BOUDGOUST, Katharina; GACHON, Erell; PELLET-MARY, Alice

doi:10.1007/978-3-031-15979-4_17

Métadonnées

Licence d’utilisation du document

BOUDGOUST, Katharina
Aarhus University [Aarhus]

GACHON, Erell
Université de Bordeaux [UB]

PELLET-MARY, Alice
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]

Langue

Communication dans un congrès

Ce document a été publié dans

CRYPTO 2022, 2022-08-13, Santa Barbara / Hybrid. vol. 13508

Résumé en anglais

In this article, we generalize the works of Pan et al. (Eurocrypt’21) and Porter et al. (ArXiv’21) and provide a simple condition under which an ideal lattice defines an easy instance of the shortest vector problem. Namely, we show that the more automorphisms stabilize the ideal, the easier it is to find a short vector in it. This observation was already made for prime ideals in Galois fields, and we generalize it to any ideal (whose prime factors are not ramified) of any number field. We then provide a cryptographic application of this result by showing that particular instances of the partial Vandermonde knapsack problem, also known as partial Fourier recovery problem, can be solved classically in polynomial time. As a proof of concept, we implemented our attack and managed to solve those particular instances for concrete parameter settings proposed in the literature. For random instances, we can halve the lattice dimension with non-negligible probability.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191053

DOI

http://dx.doi.org/10.1007/978-3-031-15979-4_17

Project ANR

Sécurité cryptographique des réseaux modules - ANR-21-CE94-0003
Calcul réparti sécurisé : Cryptographie, Combinatoire, Calcul Formel - ANR-21-CE39-0006

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251