A Taxonomy of Pairing-Friendly Elliptic Curves

作者：Freeman David^*; Scott Michael; Teske Edlyn

来源：Journal of Cryptology, 2010, 23(2): 224-280.

DOI：10.1007/s00145-009-9048-z

• Elliptic curves
• Pairing-based cryptosystems
• Embedding degree
• Efficient implementation

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.

• 出版日期2010-4