Checking the Quality of Approximation of $p$-values in Statistical Tests for Random Number Generators by Using a Three-Level Test

TL;DR

This paper introduces a three-level testing method to evaluate the accuracy of p-value approximations in statistical tests for PRNGs, focusing on common test suites like NIST and TestU01.

Contribution

It presents an experimental approach to identify defects in statistical tests and assesses modifications to improve their reliability.

Findings

The three-level test effectively reveals approximation errors.

Certain modifications improve the accuracy of specific tests.

The method helps identify unreliable tests in standard suites.

Abstract

Statistical tests of pseudorandom number generators (PRNGs) are applicable to any type of random number generators and are indispensable for evaluation. While several practical packages for statistical tests of randomness exist, they may suffer from a lack of reliability: for some tests, the amount of approximation error can be deemed significant. Reducing this error by finding a better approximation is necessary, but it generally requires an enormous amount of effort. In this paper, we introduce an experimental method for revealing defects in statistical tests by using a three-level test proposed by Okutomi and Nakamura. In particular, we investigate the NIST test suite and the test batteries in TestU01, which are widely used statistical packages. Furthermore, we show the efficiency of several modifications for some tests.