一种新的七元联合稀疏型表示及其应用
doi: 10.3724/SP.J.1146.2011.00686
New Seven-element Joint Sparse Form for Pairs of Integers and Its Applications
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摘要: 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。
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关键词:
- 椭圆曲线密码体制 /
- 新七元联合稀疏型 /
- 标量乘法 /
- 联合Hamming密度
Abstract: 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. -
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