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为了抵抗椭圆曲线密码的边信道攻击,提出了一种新型快速安全的标量乘算法.该算法是一种基于仅有点加运算的特殊加法链,可自然地抵抗边信道攻击.此外,提出在一种新型点加运算公式中引进特殊结构的加法链,可以大大提高标量乘算法的运算效率.对于长度为160比特的整数,其特殊加法链长度为260时,仅仅需要1 719次乘法运算.特殊加法链长度为280 ~260时,运行标量乘算法比倍点-点加算法效率上提高26%~31%,比NAF算法快16%~22%,比4-NAF算法快7%~13%,比目前最好的方法双基链算法还要快1%~8%.
In order to resist the edge channel attack of elliptic curve cryptography, a new fast and secure scalar multiplication algorithm is proposed, which is a kind of special additive chain based on only adding and adding points and can naturally resist side channel attacks. In addition, The introduction of a special structure of the addition chain in the new dot addition formula can greatly improve the computational efficiency of the scalar multiplication algorithm. For a length of 160 bits, its special addition chain length of 260, only need 1 719 multiplications. Addition chain length 280 ~ 260, the running scalar multiplication algorithm than the double point - point plus algorithm efficiency increased by 26% ~ 31%, 16% ~ 22% faster than NAF algorithm, faster than 4-NAF algorithm 7% to 13% , Which is even 1% ~ 8% faster than the best double-stranded algorithm currently in use.