This paper presents two new improved attacks on the KMOV cryptosystem. KMOV is an encryption algorithm based on elliptic curves over the ring (formula presented) is a product of two large primes of equal bit size. The first attack uses the properties of the convergents of the continued fraction expansion of a specific value derived from the KMOV public key. The second attack is based on Coppersmith’s method for finding small solutions of a multivariate polynomial modular equation. Both attacks improve the existing attacks on the KMOV cryptosystem.