A Markov-Chain Based Performance Analysis Method for Scalar Multiplication on Elliptic Curve

TANG Wen; TANG Li-yong; CHEN Zhong

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A Markov-Chain Based Performance Analysis Method for Scalar Multiplication on Elliptic Curve

更新时间：2025-07-16

- A Markov-Chain Based Performance Analysis Method for Scalar Multiplication on Elliptic Curve
- Acta Electronica Sinica Vol. 32, Issue 11, Pages: 1778-1781(2004)
- 作者机构：
  
  北京大学信息科学技术学院信息安全实验室,北京,100871
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN309
- Published：2004
- 稿件说明：
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TANG Wen, TANG Li-yong, CHEN Zhong. A Markov-Chain Based Performance Analysis Method for Scalar Multiplication on Elliptic Curve[J]. Acta Electronica Sinica, 2004, 32(11): 1778-1781.
DOI：

TANG Wen, TANG Li-yong, CHEN Zhong. A Markov-Chain Based Performance Analysis Method for Scalar Multiplication on Elliptic Curve[J]. Acta Electronica Sinica, 2004, 32(11): 1778-1781. DOI：

摘要

在椭圆曲线密码系统中

采用规范重编码、滑动窗口等优化技术可以有效提高椭圆曲线上点的标量乘法

k·P

的运算性能

但在实现中

需要对不同优化技术的算法性能进行定量分析

才能确定标量乘法的最优实现.本文运用Markov链对标量

规范重编码表示的滑动窗口划分过程进行了建模

提出了一种对椭圆曲线标量乘法的平均算法性能进行定量分析的方法

并运用该方法分析了不同参数下标量乘法运算的平均性能

计算了滑动窗口的最优窗口大小.最后

通过比较说明

采用规范重编码和滑动窗口技术的椭圆曲线标量乘法的运算开销比用m-ary法少10.32~17.32％

比单纯采用滑动窗口法也要少4.53~8.40％.

Abstract

The canonical re-coding and sliding window techniques are often used in computation of scalar multiplication

k·P

on elliptic curves for reducing the average number of required operation.In this paper

scalar multiplication with canonical re-coding and sliding window techniques is analyzed by modeling the window partition process of canonical re-coding expression of

as Markov-chain

the average performance of scalar multiplication under different parameters are given and the optimal window sizes are computed.Finally

the comparison shows that scalar multiplication with canonical re-coding and sliding window techniques requires 10.32~17.32% fewer operations than m-ary method

and 4.53~8.40% fewer operations than simple sliding window method.

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