Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 5 (2010), 17 -- 34


T. G. Jaiyéolá and J. O. Adéníran

Abstract. In this study, by establishing an identity for universal Osborn loops, two other identities (of degrees 4 and 6) are deduced from it and they are recognized and recommended for cryptography in a similar spirit in which the cross inverse property (of degree 2) has been used by Keedwell following the fact that it was observed that universal Osborn loops that do not have the 3-power associative property or weaker forms of; inverse property, power associativity and diassociativity to mention a few, will have cycles (even long ones). These identities are found to be cryptographic in nature for universal Osborn loops and thereby called cryptographic identities. They were also found applicable to security patterns, arrangements and networks which the CIP may not be applicable to.

2000 Mathematics Subject Classification: 20NO5; 08A05.
Keywords: Universal Osborn loops; Cryptography.

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T. G. Jaiyéolá
Obafemi Awolowo University,
Department of Mathematics,
Ile Ife 220005, Nigeria.

J. O. Adéníran
University of Agriculture,
Department of Mathematics,
Abeokuta 110101, Nigeria.