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 is a positive even integer, then, a quasigroup is an -inverse quasigroup with an inverse cycle of length if and only if its quasigroup isotope is an -inverse quasigroup with an inverse cycle of length . But when is an odd positive integer. Then, if a quasigroup is an -inverse quasigroup with an inverse cycle of length , its quasigroup isotope is an -inverse quasigroup with an inverse cycle of length if and only if the two quasigroups are isomorphic. Hence, they are isomorphic -inverse quasigroups. Explanations and procedures are given on how these results can be used to apply -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
-inverse quasigroups 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

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}
}
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