A Taxonomy of Pairing-Friendly Elliptic Curves

13 years 2 months ago

Download theory.stanford.edu

Elliptic curves with small embedding degree and large prime-order subgroup are key ingredients for implementing pairingbased 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. Keywords. Elliptic curves, pairing-based cryptosystems, embedding degree, eﬃcient implementation. 1

David Freeman, Michael Scott, Edlyn Teske

Real-time Traffic