One-dimensional bit-table
filled randomly with equal numbers of '0' and '1' bits. The
dimension (total of the random bits) has to be an exponent of two. Depending on the type of
application the exponent may vary between 16 and a technical limit of 32.
The technical limit refers to a 32bit
processor architecture. Thus the number of bits may be
65'536 bit (8 KB), 131'072 bit (16 KB), 262'144 bit (32 KB), 524'288 bit (64 KB), and so on.
The random bits in the BFT form the basis for the "endless" variations and the
unpredictability of the produced random number output of AHS-RNG.
For crypto applications the 8KB, 16KB, 32KB and 64KB versions are of special interest, as
they fit easily into the secured memories of smart-cards or USB tokens.
Considering that the BFT, and not the seed, is the only element to be held secret in crypto
applications, one might wonder how a "secret" of only 8KB may be sufficient for top secured
applications.
From the 2.003529 * 10exp19'728 possible tables of 8KB (2exp65'536), there are
6.244451 * 10exp19'725 different tables with 32'768 zerobits
and 32'768 onebits.
If we have a given BFT of 8 KByte, we would need to produce approximately 10exp141
tables before we would find one with 55 % or more identical bits compared to the original.
To find one with 60 % or more identical bits, we need to produce approximately 10exp572
tables, and to come up to 70 % identical bits, we need to produce some 10exp2'341 tables,
and so on. If we suppose that the population on earth will reach 100 billion people, and that
everybody will need one table per second, the odds are very, very strong that in 1'000 years,
we will not see two tables having 55% or more identical bitpositions.
Indeed, as the
probability is 1 to 10exp141 to get a table with 55% or more bitpositions
identical to a given
table, we need more than 10exp70 tables to find two tables with more than 55% identical bits,
by applying the socalled
"birthdayparadox"
(which, by the way, is not a paradox, but a fact
that can easily be explained by means of the principles of the probability). Considering that
the total number of produced tables in 1'000 years would sum up to 3.153 * 10exp21, we have
to admit that the odds are very, very strong.
The new invented method in AHS-Random
efficiently transforms this enormous potential of
a simple 8 KByte secret table into billions of billions unpredictable and well distributed
random numbers.
Every time we double the size of the BFT, the exponents indicated in the example double as
well. To find a 64 Kbyte (524'288 bits) BFTtable
with 55% or more identical bits compared
to a given table, we need to produce approximately 10exp1128 BFT-tables