| 引用本文: | 宋承根,徐茂智,周正华.j不变量等于1728的GLS椭圆曲线上四维.[J].国防科技大学学报,2012,34(2):25-28.[点击复制] |
| SONG Chenggen,XU Maozhi,ZHOU Zhenghua.4-dimensional GLV method on GLS elliptic curves with j-invariant 1728[J].Journal of National University of Defense Technology,2012,34(2):25-28[点击复制] |
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| j不变量等于1728的GLS椭圆曲线上四维 |
| 宋承根, 徐茂智, 周正华 |
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(北京大学 数学科学学院,北京 100871)
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| 摘要: |
| 为了实现椭圆曲线的快速倍乘，Gallant-Lamber-Vanstone(GLV)方法被推广到四维的一般情形。文章中回答了Galbraith，Lin和Scott(J. Cryptol. DOI: 10.1007/s00145-010-9065-y)提出的一个公开问题：研究Fp2上j不变量等于1728的GLS椭圆曲线上的四维GLV方法，并给出时间周期。尤其指出GLV的四维分解能够在很大的概率上实现，给出了一些结果和例子。特别指出在同一类曲线上，四维GLV方法的时间周期大概是二维GLV方法的70%～73%。 |
| 关键词: 椭圆曲线 点的倍乘 GLV方法 |
| DOI： |
| 投稿日期：2011-07-28 |
| 基金项目:国家自然科学基金资助项目（10990011） |
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| 4-dimensional GLV method on GLS elliptic curves with j-invariant 1728 |
| SONG Chenggen, XU Maozhi, ZHOU Zhenghua |
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(School of Mathematical Sciences, Peking University, Beijing 100871, China)
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| Abstract: |
| In order to obtain a fast multiplication on elliptic curves, the Gallant-Lambert-Vanstone(GLV) method is introduced to the general situation in dimension 4, one of the open problems in Galbraith, Lin and Scott's work(J. Cryptol. DOI: 10.1007/s00145-010-9065-y) is answered, that is, studying the performance of 4-dimensional GLV method for faster point multiplication on some GLS curves over Fp2 with j-invariant 1728. Finally some results and examples are presented, showing that the 4-dimensional GLV method runs in between 70% and 73% the time of the 2-dimensional GLV method which Galbraith et al. did in their work. |
| Keywords: elliptic curve point multiplication GLV method |
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