ElGamal public key cryptosystem and signature scheme in GU(m, p,n)

Abstract

ElGamal public key cryptosystem and signature scheme is extended to the recently discovered group GU(m, p,n) of numbers co-prime to mpn and having analytical representation and known order. Elements of GU(m, p,n) with the maximal order are used as the base elements in the proposed extension instead of primitive roots used in the original scheme. Proposed scheme allows easy periodic change of the group and base elements to provide necessary security level without change of the prime number p contrary to the case of GF( p) used in the original ElGamal scheme. Computation of discrete logarithms in the proposed scheme is difficult for large p. Copyright 2010 ACM.