International Association
for Cryptologic Research

We introduce a new tool for the study of isogeny-based cryptography, namely pairings which are sesquilinear (conjugate linear) with respect to the O-module structure of an elliptic curve with CM by an imaginary quadratic field O. We use these pairings to study the security of problems based on the class group action on collections of oriented ordinary or supersingular elliptic curves. This extends work of [CHM+23] and [FFP24].