The public-key cryptosystem based on discrete logarithm over group rings is proposed. Using the fact that the order of a matrix in the general linear group on a finite field is equal to that of its Jordan′s normal form and the linear algebra theory over finite field, the existence and construction of invertible elements in a kind of commutative group rings based on a general linear group are given, and it is shown that the problem of discrete logarithm problem exists in these group rings. Using these good cryptography properties in these group rings, a public-key cryptosystem based on them is given. At last, the security level of this cryptosystem, the cost of computation and the method of implementation are discussed. Also, the feasibility of this cryptography is proved by an example.

group ring; automorphism; discrete logarithm problem; general linear group