基于折半运算的带符号阶乘展开式标量乘算法  

The Scalar Multiplication Algorithm of Signed Factorial Expansion Based on Point Halving

作　　者：庞根明[1] 

机构地区：[1]晋城职业技术学院信息工程系

出　　处：《控制工程》2018年第3期504-508,共5页Control Engineering of China

基　　金：国家自然科学基金资助项目(51308126)

摘　　要：阶乘展开表示形式标量乘算法是椭圆曲线密码的一种快速标量乘算法。为能进一步有效提升阶乘展开表示形式的标量乘算法的计算效率，且因折半运算比倍点运算的执行效率更加高效，通过把折半运算的方法应用在带符号的阶乘展开表示形式的标量乘算法中，在预计算和主循环计算阶段分别用折半运算替代倍点运算，提出了一种基于折半运算的带符号阶乘展开式标量乘算法。算法的性能分析结果表明：与传统的阶乘展开表示形式标量乘算法相比，新算法的运算效率提高了约60．78％。The scalar multiplication algorithm of factorial expansion representation is a fast scalar multiplication algorithm in elliptic curve cryptography. Due to that point halving has higher execution efficiency than double operations, point halving is applied in the signed factorial expansion scalar multiplication algorithm in order to further improve the factorial expansion scalar multiplication algorithms, and then a signed factorial expansion scalar multiplication based on point halving is proposed in which the double operation is replaced by the point halving in the stage of pre-computation and the main loop. The performance analysis results show that the new algorithm could improve the efficiency by 60.78 % compared with the traditional factorial expansion scalar multiplication algorithm.

关 键 词：圆曲线密码 标量乘法 带符号阶乘展开式算法 折半运算 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]