| 优化的无预计算标量乘法算法 |
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| 引用本文： | 李忠,彭代渊.优化的无预计算标量乘法算法[J].铁道学报,2012,34(7):77-82. |
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| 作者姓名： | 李忠 彭代渊 |
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| 作者单位： | 1. 西南交通大学信息科学与技术学院,四川成都610031;宜宾学院计算机与信息工程学院,四川宜宾644000
2. 西南交通大学信息科学与技术学院,四川成都,610031 |
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| 基金项目： | 四川省教育厅重点科研项目 |
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| 摘 要： | 标量乘法是椭圆曲线密码的基本运算,也是最耗时的运算,其运算效率直接决定着椭圆曲线密码的性能。本文给出数字集{-1,0,1}上编码简单、具有最小汉明重量、长度最短、平均‘0’间隔长度大的带符号二进制标量表示法,利用直接计算2kQ+P策略,得到高效无预计算标量乘法算法。理论及实例分析表明,所得算法的平均效率比传统NAF方法标量乘法算法高26.1%,能有效提高ECC在存储受限环境的实现效率。
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| 关 键 词： | 椭圆曲线密码 标量乘法 标量表示 汉明重量 平均‘0’间隔长度 预计算 |
Efficient Scalar Multiplication without Precomputation |
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| LI Zhong
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PENG Dai-yuan.Efficient Scalar Multiplication without Precomputation[J].Journal of the China railway Society,2012,34(7):77-82. |
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| Authors: | LI Zhong PENG Dai-yuan |
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| Institution: | 1(1.School of Information Science &Technology,Southwest Jiaotong University,Chengdu 610031,China; 2.School of Computer & Information Engineering,Yibin University,Yibin 644000,China) |
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| Abstract: | Scalar multiplication is the fundamental and time-consuming operation in elliptic curve cryptosystems,the performance of the elliptic curve cryptosysytem deeply depends on the efficiency of scalar multiplication.In this paper,the new signed binary scalar representation method of the digit set {-1,0,1},with the minimal Hamming weight,shortest significant length and longer average zero-run length,was presented,and the efficient scalar multiplication algorithm was obtained by using direct computation of the 2kQ+P strategy.The analysis results show that the average calculation time is shortened by 26.1% in comparison to the traditional NAF method. |
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| Keywords: | elliptic curve cryptosysytem scalar multiplication scalar representation hamming weight average zero-run length precomputation |
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