 476 540 495 497 | 500 < 0.001 5 2 5 2 4 | 5 | 5 5 4 2 2 > 0.999 || = 0.44 488 510 493 497 512 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 472 513 464 542 513 | 500 < 0.001 50 42 40 39 47 | 50 | 44 44 45 49 58 > 0.999 || = 0.42 495 499 522 531 475 | 500 < 0.002 47 43 46 58 53 | 50 | 55 48 58 63 45 > 0.998 || = 0.41 510 509 495 502 502 | 500 < 0.003 48 49 60 45 58 | 50 | 66 37 48 48 48 > 0.997 || = 0.40 490 483 502 503 495 | 500 < 0.004 66 65 38 61 33 | 50 | 49 43 46 53 50 > 0.996 || = 0.39 490 469 489 477 503 | 500 < 0.005 46 36 50 34 48 | 50 | 45 39 46 59 40 > 0.995 || = 0.38 492 519 476 540 496 | 500 < 0.006 51 51 59 62 55 | 50 | 58 45 52 55 63 > 0.994 || = 0.37 469 531 520 477 516 | 500 < 0.007 60 44 48 47 62 | 50 | 60 43 58 44 51 > 0.993 || = 0.36 504 477 461 476 504 | 500 < 0.008 48 41 54 51 58 | 50 | 46 57 51 55 50 > 0.992 || = 0.35 518 524 516 481 467 | 500 < 0.009 51 66 61 50 50 | 50 | 55 39 53 48 41 > 0.991 || = 0.34 504 533 490 547 513 | 500 < 0.01 54 54 41 48 49 | 50 | 43 46 46 53 53 > 0.99 || = 0.33 474 503 473 524 498 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 495 495 480 520 480 | 500 < 0.01 521 491 497 495 513 | 497.5 | 521 441 503 527 499 > 0.99 || = 0.31 465 516 490 490 499 | 500 = 0.01 242 273 263 264 212 | 252.5 | 245 248 269 268 256 = 0.99 || = 0.30 521 492 471 521 492 | 500 = 0.02 504 456 517 500 536 | 500 | 493 517 465 494 476 = 0.98 || = 0.29 478 491 535 514 490 | 500 =================================================================| 500 | 519 499 488 487 510 = 0.97 || = 0.28 530 502 488 501 480 | 500 sstring_AutoCor test: | 500 | 513 476 461 501 514 = 0.96 || = 0.27 479 468 533 514 530 | 500 ----------------------------------------------- | 500 | 516 497 514 528 489 = 0.95 || = 0.26 462 490 479 532 471 | 500 N = 10, n = 1000000029, r = 0, s = 3, d = 3 | 500 | 456 493 510 520 471 = 0.94 || = 0.25 485 473 524 453 514 | 500 Tests on the sum of all N observations | 500 | 515 495 514 556 480 = 0.93 || = 0.24 485 533 507 472 526 | 500 | 500 | 487 484 489 489 510 = 0.92 || = 0.23 486 508 506 488 478 | 500 =================================================================| 500 | 507 534 488 494 512 = 0.91 || = 0.22 496 495 534 471 498 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 503 533 489 485 498 = 0.90 || = 0.21 523 498 465 498 519 | 500 -----------------------------------------------------------------| 500 | 508 493 513 496 498 = 0.89 || = 0.20 515 504 488 500 492 | 500 SD Bern.: d 0.92780 0.90266 1.09324 | 500 | 487 510 522 502 502 = 0.88 || = 0.19 511 507 530 505 508 | 500 s 0.91657 1.36082 1.13104 | 500 | 515 533 534 522 510 = 0.87 || = 0.18 497 485 529 464 480 | 500 t 0.97441 1.15209 0.66213 | 500 | 501 493 491 513 517 = 0.86 || = 0.17 478 497 465 515 537 | 500 m 0.98566 1.22126 0.85247 | 500 | 523 496 489 492 524 = 0.85 || = 0.16 501 476 524 494 530 | 500 x 0.93660 1.10417 0.95230 | 500 | 557 477 499 511 493 = 0.84 || = 0.15 506 475 469 486 501 | 500 | 500 | 491 515 549 525 519 = 0.83 || = 0.14 481 486 499 520 508 | 500 Changes: d 50 5 6 | 500 | 526 502 496 501 499 = 0.82 || = 0.13 485 479 441 458 458 | 500 s 46 5 2 | 500 | 485 477 499 485 523 = 0.81 || = 0.12 510 496 506 475 490 | 500 t 51 6 4 | 500 | 500 502 484 500 513 = 0.80 || = 0.11 535 490 498 524 540 | 500 m 41 8 7 | 500 | 519 503 479 476 464 = 0.79 || = 0.10 465 484 495 505 485 | 500 x 62 4 4 | 500 | 492 516 518 433 482 = 0.78 || = 0.09 497 473 500 478 497 | 500 -----------------------------------------------------------------| 500 | 509 512 510 491 504 = 0.77 || = 0.08 494 507 503 492 483 | 500 Aver./ d 0.50219 497 > 500: 4 5 3 4 2 5 3 6 7 6 | 500 | 497 501 549 480 500 = 0.76 || = 0.07 460 468 520 497 502 | 500 median s 0.50119 499 ----- 4 1 4 6 6 6 6 8 5 2 | 500 | 507 542 464 478 483 = 0.75 || = 0.06 475 529 472 491 510 | 500 t 0.50054 499 6 4 6 2 6 5 6 5 4 5 | 500 | 554 510 525 484 506 = 0.74 || = 0.05 490 498 505 476 520 | 500 m 0.50088 500 3 5 4 5 6 7 5 1 6 6 | 500 | 508 497 507 478 487 = 0.73 || = 0.04 513 543 506 528 483 | 500 x 0.49986 502 6 6 4 4 5 6 6 3 6 6 | 500 | 550 508 462 484 462 = 0.72 || = 0.03 546 494 487 517 504 | 500 -----------------------------------------------------------------| 500 | 482 481 499 525 496 = 0.71 || = 0.02 504 456 517 500 536 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 495 463 493 505 549 = 0.70 || = 0.01 242 273 263 264 212 | 252.5 d 0 0 0 11 76 9 5 0 0 | 500 | 498 503 501 526 488 = 0.69 || < 0.01 521 491 497 495 513 | 497.5 s 0 0 1 16 69 15 0 0 0 | 500 | 505 513 522 468 511 = 0.68 ||========================================================================= t 0 0 1 13 73 12 2 0 0 | 500 | 487 533 478 506 512 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 1 1 15 67 15 2 0 0 | 500 | 496 517 521 498 449 = 0.66 ||========================================================================= x 0 1 2 9 77 11 1 0 0 | 500 | 506 536 481 494 529 = 0.65 || sstring_AutoCor test: no 243 test no 244 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 244 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 1 0 | 0.5 | 1 0 1 0 0 > 0.99999 || = 0.64 510 524 482 524 511 | 500 < 0.00002 1 0 1 0 2 | 0.5 | 0 0 1 0 1 > 0.99998 || = 0.63 490 514 489 503 505 | 500 < 0.00003 2 2 2 0 0 | 0.5 | 0 1 1 1 0 > 0.99997 || = 0.62 538 491 515 469 488 | 500 < 0.00004 0 0 1 1 0 | 0.5 | 0 1 0 1 1 > 0.99996 || = 0.61 482 510 538 494 485 | 500 < 0.00005 0 0 0 1 0 | 0.5 | 0 0 1 2 0 > 0.99995 || = 0.60 485 465 519 504 535 | 500 < 0.00006 1 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99994 || = 0.59 465 478 478 529 508 | 500 < 0.00007 0 0 1 0 0 | 0.5 | 1 0 0 0 0 > 0.99993 || = 0.58 499 519 470 511 519 | 500 < 0.00008 1 0 1 0 0 | 0.5 | 0 0 0 2 2 > 0.99992 || = 0.57 517 515 478 500 483 | 500 < 0.00009 1 0 0 1 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 498 505 540 527 465 | 500 < 0.0001 1 0 0 0 0 | 0.5 | 1 0 0 1 1 > 0.9999 || = 0.55 478 487 463 515 490 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 499 503 503 466 542 | 500 < 0.0001 8 3 6 4 2 | 5 | 4 2 4 7 5 > 0.9999 || = 0.53 489 516 503 486 533 | 500 < 0.0002 6 5 1 2 6 | 5 | 2 2 3 1 1 > 0.9998 || = 0.52 503 514 502 489 529 | 500 < 0.0003 8 4 4 3 3 | 5 | 4 7 7 5 6 > 0.9997 || = 0.51 487 482 474 468 480 | 500 < 0.0004 7 2 4 8 6 | 5 | 5 1 3 5 4 > 0.9996 || = 0.50 506 502 496 490 541 | 500 < 0.0005 8 6 3 3 7 | 5 | 3 6 12 6 4 > 0.9995 || = 0.49 478 501 489 522 504 | 500 < 0.0006 11 9 3 3 7 | 5 | 2 6 3 4 8 > 0.9994 || = 0.48 493 476 517 505 558 | 500 < 0.0007 6 3 8 7 6 | 5 | 7 9 7 6 4 > 0.9993 || = 0.47 501 501 531 508 516 | 500 < 0.0008 4 2 6 7 4 | 5 | 4 3 3 5 7 > 0.9992 || = 0.46 460 484 512 458 477 | 500 < 0.0009 2 5 10 7 6 | 5 | 4 7 7 4 8 > 0.9991 || = 0.45 516 481 514 516 523 | 500 < 0.001 8 4 6 5 7 | 5 | 2 0 11 2 5 > 0.999 || = 0.44 470 538 462 515 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 464 495 515 521 511 | 500 < 0.001 68 43 51 49 54 | 50 | 37 43 60 45 52 > 0.999 || = 0.42 490 504 493 481 477 | 500 < 0.002 52 35 40 49 46 | 50 | 64 36 37 51 55 > 0.998 || = 0.41 548 482 509 468 476 | 500 < 0.003 59 50 44 42 47 | 50 | 47 63 51 48 48 > 0.997 || = 0.40 493 517 486 487 479 | 500 < 0.004 50 52 57 43 41 | 50 | 47 47 44 44 56 > 0.996 || = 0.39 525 527 538 491 459 | 500 < 0.005 53 61 56 46 51 | 50 | 58 56 49 46 54 > 0.995 || = 0.38 516 495 486 507 495 | 500 < 0.006 54 56 36 40 50 | 50 | 54 43 46 51 47 > 0.994 || = 0.37 509 489 530 487 525 | 500 < 0.007 53 55 52 53 54 | 50 | 50 48 48 51 40 > 0.993 || = 0.36 454 472 501 494 536 | 500 < 0.008 52 56 59 63 45 | 50 | 37 56 44 55 54 > 0.992 || = 0.35 481 466 514 507 499 | 500 < 0.009 41 50 63 58 53 | 50 | 40 54 64 49 57 > 0.991 || = 0.34 532 470 493 492 505 | 500 < 0.01 32 50 42 60 53 | 50 | 56 45 58 48 46 > 0.99 || = 0.33 490 481 470 489 524 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 517 522 495 530 515 | 500 < 0.01 514 508 500 503 494 | 497.5 | 490 491 501 488 509 > 0.99 || = 0.31 491 515 506 498 493 | 500 = 0.01 260 246 273 254 246 | 252.5 | 221 231 238 245 233 = 0.99 || = 0.30 508 502 521 492 468 | 500 = 0.02 488 530 476 503 506 | 500 | 517 486 489 504 514 = 0.98 || = 0.29 485 530 487 505 512 | 500 =================================================================| 500 | 508 476 506 472 523 = 0.97 || = 0.28 532 517 493 511 514 | 500 sstring_AutoCor test: | 500 | 494 528 497 514 484 = 0.96 || = 0.27 508 477 484 483 546 | 500 ----------------------------------------------- | 500 | 541 486 490 481 498 = 0.95 || = 0.26 434 478 497 524 484 | 500 N = 10, n = 1000000029, r = 0, s = 3, d = 3 | 500 | 503 480 514 527 498 = 0.94 || = 0.25 446 502 502 495 428 | 500 Sample variance | 500 | 490 496 511 475 489 = 0.93 || = 0.24 518 494 519 539 469 | 500 | 500 | 482 481 481 481 475 = 0.92 || = 0.23 515 489 519 488 508 | 500 =================================================================| 500 | 499 507 483 486 502 = 0.91 || = 0.22 516 482 502 528 532 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 504 510 486 553 529 = 0.90 || = 0.21 508 486 460 495 504 | 500 -----------------------------------------------------------------| 500 | 505 471 507 466 506 = 0.89 || = 0.20 525 514 512 490 487 | 500 SD Bern.: d 1.04766 1.30602 1.23996 | 500 | 493 519 495 509 515 = 0.88 || = 0.19 509 493 518 475 475 | 500 s 0.86690 0.99648 1.08589 | 500 | 493 515 477 493 469 = 0.87 || = 0.18 549 534 512 481 508 | 500 t 0.90847 1.21386 1.11679 | 500 | 506 497 516 513 492 = 0.86 || = 0.17 535 514 529 506 453 | 500 m 0.95896 1.07104 0.47771 | 500 | 483 469 506 477 499 = 0.85 || = 0.16 501 525 468 531 485 | 500 x 0.99132 0.60362 0.74198 | 500 | 522 487 500 466 509 = 0.84 || = 0.15 461 490 507 516 500 | 500 | 500 | 495 526 505 512 490 = 0.83 || = 0.14 499 490 504 495 507 | 500 Changes: d 55 3 5 | 500 | 522 479 480 535 493 = 0.82 || = 0.13 520 497 477 482 544 | 500 s 49 2 6 | 500 | 501 506 528 524 501 = 0.81 || = 0.12 503 518 487 540 508 | 500 t 48 5 4 | 500 | 496 489 501 520 486 = 0.80 || = 0.11 443 506 482 507 521 | 500 m 51 1 4 | 500 | 529 481 477 523 510 = 0.79 || = 0.10 522 521 528 503 464 | 500 x 45 6 5 | 500 | 468 505 458 465 490 = 0.78 || = 0.09 494 487 487 538 516 | 500 -----------------------------------------------------------------| 500 | 506 509 488 470 471 = 0.77 || = 0.08 487 496 502 507 494 | 500 Aver./ d 0.49987 501 > 500: 6 7 7 6 3 2 4 7 6 4 | 500 | 546 511 511 545 509 = 0.76 || = 0.07 542 490 513 466 502 | 500 median s 0.49968 497 ----- 3 6 4 4 5 6 7 6 5 2 | 500 | 508 495 548 479 497 = 0.75 || = 0.06 501 470 503 508 520 | 500 t 0.49912 502 7 6 5 6 6 5 7 5 5 4 | 500 | 485 529 518 524 470 = 0.74 || = 0.05 501 474 508 523 495 | 500 m 0.49893 502 7 6 5 3 6 5 5 5 6 3 | 500 | 502 556 446 514 488 = 0.73 || = 0.04 516 496 533 488 489 | 500 x 0.49980 500 4 5 6 5 6 6 5 3 5 4 | 500 | 529 489 468 465 499 = 0.72 || = 0.03 474 519 482 485 493 | 500 -----------------------------------------------------------------| 500 | 502 531 512 496 512 = 0.71 || = 0.02 488 530 476 503 506 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 549 532 534 471 473 = 0.70 || = 0.01 260 246 273 254 246 | 252.5 d 0 0 4 10 73 10 4 0 0 | 500 | 473 503 505 491 507 = 0.69 || < 0.01 514 508 500 503 494 | 497.5 s 0 0 0 13 74 13 1 0 0 | 500 | 506 499 517 512 523 = 0.68 ||========================================================================= t 0 0 1 13 75 11 1 0 0 | 500 | 479 532 493 520 508 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 0 17 66 16 2 0 0 | 500 | 488 476 505 461 490 = 0.66 ||========================================================================= x 0 1 1 16 67 14 2 0 0 | 500 | 477 506 513 511 475 = 0.65 || sstring_AutoCor test: no 244 test no 245 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 245 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 1 0 0 1 | 0.5 | 0 0 2 0 0 > 0.99999 || = 0.64 519 502 476 536 472 | 500 < 0.00002 1 1 0 0 2 | 0.5 | 0 1 0 0 0 > 0.99998 || = 0.63 496 504 487 478 500 | 500 < 0.00003 0 0 0 1 0 | 0.5 | 1 0 0 0 0 > 0.99997 || = 0.62 529 515 547 493 493 | 500 < 0.00004 0 0 1 1 0 | 0.5 | 0 1 1 0 0 > 0.99996 || = 0.61 491 485 512 472 509 | 500 < 0.00005 1 0 1 1 0 | 0.5 | 1 1 0 0 1 > 0.99995 || = 0.60 482 511 484 481 508 | 500 < 0.00006 0 1 1 0 1 | 0.5 | 1 0 0 0 1 > 0.99994 || = 0.59 562 487 505 474 498 | 500 < 0.00007 0 1 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99993 || = 0.58 463 501 485 481 478 | 500 < 0.00008 0 0 2 0 0 | 0.5 | 0 0 0 2 0 > 0.99992 || = 0.57 477 494 514 451 523 | 500 < 0.00009 1 0 1 0 1 | 0.5 | 1 0 1 0 0 > 0.99991 || = 0.56 534 510 528 473 551 | 500 < 0.0001 1 0 2 1 0 | 0.5 | 1 0 0 1 0 > 0.9999 || = 0.55 505 468 487 515 506 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 502 489 506 489 505 | 500 < 0.0001 6 4 8 4 5 | 5 | 5 3 4 3 2 > 0.9999 || = 0.53 529 520 483 476 523 | 500 < 0.0002 6 4 3 5 4 | 5 | 1 1 3 1 1 > 0.9998 || = 0.52 482 489 512 500 493 | 500 < 0.0003 5 5 3 7 1 | 5 | 5 5 7 4 5 > 0.9997 || = 0.51 507 507 502 543 500 | 500 < 0.0004 3 8 4 2 6 | 5 | 5 5 5 5 6 > 0.9996 || = 0.50 457 469 551 510 492 | 500 < 0.0005 6 2 7 4 3 | 5 | 5 5 8 4 4 > 0.9995 || = 0.49 517 454 481 486 498 | 500 < 0.0006 3 8 3 7 4 | 5 | 5 9 5 5 8 > 0.9994 || = 0.48 501 566 507 517 447 | 500 < 0.0007 3 11 2 3 6 | 5 | 6 6 2 7 5 > 0.9993 || = 0.47 504 519 494 492 492 | 500 < 0.0008 4 5 3 5 4 | 5 | 5 8 2 5 6 > 0.9992 || = 0.46 504 524 478 502 479 | 500 < 0.0009 5 1 5 4 3 | 5 | 7 8 7 9 5 > 0.9991 || = 0.45 491 457 478 476 555 | 500 < 0.001 6 6 6 11 11 | 5 | 1 4 8 8 9 > 0.999 || = 0.44 494 488 549 477 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 504 533 480 531 496 | 500 < 0.001 47 54 44 52 47 | 50 | 45 54 51 51 51 > 0.999 || = 0.42 485 506 459 504 515 | 500 < 0.002 45 55 61 51 45 | 50 | 43 54 33 50 54 > 0.998 || = 0.41 507 523 495 524 488 | 500 < 0.003 58 45 40 55 61 | 50 | 50 46 49 61 51 > 0.997 || = 0.40 488 494 511 528 495 | 500 < 0.004 48 52 53 64 55 | 50 | 52 37 48 46 47 > 0.996 || = 0.39 484 502 477 520 475 | 500 < 0.005 49 51 53 50 50 | 50 | 53 53 51 52 36 > 0.995 || = 0.38 493 517 517 486 507 | 500 < 0.006 32 53 41 42 63 | 50 | 44 43 64 44 38 > 0.994 || = 0.37 497 522 500 539 504 | 500 < 0.007 55 50 52 33 52 | 50 | 47 37 48 50 44 > 0.993 || = 0.36 479 508 498 511 487 | 500 < 0.008 38 49 44 60 44 | 50 | 48 51 38 54 45 > 0.992 || = 0.35 521 496 485 513 512 | 500 < 0.009 57 55 49 51 48 | 50 | 45 54 57 52 59 > 0.991 || = 0.34 453 550 491 502 523 | 500 < 0.01 50 40 51 53 53 | 50 | 53 59 61 52 50 > 0.99 || = 0.33 491 505 483 514 508 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 521 488 471 541 486 | 500 < 0.01 479 504 488 511 518 | 497.5 | 480 488 500 512 475 > 0.99 || = 0.31 506 515 470 526 515 | 500 = 0.01 239 249 272 240 243 | 252.5 | 243 251 272 239 231 = 0.99 || = 0.30 507 489 534 506 504 | 500 = 0.02 490 508 496 459 499 | 500 | 450 524 523 476 488 = 0.98 || = 0.29 522 496 556 485 490 | 500 =================================================================| 500 | 488 494 451 540 474 = 0.97 || = 0.28 533 551 483 500 510 | 500 sstring_AutoCor test: | 500 | 522 498 490 525 499 = 0.96 || = 0.27 506 482 502 468 467 | 500 ----------------------------------------------- | 500 | 482 514 527 506 540 = 0.95 || = 0.26 527 484 490 499 510 | 500 N = 10, n = 1000000030, r = 27, s = 3, d = 1 | 500 | 482 512 492 484 496 = 0.94 || = 0.25 520 490 520 490 529 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 510 536 478 464 488 = 0.93 || = 0.24 469 483 499 508 513 | 500 | 500 | 504 521 477 474 553 = 0.92 || = 0.23 512 458 511 496 501 | 500 =================================================================| 500 | 500 477 459 510 477 = 0.91 || = 0.22 495 525 510 453 499 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 513 487 478 516 507 = 0.90 || = 0.21 462 537 520 508 471 | 500 -----------------------------------------------------------------| 500 | 526 547 517 527 495 = 0.89 || = 0.20 448 502 491 499 521 | 500 SD Bern.: d 1.09802 1.13634 0.58337 | 500 | 559 473 498 531 533 = 0.88 || = 0.19 510 524 484 505 529 | 500 s 1.05691 0.64218 1.04166 | 500 | 463 496 503 487 485 = 0.87 || = 0.18 546 448 492 477 538 | 500 t 0.99235 0.89262 1.27342 | 500 | 481 493 481 471 491 = 0.86 || = 0.17 495 484 560 492 499 | 500 m 0.99781 1.17446 0.63591 | 500 | 493 501 475 510 515 = 0.85 || = 0.16 470 504 488 500 491 | 500 x 0.96925 0.89710 1.00945 | 500 | 503 492 504 482 481 = 0.84 || = 0.15 530 517 516 500 521 | 500 | 500 | 487 469 500 496 515 = 0.83 || = 0.14 493 498 488 515 490 | 500 Changes: d 50 6 3 | 500 | 480 492 506 463 478 = 0.82 || = 0.13 493 490 477 513 503 | 500 s 57 5 4 | 500 | 507 514 527 496 509 = 0.81 || = 0.12 489 525 490 484 516 | 500 t 55 7 4 | 500 | 496 495 470 510 483 = 0.80 || = 0.11 498 482 496 526 497 | 500 m 42 2 6 | 500 | 487 513 497 488 508 = 0.79 || = 0.10 497 563 513 487 487 | 500 x 53 5 3 | 500 | 513 474 488 496 516 = 0.78 || = 0.09 506 503 527 476 486 | 500 -----------------------------------------------------------------| 500 | 476 443 492 454 447 = 0.77 || = 0.08 493 475 507 496 490 | 500 Aver./ d 0.49884 497 > 500: 6 3 6 4 6 6 3 5 5 3 | 500 | 519 499 475 516 522 = 0.76 || = 0.07 514 479 529 537 480 | 500 median s 0.49984 498 ----- 4 5 4 7 6 5 6 4 3 5 | 500 | 472 507 523 545 498 = 0.75 || = 0.06 521 462 524 519 464 | 500 t 0.49816 498 6 3 6 2 3 6 5 3 5 4 | 500 | 509 512 542 474 493 = 0.74 || = 0.05 514 487 525 481 472 | 500 m 0.49985 500 4 4 2 9 6 2 7 4 4 5 | 500 | 479 487 490 501 513 = 0.73 || = 0.04 513 521 498 512 512 | 500 x 0.49944 499 3 5 6 7 3 6 4 4 5 2 | 500 | 553 513 509 497 482 = 0.72 || = 0.03 569 483 479 498 523 | 500 -----------------------------------------------------------------| 500 | 578 475 498 472 487 = 0.71 || = 0.02 490 508 496 459 499 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 473 506 514 532 517 = 0.70 || = 0.01 239 249 272 240 243 | 252.5 d 0 0 3 11 74 7 4 2 0 | 500 | 481 547 479 518 453 = 0.69 || < 0.01 479 504 488 511 518 | 497.5 s 0 0 3 13 70 9 6 0 0 | 500 | 507 469 510 525 523 = 0.68 ||========================================================================= t 0 0 1 12 69 14 5 0 0 | 500 | 471 506 497 515 474 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 3 17 63 17 1 0 0 | 500 | 486 487 462 522 556 = 0.66 ||========================================================================= x 0 0 3 11 73 10 4 0 0 | 500 | 492 467 528 525 488 = 0.65 || sstring_AutoCor test: no 245 test no 246 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 246 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 0 1 1 | 0.5 | 1 0 0 3 1 > 0.99999 || = 0.64 479 535 507 504 471 | 500 < 0.00002 0 0 1 0 0 | 0.5 | 0 2 1 0 0 > 0.99998 || = 0.63 526 494 470 534 486 | 500 < 0.00003 0 1 0 0 0 | 0.5 | 0 0 1 1 0 > 0.99997 || = 0.62 544 529 475 520 490 | 500 < 0.00004 1 0 0 3 1 | 0.5 | 0 1 0 0 1 > 0.99996 || = 0.61 504 491 476 505 523 | 500 < 0.00005 0 0 0 1 2 | 0.5 | 0 1 1 1 0 > 0.99995 || = 0.60 517 462 527 492 508 | 500 < 0.00006 0 1 0 1 0 | 0.5 | 0 0 0 0 1 > 0.99994 || = 0.59 506 475 489 527 477 | 500 < 0.00007 0 0 0 0 2 | 0.5 | 0 1 3 0 0 > 0.99993 || = 0.58 513 516 499 451 546 | 500 < 0.00008 0 0 0 0 1 | 0.5 | 1 1 1 1 0 > 0.99992 || = 0.57 503 471 519 508 502 | 500 < 0.00009 0 0 0 0 1 | 0.5 | 0 1 1 1 2 > 0.99991 || = 0.56 500 510 506 464 495 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 1 0 0 2 > 0.9999 || = 0.55 495 466 507 473 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 455 484 495 479 496 | 500 < 0.0001 1 3 1 6 8 | 5 | 2 8 8 7 7 > 0.9999 || = 0.53 494 500 502 508 497 | 500 < 0.0002 4 8 7 7 5 | 5 | 5 2 2 1 4 > 0.9998 || = 0.52 492 508 495 527 504 | 500 < 0.0003 5 6 7 4 3 | 5 | 6 2 5 8 4 > 0.9997 || = 0.51 474 525 558 503 479 | 500 < 0.0004 8 4 4 6 5 | 5 | 8 6 2 2 4 > 0.9996 || = 0.50 530 496 506 481 509 | 500 < 0.0005 3 5 5 6 10 | 5 | 6 7 7 3 8 > 0.9995 || = 0.49 504 497 518 492 515 | 500 < 0.0006 2 4 5 5 5 | 5 | 8 7 8 5 7 > 0.9994 || = 0.48 531 492 470 496 521 | 500 < 0.0007 5 2 8 8 6 | 5 | 5 3 9 6 2 > 0.9993 || = 0.47 503 532 532 510 487 | 500 < 0.0008 7 5 4 4 4 | 5 | 4 3 1 2 2 > 0.9992 || = 0.46 506 529 489 501 531 | 500 < 0.0009 8 6 3 3 5 | 5 | 7 9 4 7 3 > 0.9991 || = 0.45 510 500 504 512 545 | 500 < 0.001 8 4 6 4 4 | 5 | 9 4 4 7 6 > 0.999 || = 0.44 509 563 524 528 542 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 496 515 515 511 498 | 500 < 0.001 51 47 50 53 55 | 50 | 60 51 50 48 47 > 0.999 || = 0.42 517 467 496 506 509 | 500 < 0.002 51 42 60 36 40 | 50 | 53 54 57 53 58 > 0.998 || = 0.41 437 517 534 496 490 | 500 < 0.003 49 59 44 47 42 | 50 | 48 58 51 50 51 > 0.997 || = 0.40 477 500 545 524 478 | 500 < 0.004 53 49 47 41 50 | 50 | 63 52 53 52 57 > 0.996 || = 0.39 508 493 463 480 509 | 500 < 0.005 49 58 57 43 38 | 50 | 64 46 50 41 64 > 0.995 || = 0.38 502 485 475 507 480 | 500 < 0.006 50 53 52 41 53 | 50 | 47 46 35 45 42 > 0.994 || = 0.37 501 535 510 475 470 | 500 < 0.007 60 57 65 51 60 | 50 | 61 53 52 63 45 > 0.993 || = 0.36 492 498 499 508 510 | 500 < 0.008 47 59 69 56 47 | 50 | 49 27 47 50 52 > 0.992 || = 0.35 470 522 510 465 508 | 500 < 0.009 53 49 68 54 46 | 50 | 53 41 60 49 47 > 0.991 || = 0.34 467 528 522 504 524 | 500 < 0.01 32 42 50 45 44 | 50 | 43 35 42 57 54 > 0.99 || = 0.33 475 521 501 498 520 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 498 539 514 486 517 | 500 < 0.01 495 515 562 467 475 | 497.5 | 541 463 497 508 517 > 0.99 || = 0.31 470 473 485 485 498 | 500 = 0.01 256 236 264 288 215 | 252.5 | 241 243 284 263 235 = 0.99 || = 0.30 519 513 478 474 528 | 500 = 0.02 478 500 472 504 496 | 500 | 494 487 508 498 514 = 0.98 || = 0.29 542 468 489 488 515 | 500 =================================================================| 500 | 485 496 468 475 504 = 0.97 || = 0.28 521 508 484 509 492 | 500 sstring_AutoCor test: | 500 | 496 489 535 477 506 = 0.96 || = 0.27 513 517 517 516 474 | 500 ----------------------------------------------- | 500 | 500 493 488 508 522 = 0.95 || = 0.26 459 484 486 491 498 | 500 N = 10, n = 1000000030, r = 27, s = 3, d = 1 | 500 | 519 510 436 495 521 = 0.94 || = 0.25 508 519 497 512 501 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 519 499 504 532 503 = 0.93 || = 0.24 506 477 506 479 498 | 500 | 500 | 513 467 546 510 537 = 0.92 || = 0.23 548 485 528 498 522 | 500 =================================================================| 500 | 517 493 505 483 484 = 0.91 || = 0.22 521 474 487 519 496 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 504 529 501 478 536 = 0.90 || = 0.21 461 507 499 474 516 | 500 -----------------------------------------------------------------| 500 | 478 487 543 487 532 = 0.89 || = 0.20 545 537 489 514 518 | 500 SD Bern.: d 1.01455 0.95441 1.15555 | 500 | 491 481 489 498 527 = 0.88 || = 0.19 467 540 506 510 496 | 500 s 0.98240 0.92023 1.38704 | 500 | 499 501 486 565 474 = 0.87 || = 0.18 486 491 474 462 475 | 500 t 1.03054 1.48936 0.96068 | 500 | 509 529 491 499 507 = 0.86 || = 0.17 473 492 486 513 474 | 500 m 0.98075 1.00349 0.82744 | 500 | 466 475 475 510 517 = 0.85 || = 0.16 504 521 523 492 504 | 500 x 0.94277 1.00349 0.93533 | 500 | 466 478 521 490 504 = 0.84 || = 0.15 498 483 514 473 502 | 500 | 500 | 485 549 517 474 470 = 0.83 || = 0.14 492 496 484 505 473 | 500 Changes: d 37 7 7 | 500 | 506 484 555 509 487 = 0.82 || = 0.13 470 506 503 542 479 | 500 s 53 4 3 | 500 | 476 496 489 519 483 = 0.81 || = 0.12 497 488 475 484 507 | 500 t 51 4 6 | 500 | 499 513 523 506 462 = 0.80 || = 0.11 437 506 511 511 522 | 500 m 55 3 7 | 500 | 536 459 454 495 460 = 0.79 || = 0.10 504 516 489 524 515 | 500 x 45 3 5 | 500 | 495 504 467 518 476 = 0.78 || = 0.09 491 490 462 495 514 | 500 -----------------------------------------------------------------| 500 | 478 520 493 501 517 = 0.77 || = 0.08 532 470 498 537 515 | 500 Aver./ d 0.50086 502 > 500: 7 2 8 4 7 4 8 5 3 5 | 500 | 515 480 501 537 482 = 0.76 || = 0.07 513 476 493 479 479 | 500 median s 0.49928 497 ----- 2 5 5 6 5 4 6 6 4 1 | 500 | 512 482 498 531 496 = 0.75 || = 0.06 503 487 476 501 495 | 500 t 0.50104 499 3 5 3 5 7 6 2 3 5 6 | 500 | 473 506 499 487 504 = 0.74 || = 0.05 513 528 477 520 492 | 500 m 0.50061 503 6 6 5 3 7 5 6 7 4 5 | 500 | 498 502 516 467 539 = 0.73 || = 0.04 519 460 503 508 479 | 500 x 0.50076 501 3 5 5 7 6 5 2 3 6 8 | 500 | 502 486 497 516 499 = 0.72 || = 0.03 512 482 466 450 517 | 500 -----------------------------------------------------------------| 500 | 529 526 491 529 476 = 0.71 || = 0.02 478 500 472 504 496 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 515 506 480 525 475 = 0.70 || = 0.01 256 236 264 288 215 | 252.5 d 0 0 3 15 71 9 3 0 0 | 500 | 481 478 521 478 486 = 0.69 || < 0.01 495 515 562 467 475 | 497.5 s 0 0 0 17 68 14 2 0 0 | 500 | 515 494 500 521 504 = 0.68 ||========================================================================= t 0 0 2 16 68 10 5 0 0 | 500 | 511 521 500 468 457 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 16 68 13 2 0 0 | 500 | 502 516 491 472 498 = 0.66 ||========================================================================= x 0 0 1 18 70 10 2 0 0 | 500 | 546 518 496 472 468 = 0.65 || sstring_AutoCor test: no 246 test no 247 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 247 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 0 0 1 0 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 498 504 502 502 548 | 500 < 0.00002 1 0 0 1 0 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 492 511 511 529 513 | 500 < 0.00003 0 2 1 0 2 | 0.5 | 0 0 0 0 1 > 0.99997 || = 0.62 491 518 503 497 475 | 500 < 0.00004 1 0 1 0 1 | 0.5 | 0 0 1 1 0 > 0.99996 || = 0.61 492 485 511 534 541 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99995 || = 0.60 508 502 527 515 498 | 500 < 0.00006 1 0 1 0 2 | 0.5 | 0 1 0 0 1 > 0.99994 || = 0.59 486 532 505 490 474 | 500 < 0.00007 1 1 0 0 0 | 0.5 | 1 1 0 0 1 > 0.99993 || = 0.58 535 498 496 503 515 | 500 < 0.00008 0 0 0 1 0 | 0.5 | 1 0 1 0 0 > 0.99992 || = 0.57 534 513 487 513 518 | 500 < 0.00009 0 0 1 0 0 | 0.5 | 0 0 0 1 0 > 0.99991 || = 0.56 493 526 470 517 475 | 500 < 0.0001 1 0 0 0 0 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 501 504 519 507 479 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 487 469 507 474 500 | 500 < 0.0001 7 3 4 3 5 | 5 | 3 2 3 3 3 > 0.9999 || = 0.53 505 477 519 526 538 | 500 < 0.0002 2 6 4 8 7 | 5 | 2 3 2 0 0 > 0.9998 || = 0.52 512 498 481 537 502 | 500 < 0.0003 5 3 3 6 6 | 5 | 2 2 7 4 1 > 0.9997 || = 0.51 523 504 475 464 534 | 500 < 0.0004 5 2 2 6 4 | 5 | 1 2 4 6 1 > 0.9996 || = 0.50 499 496 495 478 532 | 500 < 0.0005 4 3 4 7 4 | 5 | 6 6 3 1 4 > 0.9995 || = 0.49 479 503 489 490 512 | 500 < 0.0006 9 5 10 5 6 | 5 | 4 4 7 4 6 > 0.9994 || = 0.48 497 509 495 510 475 | 500 < 0.0007 2 12 4 4 3 | 5 | 3 1 5 3 1 > 0.9993 || = 0.47 505 467 517 487 529 | 500 < 0.0008 5 4 11 7 3 | 5 | 2 0 1 3 2 > 0.9992 || = 0.46 496 498 533 510 551 | 500 < 0.0009 4 9 7 3 6 | 5 | 5 6 6 1 6 > 0.9991 || = 0.45 494 501 463 490 531 | 500 < 0.001 3 3 4 4 5 | 5 | 6 3 2 4 4 > 0.999 || = 0.44 526 461 520 477 452 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 525 539 470 528 490 | 500 < 0.001 46 50 53 53 49 | 50 | 34 29 40 29 28 > 0.999 || = 0.42 505 506 501 480 486 | 500 < 0.002 50 51 58 43 49 | 50 | 42 38 49 46 43 > 0.998 || = 0.41 492 493 473 508 510 | 500 < 0.003 47 49 64 60 44 | 50 | 44 51 41 31 59 > 0.997 || = 0.40 465 543 510 471 509 | 500 < 0.004 44 55 53 52 38 | 50 | 38 55 55 41 40 > 0.996 || = 0.39 472 509 514 531 464 | 500 < 0.005 50 57 49 40 43 | 50 | 30 49 56 48 45 > 0.995 || = 0.38 470 516 457 491 515 | 500 < 0.006 47 53 46 37 57 | 50 | 51 50 54 50 41 > 0.994 || = 0.37 506 516 508 514 556 | 500 < 0.007 53 61 55 41 55 | 50 | 46 45 54 49 55 > 0.993 || = 0.36 531 525 461 513 479 | 500 < 0.008 49 52 50 55 56 | 50 | 61 47 50 49 44 > 0.992 || = 0.35 534 507 540 533 470 | 500 < 0.009 52 61 44 50 37 | 50 | 44 52 47 52 52 > 0.991 || = 0.34 502 508 473 449 507 | 500 < 0.01 43 46 64 46 60 | 50 | 52 62 59 40 50 > 0.99 || = 0.33 520 506 479 526 480 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 503 471 487 517 538 | 500 < 0.01 481 535 536 477 488 | 497.5 | 442 478 505 435 457 > 0.99 || = 0.31 450 501 509 516 464 | 500 = 0.01 253 234 244 255 231 | 252.5 | 269 266 239 264 240 = 0.99 || = 0.30 507 500 524 490 511 | 500 = 0.02 511 487 492 525 493 | 500 | 521 484 521 541 510 = 0.98 || = 0.29 484 527 500 535 511 | 500 =================================================================| 500 | 489 525 495 492 489 = 0.97 || = 0.28 487 486 515 470 515 | 500 sstring_AutoCor test: | 500 | 479 513 499 517 492 = 0.96 || = 0.27 467 461 542 480 503 | 500 ----------------------------------------------- | 500 | 555 457 475 508 493 = 0.95 || = 0.26 527 519 515 499 505 | 500 N = 10, n = 1000000030, r = 27, s = 3, d = 1 | 500 | 474 480 508 511 518 = 0.94 || = 0.25 493 477 492 500 501 | 500 Anderson-Darling statistic = A2 | 500 | 526 522 505 502 556 = 0.93 || = 0.24 522 519 507 505 496 | 500 | 500 | 511 470 521 481 524 = 0.92 || = 0.23 498 465 465 514 484 | 500 =================================================================| 500 | 496 505 510 487 504 = 0.91 || = 0.22 509 503 485 464 472 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 523 499 499 532 507 = 0.90 || = 0.21 463 496 519 501 481 | 500 -----------------------------------------------------------------| 500 | 484 506 507 508 528 = 0.89 || = 0.20 474 472 475 519 519 | 500 SD Bern.: d 0.94196 0.51600 1.46906 | 500 | 496 516 509 455 482 = 0.88 || = 0.19 498 475 514 483 529 | 500 s 0.89979 0.83347 1.26078 | 500 | 526 486 492 498 504 = 0.87 || = 0.18 510 502 486 454 514 | 500 t 0.93504 1.05123 0.85481 | 500 | 455 522 505 497 501 = 0.86 || = 0.17 513 499 492 503 466 | 500 m 1.02526 1.05218 1.42126 | 500 | 528 486 482 472 495 = 0.85 || = 0.16 504 530 458 500 517 | 500 x 1.16051 1.10508 1.33107 | 500 | 503 502 538 505 519 = 0.84 || = 0.15 494 509 521 474 518 | 500 | 500 | 482 530 488 524 473 = 0.83 || = 0.14 511 499 512 530 519 | 500 Changes: d 49 4 5 | 500 | 486 492 532 483 486 = 0.82 || = 0.13 474 472 469 508 469 | 500 s 53 4 3 | 500 | 478 480 477 497 473 = 0.81 || = 0.12 512 489 520 490 463 | 500 t 54 4 3 | 500 | 497 507 512 512 444 = 0.80 || = 0.11 507 540 496 476 510 | 500 m 58 5 2 | 500 | 487 516 516 486 546 = 0.79 || = 0.10 503 511 495 517 492 | 500 x 48 3 6 | 500 | 517 468 485 527 500 = 0.78 || = 0.09 508 477 485 537 475 | 500 -----------------------------------------------------------------| 500 | 514 481 515 491 478 = 0.77 || = 0.08 504 501 478 489 497 | 500 Aver./ d 0.49976 501 > 500: 8 7 3 7 4 7 2 5 4 5 | 500 | 480 494 504 500 485 = 0.76 || = 0.07 504 509 488 500 508 | 500 median s 0.50024 501 ----- 3 5 4 8 6 6 7 3 5 5 | 500 | 505 499 484 517 479 = 0.75 || = 0.06 516 482 548 563 500 | 500 t 0.50064 501 4 4 5 5 5 5 5 7 5 6 | 500 | 502 490 548 493 472 = 0.74 || = 0.05 523 495 520 475 518 | 500 m 0.49975 502 5 4 5 7 4 7 7 4 4 6 | 500 | 560 529 512 483 533 = 0.73 || = 0.04 473 479 526 507 443 | 500 x 0.50021 501 3 6 6 5 6 5 6 3 5 5 | 500 | 465 500 498 447 464 = 0.72 || = 0.03 519 498 474 463 558 | 500 -----------------------------------------------------------------| 500 | 493 485 501 501 524 = 0.71 || = 0.02 511 487 492 525 493 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 494 481 518 485 501 = 0.70 || = 0.01 253 234 244 255 231 | 252.5 d 0 0 3 10 71 15 2 0 0 | 500 | 480 484 483 512 485 = 0.69 || < 0.01 481 535 536 477 488 | 497.5 s 0 0 0 16 72 12 1 0 0 | 500 | 496 512 482 479 470 = 0.68 ||========================================================================= t 0 0 0 16 74 9 2 0 0 | 500 | 479 513 466 521 516 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 5 11 68 16 1 0 0 | 500 | 527 550 489 503 522 = 0.66 ||========================================================================= x 0 0 3 20 60 12 6 0 0 | 500 | 504 508 480 504 464 = 0.65 || sstring_AutoCor test: no 247 test no 248 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 248 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 1 0 | 0.5 | 1 2 0 0 0 > 0.99999 || = 0.64 499 491 480 519 476 | 500 < 0.00002 1 0 1 0 1 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 482 511 503 485 474 | 500 < 0.00003 0 0 1 1 2 | 0.5 | 0 1 0 0 1 > 0.99997 || = 0.62 523 478 513 506 490 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 3 0 0 0 1 > 0.99996 || = 0.61 489 477 503 509 468 | 500 < 0.00005 0 0 2 1 0 | 0.5 | 0 0 1 1 1 > 0.99995 || = 0.60 521 486 495 503 532 | 500 < 0.00006 0 0 0 2 0 | 0.5 | 1 1 0 2 0 > 0.99994 || = 0.59 498 527 482 500 505 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 1 0 0 1 0 > 0.99993 || = 0.58 498 515 505 528 503 | 500 < 0.00008 1 0 0 0 0 | 0.5 | 0 0 2 0 0 > 0.99992 || = 0.57 518 511 482 505 545 | 500 < 0.00009 0 0 1 2 0 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 480 502 477 469 501 | 500 < 0.0001 0 0 1 3 1 | 0.5 | 0 2 0 0 0 > 0.9999 || = 0.55 487 510 524 518 478 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 543 491 502 514 489 | 500 < 0.0001 3 0 6 12 4 | 5 | 6 7 3 4 4 > 0.9999 || = 0.53 496 488 486 464 509 | 500 < 0.0002 5 6 2 8 7 | 5 | 5 3 2 1 1 > 0.9998 || = 0.52 500 498 510 463 522 | 500 < 0.0003 9 2 7 3 4 | 5 | 9 9 7 4 12 > 0.9997 || = 0.51 500 490 507 535 524 | 500 < 0.0004 4 1 5 4 2 | 5 | 5 9 3 5 1 > 0.9996 || = 0.50 502 516 548 504 467 | 500 < 0.0005 8 1 7 3 5 | 5 | 5 3 9 10 5 > 0.9995 || = 0.49 486 537 474 487 474 | 500 < 0.0006 3 7 4 4 3 | 5 | 1 7 10 5 5 > 0.9994 || = 0.48 551 496 524 453 480 | 500 < 0.0007 4 6 7 3 7 | 5 | 4 3 6 4 6 > 0.9993 || = 0.47 483 491 533 539 522 | 500 < 0.0008 2 4 11 6 3 | 5 | 9 3 5 3 6 > 0.9992 || = 0.46 480 461 480 519 501 | 500 < 0.0009 1 6 8 7 3 | 5 | 8 5 3 6 6 > 0.9991 || = 0.45 491 508 524 513 514 | 500 < 0.001 5 6 6 2 2 | 5 | 3 8 2 5 8 > 0.999 || = 0.44 525 489 539 491 464 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 511 498 512 468 524 | 500 < 0.001 44 39 63 52 40 | 50 | 55 57 50 47 54 > 0.999 || = 0.42 487 566 519 486 455 | 500 < 0.002 47 46 55 35 39 | 50 | 31 53 46 44 51 > 0.998 || = 0.41 508 485 548 512 537 | 500 < 0.003 50 49 52 56 46 | 50 | 55 56 58 40 44 > 0.997 || = 0.40 461 497 481 465 518 | 500 < 0.004 61 39 48 60 39 | 50 | 51 49 46 49 40 > 0.996 || = 0.39 492 498 505 500 513 | 500 < 0.005 54 50 46 51 45 | 50 | 61 44 49 50 52 > 0.995 || = 0.38 471 475 517 506 492 | 500 < 0.006 37 40 48 48 60 | 50 | 59 49 51 59 42 > 0.994 || = 0.37 497 468 491 507 534 | 500 < 0.007 47 49 50 53 49 | 50 | 50 63 45 66 53 > 0.993 || = 0.36 511 536 476 496 559 | 500 < 0.008 49 56 53 55 52 | 50 | 45 51 54 38 56 > 0.992 || = 0.35 508 520 494 511 495 | 500 < 0.009 46 53 56 51 50 | 50 | 58 54 42 52 47 > 0.991 || = 0.34 486 458 500 491 504 | 500 < 0.01 41 49 49 51 44 | 50 | 50 49 51 52 54 > 0.99 || = 0.33 497 529 490 486 462 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 471 527 527 505 520 | 500 < 0.01 476 470 520 512 464 | 497.5 | 515 525 492 497 493 > 0.99 || = 0.31 529 504 486 523 521 | 500 = 0.01 247 260 264 240 267 | 252.5 | 270 252 245 247 273 = 0.99 || = 0.30 485 483 537 487 504 | 500 = 0.02 499 524 497 501 474 | 500 | 475 457 495 482 500 = 0.98 || = 0.29 508 485 496 486 492 | 500 =================================================================| 500 | 520 489 536 509 510 = 0.97 || = 0.28 500 519 486 515 511 | 500 sstring_AutoCor test: | 500 | 509 512 503 514 505 = 0.96 || = 0.27 500 496 470 516 490 | 500 ----------------------------------------------- | 500 | 471 454 459 488 503 = 0.95 || = 0.26 449 494 500 498 493 | 500 N = 10, n = 1000000030, r = 27, s = 3, d = 1 | 500 | 501 478 548 523 485 = 0.94 || = 0.25 515 489 471 485 515 | 500 Tests on the sum of all N observations | 500 | 518 515 523 497 500 = 0.93 || = 0.24 552 546 473 496 486 | 500 | 500 | 468 531 522 480 505 = 0.92 || = 0.23 515 507 511 507 518 | 500 =================================================================| 500 | 480 492 482 496 523 = 0.91 || = 0.22 517 481 505 492 481 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 543 512 464 513 539 = 0.90 || = 0.21 518 501 469 513 486 | 500 -----------------------------------------------------------------| 500 | 504 489 513 485 508 = 0.89 || = 0.20 490 505 487 504 479 | 500 SD Bern.: d 0.97142 0.95755 1.18633 | 500 | 502 504 492 532 491 = 0.88 || = 0.19 451 528 519 514 502 | 500 s 0.92677 0.90155 0.79913 | 500 | 533 516 482 535 497 = 0.87 || = 0.18 492 488 489 490 527 | 500 t 0.90821 0.73248 0.63905 | 500 | 511 471 524 524 489 = 0.86 || = 0.17 487 463 492 496 494 | 500 m 0.87368 0.90155 1.12749 | 500 | 497 524 495 502 514 = 0.85 || = 0.16 527 497 489 494 508 | 500 x 0.95665 1.02422 0.76326 | 500 | 517 488 482 483 502 = 0.84 || = 0.15 516 498 492 489 488 | 500 | 500 | 464 517 477 507 493 = 0.83 || = 0.14 469 478 515 519 512 | 500 Changes: d 53 2 5 | 500 | 494 501 474 564 484 = 0.82 || = 0.13 516 493 490 512 492 | 500 s 47 2 3 | 500 | 489 465 510 469 511 = 0.81 || = 0.12 468 521 479 478 490 | 500 t 47 3 7 | 500 | 506 512 485 512 521 = 0.80 || = 0.11 508 506 491 505 535 | 500 m 55 4 3 | 500 | 524 474 525 499 491 = 0.79 || = 0.10 511 520 487 483 489 | 500 x 50 4 6 | 500 | 503 534 512 489 520 = 0.78 || = 0.09 483 497 502 500 501 | 500 -----------------------------------------------------------------| 500 | 498 493 502 517 502 = 0.77 || = 0.08 514 493 489 503 518 | 500 Aver./ d 0.50079 500 > 500: 4 5 6 3 4 3 3 6 6 6 | 500 | 491 483 536 502 516 = 0.76 || = 0.07 513 498 477 522 483 | 500 median s 0.49945 498 ----- 4 4 5 5 3 5 4 7 6 4 | 500 | 509 524 514 458 510 = 0.75 || = 0.06 506 489 492 472 484 | 500 t 0.50131 496 4 2 2 4 7 5 6 8 3 5 | 500 | 481 503 459 485 473 = 0.74 || = 0.05 489 537 484 464 510 | 500 m 0.50058 501 6 4 5 5 4 6 5 5 7 3 | 500 | 501 504 521 477 495 = 0.73 || = 0.04 535 477 484 530 536 | 500 x 0.50078 501 5 5 3 7 6 8 2 5 5 6 | 500 | 569 505 514 536 486 = 0.72 || = 0.03 475 507 506 512 438 | 500 -----------------------------------------------------------------| 500 | 481 509 526 502 488 = 0.71 || = 0.02 499 524 497 501 474 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 461 512 510 490 485 = 0.70 || = 0.01 247 260 264 240 267 | 252.5 d 0 0 2 11 75 10 2 1 0 | 500 | 507 482 485 483 478 = 0.69 || < 0.01 476 470 520 512 464 | 497.5 s 0 0 1 12 73 13 2 0 0 | 500 | 481 505 512 515 466 = 0.68 ||========================================================================= t 0 0 0 13 71 14 3 0 0 | 500 | 495 512 488 488 473 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 10 79 10 1 0 0 | 500 | 512 489 492 502 506 = 0.66 ||========================================================================= x 0 0 2 12 73 12 2 0 0 | 500 | 488 483 501 483 526 = 0.65 || sstring_AutoCor test: no 248 test no 249 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 249 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 2 0 0 | 0.5 | 0 0 1 1 2 > 0.99999 || = 0.64 503 477 517 456 446 | 500 < 0.00002 0 0 1 0 1 | 0.5 | 0 1 1 0 0 > 0.99998 || = 0.63 508 503 522 505 524 | 500 < 0.00003 0 0 1 0 0 | 0.5 | 1 0 1 1 0 > 0.99997 || = 0.62 514 505 493 497 473 | 500 < 0.00004 1 0 0 0 1 | 0.5 | 1 5 0 0 0 > 0.99996 || = 0.61 518 519 477 493 490 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 1 0 2 0 > 0.99995 || = 0.60 515 495 528 485 519 | 500 < 0.00006 1 0 0 1 0 | 0.5 | 0 1 0 0 1 > 0.99994 || = 0.59 506 512 514 526 512 | 500 < 0.00007 0 0 0 2 0 | 0.5 | 2 1 0 1 0 > 0.99993 || = 0.58 419 507 519 504 455 | 500 < 0.00008 1 0 0 0 1 | 0.5 | 1 0 1 1 0 > 0.99992 || = 0.57 510 496 504 499 488 | 500 < 0.00009 1 1 0 1 1 | 0.5 | 0 1 0 0 0 > 0.99991 || = 0.56 503 488 484 501 477 | 500 < 0.0001 0 0 0 1 0 | 0.5 | 1 1 0 0 0 > 0.9999 || = 0.55 503 478 508 476 476 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 478 497 507 480 493 | 500 < 0.0001 4 2 4 5 4 | 5 | 6 11 4 6 3 > 0.9999 || = 0.53 516 449 562 485 491 | 500 < 0.0002 5 9 6 4 6 | 5 | 5 5 3 0 0 > 0.9998 || = 0.52 521 519 455 525 468 | 500 < 0.0003 7 3 7 6 7 | 5 | 4 1 4 9 6 > 0.9997 || = 0.51 499 481 523 467 466 | 500 < 0.0004 2 11 5 3 6 | 5 | 1 3 7 8 4 > 0.9996 || = 0.50 504 487 503 509 501 | 500 < 0.0005 5 3 2 5 8 | 5 | 5 4 3 5 7 > 0.9995 || = 0.49 509 501 517 461 494 | 500 < 0.0006 6 6 3 7 3 | 5 | 3 7 4 5 2 > 0.9994 || = 0.48 501 507 530 466 518 | 500 < 0.0007 3 3 2 6 5 | 5 | 3 4 2 5 6 > 0.9993 || = 0.47 481 484 503 544 517 | 500 < 0.0008 2 3 6 2 6 | 5 | 5 8 6 5 2 > 0.9992 || = 0.46 488 523 495 504 518 | 500 < 0.0009 6 7 5 7 4 | 5 | 6 5 6 3 3 > 0.9991 || = 0.45 515 517 493 498 510 | 500 < 0.001 7 7 4 7 2 | 5 | 6 5 6 1 5 > 0.999 || = 0.44 473 534 486 485 504 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 491 545 526 509 529 | 500 < 0.001 47 54 44 52 51 | 50 | 44 53 45 47 38 > 0.999 || = 0.42 498 481 448 486 522 | 500 < 0.002 49 54 53 43 57 | 50 | 47 59 54 61 52 > 0.998 || = 0.41 515 465 498 506 494 | 500 < 0.003 55 56 57 52 38 | 50 | 54 53 42 59 46 > 0.997 || = 0.40 461 487 535 531 506 | 500 < 0.004 53 50 46 50 73 | 50 | 60 49 62 52 45 > 0.996 || = 0.39 511 485 502 512 469 | 500 < 0.005 50 55 40 52 44 | 50 | 39 41 59 55 51 > 0.995 || = 0.38 497 480 477 518 507 | 500 < 0.006 46 54 52 45 46 | 50 | 49 50 59 38 48 > 0.994 || = 0.37 480 467 485 506 504 | 500 < 0.007 48 47 44 58 62 | 50 | 53 50 61 47 49 > 0.993 || = 0.36 515 469 480 519 493 | 500 < 0.008 44 43 60 52 44 | 50 | 47 50 44 52 62 > 0.992 || = 0.35 487 505 505 561 506 | 500 < 0.009 53 49 52 50 43 | 50 | 47 51 36 48 56 > 0.991 || = 0.34 539 472 484 535 508 | 500 < 0.01 50 44 52 64 50 | 50 | 44 38 55 46 47 > 0.99 || = 0.33 481 514 483 507 505 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 463 492 490 502 497 | 500 < 0.01 495 506 500 518 508 | 497.5 | 484 494 517 505 494 > 0.99 || = 0.31 475 499 502 524 506 | 500 = 0.01 267 273 246 226 235 | 252.5 | 254 241 260 242 239 = 0.99 || = 0.30 546 535 494 524 503 | 500 = 0.02 509 492 487 524 505 | 500 | 525 510 508 498 507 = 0.98 || = 0.29 496 524 500 469 528 | 500 =================================================================| 500 | 508 502 481 485 502 = 0.97 || = 0.28 463 462 457 497 464 | 500 sstring_AutoCor test: | 500 | 529 519 508 492 469 = 0.96 || = 0.27 515 540 497 490 492 | 500 ----------------------------------------------- | 500 | 499 479 546 492 516 = 0.95 || = 0.26 503 478 516 492 526 | 500 N = 10, n = 1000000030, r = 27, s = 3, d = 1 | 500 | 495 505 449 500 510 = 0.94 || = 0.25 514 486 504 480 515 | 500 Sample variance | 500 | 491 490 520 507 523 = 0.93 || = 0.24 523 527 527 508 496 | 500 | 500 | 489 512 537 515 510 = 0.92 || = 0.23 505 518 454 529 500 | 500 =================================================================| 500 | 497 548 515 466 487 = 0.91 || = 0.22 507 485 536 538 508 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 511 503 509 481 501 = 0.90 || = 0.21 512 517 540 538 501 | 500 -----------------------------------------------------------------| 500 | 544 511 510 449 490 = 0.89 || = 0.20 481 507 511 496 485 | 500 SD Bern.: d 0.87928 0.46712 0.83227 | 500 | 506 485 495 472 474 = 0.88 || = 0.19 498 530 539 478 485 | 500 s 0.99973 0.63906 0.80786 | 500 | 511 546 495 495 495 = 0.87 || = 0.18 470 496 497 485 475 | 500 t 1.04152 0.84658 1.25680 | 500 | 481 459 500 464 514 = 0.86 || = 0.17 485 510 498 499 502 | 500 m 1.06301 0.83707 0.91368 | 500 | 492 511 506 494 498 = 0.85 || = 0.16 471 509 532 520 518 | 500 x 0.88982 1.41774 0.87678 | 500 | 513 515 488 488 480 = 0.84 || = 0.15 513 475 493 517 484 | 500 | 500 | 511 525 514 511 499 = 0.83 || = 0.14 514 496 485 506 513 | 500 Changes: d 40 4 4 | 500 | 483 496 528 522 493 = 0.82 || = 0.13 471 545 489 495 520 | 500 s 47 3 3 | 500 | 511 513 469 472 515 = 0.81 || = 0.12 476 489 519 520 536 | 500 t 48 5 5 | 500 | 503 550 441 507 503 = 0.80 || = 0.11 485 469 493 532 512 | 500 m 44 8 4 | 500 | 507 525 487 480 549 = 0.79 || = 0.10 477 462 500 508 490 | 500 x 49 5 6 | 500 | 492 500 478 506 469 = 0.78 || = 0.09 501 473 481 492 512 | 500 -----------------------------------------------------------------| 500 | 492 468 500 451 501 = 0.77 || = 0.08 536 495 488 531 496 | 500 Aver./ d 0.50142 503 > 500: 7 2 7 4 4 7 6 7 7 4 | 500 | 504 519 506 516 488 = 0.76 || = 0.07 521 479 525 569 523 | 500 median s 0.50093 501 ----- 6 4 6 3 6 3 4 6 7 6 | 500 | 510 475 492 531 497 = 0.75 || = 0.06 471 503 496 502 480 | 500 t 0.50090 500 3 3 6 3 5 8 4 3 5 8 | 500 | 529 508 518 478 536 = 0.74 || = 0.05 499 516 440 449 544 | 500 m 0.49581 501 6 6 4 10 5 4 5 5 2 3 | 500 | 483 501 498 479 462 = 0.73 || = 0.04 504 504 503 486 513 | 500 x 0.49874 501 6 6 5 7 8 2 6 4 3 6 | 500 | 504 528 504 481 469 = 0.72 || = 0.03 506 511 493 524 477 | 500 -----------------------------------------------------------------| 500 | 541 468 466 510 485 = 0.71 || = 0.02 509 492 487 524 505 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 508 492 527 455 497 = 0.70 || = 0.01 267 273 246 226 235 | 252.5 d 0 1 0 11 80 8 1 0 0 | 500 | 502 497 447 510 540 = 0.69 || < 0.01 495 506 500 518 508 | 497.5 s 0 0 1 16 67 12 5 0 0 | 500 | 499 476 524 514 515 = 0.68 ||========================================================================= t 0 0 7 5 72 15 2 0 0 | 500 | 483 468 490 510 512 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 4 12 68 15 1 1 0 | 500 | 484 528 487 477 512 = 0.66 ||========================================================================= x 0 0 2 15 73 10 1 0 0 | 500 | 494 481 485 521 517 = 0.65 || sstring_AutoCor test: no 249 test no 250 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 250 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 2 1 1 0 3 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 508 476 501 474 478 | 500 < 0.00002 0 0 0 1 1 | 0.5 | 1 1 0 2 0 > 0.99998 || = 0.63 451 478 521 545 533 | 500 < 0.00003 1 0 1 0 0 | 0.5 | 0 0 0 2 1 > 0.99997 || = 0.62 501 525 494 523 481 | 500 < 0.00004 0 0 0 1 0 | 0.5 | 0 0 0 1 0 > 0.99996 || = 0.61 483 453 489 475 525 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 1 0 1 0 0 > 0.99995 || = 0.60 512 526 506 488 559 | 500 < 0.00006 1 0 0 0 0 | 0.5 | 0 0 1 0 1 > 0.99994 || = 0.59 503 493 467 517 457 | 500 < 0.00007 1 0 0 1 1 | 0.5 | 0 2 0 1 1 > 0.99993 || = 0.58 486 515 543 506 486 | 500 < 0.00008 1 0 0 0 0 | 0.5 | 0 0 0 0 0 > 0.99992 || = 0.57 490 483 528 477 495 | 500 < 0.00009 0 0 0 0 0 | 0.5 | 0 0 0 0 1 > 0.99991 || = 0.56 508 533 502 525 486 | 500 < 0.0001 0 0 0 0 1 | 0.5 | 0 1 0 1 0 > 0.9999 || = 0.55 505 514 553 486 481 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 524 482 472 484 511 | 500 < 0.0001 6 1 2 3 6 | 5 | 2 4 2 8 4 > 0.9999 || = 0.53 474 492 527 489 526 | 500 < 0.0002 6 1 12 6 7 | 5 | 4 3 3 2 2 > 0.9998 || = 0.52 487 507 504 485 514 | 500 < 0.0003 9 6 4 4 5 | 5 | 8 7 5 5 5 > 0.9997 || = 0.51 483 486 468 495 517 | 500 < 0.0004 4 10 3 2 2 | 5 | 6 3 5 6 7 > 0.9996 || = 0.50 494 514 510 472 460 | 500 < 0.0005 8 6 8 5 3 | 5 | 6 5 2 2 3 > 0.9995 || = 0.49 493 514 479 515 487 | 500 < 0.0006 4 7 4 6 5 | 5 | 5 3 4 6 4 > 0.9994 || = 0.48 506 517 483 487 470 | 500 < 0.0007 8 3 6 3 6 | 5 | 2 10 4 7 9 > 0.9993 || = 0.47 504 515 540 466 481 | 500 < 0.0008 4 5 3 5 4 | 5 | 2 3 1 7 5 > 0.9992 || = 0.46 442 493 476 496 493 | 500 < 0.0009 3 6 6 10 5 | 5 | 7 7 2 4 5 > 0.9991 || = 0.45 509 511 501 569 495 | 500 < 0.001 5 5 7 4 4 | 5 | 6 4 6 12 4 > 0.999 || = 0.44 505 526 494 514 498 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 515 516 502 464 529 | 500 < 0.001 57 50 55 48 47 | 50 | 48 49 34 59 48 > 0.999 || = 0.42 530 533 500 504 498 | 500 < 0.002 52 42 44 44 59 | 50 | 42 61 48 43 51 > 0.998 || = 0.41 535 520 504 524 538 | 500 < 0.003 56 53 52 46 59 | 50 | 50 51 53 43 36 > 0.997 || = 0.40 489 498 488 506 489 | 500 < 0.004 53 46 36 49 52 | 50 | 49 52 51 44 62 > 0.996 || = 0.39 470 484 486 443 526 | 500 < 0.005 52 40 44 57 46 | 50 | 49 48 59 49 46 > 0.995 || = 0.38 497 506 512 502 482 | 500 < 0.006 51 53 54 63 49 | 50 | 43 47 45 60 49 > 0.994 || = 0.37 481 512 465 518 480 | 500 < 0.007 44 46 51 45 64 | 50 | 55 47 36 60 44 > 0.993 || = 0.36 504 487 513 519 507 | 500 < 0.008 51 56 51 51 52 | 50 | 56 56 52 55 44 > 0.992 || = 0.35 498 540 495 496 498 | 500 < 0.009 59 55 47 31 52 | 50 | 38 57 55 50 65 > 0.991 || = 0.34 500 492 504 452 479 | 500 < 0.01 58 49 49 45 53 | 50 | 51 50 46 46 54 > 0.99 || = 0.33 508 503 475 463 525 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 510 504 525 461 510 | 500 < 0.01 533 490 483 479 533 | 497.5 | 481 518 479 509 499 > 0.99 || = 0.31 518 465 533 503 489 | 500 = 0.01 245 233 268 243 285 | 252.5 | 277 259 243 241 257 = 0.99 || = 0.30 477 504 503 487 500 | 500 = 0.02 513 448 502 497 442 | 500 | 504 475 517 507 492 = 0.98 || = 0.29 500 542 468 501 481 | 500 =================================================================| 500 | 505 526 500 534 502 = 0.97 || = 0.28 507 505 466 518 502 | 500 sstring_AutoCor test: | 500 | 497 524 459 509 488 = 0.96 || = 0.27 525 521 478 467 463 | 500 ----------------------------------------------- | 500 | 510 501 461 504 498 = 0.95 || = 0.26 483 492 498 526 527 | 500 N = 10, n = 1000000029, r = 27, s = 3, d = 3 | 500 | 455 488 503 517 461 = 0.94 || = 0.25 528 500 488 482 484 | 500 Kolmogorov-Smirnov+ statistic = D+ | 500 | 506 529 507 510 496 = 0.93 || = 0.24 509 491 464 489 502 | 500 | 500 | 513 497 510 501 516 = 0.92 || = 0.23 516 470 515 556 550 | 500 =================================================================| 500 | 525 483 512 501 462 = 0.91 || = 0.22 481 492 536 518 519 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 508 512 509 452 514 = 0.90 || = 0.21 492 502 495 512 498 | 500 -----------------------------------------------------------------| 500 | 484 512 468 450 523 = 0.89 || = 0.20 473 479 507 467 505 | 500 SD Bern.: d 0.83465 0.75535 0.80661 | 500 | 511 504 498 508 482 = 0.88 || = 0.19 487 514 494 535 509 | 500 s 0.94555 0.74333 0.68443 | 500 | 496 469 506 495 505 = 0.87 || = 0.18 506 470 478 519 495 | 500 t 0.94500 0.80662 1.11140 | 500 | 531 500 472 514 516 = 0.86 || = 0.17 469 503 485 521 524 | 500 m 1.08165 1.17275 0.95650 | 500 | 515 509 482 512 493 = 0.85 || = 0.16 511 530 485 505 481 | 500 x 1.04386 0.90044 1.16246 | 500 | 463 478 484 512 520 = 0.84 || = 0.15 513 526 534 524 502 | 500 | 500 | 525 481 489 524 496 = 0.83 || = 0.14 495 464 505 529 524 | 500 Changes: d 51 2 3 | 500 | 524 526 485 501 520 = 0.82 || = 0.13 502 469 540 517 499 | 500 s 47 6 4 | 500 | 502 511 518 483 482 = 0.81 || = 0.12 495 536 498 513 499 | 500 t 48 5 4 | 500 | 486 503 506 483 517 = 0.80 || = 0.11 470 522 493 497 530 | 500 m 43 4 3 | 500 | 502 493 484 499 499 = 0.79 || = 0.10 480 477 495 447 479 | 500 x 58 3 5 | 500 | 488 508 491 471 483 = 0.78 || = 0.09 474 508 540 522 509 | 500 -----------------------------------------------------------------| 500 | 526 513 513 483 537 = 0.77 || = 0.08 522 485 525 526 550 | 500 Aver./ d 0.50048 502 > 500: 6 4 5 4 7 5 5 5 7 7 | 500 | 500 509 483 495 495 = 0.76 || = 0.07 485 468 503 529 495 | 500 median s 0.50228 502 ----- 1 6 4 6 8 5 2 7 6 6 | 500 | 485 504 492 508 497 = 0.75 || = 0.06 495 477 512 472 504 | 500 t 0.49806 500 9 3 3 6 4 7 3 6 3 5 | 500 | 505 540 523 533 532 = 0.74 || = 0.05 511 474 536 520 465 | 500 m 0.49924 501 5 8 6 4 6 3 4 3 6 9 | 500 | 511 540 521 490 460 = 0.73 || = 0.04 524 473 507 512 468 | 500 x 0.49945 498 5 5 6 4 2 5 5 4 6 4 | 500 | 496 488 528 477 481 = 0.72 || = 0.03 501 500 512 498 480 | 500 -----------------------------------------------------------------| 500 | 512 489 536 540 502 = 0.71 || = 0.02 513 448 502 497 442 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 476 495 496 473 533 = 0.70 || = 0.01 245 233 268 243 285 | 252.5 d 0 0 3 9 75 14 0 0 0 | 500 | 492 491 475 498 486 = 0.69 || < 0.01 533 490 483 479 533 | 497.5 s 0 0 2 16 67 16 0 0 0 | 500 | 499 477 517 470 509 = 0.68 ||========================================================================= t 0 0 0 15 70 15 1 0 0 | 500 | 512 471 493 509 530 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 5 15 64 14 2 1 0 | 500 | 526 479 500 488 467 = 0.66 ||========================================================================= x 0 0 1 11 68 17 4 0 0 | 500 | 507 520 467 528 463 = 0.65 || sstring_AutoCor test: no 250 test no 251 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 251 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 0 0 1 0 | 0.5 | 0 0 0 1 0 > 0.99999 || = 0.64 487 465 543 528 486 | 500 < 0.00002 0 0 1 0 1 | 0.5 | 0 0 1 0 0 > 0.99998 || = 0.63 502 481 526 535 524 | 500 < 0.00003 0 2 2 0 1 | 0.5 | 2 1 1 0 0 > 0.99997 || = 0.62 485 464 479 479 506 | 500 < 0.00004 2 1 1 1 0 | 0.5 | 1 0 0 0 0 > 0.99996 || = 0.61 508 508 545 496 496 | 500 < 0.00005 0 1 1 0 0 | 0.5 | 1 1 1 0 0 > 0.99995 || = 0.60 514 479 558 504 524 | 500 < 0.00006 0 0 1 1 0 | 0.5 | 0 0 0 1 0 > 0.99994 || = 0.59 489 504 475 508 510 | 500 < 0.00007 0 0 0 2 0 | 0.5 | 0 0 1 0 0 > 0.99993 || = 0.58 496 493 505 519 497 | 500 < 0.00008 1 0 0 1 0 | 0.5 | 1 0 0 2 1 > 0.99992 || = 0.57 476 488 506 542 450 | 500 < 0.00009 2 1 1 1 1 | 0.5 | 0 1 1 0 1 > 0.99991 || = 0.56 533 517 501 502 503 | 500 < 0.0001 0 0 0 0 0 | 0.5 | 0 1 0 1 2 > 0.9999 || = 0.55 494 500 486 520 510 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 487 534 512 513 522 | 500 < 0.0001 6 5 7 7 3 | 5 | 5 4 5 5 4 > 0.9999 || = 0.53 492 528 493 489 447 | 500 < 0.0002 4 3 7 5 7 | 5 | 4 1 3 2 1 > 0.9998 || = 0.52 472 484 487 513 487 | 500 < 0.0003 2 4 4 7 5 | 5 | 6 6 2 4 4 > 0.9997 || = 0.51 531 489 499 514 502 | 500 < 0.0004 2 8 2 5 2 | 5 | 8 2 5 5 4 > 0.9996 || = 0.50 501 497 507 546 488 | 500 < 0.0005 6 6 6 10 2 | 5 | 3 7 3 6 1 > 0.9995 || = 0.49 526 513 485 474 509 | 500 < 0.0006 5 2 7 3 7 | 5 | 3 4 4 2 3 > 0.9994 || = 0.48 503 480 564 462 509 | 500 < 0.0007 5 4 5 7 7 | 5 | 7 6 5 5 5 > 0.9993 || = 0.47 467 536 486 509 496 | 500 < 0.0008 4 5 6 4 4 | 5 | 3 5 2 4 5 > 0.9992 || = 0.46 488 510 504 520 507 | 500 < 0.0009 7 6 3 8 5 | 5 | 6 0 4 8 7 > 0.9991 || = 0.45 504 516 486 493 482 | 500 < 0.001 3 4 5 4 3 | 5 | 5 4 5 5 4 > 0.999 || = 0.44 473 492 515 501 490 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 488 476 497 497 486 | 500 < 0.001 44 47 52 60 45 | 50 | 50 39 38 46 38 > 0.999 || = 0.42 483 498 515 514 508 | 500 < 0.002 58 46 45 49 65 | 50 | 41 50 50 51 63 > 0.998 || = 0.41 477 497 488 500 489 | 500 < 0.003 57 46 39 48 38 | 50 | 58 54 64 56 48 > 0.997 || = 0.40 525 507 525 496 483 | 500 < 0.004 60 51 47 44 58 | 50 | 55 56 51 47 42 > 0.996 || = 0.39 487 496 494 531 484 | 500 < 0.005 58 46 47 52 46 | 50 | 50 65 62 41 67 > 0.995 || = 0.38 512 537 495 512 467 | 500 < 0.006 49 50 55 59 45 | 50 | 57 37 54 45 58 > 0.994 || = 0.37 546 495 473 499 511 | 500 < 0.007 45 59 53 58 53 | 50 | 50 50 45 51 53 > 0.993 || = 0.36 508 499 491 540 520 | 500 < 0.008 39 53 48 55 57 | 50 | 47 43 59 59 63 > 0.992 || = 0.35 487 505 478 510 525 | 500 < 0.009 58 53 58 56 46 | 50 | 61 46 52 46 65 > 0.991 || = 0.34 480 480 439 491 500 | 500 < 0.01 54 54 53 49 50 | 50 | 40 58 48 57 42 > 0.99 || = 0.33 507 458 521 490 488 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 459 539 531 503 509 | 500 < 0.01 522 505 497 530 503 | 497.5 | 509 498 523 499 539 > 0.99 || = 0.31 477 508 519 493 485 | 500 = 0.01 269 283 258 273 256 | 252.5 | 248 237 250 269 272 = 0.99 || = 0.30 460 508 479 507 492 | 500 = 0.02 485 484 498 484 527 | 500 | 491 468 469 471 511 = 0.98 || = 0.29 550 456 521 505 466 | 500 =================================================================| 500 | 501 480 486 489 473 = 0.97 || = 0.28 505 529 478 508 493 | 500 sstring_AutoCor test: | 500 | 519 476 527 480 459 = 0.96 || = 0.27 544 524 449 527 490 | 500 ----------------------------------------------- | 500 | 507 481 520 465 515 = 0.95 || = 0.26 521 487 483 518 509 | 500 N = 10, n = 1000000029, r = 27, s = 3, d = 3 | 500 | 528 495 529 483 548 = 0.94 || = 0.25 508 513 493 511 497 | 500 Kolmogorov-Smirnov- statistic = D- | 500 | 473 485 497 499 508 = 0.93 || = 0.24 555 525 464 502 517 | 500 | 500 | 503 483 512 489 474 = 0.92 || = 0.23 518 506 498 522 515 | 500 =================================================================| 500 | 480 483 479 469 476 = 0.91 || = 0.22 525 547 471 507 522 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 489 523 498 504 536 = 0.90 || = 0.21 487 517 471 532 531 | 500 -----------------------------------------------------------------| 500 | 521 477 483 531 496 = 0.89 || = 0.20 490 515 455 486 492 | 500 SD Bern.: d 0.94342 1.03974 0.94809 | 500 | 493 494 485 454 469 = 0.88 || = 0.19 509 483 463 465 501 | 500 s 0.99360 0.58850 1.18041 | 500 | 497 518 516 498 532 = 0.87 || = 0.18 484 482 490 460 509 | 500 t 1.06945 0.74736 1.10959 | 500 | 467 514 490 457 491 = 0.86 || = 0.17 506 503 508 481 527 | 500 m 1.03869 0.83945 0.79410 | 500 | 509 493 460 534 514 = 0.85 || = 0.16 479 514 493 477 505 | 500 x 0.94119 1.07104 1.55060 | 500 | 524 495 528 539 501 = 0.84 || = 0.15 494 467 496 477 533 | 500 | 500 | 501 500 493 486 493 = 0.83 || = 0.14 506 515 510 486 524 | 500 Changes: d 54 3 6 | 500 | 474 534 532 507 506 = 0.82 || = 0.13 491 547 530 488 474 | 500 s 50 3 3 | 500 | 496 492 458 500 471 = 0.81 || = 0.12 482 472 489 508 459 | 500 t 59 4 4 | 500 | 507 511 522 509 487 = 0.80 || = 0.11 513 547 514 461 452 | 500 m 44 3 5 | 500 | 498 480 493 510 512 = 0.79 || = 0.10 506 474 515 474 495 | 500 x 48 6 4 | 500 | 482 501 529 545 466 = 0.78 || = 0.09 522 481 485 470 511 | 500 -----------------------------------------------------------------| 500 | 516 523 524 507 516 = 0.77 || = 0.08 476 477 525 517 492 | 500 Aver./ d 0.49906 498 > 500: 5 5 8 4 4 3 6 4 4 6 | 500 | 443 545 512 505 515 = 0.76 || = 0.07 535 481 468 469 493 | 500 median s 0.49818 498 ----- 3 5 8 5 5 4 4 7 4 1 | 500 | 527 495 480 483 484 = 0.75 || = 0.06 488 499 512 475 466 | 500 t 0.50278 498 4 5 1 3 5 5 7 6 3 5 | 500 | 473 504 492 473 483 = 0.74 || = 0.05 492 534 490 521 495 | 500 m 0.49963 501 5 1 9 6 4 9 4 6 5 2 | 500 | 523 524 501 467 497 = 0.73 || = 0.04 490 489 449 472 514 | 500 x 0.50070 501 5 6 5 4 4 6 7 4 5 6 | 500 | 490 470 533 482 497 = 0.72 || = 0.03 506 490 507 551 490 | 500 -----------------------------------------------------------------| 500 | 480 511 498 519 505 = 0.71 || = 0.02 485 484 498 484 527 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 522 480 538 474 497 = 0.70 || = 0.01 269 283 258 273 256 | 252.5 d 0 0 1 13 71 13 3 0 0 | 500 | 522 458 497 505 511 = 0.69 || < 0.01 522 505 497 530 503 | 497.5 s 0 0 0 14 68 15 4 0 0 | 500 | 488 489 504 492 522 = 0.68 ||========================================================================= t 0 0 4 10 68 16 3 0 0 | 500 | 521 515 498 464 524 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 1 20 63 14 3 0 0 | 500 | 481 536 518 544 545 = 0.66 ||========================================================================= x 0 0 3 12 71 13 2 0 0 | 500 | 515 505 539 491 505 = 0.65 || sstring_AutoCor test: no 251 test no 252 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 252 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 1 1 0 0 1 | 0.5 | 0 0 0 0 0 > 0.99999 || = 0.64 486 502 484 550 488 | 500 < 0.00002 0 0 0 0 2 | 0.5 | 0 0 0 0 1 > 0.99998 || = 0.63 542 513 510 481 496 | 500 < 0.00003 2 0 2 1 2 | 0.5 | 0 0 0 0 0 > 0.99997 || = 0.62 483 523 502 511 494 | 500 < 0.00004 1 0 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99996 || = 0.61 515 490 500 491 530 | 500 < 0.00005 0 0 2 1 1 | 0.5 | 0 0 1 1 0 > 0.99995 || = 0.60 488 500 484 500 527 | 500 < 0.00006 0 0 2 0 0 | 0.5 | 0 0 0 0 0 > 0.99994 || = 0.59 501 563 526 541 508 | 500 < 0.00007 2 0 0 1 0 | 0.5 | 0 1 0 1 0 > 0.99993 || = 0.58 497 440 539 482 509 | 500 < 0.00008 0 0 0 1 1 | 0.5 | 1 0 1 1 0 > 0.99992 || = 0.57 485 504 498 498 461 | 500 < 0.00009 0 0 1 2 0 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 514 528 479 506 472 | 500 < 0.0001 0 0 1 0 0 | 0.5 | 1 0 0 0 0 > 0.9999 || = 0.55 482 485 479 504 469 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 522 498 491 517 479 | 500 < 0.0001 6 1 9 6 8 | 5 | 2 1 2 3 1 > 0.9999 || = 0.53 479 492 485 540 460 | 500 < 0.0002 4 2 5 3 7 | 5 | 1 1 0 1 2 > 0.9998 || = 0.52 510 503 468 487 494 | 500 < 0.0003 2 2 3 4 5 | 5 | 9 0 5 4 5 > 0.9997 || = 0.51 517 468 507 524 494 | 500 < 0.0004 3 4 5 4 8 | 5 | 5 5 2 7 0 > 0.9996 || = 0.50 544 482 481 490 519 | 500 < 0.0005 5 6 7 6 6 | 5 | 1 4 2 1 2 > 0.9995 || = 0.49 532 548 472 486 486 | 500 < 0.0006 3 7 2 4 4 | 5 | 5 5 3 5 4 > 0.9994 || = 0.48 497 501 518 497 482 | 500 < 0.0007 6 10 2 5 5 | 5 | 4 8 2 4 2 > 0.9993 || = 0.47 505 519 475 516 477 | 500 < 0.0008 4 4 4 3 4 | 5 | 6 7 3 7 7 > 0.9992 || = 0.46 484 482 528 521 534 | 500 < 0.0009 5 4 5 6 7 | 5 | 8 3 3 2 9 > 0.9991 || = 0.45 533 472 473 505 495 | 500 < 0.001 4 3 4 2 4 | 5 | 2 6 4 5 4 > 0.999 || = 0.44 523 495 491 487 517 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 498 528 504 488 539 | 500 < 0.001 42 43 46 43 58 | 50 | 43 40 26 39 36 > 0.999 || = 0.42 518 495 515 489 504 | 500 < 0.002 55 45 58 51 43 | 50 | 33 46 50 42 44 > 0.998 || = 0.41 480 539 508 480 504 | 500 < 0.003 50 50 52 46 49 | 50 | 46 48 53 34 49 > 0.997 || = 0.40 535 519 474 483 495 | 500 < 0.004 39 47 55 36 37 | 50 | 64 44 39 36 43 > 0.996 || = 0.39 493 472 494 513 499 | 500 < 0.005 56 47 39 47 43 | 50 | 43 47 50 60 47 > 0.995 || = 0.38 543 505 477 471 498 | 500 < 0.006 60 55 53 70 57 | 50 | 50 49 40 51 46 > 0.994 || = 0.37 490 486 466 483 540 | 500 < 0.007 56 41 52 44 54 | 50 | 60 48 48 41 53 > 0.993 || = 0.36 507 521 544 495 505 | 500 < 0.008 57 48 47 46 54 | 50 | 54 53 45 44 50 > 0.992 || = 0.35 480 492 482 522 471 | 500 < 0.009 47 53 59 36 54 | 50 | 42 55 54 44 56 > 0.991 || = 0.34 461 523 548 534 488 | 500 < 0.01 49 35 60 52 44 | 50 | 46 60 53 40 73 > 0.99 || = 0.33 507 452 506 475 487 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 491 513 506 472 431 | 500 < 0.01 511 464 521 471 493 | 497.5 | 481 490 458 431 497 > 0.99 || = 0.31 500 528 549 478 513 | 500 = 0.01 278 253 240 263 254 | 252.5 | 282 262 259 267 265 = 0.99 || = 0.30 479 490 478 526 474 | 500 = 0.02 511 495 468 545 529 | 500 | 521 502 546 532 515 = 0.98 || = 0.29 509 478 520 473 510 | 500 =================================================================| 500 | 516 502 532 552 510 = 0.97 || = 0.28 485 520 502 536 516 | 500 sstring_AutoCor test: | 500 | 512 524 507 479 507 = 0.96 || = 0.27 504 514 523 513 499 | 500 ----------------------------------------------- | 500 | 511 524 515 531 517 = 0.95 || = 0.26 496 522 437 499 480 | 500 N = 10, n = 1000000029, r = 27, s = 3, d = 3 | 500 | 500 490 488 506 496 = 0.94 || = 0.25 504 513 495 491 505 | 500 Anderson-Darling statistic = A2 | 500 | 477 511 494 496 537 = 0.93 || = 0.24 499 476 501 541 494 | 500 | 500 | 448 478 524 505 452 = 0.92 || = 0.23 497 477 493 494 496 | 500 =================================================================| 500 | 500 530 517 502 481 = 0.91 || = 0.22 489 469 489 514 529 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 475 454 478 464 508 = 0.90 || = 0.21 496 482 511 466 534 | 500 -----------------------------------------------------------------| 500 | 536 518 501 515 486 = 0.89 || = 0.20 491 482 496 470 514 | 500 SD Bern.: d 1.00134 0.93961 1.26157 | 500 | 497 511 505 521 503 = 0.88 || = 0.19 444 476 438 467 482 | 500 s 1.01153 0.93426 0.78012 | 500 | 498 481 531 525 493 = 0.87 || = 0.18 512 517 532 565 482 | 500 t 1.06114 0.93105 1.31213 | 500 | 464 498 515 512 485 = 0.86 || = 0.17 457 475 503 486 488 | 500 m 1.09673 1.35935 1.40853 | 500 | 435 496 521 509 478 = 0.85 || = 0.16 518 512 530 468 487 | 500 x 0.93338 0.96484 1.32805 | 500 | 459 541 541 513 507 = 0.84 || = 0.15 530 482 491 492 515 | 500 | 500 | 481 465 523 499 484 = 0.83 || = 0.14 501 510 478 485 499 | 500 Changes: d 55 4 4 | 500 | 482 488 522 476 515 = 0.82 || = 0.13 540 495 479 445 514 | 500 s 52 4 1 | 500 | 475 514 490 493 504 = 0.81 || = 0.12 483 500 492 485 533 | 500 t 41 5 3 | 500 | 506 505 500 504 477 = 0.80 || = 0.11 529 467 539 480 498 | 500 m 50 5 2 | 500 | 481 509 490 507 496 = 0.79 || = 0.10 508 504 532 535 503 | 500 x 44 3 3 | 500 | 517 514 477 507 497 = 0.78 || = 0.09 500 511 512 494 534 | 500 -----------------------------------------------------------------| 500 | 486 519 461 469 455 = 0.77 || = 0.08 525 529 548 484 496 | 500 Aver./ d 0.49801 500 > 500: 7 7 3 3 6 5 7 4 1 5 | 500 | 497 476 485 470 509 = 0.76 || = 0.07 525 520 474 492 478 | 500 median s 0.50154 500 ----- 6 4 4 5 6 4 4 7 4 7 | 500 | 504 502 488 511 523 = 0.75 || = 0.06 467 462 510 538 486 | 500 t 0.50069 500 6 5 5 5 5 3 5 0 8 7 | 500 | 510 529 494 525 506 = 0.74 || = 0.05 505 512 477 494 478 | 500 m 0.50115 498 4 2 4 4 3 6 5 6 6 7 | 500 | 476 527 471 460 520 = 0.73 || = 0.04 498 525 508 492 498 | 500 x 0.49988 499 4 4 6 3 5 3 6 5 5 6 | 500 | 481 489 490 503 508 = 0.72 || = 0.03 506 469 502 507 511 | 500 -----------------------------------------------------------------| 500 | 490 481 480 462 476 = 0.71 || = 0.02 511 495 468 545 529 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 494 481 518 505 509 = 0.70 || = 0.01 278 253 240 263 254 | 252.5 d 0 0 3 9 73 16 0 0 0 | 500 | 515 496 527 495 525 = 0.69 || < 0.01 511 464 521 471 493 | 497.5 s 0 0 3 14 67 15 2 0 0 | 500 | 536 480 487 476 537 = 0.68 ||========================================================================= t 0 0 2 14 65 16 4 0 0 | 500 | 503 542 481 525 531 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 16 64 15 4 0 0 | 500 | 505 499 516 492 493 = 0.66 ||========================================================================= x 0 1 2 9 73 16 0 0 0 | 500 | 510 490 486 533 524 = 0.65 || sstring_AutoCor test: no 252 test no 253 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 253 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 1 1 0 0 | 0.5 | 1 0 0 0 1 > 0.99999 || = 0.64 494 494 485 479 454 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 0 0 1 0 2 > 0.99998 || = 0.63 456 532 513 521 493 | 500 < 0.00003 0 0 1 0 0 | 0.5 | 0 0 1 0 2 > 0.99997 || = 0.62 513 511 457 537 468 | 500 < 0.00004 1 0 0 1 0 | 0.5 | 1 0 1 0 1 > 0.99996 || = 0.61 510 498 503 495 514 | 500 < 0.00005 0 1 0 0 0 | 0.5 | 1 0 0 0 0 > 0.99995 || = 0.60 496 476 550 470 506 | 500 < 0.00006 0 0 4 2 0 | 0.5 | 1 1 1 0 1 > 0.99994 || = 0.59 523 504 566 514 466 | 500 < 0.00007 1 0 0 2 1 | 0.5 | 1 0 0 0 1 > 0.99993 || = 0.58 490 511 511 522 514 | 500 < 0.00008 1 1 0 0 1 | 0.5 | 0 0 0 0 1 > 0.99992 || = 0.57 470 513 508 504 500 | 500 < 0.00009 0 1 1 0 1 | 0.5 | 0 0 0 0 0 > 0.99991 || = 0.56 474 506 494 486 529 | 500 < 0.0001 0 0 1 2 1 | 0.5 | 0 0 0 1 0 > 0.9999 || = 0.55 480 519 535 528 456 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 498 477 480 493 507 | 500 < 0.0001 3 4 8 7 4 | 5 | 5 1 4 1 9 > 0.9999 || = 0.53 494 481 491 510 547 | 500 < 0.0002 0 3 2 4 7 | 5 | 4 2 3 1 2 > 0.9998 || = 0.52 487 508 505 520 510 | 500 < 0.0003 2 3 5 3 4 | 5 | 7 2 6 7 6 > 0.9997 || = 0.51 476 548 538 498 525 | 500 < 0.0004 3 7 4 5 6 | 5 | 6 6 7 8 5 > 0.9996 || = 0.50 477 493 522 493 470 | 500 < 0.0005 2 3 4 7 4 | 5 | 9 6 5 4 2 > 0.9995 || = 0.49 513 494 510 509 455 | 500 < 0.0006 4 3 7 6 5 | 5 | 9 6 7 5 3 > 0.9994 || = 0.48 481 494 522 485 523 | 500 < 0.0007 6 6 7 2 4 | 5 | 2 4 5 7 6 > 0.9993 || = 0.47 477 508 481 511 518 | 500 < 0.0008 7 6 4 5 4 | 5 | 5 5 4 5 6 > 0.9992 || = 0.46 474 521 518 475 509 | 500 < 0.0009 2 3 4 2 5 | 5 | 10 2 7 2 9 > 0.9991 || = 0.45 511 495 438 495 487 | 500 < 0.001 2 5 2 3 5 | 5 | 7 6 6 3 2 > 0.999 || = 0.44 502 552 513 521 507 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 467 520 526 495 515 | 500 < 0.001 31 43 47 44 48 | 50 | 64 40 54 43 50 > 0.999 || = 0.42 472 512 513 498 503 | 500 < 0.002 40 65 51 53 54 | 50 | 47 49 55 45 31 > 0.998 || = 0.41 486 501 514 500 539 | 500 < 0.003 53 59 59 49 37 | 50 | 48 36 57 38 64 > 0.997 || = 0.40 504 532 503 506 490 | 500 < 0.004 57 45 46 53 40 | 50 | 51 42 58 45 60 > 0.996 || = 0.39 494 524 491 519 494 | 500 < 0.005 57 41 42 53 53 | 50 | 51 42 55 53 51 > 0.995 || = 0.38 493 501 517 488 509 | 500 < 0.006 58 47 44 52 48 | 50 | 39 48 51 47 50 > 0.994 || = 0.37 500 474 472 495 508 | 500 < 0.007 59 43 45 57 61 | 50 | 61 46 49 52 51 > 0.993 || = 0.36 525 499 487 517 509 | 500 < 0.008 68 63 40 62 45 | 50 | 58 64 49 47 52 > 0.992 || = 0.35 512 503 466 481 504 | 500 < 0.009 57 42 59 61 46 | 50 | 56 59 45 47 49 > 0.991 || = 0.34 522 502 508 472 508 | 500 < 0.01 42 39 59 56 49 | 50 | 37 36 50 54 68 > 0.99 || = 0.33 524 497 500 496 537 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 506 483 515 497 486 | 500 < 0.01 522 487 492 540 481 | 497.5 | 512 462 523 471 526 > 0.99 || = 0.31 526 502 532 504 518 | 500 = 0.01 245 274 233 257 274 | 252.5 | 263 263 251 249 259 = 0.99 || = 0.30 520 495 517 502 504 | 500 = 0.02 476 495 498 506 513 | 500 | 514 471 465 529 496 = 0.98 || = 0.29 542 505 523 508 472 | 500 =================================================================| 500 | 514 507 502 438 532 = 0.97 || = 0.28 483 509 521 470 479 | 500 sstring_AutoCor test: | 500 | 491 503 589 477 486 = 0.96 || = 0.27 514 481 518 515 479 | 500 ----------------------------------------------- | 500 | 494 439 499 492 528 = 0.95 || = 0.26 548 476 453 517 503 | 500 N = 10, n = 1000000029, r = 27, s = 3, d = 3 | 500 | 467 499 508 495 473 = 0.94 || = 0.25 469 549 491 488 525 | 500 Tests on the sum of all N observations | 500 | 485 513 500 500 520 = 0.93 || = 0.24 472 493 477 462 467 | 500 | 500 | 501 489 516 562 465 = 0.92 || = 0.23 476 449 475 503 493 | 500 =================================================================| 500 | 505 482 510 472 495 = 0.91 || = 0.22 478 496 480 517 495 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 551 491 489 500 503 = 0.90 || = 0.21 521 501 455 505 493 | 500 -----------------------------------------------------------------| 500 | 475 507 509 492 529 = 0.89 || = 0.20 495 503 486 506 486 | 500 SD Bern.: d 0.98349 1.51732 1.20225 | 500 | 496 536 471 488 505 = 0.88 || = 0.19 516 496 482 500 470 | 500 s 0.95841 1.32202 1.35565 | 500 | 529 506 523 483 483 = 0.87 || = 0.18 506 500 529 532 487 | 500 t 1.12447 0.99447 0.64373 | 500 | 496 492 530 519 467 = 0.86 || = 0.17 512 519 468 482 518 | 500 m 0.94462 0.91478 0.77367 | 500 | 446 481 496 518 470 = 0.85 || = 0.16 479 520 485 525 468 | 500 x 1.04191 0.96484 1.40639 | 500 | 496 472 484 511 505 = 0.84 || = 0.15 528 529 497 483 506 | 500 | 500 | 510 482 489 528 495 = 0.83 || = 0.14 484 535 476 529 491 | 500 Changes: d 50 2 5 | 500 | 513 478 480 486 476 = 0.82 || = 0.13 491 494 524 472 488 | 500 s 44 4 2 | 500 | 482 476 542 501 529 = 0.81 || = 0.12 504 461 485 465 499 | 500 t 49 3 1 | 500 | 522 510 498 523 548 = 0.80 || = 0.11 530 489 494 471 493 | 500 m 51 3 5 | 500 | 497 486 518 504 504 = 0.79 || = 0.10 484 489 523 500 502 | 500 x 49 6 5 | 500 | 505 517 477 470 478 = 0.78 || = 0.09 484 507 494 488 502 | 500 -----------------------------------------------------------------| 500 | 490 490 516 518 521 = 0.77 || = 0.08 510 488 516 480 496 | 500 Aver./ d 0.49984 496 > 500: 4 6 4 7 4 1 5 6 4 6 | 500 | 559 496 495 455 551 = 0.76 || = 0.07 483 532 461 498 546 | 500 median s 0.49799 501 ----- 6 4 5 5 7 7 4 7 3 4 | 500 | 484 503 466 505 521 = 0.75 || = 0.06 487 504 490 514 512 | 500 t 0.50241 498 2 3 3 5 8 7 4 4 4 6 | 500 | 522 506 520 464 505 = 0.74 || = 0.05 484 528 498 504 491 | 500 m 0.50033 500 5 3 7 4 4 6 6 6 5 2 | 500 | 506 535 504 499 460 = 0.73 || = 0.04 508 474 505 491 452 | 500 x 0.50092 503 6 3 2 8 7 7 3 7 5 5 | 500 | 484 508 494 532 541 = 0.72 || = 0.03 558 511 488 463 509 | 500 -----------------------------------------------------------------| 500 | 503 509 468 523 465 = 0.71 || = 0.02 476 495 498 506 513 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 496 514 497 535 500 = 0.70 || = 0.01 245 274 233 257 274 | 252.5 d 0 0 1 15 70 11 4 0 0 | 500 | 512 527 476 491 524 = 0.69 || < 0.01 522 487 492 540 481 | 497.5 s 0 0 4 10 73 11 3 0 0 | 500 | 483 453 533 526 498 = 0.68 ||========================================================================= t 0 0 4 15 66 13 2 0 1 | 500 | 541 494 518 519 484 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 14 71 13 1 0 0 | 500 | 487 449 490 491 519 = 0.66 ||========================================================================= x 0 0 3 16 64 14 4 0 0 | 500 | 533 480 436 507 467 = 0.65 || sstring_AutoCor test: no 253 test no 254 TestU01 250000 runs BigCrush Test smarsa_S sstring_AutoCor test: test no 254 ======================================================================================================================================================================================================================= p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** |Expect.| AHS-det.:-secret A:-secret B: MT19937: XO256** : p-Value || p-Value : AHS-det.:-secret A:-secret B: MT19937: XO256** | Expect. -----------------------------------------------------------------|-------|------------------------------------------------------------------||--------------------------------------------------------------|---------- < 0.00001 0 0 0 0 0 | 0.5 | 2 2 0 0 0 > 0.99999 || = 0.64 521 507 455 472 495 | 500 < 0.00002 0 0 0 0 0 | 0.5 | 1 0 1 0 2 > 0.99998 || = 0.63 516 535 473 493 545 | 500 < 0.00003 1 0 0 0 1 | 0.5 | 1 0 1 0 0 > 0.99997 || = 0.62 507 548 507 499 476 | 500 < 0.00004 1 1 0 0 0 | 0.5 | 0 1 0 0 1 > 0.99996 || = 0.61 483 499 505 516 489 | 500 < 0.00005 0 0 0 0 0 | 0.5 | 0 2 0 1 2 > 0.99995 || = 0.60 482 487 490 520 482 | 500 < 0.00006 0 0 0 1 1 | 0.5 | 0 1 1 0 0 > 0.99994 || = 0.59 539 454 488 525 500 | 500 < 0.00007 0 0 0 1 0 | 0.5 | 0 0 1 0 2 > 0.99993 || = 0.58 511 498 489 498 526 | 500 < 0.00008 0 1 0 0 1 | 0.5 | 0 5 1 0 1 > 0.99992 || = 0.57 492 483 492 507 506 | 500 < 0.00009 0 0 0 2 1 | 0.5 | 2 1 1 0 0 > 0.99991 || = 0.56 513 471 482 487 465 | 500 < 0.0001 0 0 2 1 0 | 0.5 | 1 1 1 0 0 > 0.9999 || = 0.55 530 475 499 484 507 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.54 474 512 512 469 541 | 500 < 0.0001 2 2 2 5 4 | 5 | 7 13 7 1 8 > 0.9999 || = 0.53 499 496 528 521 468 | 500 < 0.0002 5 6 2 2 6 | 5 | 3 2 4 3 2 > 0.9998 || = 0.52 554 463 498 507 498 | 500 < 0.0003 8 4 9 6 4 | 5 | 7 8 3 4 5 > 0.9997 || = 0.51 468 468 519 510 480 | 500 < 0.0004 2 3 1 6 7 | 5 | 7 2 6 5 9 > 0.9996 || = 0.50 475 521 487 558 480 | 500 < 0.0005 8 4 2 4 3 | 5 | 5 4 7 8 1 > 0.9995 || = 0.49 507 489 472 523 478 | 500 < 0.0006 9 3 9 4 3 | 5 | 5 4 3 6 6 > 0.9994 || = 0.48 508 482 521 528 545 | 500 < 0.0007 5 7 5 8 2 | 5 | 6 3 2 6 5 > 0.9993 || = 0.47 474 474 487 487 500 | 500 < 0.0008 5 6 6 8 8 | 5 | 6 8 5 4 5 > 0.9992 || = 0.46 492 492 485 518 522 | 500 < 0.0009 9 3 2 3 5 | 5 | 3 4 1 5 6 > 0.9991 || = 0.45 522 517 495 510 510 | 500 < 0.001 5 5 3 4 5 | 5 | 6 5 2 8 7 > 0.999 || = 0.44 506 510 491 490 525 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.43 488 483 527 474 500 | 500 < 0.001 58 43 41 50 47 | 50 | 55 53 40 50 54 > 0.999 || = 0.42 503 491 509 474 506 | 500 < 0.002 46 44 47 51 42 | 50 | 51 52 37 43 56 > 0.998 || = 0.41 505 523 491 514 503 | 500 < 0.003 60 56 39 59 49 | 50 | 58 42 52 50 42 > 0.997 || = 0.40 476 506 501 475 526 | 500 < 0.004 55 58 40 39 43 | 50 | 61 43 43 53 39 > 0.996 || = 0.39 497 531 481 494 501 | 500 < 0.005 47 57 54 56 61 | 50 | 50 44 49 52 62 > 0.995 || = 0.38 483 474 515 494 476 | 500 < 0.006 58 54 56 45 49 | 50 | 63 53 36 61 54 > 0.994 || = 0.37 517 547 513 537 500 | 500 < 0.007 61 52 44 47 40 | 50 | 50 62 37 50 52 > 0.993 || = 0.36 509 511 525 520 504 | 500 < 0.008 59 53 51 49 42 | 50 | 51 52 51 51 54 > 0.992 || = 0.35 479 466 516 480 497 | 500 < 0.009 50 46 59 42 55 | 50 | 57 44 42 61 50 > 0.991 || = 0.34 473 544 488 536 529 | 500 < 0.01 51 48 59 51 42 | 50 | 59 53 46 45 52 > 0.99 || = 0.33 501 484 505 488 514 | 500 -----------------------------------------------------------------| |------------------------------------------------------------------|| = 0.32 505 487 477 486 500 | 500 < 0.01 545 511 490 489 470 | 497.5 | 555 498 433 516 515 > 0.99 || = 0.31 518 501 515 489 494 | 500 = 0.01 268 254 257 287 256 | 252.5 | 262 241 243 254 265 = 0.99 || = 0.30 406 493 431 515 522 | 500 = 0.02 490 525 526 485 507 | 500 | 510 497 498 518 518 = 0.98 || = 0.29 513 497 490 509 444 | 500 =================================================================| 500 | 513 461 502 495 486 = 0.97 || = 0.28 494 506 532 476 469 | 500 sstring_AutoCor test: | 500 | 522 497 510 475 516 = 0.96 || = 0.27 502 512 508 516 467 | 500 ----------------------------------------------- | 500 | 491 500 472 516 510 = 0.95 || = 0.26 523 495 502 527 480 | 500 N = 10, n = 1000000029, r = 27, s = 3, d = 3 | 500 | 484 488 477 488 502 = 0.94 || = 0.25 466 475 522 518 492 | 500 Sample variance | 500 | 528 490 529 479 495 = 0.93 || = 0.24 493 487 457 492 480 | 500 | 500 | 525 518 530 516 493 = 0.92 || = 0.23 505 509 510 527 494 | 500 =================================================================| 500 | 480 513 462 475 508 = 0.91 || = 0.22 487 535 491 499 481 | 500 Statistics % bins (101) 1/1000 L 1/1000 R | 500 | 535 491 543 512 554 = 0.90 || = 0.21 470 508 501 499 526 | 500 -----------------------------------------------------------------| 500 | 456 472 496 529 516 = 0.89 || = 0.20 494 514 506 465 491 | 500 SD Bern.: d 1.02293 0.98130 1.01143 | 500 | 498 527 517 482 527 = 0.88 || = 0.19 503 500 508 509 571 | 500 s 1.01039 0.75270 0.85364 | 500 | 490 516 509 492 486 = 0.87 || = 0.18 493 529 504 451 502 | 500 t 1.06734 1.06071 1.24077 | 500 | 497 515 500 549 527 = 0.86 || = 0.17 488 508 542 505 511 | 500 m 1.04857 0.82381 0.81280 | 500 | 517 542 477 490 504 = 0.85 || = 0.16 527 485 532 521 482 | 500 x 1.03728 0.99849 0.91805 | 500 | 522 508 518 550 498 = 0.84 || = 0.15 499 503 472 459 512 | 500 | 500 | 505 488 511 482 520 = 0.83 || = 0.14 522 542 496 457 522 | 500 Changes: d 46 6 4 | 500 | 501 496 506 480 460 = 0.82 || = 0.13 488 477 508 489 496 | 500 s 46 2 4 | 500 | 523 487 509 504 451 = 0.81 || = 0.12 503 515 537 467 519 | 500 t 50 3 4 | 500 | 537 473 532 514 533 = 0.80 || = 0.11 469 472 568 478 535 | 500 m 47 5 4 | 500 | 532 520 496 504 504 = 0.79 || = 0.10 483 497 493 445 470 | 500 x 49 4 4 | 500 | 496 468 465 559 502 = 0.78 || = 0.09 457 520 507 474 489 | 500 -----------------------------------------------------------------| 500 | 492 461 444 499 485 = 0.77 || = 0.08 484 456 455 480 496 | 500 Aver./ d 0.50240 500 > 500: 4 4 4 5 6 5 5 4 6 7 | 500 | 471 508 501 506 535 = 0.76 || = 0.07 487 528 526 486 504 | 500 median s 0.49915 498 ----- 6 5 6 5 4 1 5 6 5 3 | 500 | 494 497 512 525 480 = 0.75 || = 0.06 500 484 506 479 485 | 500 t 0.49746 501 7 7 7 6 4 3 3 5 7 4 | 500 | 498 520 474 495 480 = 0.74 || = 0.05 485 529 491 521 516 | 500 m 0.50295 499 2 3 5 4 5 6 6 6 5 5 | 500 | 526 519 509 466 518 = 0.73 || = 0.04 525 496 520 498 464 | 500 x 0.50124 500 4 7 1 5 7 4 2 6 6 7 | 500 | 505 540 500 479 522 = 0.72 || = 0.03 518 466 531 487 487 | 500 -----------------------------------------------------------------| 500 | 493 527 535 505 492 = 0.71 || = 0.02 490 525 526 485 507 | 500 -4 -3 -2 -1 SD +1 +2 +3 +4 | 500 | 480 477 493 517 484 = 0.70 || = 0.01 268 254 257 287 256 | 252.5 d 1 0 0 13 72 12 3 0 0 | 500 | 516 528 500 514 460 = 0.69 || < 0.01 545 511 490 489 470 | 497.5 s 0 0 1 19 64 15 2 0 0 | 500 | 502 521 512 513 454 = 0.68 ||========================================================================= t 0 1 5 11 68 15 0 1 0 | 500 | 465 493 499 524 494 = 0.67 || Total 50000 50000 50000 50000 50000 | 497.5 m 0 0 2 15 69 10 5 0 0 | 500 | 481 461 486 466 473 = 0.66 ||========================================================================= x 0 0 3 12 71 11 3 1 0 | 500 | 484 485 443 519 505 = 0.65 || sstring_AutoCor test: no 254