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j不变量等于1728的GLS椭圆曲线上四维GLV方法

4-dimensional GLV method on GLS elliptic curves with j-invariant 1728
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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%。 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.
作者 宋承根 徐茂智 周正华
机构地区 北京大学数学科学学院
出处 《国防科技大学学报》 EI CAS CSCD 北大核心 2012年第2期25-28,共4页 Journal of National University of Defense Technology
基金 国家自然科学基金资助项目(10990011)
关键词 椭圆曲线 点的倍乘 GLV方法 elliptic curve point multiplication GLV method
分类号 TN918.1 [电子电信—通信与信息系统]
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参考文献10

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国防科技大学学报
2012年 第2期

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