STATISTICAL TESTS BASED ON ENTROPY ESTIMATES FOR CHECKING THE HYPOTHESES OF THE UNIFORM DISTRIBUTION OF A RANDOM SEQUENCE

Abstract

The actual information security problem of developing statistical tests of the hypothesis about a discrete uniform distribution (‘pure randomness’) of output sequences of cryptographic generators is considered. For the entropy functionals of Shannon, Renyi and Tsallis, the point statistical estimators based on the principle of ‘plug-in’ frequency statistics are constructed. The asymptotic probability distribution of the constructed point estimators is found when the ‘pure randomness’ hypothesis in asymptotics is valid, meaning that the number of observed data is comparable with the number of estimated parameters. With the use of the probability distributions of point estimators, the interval statistical estimators of considered information entropy functionals are constructed. On the basis of interval estimators, the decision rules for statistical testing of the hypothesis about the ‘pure randomness’ of the observed discrete sequence are developed. The results of computer experiments, in which the developed statistical tests are applied to the output sequence of cryptographic generators, are given. In these experiments, the output binary sequence was transformed to the sequence of alphabet with a larger dimension by combining the s neighboring elements in the s-grams.