Paper 2024/1172 Original: eprint.iacr.org/2024/1172 ↗
Generalized class group actions on oriented elliptic curves with level structure
Abstract
We study a large family of generalized class groups of imaginary quadratic orders $O$ and prove that they act freely and (essentially) transitively on the set of primitively $O$-oriented elliptic curves over a field $k$ (assuming this set is non-empty) equipped with appropriate level structure. This extends, in several ways, a recent observation due to Galbraith, Perrin and Voloch for the ray class group. We show that this leads to a reinterpretation of the action of the class group of a suborder $O' \subseteq O$ on the set of $O'$-oriented elliptic curves, discuss several other examples, and briefly comment on the hardness of the corresponding vectorization problems.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2024-07-19: last updated
- 2024-07-19: published
- Short URL
- https://ia.cr/2024/1172
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2024/1172,
author = {Sarah Arpin and Wouter Castryck and Jonathan Komada Eriksen and Gioella Lorenzon and Frederik Vercauteren},
title = {Generalized class group actions on oriented elliptic curves with level structure},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/1172},
year = {2024},
url = {https://eprint.iacr.org/2024/1172}
}