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
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