English

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