Diophantine Approximation Attack on a Fast Public Key Cryptosystem

Abstract

At ACISP 2000, H. Yoo etc. proposed a public key cryptosystem using matrices over a ring, which was analyzed using lattice basis reduction algorithms by Youssef etc. at ACISP 2001. In this paper, another attack, namely Diophantine approximation attack, is presented. It is shown that the decryption of the cryptosystem can be transformed into solving the simultaneous Diophantine approximation problem, which can be approximated by lattice basis reduction algorithms. So we heuristically explain that the scheme is insecure. Furthermore, our new attack is more general than lattice attack.