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Title:
ON MIDDLE UNIVERSAL m-INVERSE QUASIGROUPS AND THEIR APPLICATIONS TO CRYPTOGRAPHY
Authors: 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.
ePrint: https://eprint.iacr.org/2008/257
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