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Article Citation - WoS: 2Citation - Scopus: 4R-2 Composition Tests: a Family of Statistical Randomness Tests for a Collection of Binary Sequences(Springer, 2019) Uguz, Muhiddin; Doganaksoy, Ali; Sulak, Fatih; Kocak, OnurIn this article a family of statistical randomness tests for binary strings are introduced, based on Golomb's pseudorandomness postulate R-2 on the number of runs. The basic idea is to construct recursive formulae with computationally tenable probability distribution functions. The technique is illustrated on testing strings of 2(7), 2(8), 2(10) and 2(12) bits. Furthermore, the expected value of the number of runs with a specific length is obtained. Finally the tests are applied to several collections of strings arising from different pseudorandom number generators.Article Citation - WoS: 2Modifications of Knuth Randomness Tests for Integer and Binary Sequences(Ankara Univ, Fac Sci, 2018) Kocak, Onur; Sulak, Fatih; Doganaksoy, Ali; Uguz, MuhiddinGenerating random numbers and random sequences that are indistinguishable from truly random sequences is an important task for cryptography. To measure the randomness, statistical randomness tests are applied to the generated numbers and sequences. Knuth test suite is the one of the first statistical randomness suites. This suite, however, is mostly for real number sequences and the parameters of the tests are not given explicitly. In this work, we review the tests in Knuth Test Suite. We give test parameters in order for the tests to be applicable to integer and binary sequences and make suggestions on the choice of these parameters. We clarify how the probabilities used in the tests are calculated according to the parameters and provide formulas to calculate the probabilities. Also, some tests, like Permutation Test and Max-of-t-test, are modified so that the test can be used to test integer sequences. Finally, we apply the suite on some widely used cryptographic random number sources and present the results.Article Citation - WoS: 8Periodic Template Tests: a Family of Statistical Randomness Tests for a Collection of Binary Sequences(Elsevier, 2019) Sulak, Fatih; Doganaksoy, Ali; Uguz, Muhiddin; Kocak, OnurIn this work, we classify all templates according to their periods and for each template we evaluate the exact probabilities using generating functions. Afterwards, we propose a new family of statistical randomness tests, that is periodic template tests, for a collection of binary sequences. We apply these tests to the outputs of AES, SHA-3, SHA-2 family, SHA-1 and MD5 and the binary expansion of pi and root 2 and biased non-random data to test the power of new tests. Moreover, we give the probabilities for all templates for the overlapping template matching test in the NIST test suite. Afterwards, we analyse the power of templates and compare the periodic template tests with NIST overlapping template test. (C) 2019 Elsevier B.V. All rights reserved.
