Paper 2007/390 Original: eprint.iacr.org/2007/390 ↗
Implementing Cryptographic Pairings over Barreto-Naehrig Curves
Abstract
In this paper we describe an efficient implementation of the Tate and Ate pairings using Barreto-Naehrig pairing-friendly curves, on both a standard 32-bit PC and on a 32-bit smartcard. First we introduce a sub-family of such curves with a particularly simple representation. Next we consider the issues that arise in the efficient implementation of field arithmetic in $\F_{p^{12}}$, which is crucial to good performance. Various optimisations are suggested, including a novel approach to the `final exponentiation', which is faster and requires less memory than the methods previously recommended.
Metadata
- Available format(s)
PDF- Category
- Implementation
- Publication info
- Preprint.
- History
- 2008-10-31: last updated
- 2007-10-04: published
- Short URL
- https://ia.cr/2007/390
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2007/390,
author = {Augusto Jun Devegili and Michael Scott and Ricardo Dahab},
title = {Implementing Cryptographic Pairings over Barreto-Naehrig Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2007/390},
year = {2007},
url = {https://eprint.iacr.org/2007/390}
}