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Article Citation - WoS: 2A SECOND PRE-IMAGE ATTACK AND A COLLISION ATTACK TO CRYPTOGRAPHIC HASH FUNCTION LUX(Ankara Univ, Fac Sci, 2017) Sulak, Fatih; Kocak, Onur; Saygi, Elif; Ogunc, Merve; Bozdemir, BeyzaCryptography is a science that provides the security of information in communication. One of the most important sub-branches of cryptography is the hash functions. Hash functions are known as the digital fingerprints. Following the recent attacks on the widely used hash functions MD5 and SHA-1 and the increase in computational power, the need for a new hash function standard has arisen. For this purpose, US National Institute of Standards and Technology (NIST) had announced a competition to select a standard hash function algorithm which would eventually become the Third Secure Hash Algorithm, SHA-3. Initially 64 algorithms were submitted to NIST and 51 of them were announced as the First Round Candidates. After an analysis period, 14 of these algorithms were announced as the Second Round Candidates, and 5 algorithms were announced as Finalists. The winner of the competition, Keccak, was announced in 2012. LUX is one of the 64 algorithms submitted to the SHA-3 competition by Nikolic et al. It is designed as a byte oriented stream cipher based hash function. For LUX-256, Schmidt-Nielsen gave a distinguisher and later Wu et al. presented collision attacks, both of which for reduced rounds of LUX. As a result of these attacks, LUX is eliminated in the first round. In this work, we first give a procedure for the second preimage attack. Then we extend this to the collision and second preimage attacks for the reduced rounds of LUX hash family. Moreover, we implement the attacks and give the specific examples by taking the padding into consideration.Article Citation - WoS: 2Citation - Scopus: 4R-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 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.
