一种新的七元联合稀疏型表示及其应用

New Seven-element Joint Sparse Form for Pairs of Integers and Its Applications

为了进一步提高椭圆曲线密码体制中1 2k P+k Q的计算效率,该文提出了一种新的七元联合稀疏型。对任一整数对,给出了新七元联合稀疏型的定义和算法,证明了新七元联合稀疏型的唯一性,并证明了新七元联合稀疏型的平均联合Hamming密度约为0.3023。采用新七元联合稀疏型计算k 1 P+k 2Q时,比最优三元联合稀疏型减少了0.1977l次点加运算,比一种五元联合稀疏型减少了0.031l次点加运算,比另一种七元联合稀疏型减少了0.0392l次点加运算。

In order to improve the computing efficiency of in elliptic curve cryptosystem,a new seven-element Joint Sparse Form（JSF） is proposed in this paper.For any pair of integers,the definition and calculating algorithm of the new seven-element JSF are given,and the uniqueness of the new seven-element JSF is proven.Besides,it is also proven that the average joint Hamming density of the new seven-element JSF is 0.3023.When computing,the new seven-element JSF reduces 0.1977l point additions comparing with the optimal three-element JSF,and reduces 0.031l point additions comparing with an existing five-element JSF,and reduces 0.0392l point additions comparing with another existing seven-element JSF.