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ON MIDDLE UNIVERSAL $m$-INVERSE QUASIGROUPS AND THEIR APPLICATIONS TO CRYPTOGRAPHY
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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. |
BibTeX
@misc{eprint-2008-17934, title={ON MIDDLE UNIVERSAL $m$-INVERSE QUASIGROUPS AND THEIR APPLICATIONS TO CRYPTOGRAPHY}, booktitle={IACR Eprint archive}, keywords={$m$-inverse quasigroups, ${\cal T}_m$ condition,length of inverse cycles, cryptography}, url={http://eprint.iacr.org/2008/257}, note={Submitted for Publication tjayeola@oauife.edu.ng 14034 received 4 Jun 2008, last revised 4 Jun 2008}, author={JAIYEOLA Temitope Gbolahan}, year=2008 }