The supersingular isogeny path and endomorphism ring problems are equivalent
WESOLOWSKI, Benjamin
Lithe and fast algorithmic number theory [LFANT]
Centre National de la Recherche Scientifique [CNRS]
Lithe and fast algorithmic number theory [LFANT]
Centre National de la Recherche Scientifique [CNRS]
WESOLOWSKI, Benjamin
Lithe and fast algorithmic number theory [LFANT]
Centre National de la Recherche Scientifique [CNRS]
< Reduce
Lithe and fast algorithmic number theory [LFANT]
Centre National de la Recherche Scientifique [CNRS]
Language
en
Communication dans un congrès
This item was published in
FOCS 2021 - 62nd Annual IEEE Symposium on Foundations of Computer Science, 2022-02-07, Denver, Colorado.
English Abstract
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 ...Read more >
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.Read less <
ANR Project
Méthodes pour les variétés abéliennes de petite dimension - ANR-20-CE40-0013
Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008
Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008
Origin
Hal imported