Elliptic periods for finite fields
Number Theory
2012-05-07 v2 Algebraic Geometry
Abstract
We construct two new families of basis for finite field extensions. Basis in the first family, the so-called elliptic basis, are not quite normal basis, but they allow very fast Frobenius exponentiation while preserving sparse multiplication formulas. Basis in the second family, the so-called normal elliptic basis are normal basis and allow fast (quasi linear) arithmetic. We prove that all extensions admit models of this kind.
Cite
@article{arxiv.0802.0165,
title = {Elliptic periods for finite fields},
author = {Jean-Marc Couveignes and Reynald Lercier},
journal= {arXiv preprint arXiv:0802.0165},
year = {2012}
}