A study of the holomorphy of (<i>r, s, t</i>)-inverse loops

Oyebo, Yakub 'Tunde; Jaiyeola, Temitope Gbolahan; Adeniran, John Olushola

doi:10.1080/09720529.2021.1885810

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2023

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“…lá and Adeniran [14], Jaiyéo . lá and Smarandache [17], Oyebo et al [25]. A universal WIPL is an Osborn loop.…”

Section: Introductionmentioning

confidence: 96%

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

Ilemobade,

George,

Gbolahan

2023

QRS

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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 $t$.

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“…lá and Adeniran [14], Jaiyéo . lá and Smarandache [17], Oyebo et al [25]. A universal WIPL is an Osborn loop.…”

Section: Introductionmentioning

confidence: 96%