×

zbMATH — the first resource for mathematics

Random walk in a \({\mathsf N}\)-cube without Hamiltonian cycle to chaotic pseudorandom number generation: theoretical and practical considerations. (English) Zbl 1358.11090

MSC:
11K45 Pseudo-random numbers; Monte Carlo methods
60G50 Sums of independent random variables; random walks
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bahi, J.; Couchot, J.; Guyeux, C.; Richard, A., On the link between strongly connected iteration graphs and chaotic Boolean discrete-time dynamical systems, FCT’11, 18th Int. Symp. Fundamentals of Computation Theory, 126-137, (2011) · Zbl 1342.37044
[2] Bahi, J.; Fang, X.; Guyeux, C.; Wang, Q., On the design of a family of CI pseudo-random number generators, WICOM’11, 7th Int. IEEE Conf. Wireless Communications, Networking and Mobile Computing, 1-4, (2011)
[3] Banks, J.; Brooks, J.; Cairns, G.; Stacey, P., On devaney’s definition of chaos, Amer. Math. Monthly, 99, 332-334, (1992) · Zbl 0758.58019
[4] Bassham, L. E., III, Rukhin, A. L., Soto, J., Nechvatal, J. R., Smid, M. E., Barker, E. B., Leigh, S. D., Levenson, M., Vangel, M., Banks, D. L., Heckert, N. A., Dray, J. F. & Vo, S. [2010] “Sp 800-22 rev.1a. a statistical test suite for random and pseudorandom number generators for cryptographic applications,” Tech. Rep., National Institute of Standards & Technology, Gaithersburg, MD, United States.
[5] Bhat, G. S.; Savage, C. D., Balanced gray codes, Electr. J. Comb., 3, (1996) · Zbl 0917.94019
[6] Bykov, I. S., On locally balanced gray codes, J. Appl. Industr. Math., 10, 78-85, (2016) · Zbl 1349.94152
[7] Cao, L.; Min, L.; Zang, H., A chaos-based pseudorandom number generator and performance analysis, Int. Conf. (IEEE) Computational Intelligence and Security, 2009. CIS ’09, 494-498, (2009)
[8] Couchot, J.; Héam, P.; Guyeux, C.; Wang, Q.; Bahi, J. M.; Obaidat, M. S.; Holzinger, A.; Samarati, P., Pseudorandom number generators with balanced gray codes, SECRYPT 2014 — Proc. 11th Int. Conf. Security and Cryptography, 469-475, (2014), SciTePress
[9] Devaney, R. L., An Introduction to Chaotic Dynamical Systems, (1989), Addison-Wesley, Redwood City, CA · Zbl 0695.58002
[10] Guyeux, C.; Wang, Q.; Bahi, J., Improving random number generators by chaotic iterations application in data hiding, 2010 Int. Conf. (IEEE) Computer Application and System Modeling (ICCASM), V13-643-V13-647, (2010)
[11] L’Ecuyer, P.; Simard, R. J., Testu01: A C library for empirical testing of random number generators, ACM Trans. Math. Softw., 33, (2007) · Zbl 1365.65008
[12] Levin, D. A.; Peres, Y.; Wilmer, E. L., Markov Chains and Mixing Times, (2006), American Mathematical Society
[13] Marsaglia, G. [1996] “Diehard: A battery of tests of randomness,” http://stat.fsu.edu/geo/diehard.html.
[14] Matsumoto, M.; Nishimura, T., Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator, ACM Trans. Model. Comput. Simul. (TOMACS), 8, 3-30, (1998) · Zbl 0917.65005
[15] Mitzenmacher, M.; Upfal, E., Probability and Computing, (2005), Cambridge University Press
[16] Robinson, J. P.; Cohn, M., Counting sequences, IEEE Trans. Comput., 30, 17-23, (1981) · Zbl 0455.94053
[17] Stojanovski, T.; Kocarev, L., Chaos-based random number generators. part I: analysis [cryptography], IEEE Trans. Circuits Syst.-I: Fund. Th. Appl., 48, 281-288, (2001) · Zbl 0997.65002
[18] Stojanovski, T.; Pihl, J.; Kocarev, L., Chaos-based random number generators. part II: practical realization, IEEE Trans. Circuits Syst.-I: Fund. Th. Appl., 48, 382-385, (2001) · Zbl 0997.65003
[19] Suparta, I.; Zanten, A. V., Totally balanced and exponentially balanced gray codes, Discr. Anal. Operat. Res. (Russia), 11, 81-98, (2004) · Zbl 1078.94040
[20] Wang, Q.; Bahi, J.; Guyeux, C.; Fang, X., Randomness quality of CI chaotic generators. application to Internet security, INTERNET’2010. The 2nd Int. Conf. Evolving Internet, 125-130, (2010), IEEE Computer Society Press, Valencia, Spain
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.