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

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

Metadatos

Licencia de uso del documento

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]

Idioma

Communication dans un congrès

Este ítem está publicado en

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

Resumen en inglés

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.< Leer menos

URI

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

DOI

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

Proyecto ANR

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

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251