Testing and validating pseudo random sequences

After introducing true and pseudo-random number generators, and presenting the methods used to measure randomness, this article details a number of common statistical tests used to evaluate the quality of random number generators.

Obtaining long sequences of random numbers, as required by some cryptographic algorithms, is a delicate problem.

There are basically two types of random number generators: true random number generators, and pseudo-random number generators.

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I’ve compiled a list of sources of true randomness (capable of sufficiently fast output); please let me know in the comments if I forgot any.

The coupled inverters technique devised by Greg Taylor and George Cox at Intel is truly the most fascinating one : it relies on collapsing the wave function of two inverters put in a superposed state.

Pseudo-random number generators are very different: they act as a black box, which takes one number (called the random.

These tests are discussed in the following section; simple examples include measuring the frequency of bits and bit sequences, evaluating entropy by trying to compress the sequence, or generating random matrices and computing their rank.

A pseudo random number generator is formally defined by an .

This has a few disagreeable consequences, among which the fact that a PRNG can only generate as many sequences as it can accept different seeds.

Thus, since the range of values that the state can take is usually much wider than that of the seed, it is generally best to only seldom reset (re-seed) the generator Rule 1 ensures that eavesdropping the output of a PRNG doesn’t allow an attacker to learn more than the bits they overheard.

Rule 2 ensures that past communications wouldn’t be compromised should an attacker manage to gain knowledge of the current state of the PRNG (thereby compromising all future communications based on the same run). There are a number of statistical tests devised to distinguish pseudo-random number generators from true ones; the more a PRNG passes, the closer it is considered to be from a true random source.

This section presents general methodology, and studies a few example tests.

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