Abstract:

This paper presents a new fast scalar multiplication algorithm on elliptic curve cryptography. This algorithm greatly reduces times of addition operation which takes time for scalar multiplication algorithm by introducing signed and unsigned sliding window coding methods. By theoretic analysis and experiment, signed sliding window coding method is better than NAF algorithm and unsigned sliding window coding method, and it is also able to improve the efficiency of scalar multiplication algorithm compared with accustomed algorithm. And the optimal sliding window width is given.

Key words: Elliptic curve cryptography, Scalar multiplication, Sliding window coding, Non-adjacent form

摘要： 基于椭圆曲线密码，提出了一种快速标量乘算法。此算法通过引入有符号和无符号滑动窗口编码方法，大大减少了标量乘算法中费时的加法运算次数。经理论分析和实验结果表明，运用有符号滑动窗口编码方法比NAF算法和无符号窗口编码方法更有优势，可以使标量乘算法比通常的算法效率提高更多。并且给出了最佳滑动窗口的宽度。

关键词: 椭圆曲线密码, 标量乘, 滑动窗口编码, NAF

CLC Number: 

• TP309