New statistical randomness tests: 4-bit template matching tests

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Date

2017

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Tubitak Scientific & Technological Research Council Turkey

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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

For cryptographic algorithms, secret keys should be generated randomly as the security of the system depends on the key and therefore generation of random sequences is vital. Randomness testing is done by means of statistical randomness tests. In this work, we show that the probabilities for the overlapping template matching test in the NIST test suite are only valid for a specific template and need to be recalculated for the other templates. We calculate the exact distribution for all 4-bit templates and propose new randomness tests, namely template matching tests. The new tests can be applied to any sequence of minimum length 5504 whereas the overlapping template matching test in the NIST test suite can only be applied to sequences of minimum length 10(6). Moreover, we apply the proposed tests to biased nonrandom data and observe that the new tests detect the nonrandom behavior of the generator even for a bias of 0.001, whereas the template matching tests in NIST cannot detect that bias.

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Keywords

Cryptography, overlapping template matching test, statistical randomness testing, NIST test suite

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Citation

2

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Q2

Source

Volume

41

Issue

1

Start Page

80

End Page

95

URI

https://doi.org/10.3906/mat-1509-19
 https://hdl.handle.net/20.500.14411/591

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