ON THE ONE-WAY ALGEBRAIC HOMOMORPHISM

In this paper we discuss the relation between a one-way group homomorp hism and a one-way ring homomorphism. Let U,V be finite abelian groups with #U = n. We show that if there exists a one-way group homomorphis m f: U --> V, then there exists a one-way ring homomorphism F: Z(n) U --> Z(n) + Im f. We also give examples of such ring homomorphisms wh ich are one-way under a standard cryptographic assumption. This implie s that there is an affirmative solution to an extended version of the open question raised by Feigenbaum and Merrit: Is there an encryption function f such that both f(x + y) and f(x . y) can be efficiently com puted from f(x) and f(y) ? A multiple signature scheme is also given a s an application of one-way ring homomorphisms.