Public key cryptosystem and signature schemes over the ring of eisenstein integers

In this paper, the extended ElGamal public key cryptosystem and digital signature schemes with appendix and message recovery are described in the setting of the groups of units of the ring of Eisenstein integers modulo Eisenstein primes. This approach has many advantages over the classical ElGamal cryptosystem and digital signature scheme.Many examples are given to show the validity of the proposed extensions of the ElGamal public key cryptosystem and digital signature schemes.