Cryptology ePrint Archive: Report 2006/372

A taxonomy of pairing-friendly elliptic curves

David Freeman and 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.

Category / Keywords: Public key cryptography / elliptic curves, pairing-based cryptosystems, embedding degree, efficient implementation

Date: received 27 Oct 2006, last revised 20 Nov 2009

Contact author: dfreeman at cs stanford edu

Available format(s): PDF | BibTeX Citation

Note: Bibliography update.

Version: 20091120:154219 (All versions of this report)

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