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Fast Arithmetics in Artin-Schreier Towers over Finite Fields (1002.2594v1)
Published 12 Feb 2010 in cs.SC and cs.MS
Abstract: An Artin-Schreier tower over the finite field F_p is a tower of field extensions generated by polynomials of the form Xp - X - a. 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.
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