Performance Analysis for Statistical Testing of Random and Pseudorandom Generators by Entropy Statistics

The topical problem of performance analysis for statistical testing of "pure randomness" for random and pseudorandom cryptographic generators is considered. Statistical tests based on statistical estimators of Rényi and Tsallis entropy functionals for the observed output sequences with some fixed asymptotic significance level are used. To evaluate asymptotic values of power for these tests we consider two useful in practice families of "pure randomness" alternatives. The first one describes the mathematical model of a pseudo-random sequence generator that is close in its probabilistic properties to the "pure random" sequence. The second one is the Markovian alternative. For the alternative hypotheses, asymptotic probability distributions of entropy estimators are also found. Estimates of the power of the developed tests are calculated.