椭圆曲线标量乘算法的改进  

Improvement of Scalar Multiplication Algorithm in Elliptic Curve

作　　者：王媛[1] 辛小龙[1] 戢伟[1] 

机构地区：[1]西北大学数学系,西安710127

出　　处：《计算机工程》2008年第18期167-168,共2页Computer Engineering

基　　金：陕西省自然科学基金资助项目(2007A19)

摘　　要：椭圆曲线密码体制的快速实现依赖于标量乘(nP)的有效计算,该文改进n的二进制和三进制的混合表示方法,并且将其推广到n的二进制、三进制和五进制的混合表示。该算法在已知二倍点、三倍点和五倍点运算量的基础上,经过恰当的运算计算标量乘。试验结果表明,该算法减少计算标量乘的运算量,能有效地计算标量乘。In accordance with the problem that the fast implementation of elliptic curve cryptosystems relies on the efficient computation of scalar multiplication, this paper improves the mixed binary and ternary method to express n, generalizes the mixed binary, ternary and quinary method to express n. Based on the computation of double point, triple point, and quintuple point, it computes scalar multiplication nP by using proper operations. Results show that the approaches lead to lower complexity which contributes to the efficient implementation of elliptic curve scalar multiplication.

关 键 词：椭圆曲线密码体制 标量乘 非相邻形式 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]