WESOLOWSKI, Benjamin

Metadatos

Licencia de uso del documento

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

Idioma

Communication dans un congrès

Este ítem está publicado en

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

Resumen en inglés

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.< Leer menos

URI

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

Proyecto ANR

Méthodes pour les variétés abéliennes de petite dimension - ANR-20-CE40-0013
Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251