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Classification of quasigroups by random walk on torus

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Abstract

Quasigroups are algebraic structures closely related to Latin squares which have many different applications. There are several classifications of quasigroups based on their algebraic properties. In this paper we propose another classification based on the properties of strings obtained by specific quasigroup transformations. More precisely, in our research we identified some quasigroup transformations which can be applied to arbitrary strings to produce pseudo random sequences. We performed tests for randomness of the obtained pseudo-random sequences by random walks on torus. The randomness tests provided an empirical classification of quasi-groups.

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Authors and Affiliations

  1. Institute of Informatics, Faculty of Sciences, PoBox 162, Skopje, Macedonia

    Smile Markovski, Danilo Gligoroski & Jasen Markovski

Authors
  1. Smile Markovski
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  2. Danilo Gligoroski
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  3. Jasen Markovski
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Correspondence to Smile Markovski.

Additional information

Part of this work was carried out during the tenure of an ERCIM fellowship of the second author-D. Gligoroski visiting Q2S—Centre for Quantifiable Quality of Service in Communication Systems at Norwegian University of Science and Technology—Trondheim, Norway.

Smile Markovski, received his PhD at “Ss Ciryl and Methodius” University of Skopje in 1980 in the field of algebra. He has been elected as full professor in 1991. His research interest are Universal algebras,n-ary and vector valued groupoids, quasigroup theory, discrete mathematics, cryptography and coding theory.

Danilo Gligorski received his PhD at “Ss Ciryl and Methodius” University of Skopje in 1997 in the field of Computer Science. His research interest are Cryptography, Computer Security, Discrete algorithms and Information Theory and Coding. Currently he is using an ERCIM fellowship visiting Q2S—Centre for Quantifiable Quality of Service in Communication Systems at Norwegian University of Science and Technology-Trondheim, Norway.

Jasen Markovski received his MSc in Computer Science at “Ss Ciryl and Methodius” University in Skopje, and now he is a PhD student at Eindhoven Technology University in the Nederlands.

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Markovski, S., Gligoroski, D. & Markovski, J. Classification of quasigroups by random walk on torus. JAMC 19, 57–75 (2005). https://doi.org/10.1007/BF02935788

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  • DOI: https://doi.org/10.1007/BF02935788

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