Introduction

True hardware random number generators (TRNGs) do produce true random numbers based on true random processes like the falling of a dice or the noise of a resistor or oscillator. The true randomness of these numbers is the base of many cryptographical applications, e. g. the generation of PINs, TANs and cryptographical keys. They can also be used for many other applications like stochastic resonance, genetic algorithms, monte carlo simulations, surrogat data method, creation of lottery numbers, video roulette, and many other.

An often emerging problem of hardware random number generators, as well of pseudorandom number generators, are statistical conspicuities, which can be characterized partially by the entropy (average randomness of a single random number). The information theory entropy is not meaningful, because it only incorporates the single probabilities of the random numbers but not conditional probabilities and other. Furthermore the entropy is not invariant against a basis transformation, so the bit-wise entropy and the byte-wise entropy can have totally different values. That's the reason why there are so many different entropy tests and why in the strict sense not only one but also many information theory entropies do exist.

The statistical conspicuities can have drastic consequences. Quote from a textbook:

"If all scientific paper whose results are in doubt because of bad rand()s were to disappear from library shelves, there would be a gap on each shelf about as big as your fist."

Numerical Recipes (in C), Chapter 7.1