Paper 2024/880 Original: eprint.iacr.org/2024/880 ↗
Extending class group action attacks via sesquilinear pairings
Abstract
We introduce a new tool for the study of isogeny-based cryptography, namely pairings which are sesquilinear (conjugate linear) with respect to the $\mathcal{O}$-module structure of an elliptic curve with CM by an imaginary quadratic order $\mathcal{O}$. We use these pairings to study the security of problems based on the class group action on collections of oriented ordinary or supersingular elliptic curves. This extends work of of both (Castryck, Houben, Merz, Mula, Buuren, Vercauteren, 2023) and (De Feo, Fouotsa, Panny, 2024).
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2024-10-01: last updated
- 2024-06-02: published
- Short URL
- https://ia.cr/2024/880
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2024/880,
author = {Joseph Macula and Katherine E. Stange},
title = {Extending class group action attacks via sesquilinear pairings},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/880},
year = {2024},
url = {https://eprint.iacr.org/2024/880}
}