A family of implementation-friendly BN elliptic curves

• Published in: The Journal of systems and software Vol. 84; no. 8; pp. 1319 - 1326
• Main Authors: Pereira, Geovandro C.C.F., Simplício, Marcos A., Naehrig, Michael, Barreto, Paulo S.L.M.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.08.2011; Elsevier Sequoia S.A
• Subjects: Boron nitride; Communities; Computational efficiency; Computer programs; Cryptography; Cybersecurity; Elliptic curve cryptosystems; Keys; Optimization; Pairing-based cryptosystems; Pairing-friendly curves; Software; Studies; Systems development; 94A60; Elliptic curve cryptosystems; 14G50; Pairing-based cryptosystems; Pairing-friendly curves
• ISSN: 0164-1212; 1873-1228
• DOI: 10.1016/j.jss.2011.03.083

► We describe a new subfamily of BN elliptic curves for a wide platform scenario. ► Curves herein are simple to generate and suitable for efficient implementation. ► The implementation of the optimal ate pairing provided software speed records.. 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.