Random Self-reducibility of Ideal-SVP via Arakelov Random Walks - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2020

Random Self-reducibility of Ideal-SVP via Arakelov Random Walks

Résumé

Fixing a number field, the space of all ideal lattices, up to isometry, is naturally an Abelian group, called the Arakelov class group. This fact, well known to number theorists, has so far not been explicitly used in the literature on lattice-based cryptography. Remarkably, the Arakelov class group is a combination of two groups that have already led to significant cryptanalytic advances: the class group and the unit torus. In the present article, we show that the Arakelov class group has more to offer. We start with the development of a new versatile tool: we prove that, subject to the Riemann Hypothesis for Hecke L-functions, certain random walks on the Arakelov class group have a rapid mixing property. We then exploit this result to relate the average-case and the worst-case of the Shortest Vector Problem in ideal lattices. Our reduction appears particularly sharp: for Hermite-SVP in ideal lattices of certain cyclotomic number fields, it loses no more than $\tilde O(\sqrt{n})$ factor on the Hermite approximation factor. Furthermore, we suggest that this rapid-mixing theorem should find other applications in cryptography and in algorithmic number theory.
Fichier principal
Vignette du fichier
2020-297.pdf (622.68 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02513308 , version 1 (20-03-2020)
hal-02513308 , version 2 (22-09-2020)

Identifiants

Citer

Koen de Boer, Leo Ducas, Alice Pellet-Mary, Benjamin Wesolowski. Random Self-reducibility of Ideal-SVP via Arakelov Random Walks. CRYPTO 2020, Aug 2020, Santa Barbara, United States. ⟨10.1007/978-3-030-56880-1_9⟩. ⟨hal-02513308v2⟩
184 Consultations
109 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More