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Elliptic curves over the ring Z/nZ 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 Z/nZ.

A Public Key Cryptosystem Based on Elliptic Curves over ℤ/nℤ Equivalent to Factoring