New algorithms for the Deuring correspondence Towards practical and secure SQISign signatures
hal.structure.identifier | IBM Research [Zurich] | |
dc.contributor.author | DE FEO, Luca | |
hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
hal.structure.identifier | DGA | |
dc.contributor.author | LEROUX, Antonin | |
hal.structure.identifier | Microsoft Research | |
dc.contributor.author | LONGA, Patrick | |
hal.structure.identifier | Centre National de la Recherche Scientifique [CNRS] | |
hal.structure.identifier | Unité de Mathématiques Pures et Appliquées [UMPA-ENSL] | |
hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
dc.contributor.author | WESOLOWSKI, Benjamin | |
dc.date.accessioned | 2024-04-04T02:34:42Z | |
dc.date.available | 2024-04-04T02:34:42Z | |
dc.date.conference | 2023-04-23 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190572 | |
dc.description.abstractEn | The Deuring correspondence defines a bijection between isogenies of supersingular elliptic curves and ideals of maximal orders in a quaternion algebra. We present a new algorithm to translate ideals of prime-power norm to their corresponding isogenies — a central task of the effective Deuring correspondence. The new method improves upon the algorithm introduced in 2021 by De Feo, Kohel, Leroux, Petit and Wesolowski as a building-block of the SQISign signature scheme. SQISign is the most compact post-quantum signature scheme currently known, but is several orders of magnitude slower than competitors, the main bottleneck of the computation being the ideal-to-isogeny translation. We implement the new algorithm and apply it to SQISign, achieving a more than two-fold speedup in key generation and signing with a new choice of parameter. Moreover, after adapting the state-of-the-art Fp2 multiplication algorithms by Longa to implement SQISign’s underlying extension field arithmetic and adding various improvements, we push the total speedups to over three times for signing and four times for verification. In a second part of the article, we advance cryptanalysis by showing a very simple distinguisher against one of the assumptions used in SQISign. We present a way to impede the distinguisher through a few changes to the generic KLPT algorithm. We formulate a new assumption capturing these changes, and provide an analysis together with experimental evidence for its validity. | |
dc.description.sponsorship | Méthodes pour les variétés abéliennes de petite dimension - ANR-20-CE40-0013 | |
dc.description.sponsorship | Post-quantum padlock for web browser - ANR-22-PETQ-0008 | |
dc.description.sponsorship | Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020 | |
dc.language.iso | en | |
dc.rights.uri | http://creativecommons.org/licenses/by/ | |
dc.subject.en | Post-quantum cryptography | |
dc.subject.en | Isogenies | |
dc.subject.en | Group actions | |
dc.title.en | New algorithms for the Deuring correspondence Towards practical and secure SQISign signatures | |
dc.type | Communication dans un congrès | |
dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.conference.title | Eurocrypt 2023 | |
bordeaux.country | FR | |
bordeaux.conference.city | Lyon | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-04052502 | |
hal.version | 1 | |
hal.invited | non | |
hal.proceedings | oui | |
hal.conference.end | 2023-04-27 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-04052502v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=DE%20FEO,%20Luca&LEROUX,%20Antonin&LONGA,%20Patrick&WESOLOWSKI,%20Benjamin&rft.genre=unknown |
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