Paper 2022/996

Fast Hashing to G2 on Pairing-friendly Curves with the Lack of Twists

Yu Dai
Fangguo Zhang
Chang-An Zhao
Abstract

Pairing-friendly curves with the lack of twists, such as BW13-P310 and BW19-P286, have been receiving attention in pairing-based cryptographic protocols as they provide fast operation in the first pairing subgroup G1 at the 128-bit security level. However, they also incur a performance penalty for hashing to G2 simultaneously since G2 is totally defined over a full extension field. Furthermore, the previous methods for hashing to G2 focus on pairing-friendly curves admitting a twist, which can not be employed for our selected curves. In this paper, we propose a general method for hashing to on curves with the lack of twists. More importantly, we further optimize the general algorithm on curves with non-trival automorphisms, which is certainly suitable for BW13-P310 and BW19-P286. Theoretical estimations show that the latter would be more efficient than the former. For comparing the performance of the two proposed algorithms in detail, high speed software implementation over BW13-P310 is also provided on a 64-bit processor. Experimental results show that the general algorithm can be sped up by up to if the computational cost of cofactor multiplication for is only considered, while the improved method is up to faster than the general one for the whole process.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint.
Contact author(s)
daiy39 @ mail2 sysu edu cn
isszhfg @ mail sysu edu cn
zhaochan3 @ mail sysu edu cn
History
2023-10-08: revised
2022-08-03: received
See all versions
Short URL
https://ia.cr/2022/996
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2022/996,
      author = {Yu Dai and Fangguo Zhang and Chang-An Zhao},
      title = {Fast Hashing to $\mathbb{G}_2$ on Pairing-friendly Curves with the Lack of Twists},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/996},
      year = {2022},
      url = {https://eprint.iacr.org/2022/996}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.