Checking the Soundness of Statistical Tests for Random Number Generators by Using a Three-Level Test
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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. Although mathematically justifying such tests is necessary, doing so generally requires an enormous amount of effort. Therefore, we propose an experimental method for revealing defects in statistical tests by using a three-level test. 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 of unsound tests in these test suites.
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