A Taxonomy of Pairing-Friendly Elliptic Curves

被引：239

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：

爱尔兰科学基金会; 美国国家科学基金会;

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

页码：224 / 280

页数：57

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