Fast Subgroup Membership Testings for $\mathbb{G}_1$, $\mathbb{G}_2$ and $\mathbb{G}_T$ on Pairing-friendly Curves

Yu Dai; Kaizhan Lin; Chang-An Zhao; Zijian Zhou

Paper 2022/348

Fast Subgroup Membership Testings for $\mathbb{G}_1$, $\mathbb{G}_2$ and $\mathbb{G}_T$ on Pairing-friendly Curves

Yu Dai

Kaizhan Lin

Chang-An Zhao

Zijian Zhou

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.
Keywords: Small-subgroup attacks group membership testings pairing-friendly curves.
Contact author(s): daiy39 @ mail2 sysu edu cn
History: 2023-04-16: last of 5 revisions; 2022-03-14: received; See all versions
Short URL: https://ia.cr/2022/348
License: CC BY

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}
}