Three cryptographic identities in left universal Osborn loops

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I recommend them for or 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 left 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).

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