Browsing by Author "Uğuz, Muhiddin"

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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.
Mutual Correlation of Nist Statistical Randomness Tests and Comparison of Theirsensitivities on Transformed Sequences
(2017) Doğanaksoy, Ali; Sulak, Fatih; Uğuz, Muhiddin; Şeker, Okan; Akcengiz, Ziya; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Random sequences are widely used in many cryptographic applications and hence their generation is oneof the main research areas in cryptography. Statistical randomness tests are introduced to detect the weaknesses ornonrandom characteristics that a sequence under consideration may have. In the literature, there exist various statisticalrandomness tests and test suites, de ned as a collection of tests. An efficient test suite should consist of a number ofuncorrelated statistical tests each of which measures randomness from another point of view. `Being uncorrelated\\' is nota well-de ned or well-understood concept in the literature. In this work, we apply Pearson\\'s correlation test to measurethe correlation between the tests.In addition, we de ne ve new methods for transforming a sequence. Our motivation is to detect those testswhose results are invariant under a certain transformation. To observe the correlation, we use two methods. One is thedirect correlation between the tests and the other is the correlation between the results of a test on the sequence andits 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 testfunctions by employing transformations together with a reasonable number of statistical test functions.
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.