Abstract
In the last few years, quasigroups are finding their way to becoming a building block of cryptographic primitives. This paper extends previous work done on evolutionary search for quasigroups by defining fitness functions based on heterogeneous sequences generated during the exponentiation of quasigroups elements. In this paper, we explore how succeed a genetic algorithm in search for maximum of the best fitness function and some statistics about this fitness function is presented, too.
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References
Panda, M., Abraham, A., Das, S., Patra, M.R.: Network intrusion detection system: A machine learning approach. In: Intelligent Decision Technologies, vol. 5(4), pp. 347–356 (2011)
Gligoroski, D., Markovski, S., Knapskog, S.J.: Multivariate quadratic trapdoor functions based on multivariate quadratic quasigroups. In: American Conference on Applied Mathematics (2008)
Gligoroski, D., Markovski, S., Knapskog, S.J.: The Stream Cipher Edon80. In: Robshaw, M., Billet, O. (eds.) New Stream Cipher Designs. LNCS, vol. 4986, pp. 152–169. Springer, Heidelberg (2008)
Gligoroski, D., et al.: EdonR cryptographic hash function. Submition to NIST’s SHA-3 hash function competition (2008), http://csrc.nist.gov/groups/ST/hash/sha-3/index.html
Gligoroski, D., Markovski, S.: Cryptographic potentials of quasigroup transformations. Talk at EIDMA Cryptography Working Group, Utrecht (2003)
Markovski, S., Gligoroski, D., Markovski, J.: Classification of quasigroups by random walk on torus. Journal of Applied Mathematics and Computing 19(1-2), 57–75 (2005)
Ochodkova, E., Kromer, P., Dvorsky, J., Abraham, P.J.A., Snasel, V.: Genetic search for quasigroups with heterogeneous power sequences. In: 2011 Third World Congress on Nature and Biologically Inspired Computing (NaBIC), pp. 533–539 (October 2011)
Ochodková, E., Dvorský, J., Snášel, V., Abraham, A.: Testing quasigroup identities using product of sequence. In: Pokorný, J., Snásel, V., Richta, K. (eds.) DATESO. CEUR Workshop Proceedings, vol. 567, pp. 155–162. CEUR-WS.org (2010)
Snášel, V., Dvorský, J., Ochodková, E., Krömer, P., Platoš, J., Abraham, A.: Genetic Algorithms Evolving Quasigroups with Good Pseudorandom Properties. In: Taniar, D., Gervasi, O., Murgante, B., Pardede, E., Apduhan, B.O. (eds.) ICCSA 2010, Part III. LNCS, vol. 6018, pp. 472–482. Springer, Heidelberg (2010)
Snášel, V., Abraham, A., Dvorský, J., Ochodková, E., Platoš, J., Krömer, P.: Searching for quasigroups for hash functions with genetic algorithms. In: World Congress on Nature & Biologically Inspired Computing, NaBIC 2009, pp. 367–372. IEEE Computer Society (2009)
Belousov, V.D.: Osnovi teorii kvazigrup i lup, Nauka, Moscow (1967) (in Russian)
McKay, B.D., Wanless, I.M.: On the Number of Latin Squares. Journal Annals of Combinatorics 9(3), 335–344 (2005)
Borůvka, O.: Foundations of the theory of groupoids and groups. Wiley (1976)
Hilton, P., Pedersen, J.: Catalan Numbers, Their Generalization, and Their Uses. Journal The Mathematical Intelligencer 13(2), 64–75 (1991)
Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press, Cambridge (1996)
Kemperman, J.H.B.: Mixture with a limited number of modal intervals. Annal. Stat. 19, 2120–2144 (1991)
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Ochodková, E., Dvorský, J., Krömer, P., Tuček, P. (2013). On Fitness Function Based upon Quasigroups Power Sequences. In: Herrero, Á., et al. International Joint Conference CISIS’12-ICEUTE´12-SOCO´12 Special Sessions. Advances in Intelligent Systems and Computing, vol 189. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33018-6_14
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DOI: https://doi.org/10.1007/978-3-642-33018-6_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33017-9
Online ISBN: 978-3-642-33018-6
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