International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Cryptographic Pairings Based on Elliptic Nets

Naoki Ogura
Naoki Kanayama
Shigenori Uchiyama
Eiji Okamoto
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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.
  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},
  note={ 14788 received 17 Jun 2010, last revised 28 Jun 2010},
  author={Naoki Ogura and Naoki Kanayama and Shigenori Uchiyama and Eiji Okamoto},