A New Cryptographic Property Based On the orthogonality of Quasigroups

Mihajloska, Hristina (2012) A New Cryptographic Property Based On the orthogonality of Quasigroups. In: Proceedings of the Nineth Conference on Informatics and Information Technology. Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University in Skopje, Macedonia, Skopje, Macedonia, pp. 237-240. ISBN 978-608-4699-01-9


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In order to achieve better cryptographic properties of quasigroups of order 4, we make a new classification. In our research we use an approach with generalized quasigroup orthogonality, which leads us to this interesting classification, on reducible and irreducible quasigroups. Existence of the classes of reducible and irreducible quasigroups depends on the property of orthogonality of quasigroups which can be studied in the light of right quasigroups. Two right quasigroups r, s of order 4 are orthogonal if and only if there exists a quasigroup q of the same order and r · q = s is satisfied. Furthermore, for every quasigroup out of 576 of order 4 we find all pairs of orthogonal right quasigroups that satisfy previously mentioned property. Experimentally we show that all quasigroups which belong to the class of linear by their Boolean presentation can be presented as product of two other linear quasigroups. All this quasigroups formed the class of product reducible quasigroups and remaining belong to the class of product irreducible quasigroups.

Item Type: Book Section
Uncontrolled Keywords: cryptography, orthogonality, quasigroup, right quasigroup
Subjects: International Conference on Informatics and Information Technologies > Security and Cryptography
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/11120

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