Evaluation of Statistical Tests for Randomness Using Conditional Entropy

Abstract

Random sequences are widely used in the field of computer science. In practice, random sequences are generated by pseudorandom number generators which are in fact deterministic algorithms. Statistical tests are used to check whether there are regularities in a sequence generated by a pseudorandom number generator. Currently there are many statistical tests available, which focus on different aspects of a sequence, but it remains open how these tests are correlated. In this paper, we select a set of statistical tests from different test suites, adapt them for testing short sequences if necessary, and evaluate these tests by calculating their conditional entropy, which reflects the coverage of each test in the whole test suite. Finally we propose a new test suite which has a larger coverage than the original test suite.