Cryptology ePrint Archive: Report 2010/429

A Family of Implementation-Friendly BN Elliptic Curves

Geovandro C. C. F. Pereira and Marcos A. Simplício Jr and Michael Naehrig and Paulo S. L. M. Barreto

Abstract: 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.

Category / Keywords: pairing-based cryptosystems, elliptic curve cryptosystems, pairing-friendly curves, pairing implementation

Publication Info: Full version published in The Journal of Systems and Software 84(8), 1319--1326, Elsevier, 2011, doi:10.1016/j.jss.2011.03.083

Date: received 3 Aug 2010, last revised 11 Jun 2013

Contact author: geovandro at larc usp br

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Version: 20130611:211421 (All versions of this report)

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