## CryptoDB

### Paper: Cryptographic Pairings Based on Elliptic Nets

Authors: Naoki Ogura Naoki Kanayama Shigenori Uchiyama Eiji Okamoto URL: http://eprint.iacr.org/2010/353 Search ePrint Search Google 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
}