Two Approaches to computing the endomorphism ring of a supersingular elliptic curve

by Annamaria Iezzi

Thursday Dec 12, 2024, 2:00 PM → 3:00 PM Europe/Paris

The endomorphism ring of a supersingular elliptic curve defined over a finite field is a maximal order inside a quaternion algebra. Computing this order is a hard problem and this assumption is central to the security of protocols of isogeny-based cryptography.
In this talk, we present an algorithm for computing an inseparable endomorphism of a supersingular elliptic curve defined over F_{p^2}. Building on this, we outline two distinct approaches to computing the full endomorphism ring of such curves and discuss some open questions that arise from this work.
This is based on a joint work with Jenny G. Fuselier, Mark Kozek, Travis Morrison, and Changningphaabi Namoijam.