**The four Families of AHS-RNG**

1. Family **AHS-RNG-determ** or simply **AHS-RNG**

There are two different basic systems of the AHS-RNG program. The first is the deterministic system, abbreviated as "AHS-RNG-determ" or simply "AHS-RNG". At the initialization, the bit-fishing-table (BFT), the final address assembly parameters (FAAP table) and the parameters a, c and seed for one or two LCGs are loaded as parameters. These three pieces of information then determine the generation of the true random numbers, similar to reading true physical random numbers from a file. We would like to mention that there are different program variants, e.g. a 32-bit and a 64-bit variant working in parallel. The loading of the parameter table can also vary. However, the random numbers produced differ only for the 32-bit and 64-bit variants. All deterministic versions form the first family.

2. Family **AHS-RNG-secret**

We call the second family the program variants that work in a non-deterministic way with the physical mini-entropy "time", but without storing the random values of the mini-entropy used. This makes it impossible to recalculate the random numbers generated, even if all the parameters are known. This is why we refer to this family as AHS-RNG-secret.

3. Family **AHS-RNG-record**

The third family works in the same way as the second, with the important difference that the mini-entropies used are stored when the non-deterministic random numbers are generated. The mode of operation is therefore the same as with a purely physical random number generator, in which all random numbers generated are stored. This family is therefore called AHS-RNG-record. The big difference, however, is that the data to be stored is around 1700 times smaller than with a purely physical random number generator. The name of the write file must be specified as an additional parameter. This ensures that identical real random numbers are available later, for example to carry out a corrected simulation with identical random numbers. This corresponds to John von Neumann's requirement that purely physical random data must also be available again in order to be able to carry out new calculations with identical random numbers. AHS-RNG-record makes it possible to carry out very large simulations with non-deterministic random numbers, which would fail with purely physical random number generators due to the required storage capacity.

4. Family **AHS-RNG-replay**

The fourth family is the counterpart of the third family. By reading out the mini-entropy file created with the third family, the generation of identical random numbers is guaranteed. This is why we refer to this family as AHS-RNG-replay. It therefore corresponds to reading out the stored random numbers of a physical RNG, with the great advantage of only having to process a data volume that is 1700 times smaller. The name of the file with the mini-entropy saved by AHS-RNG-record is the additional parameter here. Of course, the same parameters BFT, FAAP and LCG must be used as for the original AHS-RNG-record.