Using Information Theory Approach to Randomness Testing

TL;DR

This paper introduces new randomness tests based on information theory and data compression, demonstrating improved power over existing methods in detecting deviations from true randomness in binary sequences.

Contribution

It proposes two novel randomness tests utilizing universal coding, enhancing the detection of non-randomness in binary sequences compared to traditional methods.

Findings

New tests outperform many existing algorithms

Data compression methods effectively detect deviations from randomness

Experiments confirm higher power of proposed tests

Abstract

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 $H_0$ that a given bit sequence is generated by Bernoulli source with equal probabilities of 0 and 1 and the alternative hypothesis $H_1$ that the sequence is generated by a stationary and ergodic source which differs from the source under $H_0$. 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.