WESOLOWSKI, Benjamin

Métadonnées

Licence d’utilisation du document

WESOLOWSKI, Benjamin
Lithe and fast algorithmic number theory [LFANT]
Centre National de la Recherche Scientifique [CNRS]

Langue

Communication dans un congrès

Ce document a été publié dans

FOCS 2021 - 62nd Annual IEEE Symposium on Foundations of Computer Science, 2022-02-07, Denver, Colorado.

Résumé en anglais

We prove that the path-finding problem in isogeny graphs and the endomorphism ring problem for supersingular elliptic curves are equivalent under reductions of polynomial expected time, assuming the generalised Riemann hypothesis. The presumed hardness of these problems is foundational for isogeny-based cryptography. As an essential tool, we develop a rigorous algorithm for the quaternion analog of the path-finding problem, building upon the heuristic method of Kohel, Lauter, Petit and Tignol. This problem, and its (previously heuristic) resolution, are both a powerful cryptanalytic tool and a building-block for cryptosystems.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191487

Project ANR

Méthodes pour les variétés abéliennes de petite dimension - ANR-20-CE40-0013
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