MODIFICATIONS OF KNUTH RANDOMNESS TESTS FOR INTEGER AND BINARY SEQUENCES

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2018

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Ankara Univ, Fac Sci

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

Generating 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.

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Knuth test suite, Statistical randomness testing

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1

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Volume

67

Issue

2

Start Page

64

End Page

81

URI

https://doi.org/10.1501/Commua1_0000000862
 https://hdl.handle.net/20.500.14411/2979

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