Browsing by Author "Koçak, Onur"

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Modifications of Knuth Randomness Tests for Integer and Binary Sequences
(2018) Koçak, Onur; Sulak, Fatih; Doğanaksoy, Ali; Uğuz, Muhiddin; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Generating random numbers and random sequences that are in-distinguishable from truly random sequences is an important task for cryptog-raphy. To measure the randomness, statistical randomness tests are applied tothe generated numbers and sequences. Knuth test suite is the one of the .rststatistical randomness suites. This suite, however, is mostly for real numbersequences and the parameters of the tests are not given explicitly.In this work, we review the tests in Knuth Test Suite. We give test para-meters in order for the tests to be applicable to integer and binary sequencesand make suggestions on the choice of these parameters. We clarify how theprobabilities used in the tests are calculated according to the parameters andprovide formulas to calculate the probabilities. Also, some tests, like Per-mutation Test and Max-of-t-test, are modi.ed so that the test can be usedto test integer sequences. Finally, we apply the suite on some widely usedcryptographic random number sources and present the results.
On the Independence of Statistical Randomness Tests Included in the Nist Test Suite
(2017) Sulak, Fatih; Uğuz, Muhiddin; Koçak, Onur; Doğanaksoy, Ali; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Random numbers and random sequences are used to produce vital parts of cryptographic algorithms such as encryption keys and therefore the generation and evaluation of random sequences in terms of randomness are vital. Test suites consisting of a number of statistical randomness tests are used to detect the nonrandom characteristics of the sequences. Construction of a test suite is not an easy task. On one hand, the coverage of a suite should be wide; that is, it should compare the sequence under consideration from many different points of view with true random sequences. On the other hand, an overpopulated suite is expensive in terms of running time and computing power. Unfortunately, this trade-off is not addressed in detail in most of the suites in use. An efficient suite should avoid use of similar tests, while still containing sufficiently many. A single statistical test gives a measure for the randomness of the data. A collection of tests in a suite give a collection of measures. Obtaining a single value from this collection of measures is a difficult task and so far there is no conventional or strongly recommended method for this purpose. This work focuses on the evaluation of the randomness of data to give a uni ed result that considers all statistical information obtained from different tests in the suite. A natural starting point of research in this direction is to investigate correlations between test results and to study the independences of each from others. It is started with the concept of independence. As it is complicated enough to work even with one test function, theoretical investigation of dependence between many of them in terms of conditional probabilities is a much more difficult task. With this motivation, in this work it is tried to get some experimental results that may lead to theoretical results in future works. As experimental results may re ect properties of the data set under consideration, work is done on various types of large data sets hoping to get results that give clues about the theoretical results. For a collection of statistical randomness tests, the tests in the NIST test suite are considered. Tests in the NIST suite that can be applied to sequences shorter than 38,912 bits are analyzed. Based on the correlation of the tests at extreme values, the dependencies of the tests are found. Depending on the coverage of a test suite, a new concept, the coverage efficiency of a test suite, is de ned, and using this concept, the most efficient, the least efficient, and the optimal subsuites of the NIST suite are determined. Moreover, the marginal bene t of each test, which also helps one to understand the contribution of each individual test to the coverage efficiency of the NIST suite, is found. Furthermore, an efficient subsuite that contains ve statistical randomness tests is proposed.
A Second Pre-Image Attack and A Collision Attack To Cryptographic Hash Function Lux
(2017) Sulak, Fatih; Koçak, Onur; Saygı, Elif; Öğünç, Merve Ö.; Bozdemır, Beyza; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Cryptography is a science that provides the security of informationin communication. One of the most important sub-branches of cryptographyis the hash functions. Hash functions are known as the digital ...ngerprints.Following the recent attacks on the widely used hash functions MD5 and SHA1 and the increase in computational power, the need for a new hash functionstandard has arisen. For this purpose, US National Institute of Standards andTechnology (NIST) had announced a competition to select a standard hashfunction algorithm which would eventually become the Third Secure HashAlgorithm, SHA-3. Initially 64 algorithms were submitted to NIST and 51 ofthem were announced as the First Round Candidates. After an analysis period,14 of these algorithms were announced as the Second Round Candidates, and5 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 byNikolic et al.function. For LUX-256, Schmidt-Nielsen gave a distinguisher and later Wu etal. presented collision attacks, both of which for reduced rounds of LUX. As aresult of these attacks, LUX is eliminated in the ...rst round. In this work, we...rst give a procedure for the second preimage attack. Then we extend this tothe collision and second preimage attacks for the reduced rounds of LUX hashfamily. Moreover, we implement the attacks and give the speci...c examples bytaking the padding into consideration.