On some constructions of shapeless quasigroups

Mileva, Aleksandra and Markovski, Smile (2011) On some constructions of shapeless quasigroups. In: The International Mathematical Conference on Quasigroups and Loops (Loops'11), 21-27 July 2011, Trešt, Czech Republic. (Unpublished)

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Official URL: http://www.karlin.mff.cuni.cz/~loops11/

Abstract

In this paper we examine algebraic properties of quasigroups produced by diagonal method from orthomorphisms and we give a construction of shapeless quasigroups of different orders. We examine different types of Extended Feistel Networks (EFN) and Generalized Feistel-Non Linear Feedback Shift Registers (GF-NLFSR) as orthomorphisms of an abelian group (G, +). It is shown that type-1 EFN produced by a bijection is an orthomorphism of the abelian group (G, +) and that GF-NLFSR produced by a bijection is an orthomorphism of the group (Z_2^m,XOR). Also, we parameterized these orthomorphisms for the need of cryptography, so we can work with different quasigroups in every iterations of the future cryptographic primitives.

Item Type: Conference or Workshop Item (Speech)
Subjects: Natural sciences > Computer and information sciences
Divisions: Faculty of Computer Science
Depositing User: Aleksandra Mileva
Date Deposited: 29 Aug 2014 09:30
Last Modified: 29 Aug 2014 09:30
URI: http://eprints.ugd.edu.mk/id/eprint/10788

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