Abstract. The authors analyze the dependence of the uniformity of distribution of signs of empirical autocorrelation function with respect to the number of overlapping symbols of intervals into which a sequence of random numbers is divided. A feasible “threshold” of overlap is established, below which the signs of the autocorrelation function are uniformly distributed. The concept of barrier function is defined and used to develop a criterion for the quality assessment of random number generators. The technique of its application and its implementation for several well-known generators are presented.
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References
R. G. Brown, Introduction to Random Signal Analysis and Kalman Filtering, John Wiley and Sons, New York (1983).
A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York (1991).
M. A. Ivanov and I. V. Chugunkov, Theory, Application, and Quality Assessment of Pseudo Random Sequence Generators [in Russian], KUDITS-OBRAZ, Moscow (2003).
D. E. Knuth, The Art of Computer Programming, in 7 Vols., Vol. 2: Seminumerical Algorithms, Addison Wesley Longman Publishing Co., Boston (1997).
Stream Ciphers. Results of Foreign Open Cryptology, http://www.ssl.stu.neva.ru/psw/crypto/potok/str_ciph.htm.
M. J. B. Robshaw, Stream Ciphers. Technical Report TR-701, V. 2.0, RSA Lab. (1995).
G. Marsaglia, “DIEHARD battery of tests of randomness,” http://www.stat.fsu.edu/pub/diehard.
A. Rukhin et al., “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” Spec. Pub. 800-22 rev. 1a, Gaithersburg, MD, NIST (2010).
P. L’ecuyer and R. Simard, “TestU01: A C library for empirical testing of random number generators,” ACM TOMS, 33, No. 4, Article 22 (2007).
M. Matsumoto and T. Nishimura, “Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM TOMACS, 8, 3–30 (1998).
J. Soto, “Statistical testing of random number generators,” in: Proc. 22nd National Inform. Systems Security Conf., Gaithersburg, MD, NIST (1999).
J. C. Collins, “Testing, selection, and implementation of random number generators,” Rep. ARL-TR-4498, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD (2008).
N. V. Smirnov and I. V. Dunin-Barkovsky, A Course in Probability Theory and Mathematical Statistics for Engineering Applications [in Russian], Nauka, Moscow (1969).
M. G. Kendall, The Advanced Theory of Statistics, Vol. 2, C. Griffin&Co, London (1946).
P. A. M. Dirac, The Principles of Quantum Mechanics, OUP, London (1958).
L. N. Bolshev and N. V. Smirnov, Tables of Mathematical Statistics, Nauka, Moscow (1983).
E. V. Faure, A. I. Shcherba, and A. A. Lavdanskii, “Analysis of correlation properties of sequences of (pseudo) random numbers,” Nauka i Tekhnika Povitr. Syl Zbroinykh Syl Ukrainy, No. 1(18), 142–150 (2015).
A. A. Lavdanskii and E. V. Faure, “A combination method to generate a sequence of pseudorandom numbers,” in: Pros. 16th Intern. Sci.-Tech. Conf. SAIT-2014 (Systems Analysis and Information Technologies), Kyiv, May 26–30, 2014 NNK IPSA NTUU KPI, Kyiv (2014), pp. 403–404.
M. Haahr, True Random Number Service, http://random.org/.
QRNG Service, http://qrng.physik.hu-berlin.de/.
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Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2016, pp. 116–124.
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Faure, E.V., Shcherba, A.I. & Rudnytskyi, V.M. The Method and Criterion for Quality Assessment of Random Number Sequences. Cybern Syst Anal 52, 277–284 (2016). https://doi.org/10.1007/s10559-016-9824-3
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DOI: https://doi.org/10.1007/s10559-016-9824-3