On asymptotically optimal tests for random number generators

TL;DR

This paper develops asymptotically optimal statistical tests for random number generators, providing theoretical estimates of p-values for known and unknown stationary ergodic sources, enhancing RNG testing methods.

Contribution

It introduces a family of tests with asymptotic p-value estimates applicable to any stationary ergodic source, advancing RNG testing theory.

Findings

Derived asymptotic p-value estimates for optimal tests

Established a family of tests effective for unknown stationary ergodic sources

Enhanced understanding of RNG test effectiveness in cryptography

Abstract

The problem of constructing effective statistical tests for random number generators (RNG) is considered. Currently, statistical tests for RNGs are a mandatory part of cryptographic information protection systems, but their effectiveness is mainly estimated based on experiments with various RNGs. We find an asymptotic estimate for the p-value of an optimal test in the case where the alternative hypothesis is a known stationary ergodic source, and then describe a family of tests each of which has the same asymptotic estimate of the p-value for any (unknown) stationary ergodic source.