Improved Cryptanalysis of the KMOV Elliptic Curve Cryptosystem

Abderrahmane Nitaj (1) , Willy Susilo (2) , Joseph Tonien (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 University of Wollongong [Australia]

This paper presents two new improved attacks on the KMOV cryptosystem. KMOV is an encryption algorithm based on elliptic curves over the ring ZN where N = pq 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.

Domains: Computer Science [cs]; Cryptography and Security [cs.CR]

Abderrahmane Nitaj, Willy Susilo, Joseph Tonien. Improved Cryptanalysis of the KMOV Elliptic Curve Cryptosystem. Provable Security ProvSec 2019, 2019, Cairns, Australia. ⟨10.1007/978-3-030-31919-9_12⟩. ⟨hal-02320906⟩