| 利用半点计算椭圆曲线双标量乘法算法 |
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| 引用本文： | 冯娟娟,祝跃飞,张亚娟.利用半点计算椭圆曲线双标量乘法算法[J].计算机工程与应用,2006,42(18):58-60. |
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| 作者姓名： | 冯娟娟 祝跃飞 张亚娟 |
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| 作者单位： | 解放军信息工程大学信息工程学院,郑州,450002 |
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| 摘 要： | 实现椭圆曲线密码体制最主要的运算是椭圆曲线点群上的标量乘法(或点乘)运算。一些基于椭圆曲线的密码协议比如ECDSA签名验证,就需要计算双标量乘法kP+lQ,其中P、Q为椭圆曲线点群上的任意两点。一个高效计算kP+lQ的方法就是同步计算两个标量乘法,而不是分别计算每个标量乘法再相加。通过对域F2m上的椭圆曲线双标量乘法算法进行研究,将半点公式应用于椭圆曲线的双标量乘法中,提出了一种新的同步计算双标量乘法算法,分析了效率,并与传统的基于倍点运算的双标量乘法算法进行了详细的比较,其效率更优。
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| 关 键 词： | 椭圆曲线 双标量乘法 半点 |
| 文章编号： | 1002-8331-（2006）18-0058-03 |
| 收稿时间： | 2005-09 |
| 修稿时间： | 2005-09 |
Algorithms for Efficient Simultaneous Elliptic Curve Scalar Multiplication Using Point Halving |
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| Feng Juanjuan,Zhu Yuefei,Zhang Yajuan.Algorithms for Efficient Simultaneous Elliptic Curve Scalar Multiplication Using Point Halving[J].Computer Engineering and Applications,2006,42(18):58-60. |
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| Authors: | Feng Juanjuan Zhu Yuefei Zhang Yajuan |
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| Affiliation: | School of Information Engineering,Information Engineering University of PLA,Zhengzhou 450002 |
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| Abstract: | The computational performance of elliptic curve cryptographic schemes strongly depends on the efficiency of the scalar multiplication.Some elliptic curve based on cryptographic protocols,such as ECDSA signature verification,require computation of multiple scalar multiplications of kP+lQ,where P and Q are points on an elliptic curve.An efficient way to compute kP+lQ is to compute two scalar multiplication simultaneously,rather than computing each scalar multiplication separately.By analysing algorithms of computing kP+lQ on an elliptic curve over finite field F■■,a new efficient algorithm for simultaneous scalar multiplication using point halving is proposed.A detailed analysis of the computational efficiency of our proposed algorithms is also given.It is faster than the traditional algorithms using point doubling. |
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| Keywords: | elliptic curve multiple scalar multiplications point halving |
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