Geometry Seminar

University of Tor Vergata, Department of Mathematics

4th of April 2023, 14:30-15:30, room “Dal Passo”

Speaker

Sarah Arpin

(Leiden)

Title

 Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs

Abstract

:

Abstract: The classical Deuring correspondence provides a roadmap between supersingular elliptic curves and the maximal orders which are isomorphic to their endomorphism rings. Building on this idea, we add the information of a cyclic subgroup of prime order N to supersingular elliptic curves, and prove a generalisation of the Deuring correspondence for these objects. We also study the resulting ell-isogeny graphs supersingular elliptic curve with level-N structure, and the corresponding graphs in the realm of quaternion algebras. The structure of the supersingular elliptic curve ell-isogeny graph underlies the security of a new cryptographic signature protocol, SQISign, which is proposed to be resistant against both classical and quantum attack.