Paper 2022/1164

Point-Halving and Subgroup Membership in Twisted Edwards Curves

Thomas Pornin, NCC Group
Abstract

In this short note, we describe a process for halving a point on a twisted Edwards curve. This can be used to test whether a given point is in the subgroup of prime order $\ell$, which is used by some cryptographic protocols. On Curve25519, this new test is about twice faster than the classic method consisting of multiplying the source point by $\ell$.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint.
Keywords
twisted Edwards curve subgroup point halving
Contact author(s)
thomas pornin @ nccgroup com
History
2022-09-06: approved
2022-09-06: received
See all versions
Short URL
https://ia.cr/2022/1164
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2022/1164,
      author = {Thomas Pornin},
      title = {Point-Halving and Subgroup Membership in Twisted Edwards Curves},
      howpublished = {Cryptology ePrint Archive, Paper 2022/1164},
      year = {2022},
      note = {\url{https://eprint.iacr.org/2022/1164}},
      url = {https://eprint.iacr.org/2022/1164}
}
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