一种新的七元联合稀疏型表示及其应用

摘要

In order to improve the computing efficiency of k1P + k2Q 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 k1P + k2Q , the new seven-element JSF reduces 0.1977/ point additions comparing with the optimal three-element JSF, and reduces 0.031/ point additions comparing with an existing five-element JSF, and reduces 0.0392l point additions comparing with another existing seven-element JSF.%为了进一步提高椭圆曲线密码体制中k1P +k2Q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k1P+ k2Q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.