一种改进的Fixed-base Comb安全快速算法

An Improved Fixed-base Comb Method with High Speed and Security

本文从分析椭圆曲线上Fixed-baseComb算法出发,根据其特点,利用牺牲乘法操作以降低求逆操作的方法,分别用2kP、2P+Q的快速算法对Fixed-baseComb算法的预计算阶段和赋值阶段进行改进,极大地提高了计算效率:在素数域上预计算阶段提高70%～80%,而赋值阶段提高38%～43%,同时,改进算法通过对k的预处理,使得算法能够抵抗边际信道攻击.

According to the Fixed-base comb method＇s features, this paper apply the direct computations of 2^kP and 2P＋Q to the comb method＇s precomputation and evaluation stage respectively. Taking advantage of trading inversions for multiplications, the improved method is able to obtain about 70-80% improvement in precomputation stage and a range of 38%- 43 % in evaluation stage over prime field, furthermore, our improved method is resistant to side channel attack by pretreating the scalar k.