Statistical Randomness Tests of Long Sequences by Dynamic Partitioning

Akcengiz, Ziya; Aslan, Melis; Karabayir, Ozgur; Doğanaksoy, Ali; Uğuz, Muhiddin; Sulak, Fatih

doi:10.1109/iscturkey51113.2020.9308005

Cited by 2 publications

(9 citation statements)

References 6 publications

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“…• Fixed-length weight test [19]: Partition the long sequence to obtain a collection of fixed length short sequences and evaluate the collection using χ 2 distribution. • Dynamic partition weight test [2]: Partition the long sequence into short sequences of variable length determined by a prefixed value for the weight. Then evaluate the collection of the lengths of subsequences using χ 2 distribution.…”

Section: Weight Testmentioning

confidence: 99%

“…We used linear complexity test in two ways, fixed length linear complexity test [19], [29] and dynamic partition linear complexity test [2].…”

Section: Linear Complexity Testmentioning

confidence: 99%

“…Then, the probability of the sequence S having c different integers is: In the literature, collision test is one of the most appropriate randomness tests for the dynamic partitioning method. Two types of collision test [2] are used in the test suite.…”

Section: Integer Coverage Testmentioning

confidence: 99%

“…• those applied to the collection obtained from the sequence using a fixed-length partition, • a new approach called dynamically partitioned subsequences defined by [2].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we propose a new test suite to test long sequences. We use tests defined in [2] and tests for the entire sequence and fixed-length partitioning method in order to complete the test suite. In the entire sequence method, two basic tests named as weight and run [29] are used, while in the fixed-length partitioning method, five different tests named weight test, run test, linear complexity test, and integer coverage test [20] are used.…”

Section: Introductionmentioning

confidence: 99%

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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: Weight Testmentioning

confidence: 99%

“…We used linear complexity test in two ways, fixed length linear complexity test [19], [29] and dynamic partition linear complexity test [2].…”

Section: Linear Complexity Testmentioning

confidence: 99%

Section: Integer Coverage Testmentioning

confidence: 99%

“…• those applied to the collection obtained from the sequence using a fixed-length partition, • a new approach called dynamically partitioned subsequences defined by [2].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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