RO  EN
IMI/Publicaţii/QRS/Ediţii/QRS v.31, n.1 (49), 2023/

On the universality and isotopy-isomorphy of (r,s,t)-inverse quasigroups and loops with applications to cryptography

Authors: R. Ilemobade, O. George and T. G. Jaiyeola

Abstract

This paper introduced a condition called $\mathcal{R}$-condition under which $(r,s,t)$-inverse quasigroups are universal. Middle isotopic $(r,s,t)$-inverse loops, satisfying the $\mathcal{R}$-condition and possessing a trivial set of $r$-weak inverse permutations were shown to be isomorphic; isotopy-isomorphy for $(r,s,t)$-inverse loops. Isotopy-isomorphy for $(r,s,t)$-inverse loops was generally characterized. With the $\mathcal{R}$-condition, it was shown that for positive integers $r$, $s$ and $t$, if there is a $(r,s,t)$-inverse quasigroup of order $3k$ with an inverse-cycle of length $gcd(k,r+s+t)>1$, then there exists an $(r,s,t)$-inverse quasigroup of order $3k$ with an inverse-cycle of length $gcd\big(k(r+s+t), (r+s+t)^2\big)$. The procedure of application of such $(r,s,t)$-inverse quasigroups to cryptography was described and explained, while the feasibility of such $(r,s,t)$-inverse quasigroups was illustrated with sample values of $k,r,s$ and $t$.

R. Ilemobade and T. G. Jaiyeola
Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
E-mail: , ,

G.Olufemi
Department of Mathematics, University of Lagos, Akoka, Yaba, Nigeria.
E-mail:

DOI

https://doi.org/10.56415/qrs.v31.04

Fulltext

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