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计算机工程 ›› 2009, Vol. 35 ›› Issue (8): 169-170. doi: 10.3969/j.issn.1000-3428.2009.08.057

• 安全技术 • 上一篇    下一篇

椭圆曲线密码标量乘的 -NAFw分解

丁 勇1,2   

  1. (1. 桂林电子科技大学数学与计算科学学院,桂林 541004;2. 西安电子科技大学计算机网络与信息安全国家重点实验室,西安 710071)
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2009-04-20 发布日期:2009-04-20

-NAFw Decomposition of Scalar Multiplication of ECC

DING Yong1,2   

  1. (1. School of Mathematics and Computational Science, Guilin University of Electronic and Technology, Guilin 541004;2. National Key Laboratory of Computer Networks and Information Security, Ministry of Education, Xidian University, Xi’an 710071)
  • Received:1900-01-01 Revised:1900-01-01 Online:2009-04-20 Published:2009-04-20

摘要: 对于GF(p)上的椭圆曲线的标量乘计算,Ciet通过引入特征多项式为 的自同态 ,提出一种整数k的 -NAF分解。对 -NAF分解使用窗口技术得到k的 -NAF 分解,通过一定量的存储可以获取更快的计算速度。对该分解的长度和Hamming密度进行较为准确的估计。

关键词: 椭圆曲线密码, 标量乘, 窗口技术, 自同态

Abstract: For fast computation of scalar multiplication of the elliptic curve over GF(p), with the utilization of the endomorphism whose characteristic polynomial is , -NAF expansion of the integer k is proposed by Ciet in order to speed up the computation of scalar multiplication kP. In this paper, a window technic is applied to the -NAF representation, which gets the -NAF decomposition of k and can obtain better result than -NAF representation with the cost of some quantities of storages. The length and the density of the expansion is accurately estimated.

Key words: Elliptic Crypty Curves(ECC), scalar multiplication, window technic, endomorphism

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