A family of implementation-friendly BN elliptic curves

作者：Pereira Geovandro C C F^*; Simplicio Marcos A Jr; Naehrig Michael; Barreto Paulo S L M

来源：Journal of Systems and Software, 2011, 84(8): 1319-1326.

DOI：10.1016/j.jss.2011.03.083

• Pairing-based cryptosystems
• Elliptic curve cryptosystems
• Pairing-friendly curves

For the last decade, elliptic curve cryptography has gained increasing interest in industry and in the academic community. This is especially due to the high level of security it provides with relatively small keys and to its ability to create very efficient and multifunctional cryptographic schemes by means of bilinear pairings. Pairings require pairing-friendly elliptic curves and among the possible choices, Barreto-Naehrig (BN) curves arguably constitute one of the most versatile families.
In this paper, we further expand the potential of the BN curve family. We describe BN curves that are not only computationally very simple to generate, but also specially suitable for efficient implementation on a very broad range of scenarios. We also present implementation results of the optimal ate pairing using such a curve defined over a 254-bit prime field.

• 出版日期2011-8
• 单位Microsoft