CM算法的一种改进

为了抵抗诸如MOV等算法可能的攻击，在CM算法的基础上，对有限域上椭圆曲线的构造方法进行了改进，使椭圆曲线子群且其阶中含有多个大素因子，并在满足安全性条件下对形式为2p+1的大素因子放宽到包括形式为2ip+1的素数(i 是一个小整数).这类椭圆曲线可用于密码技术中各种合数阶群的情形.在这类椭圆曲线上建立密码体制，降低了离散对数型保密或数字签名方案信息泄露的隐患，为建立可抗击各种攻击的椭圆曲线密码体制提供了基础.同时，还对改进后的算法进行了算法分析，表明用该算法来产生安全椭圆曲线在速度上比CM算法快.

An improved complex multiplication algorithm

An efficient algorithm of generate elliptic curves for public key cryptosystems based on discrete logarithm is presented to resist possible attacks such as MOV reduction.The algorithm differs from the(existing) methods of building an elliptic curve with nearly prime order.An elliptic curve constructed by this method contains two large prime factors and satisfies conditions of security.This kind of elliptic curve can be used for various situations where composite order groups are needed.In the cryptosystems based on such elliptic curves,the leakage of information is prevented,and then the cryptosystems are also robust against attacks.Algorithm analysis has been done.Results show that it is much faster to generate a suitable(elliptic) curve with new-scheme than with original scheme.