[Resource Topic] 2006/372: A taxonomy of pairing-friendly elliptic curves

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A taxonomy of pairing-friendly elliptic curves

Authors: David Freeman, Michael Scott, Edlyn Teske


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.

ePrint: https://eprint.iacr.org/2006/372

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