A Taxonomy of Pairing-Friendly Elliptic Curves

被引：238
作者：
Freeman, David [1 ,2 ]
Scott, Michael [3 ]
Teske, Edlyn [4 ]
机构：
[1] CWI, NL-1098 XG Amsterdam, Netherlands
[2] Leiden Univ, NL-1098 XG Amsterdam, Netherlands
[3] Dublin City Univ, Sch Comp Applicat, Dublin 9, Ireland
[4] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada
来源：
JOURNAL OF CRYPTOLOGY | 2010年 / 23卷 / 02期
基金：
美国国家科学基金会; 爱尔兰科学基金会;
关键词：
Elliptic curves; Pairing-based cryptosystems; Embedding degree; Efficient implementation; ABELIAN-VARIETIES; DIFFIE-HELLMAN; FINITE-FIELDS; COMPUTATION; LOGARITHMS; CRYPTOGRAPHY; ISOMORPHISM; ALGORITHMS; SIGNATURES; ISOGENIES;
D O I：
10.1007/s00145-009-9048-z
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Elliptic curves with small embedding degree and large prime-order subgroup are key ingredients for implementing pairing-based cryptographic systems. Such "pairing-friendly" curves are rare and thus require specific constructions. In this paper we give a single coherent framework that encompasses all of the constructions of pairing-friendly elliptic curves currently existing in the literature. We also include new constructions of pairing-friendly curves that improve on the previously known constructions for certain embedding degrees. Finally, for all embedding degrees up to 50, we provide recommendations as to which pairing-friendly curves to choose to best satisfy a variety of performance and security requirements.
引用
收藏
页码：224 / 280
页数：57
相关论文
共 88 条
[1]  
[Anonymous], LECT NOTES COMPUTER
[2]  
[Anonymous], 2000, 2000 S CRYPT INF SEC
[3]  
[Anonymous], 2001, IDENTITY BASED UNPUB
[4]  
[Anonymous], 2001, LNCS
[5]  
[Anonymous], 2000, Expo. Math
[6]  
[Anonymous], 2002, ALGEBRA
[7]   ELLIPTIC-CURVES AND PRIMALITY PROVING [J].
ATKIN, AOL ;
MORAIN, F .
MATHEMATICS OF COMPUTATION, 1993, 61 (203) :29-68
[8]  
Bailey DV, 2001, J CRYPTOL, V14, P153, DOI 10.1007/s00145-001-0012
[9]   The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm [J].
Balasubramanian, R ;
Koblitz, N .
JOURNAL OF CRYPTOLOGY, 1998, 11 (02) :141-145
[10]   Efficient pairing computation on supersingular Abelian varieties [J].
Barreto, Paulo S. L. M. ;
Galbraith, Steven D. ;
O'hEigeartaigh, Colm ;
Scott, Michael .
DESIGNS CODES AND CRYPTOGRAPHY, 2007, 42 (03) :239-271
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