j不变量等于1728的GLS椭圆曲线上四维

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％.

4-dimensional GLV method on GLS elliptic curves with j-invariant 1728

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.