#### 2. Generation (perfect random number generators, no after-treatment necessary)

The second generation of hardware random number generators is based on the first generation and the central limit theorem. A complete description, which is mainly a chapter of my doctoral thesis, can be found here.

Short said it can be shown by the central limit theorem that by modulo addition of sufficient many true random numbers the memory length m of the markov process is effectively reduced to one and the transition probabilities are approximated to equal values. This means that the entropies and the entropy cover do have the theory maximum value of one. It is only necessary to verify that sufficient many true random numbers are used, because this means that the Lindeberg condition is fulfilled. The main advantage is that while production of a new random number takes only one clock cycle, these random numbers do pass all tests, i. e. the 15 diehard tests, without after-treatment and that this can be shown both experimental and in theory. Furthermore no shielding is necessary and the slowest generators here are at minimum eight million times faster than /dev/random, the standard hardware random number generator on Linux and other Unix derivatives.

This mathematical proven technique is patented (german patent number 199 26 640) and makes these random number generators unique.

For showing that the random numbers do need no after-treatment the software is completely open source. Because no after-treatment is necessary, these generators can be used without software. That's the reason why some of them (rw2) do have one mono and two stereo outputs with the random bits, which can be used e. g. as perfect white noise for audio measurements or for switching a Laser for crosscorrelation measurements.

It could be shown that these generators do pass all statistical tests even in climate chambers at -10...+60°C, as certified e. g. from Kryptografics.

These generators are optimised for a) autonomous operation, b) hard real time and c) high quality at high speed. Therefore they can also be used for noise radar, stealth radar, as interfering transmitter and as random clock generator (with discrete exponential distributed cycle duration).

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