A new ElGamal-like cryptosystem based on matrices over groupring

In this paper, we have developed a new ElGamal-like public key cryptosystem based on the matrices over a groupring. The underlying hard problem for this cryptosystem is the conjugacy search problem. That is, we have replaced the exponentiation of elements by conjugacy. This makes the key generation step more efficient. We also talk about different security aspects against known attacks. The proposed scheme is found to be secure against known plaintext attack when encryption uses a different random key for every new plaintext.