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

In order to improve the computing efficiency ofk1P+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 0.1977l 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.