Bruhat-Tits trees and supersingular elliptic curves

Abstract: Cryptographic schemes based on computing isogenies of supersingular elliptic curves are a fairly young topic in post-quantum cryptography. Their main benefits are their size: public keys are just a few field elements. Their main drawbacks are their speed - and underlying algebraic structure, which has not been explored fully. We will focus on the SIDH family of proposals and propose studying them from the view of Bruhat-Tits trees. These trees are simple combinatorial objects, we can describe them using 2x2 matrices, and use them to capture the information on torsion points coming from SIDH. This is joint work with Laia Amorós, Annamaria Iezzi, Kristin Lauter, and Chloe Martindale.

algebraic geometrynumber theory

Audience: researchers in the topic

Leiden Algebra, Geometry, and Number Theory Seminar