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. 152160. ISBN 9789989668692

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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 errorcorrecting 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 nonfractal 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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