Fast arithmetics in Artin–Schreier towers over finite fields

Luca De Feo, Éric Schost
2012 Journal of symbolic computation  
An Artin-Schreier tower over the finite field Fp is a tower of field extensions generated by polynomials of the form X p − 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.
doi:10.1016/j.jsc.2011.12.008 fatcat:iifmqekumvb3lattsy3pcdzrfy