## Cryptology ePrint Archive: Report 2008/257

ON MIDDLE UNIVERSAL $m$-INVERSE QUASIGROUPS AND THEIR APPLICATIONS TO CRYPTOGRAPHY

JAIYEOLA Temitope Gbolahan

Abstract: This study presents a special type of middle isotopism under which $m$-inverse quasigroups are isotopic invariant. A sufficient condition for an $m$-inverse quasigroup that is specially isotopic to a quasigroup to be isomorphic to the quasigroup isotope is established. It is shown that under this special type of middle isotopism, if $n$ is a positive even integer, then, a quasigroup is an $m$-inverse quasigroup with an inverse cycle of length $nm$ if and only if its quasigroup isotope is an $m$-inverse quasigroup with an inverse cycle of length $nm$. But when $n$ is an odd positive integer. Then, if a quasigroup is an $m$-inverse quasigroup with an inverse cycle of length $nm$, its quasigroup isotope is an $m$-inverse quasigroup with an inverse cycle of length $nm$ if and only if the two quasigroups are isomorphic. Hence, they are isomorphic $m$-inverse quasigroups. Explanations and procedures are given on how these results can be used to apply $m$-inverse quasigroups to cryptography, double cryptography and triple cryptography.

Category / Keywords: $m$-inverse quasigroups, ${\cal T}_m$ condition,length of inverse cycles, cryptography

Publication Info: Submitted for Publication

Date: received 4 Jun 2008, last revised 4 Jun 2008

Contact author: tjayeola at oauife edu ng

Available format(s): PDF | BibTeX Citation

Note: m-inverse quasigroups are generalizations of weak and cross inverse loops which are useful in cryptography.

[ Cryptology ePrint archive ]