Using Information Theory Approach to Randomness Testing

We address the problem of detecting deviations of binary sequence from randomness,which is very important for random number (RNG) and pseudorandom number generators (PRNG). Namely, we consider a null hypothesis H0 that a given bit sequence is generated by Bernoulli source with equal probabilities of 0 and 1 and the alternative hypothesis H1 that the sequence is generated by a stationary and ergodic source which differs from the source under H0. We show that data compression methods can be used as a basis for such testing and describe two new tests for randomness, which are based on ideas of universal coding. Known statistical tests and suggested ones are applied for testing PRNGs. Those experiments show that the power of the new tests is greater than of many known algorithms. © 2004 Elsevier B.V. All rights reserved. MSC: 62B10; 62G10; 62M07; 62M10; 94A29