The status of attack on the discrete logarithm of elliptic curves

The study of elliptic curve cryptography is now becoming a focus in public key cryptosystems, and its security relies on the difficulty to solve the discrete logarithm problem of the elliptic curve abelian group. Because of the rich group structure, multi-selectivity and the highest security per bit key, the elliptic curve is of endless use in cryptography field. In this paper, we first discussed the discrete logarithm problem of elliptic curves and the available attack in theory, and then analyzed some attack methods on a few special curves and a new attack: Weil descent attack. Finally we presented the practical attack status on the discrete logarithm problem of the elliptic curve-attack by software and hardware.