On Statistical Testing of Random Numbers Generators

Maurer’s test is nowadays a basic statistical tool for testing physical random number generators in cryptographic applications. Based on a statistical analysis of this test we propose simple and effective methods for its improvement. These methods are related to the m- spacing technique common in goodness-of-fit problems and the L- leave out method used for a noise reduction in the final Maurer test statistic. We also show that the spacing distribution test represents a serious competitor for Maurer’s test in the case when the random number generator is governed by a Markov chain with a long memory. Finally we discuss some approaches to the multiple testing problem which seems essential for constructing new powerful statistical tests. Key words: maximum likelihood test, multiple testing, entropy, Maurer’s test, spacings.