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. Categories and Subject Descriptors:

• Type: Conference
• Year: 2009
• Where: ISSAC
• Authors: Luca De Feo, Éric Schost
• Keywords: Artin-Schreier Tower, ISSAC 2009, Mathematics, Quasi-linear Time Complexity, finite field Fp