R-2 composition tests: a family of statistical randomness tests for a collection of binary sequences

Uğuz, Muhiddin; Doğanaksoy, Ali; Sulak, Fatih; Koçak, Onur

doi:10.1007/s12095-018-0334-1

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…In the literature, rather than Golomb's postulates, statistical approaches are studied to decide whether the finite sequence under consideration is random with a certain probability. Statistical randomness tests use different random variables, mostly inspired by Golomb's postulates [7,10,13,14,16,26,30,34,35,38,42].…”

Section: Introductionmentioning

confidence: 99%

LS-14 test suite for long sequences

AKCENGİZ,

ASLAN,

DOĞANAKSOY

et al. 2024

Hacettepe Journal of Mathematics and Statistics

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Random number sequences are used in many branches of science. Because of many technical reasons and their practicality, pseudo random sequences are usually employed in place of true number sequences. Whether a sequence generated through a deterministic process is a pseudo random, in other words, random-looking sequence or it contains certain patterns, can be determined with the help of statistics and mathematics. Although, in the literature there are many statistical randomness tests for this purpose, there is no much work on test suites specialized for long sequences, that is sequences of length 1,000,000 bits or more. Most of the randomness tests for long sequences use some mathematical approximations to compute expected values of the random variables and hence their results contain some errors. Another approach to evaluate randomness criteria of long sequences is to partition the long sequence into a collection short sequences and evaluate the collection for the ran- domness using statistical goodness of fit tests. The main advantage of this approach is, as the individual sequences are short, there is no need to use mathematical approximations. On the other hand when the second approach is preferred, partition the long sequence into a collection of fixed length subsequences and this approach causes a loss of information in some cases. Hence the idea of dynamic partition should be included to perform a more reliable test suite. In this paper, we propose three new tests, namely the entire R2 run, dynamic saturation point, and dynamic run tests. Moreover, we introduce a new test suite, called LS-14, consisting of 14 tests to evaluate randomness of long sequences. As LS-14 employs all three approaches: testing the entire long sequence, testing the collection of fixed length partitions of it, and finally, testing the collection obtained by the dynamic partitions of it, the proposed LS-14 test suit differs from all existing suites. Mutual comparisons of all 14 tests in the LS-14 suite, with each other are computed. Moreover, results obtained from the proposed test suite and NIST SP800-22 suite are compared. Examples of sequences with certain patterns which are not observed by NIST SP800-22 suite but detected by the proposed test suite are given.

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Section: Introductionmentioning

confidence: 99%

LS-14 test suite for long sequences

AKCENGİZ,

ASLAN,

DOĞANAKSOY

et al. 2024

Hacettepe Journal of Mathematics and Statistics

Self Cite

View full text Add to dashboard Cite

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“…https://doi.org/10.55859/ijiss.1288854 are many documents outlining how these statistical randomness test can be designed, [1] gives a detailed information on this. There are many tests defined in the literature [2], [3], [4], [5], [6], [7], [8], [9] are some of them. Also many test suites are available in the literature [10], [11], [12], [13], [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Graph Theoretic Approach to Randomness Test Based on the Overlapping Blocks

Uğuz¹

2023

International Journal of Information Security Science

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Cryptographic parameters such as secret keys, should be chosen randomly and at the same time it should not be so difficult to reproduced them when necessary. Because of this, pseudorandom bit (or number) generators take the role of true random generators. Outputs of pseudorandom generators, although they are produced through some deterministic process, should be random looking, that is not distinguishable from true random sequences. In other word they should not follow any pattern. In this paper we propose a new approach using graph theory, to determine when to expected a fixed pattern to appear in a random sequence for the fist time. Using these expected values and comparing them with the observed values a randomness test can be defined. In this work patters are traced through the sequence in an overlapping manner.

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R-2 composition tests: a family of statistical randomness tests for a collection of binary sequences

Cited by 2 publications

References 8 publications

LS-14 test suite for long sequences

LS-14 test suite for long sequences

Graph Theoretic Approach to Randomness Test Based on the Overlapping Blocks

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