I am interested in the applications of algebraic number theory and arithmetic geometry to isogeny-based cryptography. My research is a mix of explorations of the mathematics underpinning proposed protocols and analysis of their concrete security. I have ongoing projects on:
Connections between class field theory, generalized class group actions, and level structures on elliptic curves
Bilinear pairings on elliptic curves
Concrete hardness of the supersingular isogeny problem
Publications
Extending Class Group Action Attacks via Sesquilinear Pairings, Advances in Cryptology – ASIACRYPT 2024. Joint with Katherine E. Stange.