Jana Sotáková – University of Amsterdam

Title: Algebraic aspects of isogeny-based cryptography

Abstract: Cryptographic schemes based on isogeny graphs of elliptic curves give interesting candidates for post-quantum cryptography. Isogenies carry with them lots of beautiful number theory, which makes them attractive to number theorists and opaque to cryptographers. We will look at the Supersingular Isogeny Diffie-Hellman key exchange (SIDH) and look at how much one can gain from studying endomorphism rings and torsion points. Finally, we propose to systematize this extra information on isogeny graphs using Bruhat-Tits trees. This is joint work with Laia Amorós, Annamaria Iezzi, Kristin Lauter, and Chloe Martindale.