On Another Two Cryptographic Identities In Universal Osborn Loops

TL;DR

This paper introduces new cryptographic identities derived from universal Osborn loops, which are useful for cryptography and security applications where traditional properties like CIP do not apply.

Contribution

It derives two novel identities of degrees 4 and 6 from a fundamental identity in universal Osborn loops, expanding cryptographic tools.

Findings

Identified cryptographic identities of degrees 4 and 6

Applicable to security patterns beyond CIP scope

Enhances cryptographic methods in non-associative loops

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.