Qlapoty: Improved analysis and eﬃciency for quaternionic ideal to isogeny transformation

Max Duparc; Antonin Leroux; Sina Schaeﬄer

Paper 2026/1700

Qlapoty: Improved analysis and eﬃciency for quaternionic ideal to isogeny transformation

Max Duparc

, École Polytechnique Fédérale de Lausanne

Antonin Leroux

, DGA-MI, IRMAR - UMR 6625, Université de Rennes

Sina Schaeﬄer

, ETH Zurich, IBM Research - Zurich

Abstract

The quaternionic ideal-to-isogeny translation is a central building block of SQIsign. While the Qlapoti algorithm by Borin, Invernizzi, Corte-Real Santos, Eriksen, Mula, Schaeffler and Vercauteren significantly simplified and accelerated this step, it does not treat several technical details in sufficient depth, resulting in a flawed analysis of its failure probability. Additionally, several discrepancies between the implementation of Qlapoti and the paper's pseudocode were never analyzed explicitly. We address these shortcomings and add further improvements, resulting in a new norm equation solving algorithm with negligible failure probability. Our C implementations shows 6x to 9x speedups compared to Qlapoti's norm equation solver, and 1.3x-2.1x speedups for a SQIsign NIST2 signature (depending on NIST levels).

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Isogenies Quaternions Ideal-to-Isogeny SQIsign
Contact author(s): max duparc @ epfl ch
antonin leroux @ polytechnique org
sschaeffle @ ethz ch
History: 2026-08-16: approved; 2026-08-15: received; See all versions
Short URL: https://ia.cr/2026/1700
License: CC BY

BibTeX

@misc{cryptoeprint:2026/1700,
      author = {Max Duparc and Antonin Leroux and Sina Schaeﬄer},
      title = {Qlapoty: Improved analysis and eﬃciency for quaternionic ideal to isogeny transformation},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1700},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1700}
}