Paper 2021/955
Higher-degree supersingular group actions
Mathilde Chenu and Benjamin Smith
Abstract
We investigate the isogeny graphs of supersingular elliptic curves over \(\mathbb{F}_{p^2}\) equipped with a \(d\)-isogeny to their Galois conjugate. These curves are interesting because they are, in a sense, a generalization of curves defined over \(\mathbb{F}_p\), and there is an action of the ideal class group of \(\mathbb{Q}(\sqrt{-dp})\) on the isogeny graphs. We investigate constructive and destructive aspects of these graphs in isogeny-based cryptography, including generalizations of the CSIDH cryptosystem and the Delfs--Galbraith algorithm.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. MathCrypt 2021 - Mathematical Cryptology
- Keywords
- Isogeny-based cryptographySupersingular elliptic curvesEndomorphisms
- Contact author(s)
-
smith @ lix polytechnique fr
mathilde chenu @ inria fr - History
- 2021-07-22: received
- Short URL
- https://ia.cr/2021/955
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/955,
author = {Mathilde Chenu and Benjamin Smith},
title = {Higher-degree supersingular group actions},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/955},
year = {2021},
url = {https://eprint.iacr.org/2021/955}
}
