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Author: Akcengiz, ZiyaSubject: Cryptography

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    Article
    Citation - WoS: 11
    Citation - Scopus: 12
    Mutual Correlation of Nist Statistical Randomness Tests and Comparison of Their Sensitivities on Transformed Sequences
    (Tubitak Scientific & Technological Research Council Turkey, 2017) Doganaksoy, Ali; Sulak, Fatih; Uguz, Muhiddin; Seker, Okan; Akcengiz, Ziya
    Random sequences are widely used in many cryptographic applications and hence their generation is one of the main research areas in cryptography. Statistical randomness tests are introduced to detect the weaknesses or nonrandom characteristics that a sequence under consideration may have. In the literature, there exist various statistical randomness tests and test suites, defined as a collection of tests. An efficient test suite should consist of a number of uncorrelated statistical tests each of which measures randomness from another point of view. `Being uncorrelated' is not a well-defined or well-understood concept in the literature. In this work, we apply Pearson's correlation test to measure the correlation between the tests. In addition, we define five new methods for transforming a sequence. Our motivation is to detect those tests whose results are invariant under a certain transformation. To observe the correlation, we use two methods. One is the direct correlation between the tests and the other is the correlation between the results of a test on the sequence and its transformed form. In light of the observations, we conclude that some of the tests are correlated with each other. Furthermore, we conclude that in designing a reliable and efficient suite we can avoid overpopulating the list of test functions by employing transformations together with a reasonable number of statistical test functions.
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    Article
    Citation - WoS: 1
    Citation - Scopus: 3
    LS-14 Test Suite for Long Sequences
    (Hacettepe Univ, Fac Sci, 2024) Akcengiz, Ziya; Aslan, Melis; Doğanaksoy, Ali; Sulak, Fatih; Uguz, Muhiddin
    Random number sequences are used in many branches of science. Because of many techni- cal 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 pat- terns, 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 ap- proximations 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 collec- tion 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 in- troduce 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.