二元域上Edwards型椭圆曲线的配对计算

北京大学学报（自然科学版）

二元域上Edwards型椭圆曲线的配对计算

徐茂智^1,2,喻洪辉³,唐春明¹,亓延峰¹

1. 北京大学数学科学学院,北京100871; 2. 网络与软件安全保障教育部重点实验室, 北京100871; 3. 国家电网公司辽宁省电力公司, 沈阳 110006;

收稿日期:2010-05-14 出版日期:2010-09-20 发布日期:2010-09-20

The Pairing Computation on Binary Edwards Curves

XU Maozhi^1,2, YU Honghui³, TANG Chunming¹, QI Yanfeng¹

1. School of Mathematical Sciences, Peking University, Beijing 100871; 2. Key Laboratory of Network and Software Security Assurance, Beijing 100871; 3. Liaoning Electronic Power Company Limited, National Grid Corporation, Shenyang 110006;

Received:2010-05-14 Online:2010-09-20 Published:2010-09-20

摘要/Abstract

摘要： 研究了二元域上 Edwards 型椭圆曲线的配对计算问题, 并且给出了两种计算配对的方法。一种是基于Edwards型曲线与Weierstrass型曲线的双有理等价; 另一种是基.LNCS 1403 于它们之间的二次可分同源。在两种情况下, 都给出了具体的Miller 型函数计算和相应的配对计算算法, 特别是基于二次同源的配对计算, 由于其更多地采用平方运算而非一般乘法运算, 因此计算将会更为有效。

关键词: 二元域上的Edwards型曲线, Tate配对, Miller函数, 二次同源

Abstract: The authors consider pairings on binary Edwards curves and give two approaches to construct pairings and implement them. One is based on the birational equivalence between a binary Edwards curve and an elliptic curve in Weierstrass form, the other is based on a 2-isogeny from a binary Edwards curve to an elliptic curve. For both approaches, the authors give the computation of their Miller functions and present two algorithms for their pairing computation. Especially in the second algorithm, more field squaring operations are included, which is more efficient.

Key words: binary Edwards curves, Tate pairings, Miller functions, 2-isogeny

中图分类号:

TN918

徐茂智,喻洪辉,唐春明,亓延峰. 二元域上Edwards型椭圆曲线的配对计算[J]. 北京大学学报（自然科学版）.

XU Maozhi,YU Honghui,TANG Chunming,QI Yanfeng. The Pairing Computation on Binary Edwards Curves[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

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链接本文: https://xbna.pku.edu.cn/CN/

https://xbna.pku.edu.cn/CN/Y2010/V46/I5/736

[1]	唐春明,亓延峰,徐茂智. 实现k=18的Brezing-Weng曲线的最优配对[J]. 北京大学学报（自然科学版）, 2010, 46(5): 743-748.
[2]	胡志,周正华,徐茂智. 用有效可计算自同态来计算Tate配对[J]. 北京大学学报（自然科学版）, 2010, 46(5): 685-690.