探测窗口的NAFω算法

摘要

The point multiplication on elliptic curves is a key operation for Elliptic Curve Cryptography.Its speed affect the speed of ECC directly.The width w of the non-adjacent form（NAF） algorithm is analyzed and a NAFω algorithm for detection window is proposed by the character of NAF in this article.This algorithm reduces the number of times for the shift operations and XOR to shorten the computing time.The modeling and simulation results show that the time consumption of detection window method is about times for the original algorithm and the computational efficiency is also improving with ω increase.%椭圆曲线上的点乘运算是椭圆曲线加密（ECC）的一个关键运算,它的速度直接影响椭圆曲线加密的速度。本文分析了窗口宽度w的非相邻表示型（NAFω）算法,根据NAF的性质提出了一个探测窗口的NAFω算法。本算法减少了运算中的移位和异或运算次数,缩短了运算时间。经建模仿真,结果表明本算法的时间消耗大约是原算法的1/（ω＋1）倍,且随ω的增大运算效率也在提高。