Paper 2023/1726 Original: eprint.iacr.org/2023/1726 ↗
CSIDH with Level Structure
Abstract
We construct a new post-quantum cryptosystem which consists of enhancing CSIDH and similar cryptosystems by adding a full level $N$ structure. We discuss the size of the isogeny graph in this new cryptosystem which consists of components which are acted on by the ray class group for the modulus $N$. We conclude by showing that, if we can efficiently find rational isogenies between elliptic curves, then we can efficiently find rational isogenies that preserve the level structure. We show that one can reduce the group action problem for the ray class group to the group action problem for the ideal class group. This reduces the security of this new cryptosystem to that of the original one
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2023-11-07: last updated
- 2023-11-07: published
- Short URL
- https://ia.cr/2023/1726
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2023/1726,
author = {Steven D. Galbraith and Derek Perrin and José Felipe Voloch},
title = {CSIDH with Level Structure},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/1726},
year = {2023},
url = {https://eprint.iacr.org/2023/1726}
}