椭圆曲线密码中抗功耗分析攻击的标量乘改进方案

J4 ›› 2014, Vol. 36 ›› Issue (04): 644-648.

椭圆曲线密码中抗功耗分析攻击的标量乘改进方案

张友桥1，周武能1，申晔2，刘玉军2

(1.东华大学信息科学与技术学院,上海 201620;2.上海华虹集成电路有限责任公司,上海 201203)

收稿日期:2012-09-17 修回日期:2012-12-30 出版日期:2014-04-25 发布日期:2014-04-25
基金资助:
国家自然科学基金资助项目(61075060);上海市教育委员会科研创新项目(12zz064)

Improved scheme for scalar multiplication against
power analysis attacks in elliptic curve cryptography

ZHANG Youqiao1,ZHOU Wuneng1,SHEN Ye2,LIU Yujun2

(1.College of Information Science and Technology,Donghua University,Shanghai 201620;
2.Shanghai Huahong Integrated Circuit Co.,Ltd.,Shanghai 201203,China)

Received:2012-09-17 Revised:2012-12-30 Online:2014-04-25 Published:2014-04-25

摘要/Abstract

摘要：

椭圆曲线标量乘法运算是椭圆曲线密码(ECC)体制中最主要的计算过程，标量乘法的效率和安全性一直是研究的热点。针对椭圆曲线标量乘运算计算量大且易受功耗分析攻击的问题，提出了一种抗功耗分析攻击的快速滑动窗口算法，在雅可比和仿射混合坐标系下采用有符号滑动窗口算法实现椭圆曲线标量乘计算，并采用随机化密钥方法抵抗功耗分析攻击。与二进制展开法、密钥分解法相比的结果表明，新设计的有符号滑动窗口标量乘算法计算效率、抗攻击性能有明显提高。

关键词: 椭圆曲线密码, 标量乘, 功耗分析攻击, 滑动窗口算法, 混合坐标系

Abstract:

Elliptic curve scalar multiplication is the main computing process in Elliptic Curve Cryptography (ECC), and the efficiency and security of scalar multiplication is always the research hotspot. Aiming at the problem that elliptic curve scalar multiplication has a tremendous computation and is vulnerable to power analysis attacks, a fast sliding window algorithm against power analysis attacks is proposed. In Jacobian and Affine mixed coordinates, the signed sliding window algorithm strategy is used to perform elliptic curve scalar multiplication, and random keys method is applied against power analysis attacks. The analysis results show that, compared with binary expansion method and key assignment method, the improved signed sliding window scalar multiplication algorithm improves calculation efficiency and antiattack performance significantly.

Key words: elliptic curve cryptography;scalar multiplication;power analysis attack;sliding window algorithm;mixed coordinates

张友桥1，周武能1，申晔2，刘玉军2. 椭圆曲线密码中抗功耗分析攻击的标量乘改进方案[J]. J4, 2014, 36(04): 644-648.

ZHANG Youqiao1,ZHOU Wuneng1,SHEN Ye2,LIU Yujun2. Improved scheme for scalar multiplication against
power analysis attacks in elliptic curve cryptography [J]. J4, 2014, 36(04): 644-648.

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