Quantum security analysis of unrestricted isogeny-based group actions

Xavier Bonnetain; Max Duparc; Dania Lazzarini; Luciano Maino; Chloe Martindale; Christophe Petit; Sina Schaeffler; André Schrottenloher; Alessandro Sferlazza

Paper 2026/2215

Quantum security analysis of unrestricted isogeny-based group actions

Xavier Bonnetain, Université de Lorraine

Max Duparc

, École Polytechnique Fédérale de Lausanne

Dania Lazzarini

, Université Libre de Bruxelles

Luciano Maino

, University of Birmingham

Chloe Martindale, University of Bristol, TSVP, Okinawa Institute of Science and Technology

Christophe Petit, Université Libre de Bruxelles, University of Birmingham

Sina Schaeffler

, IBM Research Europe, Zurich, Switzerland, ETH Zurich, TSVP, Okinawa Institute of Science and Technology

André Schrottenloher

, Univ Rennes, Inria, CNRS, IRISA, Rennes, France, TSVP, Okinawa Institute of Science and Technology

Alessandro Sferlazza

, Technical University of Munich, TSVP, Okinawa Institute of Science and Technology

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.
Keywords: Isogenies Group Actions CSIDH qt-Pegasis
Contact author(s): xavier bonnetain @ inria fr
max duparc @ epfl ch
dania lazzarini @ ulb be
l maino @ bham ac uk
chloe martindale @ bristol ac uk
Christophe Petit @ ulb be
sschaeffle @ ethz ch
andre schrottenloher @ inria fr
alessandro sferlazza @ tum de
History: 2026-09-28: revised; 2026-09-25: received; See all versions
Short URL: https://ia.cr/2026/2215
License: CC BY

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}
}