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

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

CLC Number: 

• TN918.2