On middle universal weak and cross inverse property loops with equal length of inverse cycles

This study presents a special type of middle isotopism under which the weak inverse property (WIP) is isotopic invariant in loops. A sufficient condition for a WIPL that is specially isotopic to a loop to be isomorphic to the loop isotope is established. It is shown that under this special type of middle isotopism, whenever $n$ is a positive even integer, a finite WIPL has an inverse cycle of length $n$ if and only if its isotope is a finite WIPL with an inverse cycle of length $n$. But, when $n$ is an odd positive integer and a loop (or its isotope) is a finite WIPL with only $e$ and inverse cycles of length $n$, then its isotope (or the loop) is a finite WIPL with only $e$ and inverse cycles of length $n$ if and only if they are isomorphic. Hence, both are isomorphic CIPLs. Explanations and procedures are given on how these results can be used to apply CIPLs to cryptography.

• Autores: Temitope Gbolahan, Jaiyeola
• Tipo de recurso: Article of journal
• Fecha de publicación: 2010
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/39763
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/39763; http://bdigital.unal.edu.co/29860/
• Palabra clave: Cross inverse property loops (CIPLs); Weak inverse property loops (WIPLs); Inverse cycles; 20NO5; 08A05
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional