基于多基数系统的有效标量乘算法

首先给出了椭圆曲线上点P的7倍点公式7P,当i]/m]=6时,它比直接计算节省运算量7.4%～30.56%。作为双基数系统的一个推广,多基数系统具有标量表示长度更短、汉明重量更小的特点,较适用于椭圆曲线标量乘的快速计算。结合以上给出的公式,提出了一个以2,3和7作为基底的多基数系统计算椭圆曲线标量乘的有效算法,所提方法计算量更少。

Fast Scalar Multiplication Based on MBNS

Firstly, this paper gives the 7P formula of point P which is on the elliptic curve, and it saves 7.4% - 30.56% than directly computation. Then as a generalization of double base chains, multibase number system is very suitable for efficient compu- tation of scalar multiplication of a point of elliptic curve because of shorter representation length and hamming weight. Combined with the given formulas for computing the 7 -fold of an elliptic curve point P, an efficient scalar multiplication algorithm of elliptic curve is proposed using 2, 3 and 7 as basis of the multi based number system and the proposed algorithms cost less.