DECRU, Thomas; KUNZWEILER, Sabrina

doi:10.1007/978-3-031-37679-5_3

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DECRU, Thomas
IMEC [IMEC]

KUNZWEILER, Sabrina
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]

Langue

Communication dans un congrès

Ce document a été publié dans

Lecture Notes in Computer Science, Lecture Notes in Computer Science, AfricaCrypt 2023, 2023-07-19, Sousse. 2023-07-13, vol. 14064, p. 53-78

Résumé en anglais

The parametrization of $(3, 3)$-isogenies by Bruin, Flynn and Testa requires over 37.500 multiplications if one wants to evaluate a single isogeny in a point. We simplify their formulae and reduce the amount of required multiplications by 94%. Further we deduce explicit formulae for evaluating $(3, 3)$-splitting and gluing maps in the framework of the parametrization by Bröker, Howe, Lauter and Stevenhagen. We provide implementations to compute $(3^n , 3^n)$-isogenies between principally polarized abelian surfaces with a focus on cryptographic application. Our implementation can retrieve Alice's secret isogeny in 11 seconds for the SIKEp751 parameters, which were aimed at NIST level 5 security.< Réduire

Mots clés en anglais

Isogenies

Post-quantum Cryptography

Abelian surfaces

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190446

DOI

http://dx.doi.org/10.1007/978-3-031-37679-5_3

Project ANR

Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251