Fast arithmetics in artin-schreier towers over finite fields

Luca De Feo, Éric Schost
2009 Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09  
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:10.1145/1576702.1576722 dblp:conf/issac/FeoS09 fatcat:ahsgz7hfd5axvhranfxynmkxbm