Fast Arithmetics in Artin-Schreier Towers over Finite Fields
Résumé
An Artin-Schreier tower over the finite field Fp is a tower of field extensions generated by polynomials of the form X^p-X-alpha. 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.