Calibrating random number generator tests
This addresses the need for reliable randomness testing in information security, particularly for non-stationary RNGs, though it is incremental as it extends existing test frameworks.
The paper tackles the problem that existing statistical tests for random number generators are only consistent for stationary ergodic deviations, which is too narrow for some RNGs like those based on physical effects, and proposes computable consistent tests for more general classes of deviations using information theory methods.
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.