Classification of Quasigroups By Image Patterns

Dimitrova, Vesna and Markovski, Smile (2007) Classification of Quasigroups By Image Patterns. In: Proceedings of the Fifth Conference on Informatics and Information Technology. Institute of Informatics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University in Skopje, Macedonia, Skopje, Macedonia, pp. 152-160. ISBN 978-9989-668-69-2

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Abstract

Given a finite quasigroup (Q, ∗), we define a quasigroup string transformation e over the strings of elements from Q by e(a1a2...an) = b1b2...bn if and only if bi = bi−1∗ai for each i = 1, 2,..., n, where b0 is a fixed element of Q, and a i are elements from Q. These kind of quasigroup string transformations are used for designing several cryptographic primitives and error-correcting codes. Not all quasigroups are suitable for that kind of designs. The set of quasigroups of given order can be separated in two disjoint classes, the class of so called fractal quasigroups and the class of non-fractal quasigroups. The classification is obtained by presenting several consecutive sequences generated by e−transformations and their presentation in matrix form, used to produce suitable image pattern. We note that the fractal quasigroups are usually not suitable for designing cryptographic Primitives.

Item Type: Book Section
Uncontrolled Keywords: quasigroup string transformation, classification of quasigroups
Subjects: International Conference on Informatics and Information Technologies > Industrial Mathematics
Depositing User: Vangel Ajanovski
Date Deposited: 28 Oct 2016 00:15
Last Modified: 28 Oct 2016 00:15
URI: http://eprints.finki.ukim.mk/id/eprint/11323

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