Improved against power analysis of elliptic curve scalar multiplication algorithm

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (33): 68-70.

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Improved against power analysis of elliptic curve scalar multiplication algorithm

TONG Lian1，LIU Ning2，QIAN Jiang1

1.College of Electronics and Information Engineering，Nanjing University of Technology，Nanjing 210009，China
2.ZTE Co.，Ltd，Nanjing 210001，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-11-21 Published:2011-11-21

改进的抗能量分析的椭圆曲线标量乘算法

童莲1，刘宁2，钱江1

1.南京工业大学电子与信息工程学院，南京 210009
2.中兴通讯股份有限公司，南京 210001

Abstract

Abstract: Power analysis is a common and effective means of password attack.In order to increase the anti-aggression ability to the smart card，this paper analyzes the common five kinds of power analysis and puts forward the improved scalar multiplication algorithm which considers both efficiency and safety.Random number and multi-base number system are introduced.A single scalar multiplication is rewritten to the double scalar multiplication，and the sliding window algorithm is combined to improve efficiency.When the window length is fixed and three different scalars are selected，compared with the existing comprehensive anti-aggression scalar multiplication algorithm，the efficiency in binary and prime fields are vastly improved.

Key words: elliptic curve, scalar multiplication algorithm, power analysis, multi-base number system, sliding window algorithm

摘要： 能量分析是密码攻击中常用且有效的手段，为提高智能卡的抗攻击性能，针对常见的五种能量分析方法，进行全面扼要的分析，提出兼顾效率和安全性的改进标量乘算法。引入随机数以及采用多基数系统表示标量，将单标量乘法改写为双标量乘，结合滑动窗口算法提高效率。当固定窗口长度时，选取标量的三个不同二进制位长，与已有的具有全面抗攻击性标量乘算法相比，效率在二元域及素数域上均得到大幅提高。

关键词: 椭圆曲线, 标量乘算法, 能量分析, 多基数系统, 滑动窗口算法

TONG Lian1，LIU Ning2，QIAN Jiang1. Improved against power analysis of elliptic curve scalar multiplication algorithm[J]. Computer Engineering and Applications, 2011, 47(33): 68-70.

童莲1，刘宁2，钱江1. 改进的抗能量分析的椭圆曲线标量乘算法[J]. 计算机工程与应用, 2011, 47(33): 68-70.

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Improved against power analysis of elliptic curve scalar multiplication algorithm

改进的抗能量分析的椭圆曲线标量乘算法

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