Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

31^st  of October 2023, 14:30-16:00, room “Dal Passo”

 

 

 

 

 

 

 

 

 The supersingular Endomorphism Ring and One Endomorphism problems are equivalent

 

Benjamin Wesolowski
ENS de Lyon

 

 

 

The supersingular Endomorphism Ring problem is the following: given a supersingular elliptic curve, compute all of its endo- morphisms. The presumed hardness of this problem is foundational for isogeny-based cryptography. The One Endomorphism problem only asks to find a single non-scalar endomorphism. We prove that these two problems are equivalent, under probabilistic polynomial time reductions. We prove a number of consequences: on the security of cryptosystems, on the hardness of computing isogenies between supersingular elliptic curves, and on solving the endomorphism ring problem.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry