Paper 2010/353
Cryptographic Pairings Based on Elliptic Nets
Naoki Ogura, Naoki Kanayama, Shigenori Uchiyama, and Eiji Okamoto
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.
Metadata
- Available format(s)
-
PDF
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Tate pairingAte pairingR-Ate pairingOptimal pairingelliptic netnormalization
- Contact author(s)
- ogura-naoki @ ed tmu ac jp
- History
- 2011-05-11: last of 4 revisions
- 2010-06-18: received
- See all versions
- Short URL
- https://ia.cr/2010/353
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2010/353,
author = {Naoki Ogura and Naoki Kanayama and Shigenori Uchiyama and Eiji Okamoto},
title = {Cryptographic Pairings Based on Elliptic Nets},
howpublished = {Cryptology {ePrint} Archive, Paper 2010/353},
year = {2010},
url = {https://eprint.iacr.org/2010/353}
}
