Statistical tests suites analysis methods. Cryptographic recommendations

Abstract

In many applications, it is necessary to work with long sequences of random numbers, or at least those that behave as such (pseudo-random numbers). For this purpose, it is essential to verify the goodness of the sequences under study, e.g., to verify whether the sequences meet the properties of randomness, uniformity, and, in the case of cryptographic applications, unpredictability. To verify these properties, hypothesis tests are used, which are usually grouped into sets of tests known as batteries or suites. The design of these suites is a task of vital importance, and some rules must be followed. On the one hand, the coverage of a suite must be broad; it must check the properties of the sequences from different points of view. On the other hand, a suite with a very large number of tests is not uncommonly expensive in terms of execution time and computational performance. However, this consideration is ignored in most of the test suites in use. There are approximately 50 randomization tests in the literature, and each test suite collects many of them without performing any further analysis on the suite construction. It is important to perform an analysis of the possible relationships between the tests that constitute a suite to eliminate, if necessary, those tests that are redundant and that would slow down the performance of the suite. This paper reviews all of the methods that have been used in the literature to analyze statistical test suites and establishes recommendations for their use in cryptography.