Title: Computing the endomorphism ring of a supersingular elliptic curve over a finite field

Abstract: The endomorphism ring of a supersingular elliptic curve 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 isogeny-based cryptography, a young and very active subfield of post-quantum cryptography based on the mathematical problem of finding an isogeny between two given elliptic curves.

In this talk, after reviewing the mathematical and cryptographic context, we will discuss the state-of-art of this problem and we will present some recent advances about it. This is a joint work with Jenny G. Fuselier, Mark Kozek, Travis Morrison and Changningphaabi Namoijam.

Remarks: The seminar will be given in English or Italian, depending on the audience, and it will be accessible also to master students.