A NEW ATTACK ON THE KMOV CRYPTOSYSTEM
Abderrahmane Nitaj · Bulletin of the Korean Mathematical Society · 2014
In this paper, we analyze the security of the KMOV public key cryptosystem. KMOV is based on elliptic curves over the ring $\mathbb{Z}_n$ where n = pq is the product of two large unknown primes of equal bit-size. 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.