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Implementing Cryptographic Pairings over Barreto-Naehrig Curves

Authors:
Augusto Jun Devegili
Michael Scott
Ricardo Dahab
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URL: http://eprint.iacr.org/2007/390
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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.
BibTeX
@misc{eprint-2007-13670,
  title={Implementing Cryptographic Pairings over Barreto-Naehrig Curves},
  booktitle={IACR Eprint archive},
  keywords={implementation /},
  url={http://eprint.iacr.org/2007/390},
  note={Corrected and Improved version of paper from Pairing 2007, Tokyo, Japan, LNCS 4575 mike@computing.dcu.ie 13790 received 4 Oct 2007},
  author={Augusto Jun Devegili and Michael Scott and Ricardo Dahab},
  year=2007
}