Weil配对求解椭圆曲线离散对数的实施分析

胡建军

doi:10.13568/j.cnki.651094.651316.2024.01.09.0001

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Weil配对求解椭圆曲线离散对数的实施分析

信息科学与技术 | 更新时间：2026-01-21

- Weil配对求解椭圆曲线离散对数的实施分析
- Weil配对求解椭圆曲线离散对数的实施分析
- 新疆大学学报（自然科学版中英文） 2024年41卷第3期页码：329-335
- 作者机构：
  
  兰州文理学院数字媒体学院
- 作者简介：
- 基金信息：
  
  兰州文理学院服务地方经济社会发展计划项目“椭圆曲线密码关键技术研究”（2021FWDF15）
- DOI：10.13568/j.cnki.651094.651316.2024.01.09.0001
  中图分类号： TN918.1
- 纸质出版：2024
- 稿件说明：
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[1]胡建军.Weil配对求解椭圆曲线离散对数的实施分析[J].新疆大学学报(自然科学版)(中英文),2024,41(03):329-335+343.
[1]胡建军.Weil配对求解椭圆曲线离散对数的实施分析[J].新疆大学学报(自然科学版)(中英文),2024,41(03):329-335+343. DOI： 10.13568/j.cnki.651094.651316.2024.01.09.0001.

DOI：10.13568/j.cnki.651094.651316.2024.01.09.0001.

摘要

Weil配对广泛应用于加密、解密、签名、密码交换和密码体制安全分析中. 1993年

Menezes等利用Weil配对有效地将超奇异椭圆曲线的离散对数约减到有限域上的离散对数

基于Weil配对的椭圆曲线密码体制遭受严峻挑战

然而

基于Weil配对的椭圆曲线密码体制的应用并未止步.为此

分析了适合Weil配对椭圆曲线的特征

指出适合Weil配对的椭圆曲线是具有二元循环群结构的曲线

一元群结构的超奇异椭圆曲线通过嵌入度的方式能够构造出二元群结构的超奇异椭圆曲线.同时

为了方便理解Weil配对的实施

列出了适合Weil配对安全的常见椭圆曲线.最后

聚焦了MOV攻击嵌入度为偶数的超奇异椭圆的实施过程

利用PARI软件验证了分析结论

指出了PARI和SageMath软件在设计上存在的缺陷.

Abstract

Weil pairing is widely used in encryption

decryption

signature

cryptographic exchange and cryptosystem security analysis. In 1993

Menezes et al. used Weil pairing to effectively reduce the discrete logarithm of a supersingular elliptic curve to the discrete logarithm over a finite field

so the elliptic curve cryptosystem based on Weil pairing was seriously challenged. However

the application of elliptic curve cryptosystem based on Weil pairing has not stopped. For this reason

the characteristics of elliptic curves suitable for Weil pairing are analyzed

and it is pointed out that the elliptic curves suitable for Weil pairing are curves with binary cyclic group structure

and the hypersingular elliptic curves with monadic group structure can be constructed by means of embedding degree.At the same time

in order to facilitate the understanding of the implementation of Weil pairing

common elliptic curves suitable for Weil pairing safety are listed. Finally

we focus on the implementation process of MOV attack with even embedding degree of supersingular elliptic curve

verify the analysis results by using PARI software

and point out the design flaws of PARI and SageMath software.

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references

KUMAR M.Design and analysis of pairing-friendly elliptic curves for cryptographic primitives[D].New Delhi:Jawaharlal Nehru University,2023.

MENEZES A J,OKAMOTO T,VANSTONE S A.Reducing elliptic curve logarithms to logarithms in a finite field[J].IEEE Transactions on Information Theory,1993,39(5):1639-1646.

FREY G,MULLER M,RUCK H G.The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems[J].IEEE Transactions on Information Theory,1999,45(5):1717-1719.

FREEMAN D.Constructing pairing-friendly elliptic curves with embedding degree 10[M]//Lecture Notes in Computer Science.Berlin,Heidelberg:Springer Berlin Heidelberg,2006:452-465.

YASUDA T,TAKAGI T,SAKURAI K.Constructing pairing-friendly elliptic curves using global number fields[C]//2015 Third International Symposium on Computing and Networking(CANDAR).Sapporo,Japan.IEEE,2015:477-483.

CHIESA A,CHUA L,WEIDNER M.On cycles of pairing-friendly elliptic curves[J].SIAM Journal on Applied Algebra and Geometry,2019,3(2):175-192.

KHAMSEH E.The review on elliptic curves as cryptographic pairing groups[J].Mathematics and Computational Sciences,2021,2(2):50-59.

SMIT R.The discrete logarithm problem on supersingular elliptic curves[D].Groningen:University of Groningen,2020.

MILLER V S.The Weil pairing,and its efficient calculation[J].Journal of Cryptology,2004,17(4):235-261.

胡建军，王伟，李恒杰．有限域上椭圆曲线Weil对的计算[J]．吉林大学学报(信息科学版)，2022,40(3):509-514.HU J J,WANG W,LI H J.Computation of Weil pairs for elliptic curves over finite fields[J].Journal of Jilin University(Information Science Edition),2022,40(3):509-514.(in Chinese)

SMART N P.The discrete logarithm problem on elliptic curves of trace one[J].Journal of Cryptology,1999,12(3):193-196.

胡建军，王伟，李恒杰．求解迹1椭圆曲线上的离散对数[J]．安徽大学学报(自然科学版)，2023,47(6):1-6.HU J J,WANG W,LI H J.Solving the discrete logarithm on elliptic curve of trace one[J].Journal of Anhui University(Natural Science Edition),2023,47(6):1-6.(in Chinese)

BROKER R.Constructing supersingular elliptic curves[J].Journal of Combinatorial Number Theory,2009,1(3):269-273.

SCHOOF R.Counting points on elliptic curves over finite fields[J].Journal de Theorie des Nombres de Bordeaux,1995,7(1):219-254.

ARANHA D F,EI HOUSNI Y,GUILLEVIC A.A survey of elliptic curves for proof systems[J].Designs,Codes and Cryptography,2023,91(11):3333-3378.

KHALIL ABDULLA A,BAKIRAS D S.Data privacy in online social networks with FineGrained access control[C]//Qatar Foundation Annual Research Conference Proceedings Volume 2018 Issue 3.Qatar National Convention Center(QNCC),Doha,Qatar:Hamad bin Khalifa University Press(HBKU Press),2018.

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