椭圆曲线密码体制中的快速点乘算法

点乘运算是实现椭圆曲线密码体制的基本运算,同时也是最耗时的运算,它的运算效率直接决定着ECC的性能。本文从三方面分析了椭圆曲线密码体制中快速点乘的实现,并将Marc Joye和Sung-Ming Yen提出的具有最小汉明重的从左到右带符号二进制编码应用于椭圆曲线密码体制的点乘算法中,生成了一个能快速实现的二进制编码新点乘算法,适用于计算能力和集成电路空间受限,要求高速实现的情况。

Fast Algorithm for Scalar Multiplication in Elliptic Curve Cryptography

Scalar multiplication is the basic operation in realizing elliptic curve cryptography,at the same time is the most time-consuming operation.Its efficiency determines the performance of ECC.This paper analyzes the fast realization of scalar multiplication from three aspects,and applies the minimum-weight Left-to-right Recoding Algorithm proposed by Marc Joye and Sung-Ming Yen to scalar multiplication.The new algorithm is particularly applicable in the case that we are required to operate at high speed when both computational ability and memory of integrate circuit are limited.