Paper 2022/348 Original: eprint.iacr.org/2022/348 ↗
Fast Subgroup Membership Testings for $\mathbb{G}_1$, $\mathbb{G}_2$ and $\mathbb{G}_T$ on Pairing-friendly Curves
Abstract
Pairing-based cryptographic protocols are typically vulnerable to small-subgroup attacks in the absence of protective measures. To thwart them, one of feasible measures is to execute subgroup membership testings, which are generally considered expensive. Recently, Scott proposed an efficient method of subgroup membership testings for $\mathbb{G}_1$, $\mathbb{G}_2$ and $\mathbb{G}_T$ on the BLS family. In this paper, we generalize this method proposed by Scott and show that the new technique is applicable to a large class of pairing-friendly curves. In addition, we also confirm that the new method leads to a significant speedup for membership testings on many popular pairing-friendly curves.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2023-04-16: last updated
- 2022-03-14: published
- Short URL
- https://ia.cr/2022/348
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2022/348,
author = {Yu Dai and Kaizhan Lin and Chang-An Zhao and Zijian Zhou},
title = {Fast Subgroup Membership Testings for $\mathbb{G}_1$, $\mathbb{G}_2$ and $\mathbb{G}_T$ on Pairing-friendly Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/348},
year = {2022},
url = {https://eprint.iacr.org/2022/348}
}