fast arithmetics in artin-schreier towers over finite fields
An Artin-Schreier tower over the finite field F p is a tower of field extensions generated by polynomials of the form X p - X -?. 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.
artin-schreier algorithms complexity