Fast Arithmetics in Artin-Schreier Towers over Finite Fields
Symbolic Computation
2020-01-07 v1 Mathematical Software
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.
Keywords
Cite
@article{arxiv.1002.2594,
title = {Fast Arithmetics in Artin-Schreier Towers over Finite Fields},
author = {Luca De Feo and Éric Schost},
journal= {arXiv preprint arXiv:1002.2594},
year = {2020}
}
Comments
28 pages, 4 figures, 3 tables, uses mathdots.sty, yjsco.sty Submitted to J. Symb. Comput