A New Multi-Party Key Exchange Protocol and Symmetric Key Encryption Scheme over Non-commutative Group Rings

Özet

The importance of secure communication over an insecure channel has increased day by day in almost all applications such as commercial purposes, money transactions, military and sanitary services. Therefore, many encryption algorithms based on various types of algebraic structures have become more considerable because of the underlying mathematically hard problems such as integer factorization, discrete logarithm, conjugacy search problem in group theory, finding the inverse of a given unit in group rings. Key exchange protocols also have monumental significance for generating shared keys between parties by exchanging cryptographic 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 key exchange protocol then we generalize this to a multi-party type key exchange protocol using units in a given group ring and finally we propose a symmetric key encryption scheme over a non-commutative group ring which is different from the encryption scheme in [1] by illustrating a concrete example. We also give a security analysis of the proposed protocol and comparisons with [1] and [8].