A key exchange protocol using matrices over group ring

Abstract

The first published solution to key distribution problem is due to Diffie–Hellman, which allows two parties that have never communicated earlier, to jointly establish a shared secret key over an insecure channel. In this paper, we propose a new key exchange protocol in a non-commutative semigroup over group ring whose security relies on the hardness of Factorization with Discrete Logarithm Problem (FDLP). We have also provided its security and complexity analysis. We then propose a ElGamal cryptosystem based on FDLP using the group of invertible matrices over group rings.