椭圆曲线离散对数的攻击现状

椭圆曲线密码的数学基础是基于椭圆曲线上的有理点构成的Abelian加法群构造的离散对数问题，讨论了椭圆曲线离散对数问题及其常用的理论攻击方法，分析了一些特殊曲线的攻击方法及最近的提出的一个新攻击方法-Weil Descent攻击（或GHS攻击），给出了椭圆曲线离散对数的实际攻击-软件攻击和硬件攻击现状。

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.