基于N进制位权下NAF的椭圆曲线标量乘算法

An Elliptic Curve Scalar Multiplication Algorithm Based on Non-Adjacent Forms in N-Ary Bit Weight

椭圆曲线上的标量乘是影响椭圆曲线密码体制实现效率的重要因素之一。为了提高椭圆曲线密码体制运算效率,通过分析倍点运算,点加运算,3P运算,2sP运算等实现点乘的运算细节,提出一种基于N进制位权下非相邻形式的椭圆曲线标量乘算法。该算法提出的N进制位权的非相邻形式,可以减少算法中主要循环步骤中的点加和N倍点的运算次数。实验显示,与同类算法对比,该算法的计算效率提高26.91%~31.72%。

The scalar multiplication on the elliptic curve is one of the important factors affecting the efficiency of elliptic curve cryptosystem implementation.In order to improve the efficiency of elliptic curve cryptography,An Elliptic Curve Scalar Multiplication Algorithm Based on Non-adjacent Forms in N-ary Bit Weight is proposed by analyzing double point operation,addition operation,3P operation,2s P operation and so on.The non-neighboring form of the N-ary bitwise weight proposed by the algorithm can reduce the number of times on point operation and addition operation in the main loop step in the algorithm.Experiments show that compared with similar algorithms,The computational efficiency of this algorithm has improved by 26.91%~31.72%.