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
Zijian Zhou
Chang-An Zhao
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
2022-09-29: last of 3 revisions
2022-03-14: received
See all versions
Short URL
https://ia.cr/2022/348
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2022/348,
      author = {Yu Dai and Kaizhan Lin and Zijian Zhou and Chang-An Zhao},
      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},
      note = {\url{https://eprint.iacr.org/2022/348}},
      url = {https://eprint.iacr.org/2022/348}
}
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