Paper 2026/2215 Original: eprint.iacr.org/2026/2215 ↗
Quantum security analysis of unrestricted isogeny-based group actions
Abstract
Setting concrete parameters for group action based cryptographic protocols is notoriously difficult due to the incomplete understanding of the concrete efficiency of Kuperberg's subexponential quantum attack. Estimates for the CSIDH group action do exist in the literature, but they do not easily translate into meaningful estimates for the many recent and far more efficient alternative group actions. In this paper, we implement the recent qt-Pegasis group action framework as a (simulated) quantum circuit, allowing for concrete estimation of its efficiency and Kuperberg's attack. Our results suggest that using a 2048-bit base field in qt-Pegasis offers reasonable quantum security, while a 4096-bit base field is required to reach NIST security level 1.
Metadata
- Available format(s)
PDF- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- History
- 2026-09-28: last updated
- 2026-09-25: published
- Short URL
- https://ia.cr/2026/2215
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2026/2215,
author = {Xavier Bonnetain and Max Duparc and Dania Lazzarini and Luciano Maino and Chloe Martindale and Christophe Petit and Sina Schaeffler and André Schrottenloher and Alessandro Sferlazza},
title = {Quantum security analysis of unrestricted isogeny-based group actions},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2215},
year = {2026},
url = {https://eprint.iacr.org/2026/2215}
}