Mutual correlation of NIST statistical randomness tests and comparison of their sensitivities on transformed sequences

Abstract

Random sequences are widely used in many cryptographic applications and hence their generation is one of the main research areas in cryptography. Statistical randomness tests are introduced to detect the weaknesses or nonrandom characteristics that a sequence under consideration may have. In the literature, there exist various statistical randomness tests and test suites, defined as a collection of tests. An efficient test suite should consist of a number of uncorrelated statistical tests each of which measures randomness from another point of view. `Being uncorrelated' is not a well-defined or well-understood concept in the literature. In this work, we apply Pearson's correlation test to measure the correlation between the tests. In addition, we define five new methods for transforming a sequence. Our motivation is to detect those tests whose results are invariant under a certain transformation. To observe the correlation, we use two methods. One is the direct correlation between the tests and the other is the correlation between the results of a test on the sequence and its transformed form. In light of the observations, we conclude that some of the tests are correlated with each other. Furthermore, we conclude that in designing a reliable and efficient suite we can avoid overpopulating the list of test functions by employing transformations together with a reasonable number of statistical test functions.