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Paper 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.

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

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Available format(s)
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Publication info
Published elsewhere. Submitted for Publication
Keywords
$m$-inverse quasigroups${\cal T}_m$ conditionlength of inverse cyclescryptography
Contact author(s)
tjayeola @ oauife edu ng
History
2008-06-10: received
Short URL
https://ia.cr/2008/257
License
Creative Commons Attribution
CC BY
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