利用多基链计算椭圆曲线标量乘的高效算法

椭圆曲线标量乘是椭圆曲线密码体制中最耗时的运算,多基链作为双基链的一个推广,具有标量表示长度更短、非零比特数目更少的特点,非常适宜用于椭圆曲线标量乘的快速计算。该文给出了新的五倍点公式,同时以2、3和5作为基底,给出了一个利用多基链计算椭圆曲线标量乘的高效算法。由于多基数表示的高度冗余性,该算法能够抵抗某些边信道攻击,与常用的标准倍点加和非邻接形标量乘算法相比,该算法的运算量更少。

Efficient Scalar Multiplication Algorithm Using Multibase Chains

In the elliptic curve cryptosystem, Scalar multiplication is the most important and computationally costliest operation, thus it becomes one of hot topics. As a generalization of double base chains, multibase chains are very suitable for efficient computation of scalar multiplications of elliptic curves because of shorter representation length and less Hamming weight. In this paper, the formulas for computing the 5-fold of an elliptic curve point P are given. Using 2, 3 and 5 as bases of the multibase chains, an efficient scalar multiplication algorithm of elliptic curve is proposed. This algorithm can offer some protections against some side-channel attacks for the huge redundancy of the multibase representation and cost less compared with stand double-and-add and nonadjacent form for scalar multiplications.