Paper 2007/434
Computing the Ate Pairing on Elliptic Curves with Embedding Degree $k=9$
Xibin Lin, Chang-An Zhao, Fangguo Zhang, and Yanming Wang
Abstract
For AES 128 security level there are several natural choices for pairing-friendly elliptic curves. In particular, as we will explain, one might choose curves with $k=9$ or curves with $k=12$. The case $k=9$ has not been studied in the literature, and so it is not clear how efficiently pairings can be computed in that case. In this paper, we present efficient methods for the $k=9$ case, including generation of elliptic curves with the shorter Miller loop, the denominator elimination and speed up of the final exponentiation. Then we compare the performance of these choices. From the analysis, we conclude that for pairing-based cryptography at the AES 128 security level, the Barreto-Naehrig curves are the most efficient choice, and the performance of the case $k=9$ is comparable to the Barreto-Naehrig curves.
Metadata
- Available format(s)
-
PDF PS
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Ate pairingDenominator eliminationFinal exponentiation
- Contact author(s)
- linxibin @ mail2 sysu edu cn
- History
- 2007-11-24: revised
- 2007-11-24: received
- See all versions
- Short URL
- https://ia.cr/2007/434
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2007/434,
author = {Xibin Lin and Chang-An Zhao and Fangguo Zhang and Yanming Wang},
title = {Computing the Ate Pairing on Elliptic Curves with Embedding Degree $k=9$},
howpublished = {Cryptology {ePrint} Archive, Paper 2007/434},
year = {2007},
url = {https://eprint.iacr.org/2007/434}
}