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Paper: Cryptographic Pairings Based on Elliptic Nets

Authors:
Naoki Ogura
Naoki Kanayama
Shigenori Uchiyama
Eiji Okamoto
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URL: http://eprint.iacr.org/2010/353
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Abstract: In 2007, Stange proposed a novel method of computing the Tate pairing on an elliptic curve over a finite field. This method is based on elliptic nets, which are maps from $\mathbb{Z}^n$ to a ring that satisfy a certain recurrence relation. In this paper, we explicitly give formulae for computing some variants of the Tate pairing: Ate, Ate$_i$, R-Ate and Optimal pairings, based on elliptic nets. We also discuss their efficiency by using some experimental results.
BibTeX
@misc{eprint-2010-23254,
  title={Cryptographic Pairings Based on Elliptic Nets},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Tate pairing, Ate pairing, R-Ate pairing, Optimal pairing, elliptic net},
  url={http://eprint.iacr.org/2010/353},
  note={ ogura-naoki@ed.tmu.ac.jp 14788 received 17 Jun 2010, last revised 28 Jun 2010},
  author={Naoki Ogura and Naoki Kanayama and Shigenori Uchiyama and Eiji Okamoto},
  year=2010
}