抗能量攻击的新标量乘算法

标量乘算法是椭圆曲线密码中最基础也是最关键的运算,对整个密码体制的效率和安全性具有举足轻重的作用.在分析NAF(Non-Adjacent Form)标量乘算法和能量分析攻击基础上,综合考虑标量乘算法的速度和安全性,提出一种随机高效的ECC快速算法——改进的随机标量乘算法.与已有算法相比,该算法在保证同NAF等汉明重量的基础上,克服了由于引入随机变量所导致的冗余计算,实现了速度与安全的折中；也克服了NAF标量乘中需要预存储标量的不足,提高了存储效率.同时通过引入随进变量,每次产生不同的随机NAF表示,增强了抗SPA、DPA的攻击.

NEW SCALAR MULTIPLICATION ALGORITHM WITH POWER ATTACKS RESISTANCE

Scalar multiplication is the most basic and critical operations in elliptic curve cryptography,which plays a pivotal role in the efficiency and security of the cryptography.Based on the analysis of NAF scalar multiplication algorithm and the power analysis attacks,and taking into account the speed and security of the scalar multiplication comprehensively,a stochastic efficient fast ECC algorithm,the modified scalar multiplication algorithm,is proposed.Compared with the existing algorithms,it overcomes the redundant computation resulting from the introduction of the random variables and achieves the compromise between the speed and the security on the basis of ensuring the same hamming weight for same NAF;Apart from that,it also overcomes the problem of NAF scalar multiplication which needs to pre-store the scalar and therefore improves the storage efficiency.Meanwhile,it strengthens the resistance against SPA and DPA attacks by introducing the following variable yielding different stochastic NAF expression each time.