A taxonomy of pairing-friendly elliptic curves

David Freeman; Michael Scott; Edlyn Teske

Paper 2006/372

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: elliptic curves pairing-based cryptosystems embedding degree efficient implementation
Contact author(s): dfreeman @ cs stanford edu
History: 2009-11-20: last of 8 revisions; 2006-11-03: received; See all versions
Short URL: https://ia.cr/2006/372
License: 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},
      url = {https://eprint.iacr.org/2006/372}
}