Abstract
In this paper we revisit the problem of using Genetic Algorithms to evolve 2-dimensional Cellular Automata (CA) as Pseudo-random Number Generators (PRNG). Our main contribution is two-fold. First, we review the problem of using CAs as PRNGs under the scope of the newer and more demanding batteries of pseudo-random generator tests that have been developed since the introduction of DIEHARD [1]. Second, we introduce a composite fitness metric, that incorporates elements from PRNG tests, to be used in the evolution of the CAs.
This work has been partly realized thanks to the support of the Région Lorraine and the CPER MISN TALC project.
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References
Marsaglia, G.: Diehard prng tests (1995)
Abarbanel, H.D.I., Brown, R., Sidorowich, J.J., Tsimring, L.S.: The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 65(4), 1331–1392 (1993)
Kier, L., Seybold, P., Cheng, C.K.: Modeling Chemical Systems Using Cellular Automata. Springer (2005)
Berry, H., Gracia Pérez, D., Temam, O.: Chaos in computer performance. Chaos 16, 013110 (2006)
Musti, U., Toutios, A., Ouni, S., Colotte, V., Wrobel Dautcourt, B., Berger, M.O.: HMM-based Automatic Visual Speech Segmentation Using Facial Data. In: Interspeech 2010, pp. 1401–1404 (2010)
Oran, E., Oh, C., Cybyk, B.: Direct simulation monte carlo: Recent advances and applications. Annual Review of Fluid Mechanics 30, 403–441 (1998)
Diaconis, P.: The markov chain monte carlo revolution. Bull. Amer. Math. Soc. 46, 179–205 (2009)
Hortensius, P., McLeod, R., Card, H.: Parallel random number generation for vlsi systems using cellular automata. IEEE Transactions on Computers 38(10), 1466–1473 (1989)
Kotoulas, L.G., Tsarouchis, D., Sirakoulis, G.C., Andreadis, I.: 1-d cellular automaton for pseudorandom number generation and its reconfigurable hardware implementation. In: ISCAS. IEEE (2006)
Nandi, S., Kar, B., Chaudhuri, P.: Theory and applications of cellular automata in cryptography. IEEE Transactions on Computers 43(12), 1346–1357 (1994)
Tomassini, M., Perrenoud, M.: Cryptography with cellular automata. Applied Soft Computing (1), 151–160 (2001)
Karmakar, S., Mukhopadhyay, D., Roy Chowdhury, D.: d-Monomial Tests of Nonlinear Cellular Automata for Cryptographic Design. In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds.) ACRI 2010. LNCS, vol. 6350, pp. 261–270. Springer, Heidelberg (2010)
Chowdhury, D.R., Sengupta, I., Chaudhuri, P.P.: A class of two-dimensional cellular automata and their applications in random pattern testing. J. Electron. Test. 5(1), 67–82 (1994)
Tomassini, M., Sipper, M., Zolla, M., Perrenoud, M.: Generating high-quality random numbers in parallel by cellular automata. Future Generation Computer Systems 16, 291–305 (1999)
Mitchell, M., Crutchfield, J.P., Das, R.: Evolving cellular automata with genetic algorithms: A review of recent work. In: Proceedings of the First International Conference on Evolutionary Computation and Its Applications (1996)
Mitchell, M., Hraber, P.T., Crutchfield, J.P.: Revisiting the edge of chaos: Evolving cellular automata to perform computations. Complex Systems 7, 89–130 (1993)
Mizas, C., Sirakoulis, G., Mardiris, V., Karafyllidis, I., Glykos, N., Sandaltzopoulos, R.: Reconstruction of dna sequences using genetic algorithms and cellular automata: Towards mutation prediction? Biosystems 92(1), 61–68 (2008)
Dewri, R., Chakraborti, N.: Simulating recrystallization through cellular automata and genetic algorithms. Modelling and Simulation in Materials Science and Engineering 13(2), 173 (2005)
Rongo, R., Spataro, W., D’Ambrosio, D., Vittoria Avolio, M., Trunfio, G.A., Di Gregorio, S.: Lava flow hazard evaluation through cellular automata and genetic algorithms: an application to mt etna volcano. Fundamenta Informaticae 87(2), 247–267 (2008)
Tomassini, M., Sipper, M., Perrenoud, M.: On the generation of high-quality random numbers by two-dimensional cellular automata. IEEE Transactions on Computers 49, 1146–1151 (2000)
Sipper, M., Tomassini, M.: Generating parallel random number generators by cellular programming. International Journal of Modern Physics C 7, 181–190 (1996)
Brown, R.: Dieharder prng tests (2009)
L’Ecuyer, P., Simard, R.: Testu01: A c library for empirical testing of random number generators. ACM Trans. Math. Softw. 33, 2/1–2/40 (2007)
Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)
Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press (1999)
Marsaglia, G., Tsang, W.W.: Some difficult-to-pass tests of randomness. Journal of Statistical Software 7(3), 8 (2002)
Schervish, M.J.: P values: What they are and what they are not. The American Statistician 50(3), 203–206 (1996)
Boes, D.C., Graybill, F.A., Mood, A.M.: Introduction to the Theory of Statistics, 3rd edn. McGraw-Hill (1974)
Wikipedia: Embarrassingly parallel — wikipedia, the free encyclopedia (2012) (online, accessed April 4, 2012)
Filiol, E.: A New Statistical Testing for Symmetric Ciphers and Hash Functions. In: Deng, R.H., Qing, S., Bao, F., Zhou, J. (eds.) ICICS 2002. LNCS, vol. 2513, pp. 342–353. Springer, Heidelberg (2002)
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Girau, B., Vlassopoulos, N. (2012). Evolution of 2-Dimensional Cellular Automata as Pseudo-random Number Generators. In: Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2012. Lecture Notes in Computer Science, vol 7495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33350-7_63
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DOI: https://doi.org/10.1007/978-3-642-33350-7_63
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