### A taxonomy of pairing-friendly elliptic curves

David Freeman, Michael Scott, and Edlyn Teske

##### Abstract

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.

Note: Bibliography update.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
elliptic curvespairing-based cryptosystemsembedding degreeefficient implementation
Contact author(s)
dfreeman @ cs stanford edu
History
2009-11-20: last of 8 revisions
See all versions
Short URL
https://ia.cr/2006/372

CC BY

BibTeX

@misc{cryptoeprint:2006/372,
author = {David Freeman and Michael Scott and Edlyn Teske},
title = {A taxonomy of pairing-friendly elliptic curves},
howpublished = {Cryptology ePrint Archive, Paper 2006/372},
year = {2006},
note = {\url{https://eprint.iacr.org/2006/372}},
url = {https://eprint.iacr.org/2006/372}
}

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