Paper 2025/1098 Original: eprint.iacr.org/2025/1098 ↗
Efficient post-quantum commutative group actions from orientations of large discriminant
Abstract
We describe an algorithm to efficiently evaluate class group actions on supersingular elliptic curves that are oriented by an imaginary quadratic order of arbitrarily large discriminant. Contrary to CSIDH, this allows to increase the post-quantum security of the group action without increasing the size of the base field. In particular, we describe instances where Kuperberg's algorithm loses to generic supersingular isogeny path finding. Our algorithm is fully deterministic, strictly constant time, dummy free, and can be implemented without conditional branches. We show that the (restricted effective) group action can be employed in a non-interactive key exchange protocol, that we argue is asymptotically more efficient than CSIDH.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2025-09-17: last updated
- 2025-06-11: published
- Short URL
- https://ia.cr/2025/1098
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2025/1098,
author = {Marc Houben},
title = {Efficient post-quantum commutative group actions from orientations of large discriminant},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/1098},
year = {2025},
url = {https://eprint.iacr.org/2025/1098}
}