A new attack on the KMOV cryptosystem

Abstract

In this paper, we analyze the security of the KMOV public key cryptosystem. KMOV is based on elliptic curves over the ring ℤn where n = pq is the product of two large unknown primes of equal bitsize. We consider KMOV with a public key (n, e) where the exponent e satisfies an equation ex–(p+1)(q+1)y = z, with unknown parameters x, y, z. Using Diophantine approximations and lattice reduction techniques, we show that KMOV is insecure when x, y, z are suitably small.