A New Multi-Party Key Exchange Protocol and Symmetric Key Encryption Scheme Over Non-Commutative Group Rings

Abstract

The importance of secure communication over an insecure channel has increased day by day in almost all applicationssuch as commercial purposes, money transactions, military and sanitary services. Therefore, many encryption algorithms basedon various types of algebraic structures have become more considerable because of the underlying mathematically hard problemssuch as integer factorization, discrete logarithm, conjugacy search problem in group theory, finding the inverse of a given unit ingroup rings. Key exchange protocols also have monumental significance for generating shared keys between parties by exchangingcryptographic keys to allow a secure communication.In this paper, we first briefly mention about the basics of group rings, the fundamental properties of units, Diffie-Hellman type keyexchange protocol then we generalize this to a multi-party type key exchange protocol using units in a given group ring and finallywe propose a symmetric key encryption scheme over a non-commutative group ring which is different from the encryption schemein [1] by illustrating a concrete example. We also give a security analysis of the proposed protocol and comparisons with [1] and[8].