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Article Cryptographic Randomness Testing of Block Ciphers: SAC Tests(IEEE-Inst Electrical Electronics Engineers Inc, 2026) Aslan, Melis; Doganaksoy, Ali; Kocaman, Sermin; Saygi, Zulfukar; Sulak, FatihBlock ciphers are designed to function as random mappings, making it essential for them to successfully pass statistical randomness tests. These tests evaluate whether the distribution of a test statistic, derived empirically through various data manipulations over states of the algorithm, aligns with the theoretical distribution for cryptographic randomness. Beyond this, evaluating the cryptographic properties of the algorithm is also important to ensure its security and reliability. One of the important cryptographic randomness properties is the Strict Avalanche Criterion (SAC), which assesses the impact of a one-bit alteration in the input over the output. In this work, we introduce new SAC-based tests to offer more reliable evaluation for the cryptographic randomness of block cipher algorithms. The tests are utilized for the application of AES, PRESENT, and CLEFIA block ciphers. The results are compared with Soto's evaluation methods, which are known for their comprehensive approach to block ciphers. According to this, it is apparent that our novel SAC tests improve upon Soto's results, thus providing a more comprehensive understanding of randomness.Article Citation - WoS: 4Citation - Scopus: 6R-2 Composition Tests: a Family of Statistical Randomness Tests for a Collection of Binary Sequences(Springer, 2019) Uguz, Muhiddin; Doganaksoy, Ali; Sulak, Fatih; Kocak, OnurIn this article a family of statistical randomness tests for binary strings are introduced, based on Golomb's pseudorandomness postulate R-2 on the number of runs. The basic idea is to construct recursive formulae with computationally tenable probability distribution functions. The technique is illustrated on testing strings of 2(7), 2(8), 2(10) and 2(12) bits. Furthermore, the expected value of the number of runs with a specific length is obtained. Finally the tests are applied to several collections of strings arising from different pseudorandom number generators.Article Citation - WoS: 2Citation - Scopus: 1Observations on Nist Sp 800-90b Entropy Estimators(Springer, 2025) Aslan, Melis; Doganaksoy, Ali; Saygi, Zulfukar; Turan, Meltem Sonmez; Sulak, Fatih; Sönmez Turan, MeltemRandom numbers play a crucial role in cryptography since the security of cryptographic protocols relies on the assumption of the availability of uniformly distributed and unpredictable random numbers to generate secret keys, nonce, salt, etc. However, real-world random number generators sometimes fail and produce outputs with low entropy, leading to security vulnerabilities. The NIST Special Publication (SP) 800-90 series provides guidelines and recommendations for generating random numbers for cryptographic applications and describes 10 black-box entropy estimation methods. This paper evaluates the effectiveness and limitations of the SP 800-90 methods by exploring the accuracy of these estimators using simulated random numbers with known entropy, investigating the correlation between entropy estimates, and studying the impacts of deterministic transformations on the estimators.Article Citation - WoS: 9Periodic Template Tests: a Family of Statistical Randomness Tests for a Collection of Binary Sequences(Elsevier, 2019) Sulak, Fatih; Doganaksoy, Ali; Uguz, Muhiddin; Kocak, OnurIn this work, we classify all templates according to their periods and for each template we evaluate the exact probabilities using generating functions. Afterwards, we propose a new family of statistical randomness tests, that is periodic template tests, for a collection of binary sequences. We apply these tests to the outputs of AES, SHA-3, SHA-2 family, SHA-1 and MD5 and the binary expansion of pi and root 2 and biased non-random data to test the power of new tests. Moreover, we give the probabilities for all templates for the overlapping template matching test in the NIST test suite. Afterwards, we analyse the power of templates and compare the periodic template tests with NIST overlapping template test. (C) 2019 Elsevier B.V. All rights reserved.Article RW-9: A Family of Random Walk Tests(Springer, 2025) Uguz, Muhiddin; Sulak, Fatih; Doganaksoy, Ali; Kocak, OnurIn this work, we define a family of nine statistical randomness tests for collections of short binary strings, by making use of random walk statistics. For a binary sequence of length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{n}$$\end{document}, we consider the probability of intersecting the line \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{y=t}$$\end{document} exactly at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{k}$$\end{document} distinct points. Although there are some explicit formulas for these probability values in the literature, those applicable to short sequences are not feasible for computations involving sequences of length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{256}$$\end{document} bits or more. On the other hand, approximation techniques, or asymptotic approaches, that should be used only when testing long sequences, are not useful for testing sequences of length between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{256}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{4096}$$\end{document}. The recursive formulas, derived in this paper, made it possible to obtain exact values of the corresponding probability distribution functions. Using these formulas, we provide the necessary figures for testing collections of strings of length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{2}<^>{\varvec{7}}, \ \varvec{2}<^>{\varvec{8}}, \ \varvec{2}<^>{\varvec{10}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{2}<^>{\varvec{12}}$$\end{document} bits. Finally, we apply these nine tests to various collections of strings obtained from different pseudorandom number generators as well as to biased sequences to assess whether the proposed tests can effectively detect non-random data.Correction Observations on Nist Sp 800-90b Entropy Estimators (Jan, 10.1007/S12095-025-00778-7, 2025)(Springer, 2025) Aslan, Melis; Doganaksoy, Ali; Saygi, Zulfukar; Turan, Meltem Sonmez; Sulak, Fatih
