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arXiv · 1002.2594

Fast Arithmetics in Artin-Schreier Towers over Finite Fields

Luca De Feo·Éric Schost
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Abstract

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 - 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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Luca De Feo, Éric Schost. 2010-02-12. Fast Arithmetics in Artin-Schreier Towers over Finite Fields. https://doi.org/10.1016/j.jsc.2011.12.008

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