Efficient Scalar Multiplication for Elliptic Curves over Binary Fields  

作　　者：GU Haihua GU Dawu LIU Ya 

机构地区：[1]School of Electronic, lnforamation and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

出　　处：《Wuhan University Journal of Natural Sciences》2008年第6期717-720,共4页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China (60573031)

摘　　要：Scalar multiplication [n]P is the kernel and the most time-consuming operation in elliptic curve cryptosystems. In order to improve scalar multiplication, in this paper, we propose a tripling algorithm using Lopez and Dahab projective coordinates, in which there are 3 field multiplications and 3 field squarings less than that in the Jacobian projective tripling algorithm. Furthermore, we map P to（φε^-1（P）, and compute [n]（φε^-1（P） on elliptic curve Eε, which is faster than computing [n]P on E, where φε is an isomorphism. Finally we calculate （φε（[n]φε^-1（P）） = [n]P. Combined with our efficient point tripling formula, this method leads scalar multiplication using double bases to achieve about 23% improvement, compared with Jacobian projective coordinates.Scalar multiplication [n]P is the kernel and the most time-consuming operation in elliptic curve cryptosystems. In order to improve scalar multiplication, in this paper, we propose a tripling algorithm using Lopez and Dahab projective coordinates, in which there are 3 field multiplications and 3 field squarings less than that in the Jacobian projective tripling algorithm. Furthermore, we map P to（φε^-1（P）, and compute [n]（φε^-1（P） on elliptic curve Eε, which is faster than computing [n]P on E, where φε is an isomorphism. Finally we calculate （φε（[n]φε^-1（P）） = [n]P. Combined with our efficient point tripling formula, this method leads scalar multiplication using double bases to achieve about 23% improvement, compared with Jacobian projective coordinates.

关 键 词：elliptic curve cryptosystem scalar multiplication double-base number system projective coordinates 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]