Jana Sotáková

Isogenies of elliptic curves over finite fields and genus theory

We will look at ideal class groups of imaginary quadratic orders acting on elliptic curves over finite fields via isogenies. These can be used to define public-key cryptosystems, such as CRS and CSIDH; we will show how to break some of the computational assumptions for CRS. To do this, we will compute the quadratic characters of the class group (coming from genus theory) directly from the elliptic curves. This is joint work with Wouter Castryck and Fre Vercauteren.