Fast arithmetics in Artin–Schreier towers over finite fields

An Artin–Schreier tower over the finite field Fp is a tower of field extensions generated by polynomials of the form Xp−X−α. Following Cantor and Couveignes, we give algorithms with quasi-linear time complexity for arithmetic operations in such towers. As an application, we present an implementation of Couveignes’ algorithm for computing isogenies between elliptic curves using the p-torsion.