Calibrating random number generator tests

TL;DR

This paper develops new computable statistical tests for random number generators that can detect a broader range of deviations from randomness than traditional stationary ergodic tests, using information theory.

Contribution

It introduces consistent, computable tests for non-stationary ergodic deviations, expanding the applicability of RNG testing beyond existing models.

Findings

Proposed tests are computable and consistent for broader classes of deviations.

The approach is based on information-theoretic methods.

General properties of statistical tests are described.

Abstract

Currently, statistical tests for random number generators (RNGs) are widely used in practice, and some of them are even included in information security standards. But despite the popularity of RNGs, consistent tests are known only for stationary ergodic deviations of randomness (a test is consistent if it detects any deviations from a given class when the sample size goes to $ \infty $). However, the model of a stationary ergodic source is too narrow for some RNGs, in particular, for generators based on physical effects. In this article, we propose computable consistent tests for some classes of deviations more general than stationary ergodic and describe some general properties of statistical tests. The proposed approach and the resulting test are based on the ideas and methods of information theory.