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Наслов: Classification of quasigroups by image patterns
Authors: Dimitrova, Vesna 
Markovski, Smile 
Keywords: quasigroup string transformation, classification of quasigroups
Issue Date: 2007
Publisher: Institute of Informatics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University in Skopje, Macedonia
Conference: CIIT 2007
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 ai 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.
URI: http://hdl.handle.net/20.500.12188/23868
Appears in Collections:Faculty of Computer Science and Engineering: Conference papers

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