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- Title
On the universality and isotopy-isomorphy of (r, s, t)-inverse quasigroups and loops with applications to cryptography.
- Authors
Ilemobade, Richard; George, Olufemi; Jaíyéolá, Tèmítópé Gbóláhàn
- Abstract
This paper introduced a condition called R-condition under which (r, s, t)- inverse quasigroups are universal. Middle isotopic (r, s, t)-inverse loops, satisfying the 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 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 k(r + s + t),(r + s + t) ² ) . 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.
- Publication
Quasigroups & Related Systems, 2023, Vol 31, Issue 1, p53
- ISSN
1561-2848
- Publication type
Article
- DOI
10.56415/qrs.v31.04