An Efficient Secure Elliptic Curve Scalar Multiplication Algorithm

doi:10.3969/j.issn.1000-3428.2012.18.028

Computer Engineering ›› 2012, Vol. 38 ›› Issue (18): 103-106. doi: 10.3969/j.issn.1000-3428.2012.18.028

• Networks and Communications • Previous Articles Next Articles

An Efficient Secure Elliptic Curve Scalar Multiplication Algorithm

CHEN Xi, ZHU Yue-fei

(Institute of Information Engineering, PLA Information Engineering University, Zhengzhou 450002, China)

Received:2011-11-30 Revised:2012-01-04 Online:2012-09-20 Published:2012-09-18

一种高效安全的椭圆曲线标量乘算法

陈熹，祝跃飞

(解放军信息工程大学信息工程学院，郑州 450002)

作者简介:陈熹(1988－)，男，硕士研究生，主研方向：信息安全；祝跃飞，教授、博士生导师
基金资助:
郑州市科技创新团队基金资助项目(10CXTD150)

Abstract

Abstract: Most secure Elliptic Curve Scalar Multiplication(ECSM) algorithms based on Point Verification(PV) and Coherency Check(CC) have low efficiency. Aiming at the problem, this paper proposes a new secure algorithm based on ternary representation and proves its correctness. The analysis about its efficiency in the affine coordinates and Jacobian coordinates is presented, whose result shows that the computational efficiency is improved while guaranteeing the security.

Key words: Point Verification(PV), Coherency Check(CC), Elliptic Curve Scalar Multiplication(ECSM), fault analysis attack, ternary representation, affine coordinates, Jacobian coordinates

摘要： 基于点验证和基于一致性检测的椭圆曲线标量乘安全算法一般运算效率低下。为此，通过对错误探测方法进行改进，提出一种基于三进制的椭圆曲线标量乘算法，给出算法的正确性证明，并在仿射坐标和Jacobian坐标下对其进行分析，结果表明，在保证安全性的前提下，该算法的效率有较大提高。

关键词: 点验证, 一致性检测, 椭圆曲线标量乘, 错误分析攻击, 三进制表示, 仿射坐标, Jacobian坐标

CLC Number:

TP301.6

CHEN Xi, CHU Ti-Fei. An Efficient Secure Elliptic Curve Scalar Multiplication Algorithm[J]. Computer Engineering, 2012, 38(18): 103-106.

陈熹, 祝跃飞. 一种高效安全的椭圆曲线标量乘算法[J]. 计算机工程, 2012, 38(18): 103-106.

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