Fast Arithmetics in Artin-Schreier Towers over Finite Fields

Details Fast Arithmetics in Artin-Schreier Towers over Finite Fields Fast Arithmetics in Artin-Schreier Towers over Finite Fields

2010-02-12

arxiv.org/abs/1002.2594v1

Computer Science

Symbolic Computation

28 pages, 4 figures, 3 tables, uses mathdots.sty, yjsco.sty Submitted to J. Symb. Comput

Scientific paper

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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