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.
Metadata
- Available format(s)
-
PDF
- 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
-
CC BY
BibTeX
@misc{cryptoeprint:2008/257,
author = {JAIYEOLA Temitope Gbolahan},
title = {{ON} {MIDDLE} {UNIVERSAL} $m$-{INVERSE} {QUASIGROUPS} {AND} {THEIR} {APPLICATIONS} {TO} {CRYPTOGRAPHY}},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/257},
year = {2008},
url = {https://eprint.iacr.org/2008/257}
}
