A Randomness test based on postulate r-2 on the number of runs

Şeker, Okan
Random values are considered as an indispensable part of cryptography, since they are necessary for almost all cryptographic protocols. Most importantly, key generation is done by random values and key itself should behave like a random value. Randomness is tested by statistical tests and hence, security evaluation of a cryptographic algorithm deeply depends on statistical randomness tests. In this thesis we focus on randomness postulates of Solomon W. Golomb in particular, second postulate which is about runs of a sequence and their distributions. The distributions of runs of length one, two and three are underlined. And by these distributions we state three new statistical randomness tests. New tests use chi-square distribution therefore, exact probabilities are needed. We calculate the probabilities in a combinatorial approach. In order to using in the tests, probabilities are divided into five intervals, which are called as subintervals. Subintverval are selected in such a manner that each interval has nearly equal probabilities. Finally, three new statistical tests are defined and pseudocodes for new statistical tests are given. New statistical tests are designed to detect deviations of number of different length from a random sequence. Since other tests are not interested in runs of different length, they cannot be detected this deviation. The tests are implemented with some other statistical tests, on some well-known algorithms and binary expansion of irrational numbers. Experiment results show the performance and sensitivity of our tests.


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Citation Formats
O. Şeker, “A Randomness test based on postulate r-2 on the number of runs,” M.S. - Master of Science, Middle East Technical University, 2014.