Abstract

. Elliptic curves over the ring ZZ=nZZ where n is the product of two large primes have first been proposed for public key cryptosystems in [4]. The security of this system is based on the integer factorization problem, but it is unknown whether breaking the system is equivalent to factoring. In this paper, we present a variant of this cryptosystem for which breaking the system is equivalent to factoring the modulus n. Moreover, we extend the ideas to get a signature scheme based on elliptic curves over ZZ=nZZ. 1 Introduction In recent years, elliptic curves over finite fields have gained a lot of attention. The use of elliptic curves over finite fields in public key cryptography was suggested by Koblitz [3] and Miller [7]. The security of these cryptosystems is based on the difficulty of the discrete logarithm problem in the group of points on an elliptic curve. Later Vanstone et. al. proposed to use elliptic curves over the ring ZZ=nZZ, where n is the product of two large prime num...

Citations