基于青铜比例加法链的椭圆曲线标量乘算法  

Elliptic curve scalar multiplication algorithm based on bronze ratio addition chain

作　　者：刘双根 李丹丹 李潇 LIU Shuang-gen;LI Dan-dan;LI Xiao(School of Telecommunication and Information Engineering,Xi’an University of Posts and Telecommunications,Xi’an 710121,Shaanxi,China)

机构地区：[1]西安邮电大学通信与信息工程学院

出　　处：《山东大学学报（理学版）》2019年第11期12-19,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61872292);陕西省自然科学基金资助项目(2017JQ6010)

摘　　要：提出一种新的高效安全的椭圆曲线标量乘算法。基于广义的斐波那契数列,提出一个新的加法链,称之为青铜比例加法链(bronze ratio addition chain, BRAC)。该算法每次都迭代执行"3P1+P2"运算,天然具有抵抗简单功耗攻击的性质。BRAC链长较短,结合新的投影坐标,提高了运算效率。实验结果表明,BRAC的标量乘算法比黄金比例加法链(GRAC)快31.73%。A new efficient and secure elliptic curve scalar multiplication algorithm is proposed. There is an new addition chain based on generalized Fibonacci sequences, which is called bronze ratio addition chain(BRAC). Each iteration of this algorithm executes fixed "3P1+P2" operation, which can resist the simple power analysis naturally. BRAC has a shorter chain length, combined with the new projection coordinates can improve efficiency of the previous ones. The experimental results show that the new algorithm is 31.73% faster than golden ratio addition chain(GRAC).

关 键 词：标量乘 青铜比例加法链 简单功耗攻击 效率 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]