%0 Journal Article
%T Elliptic periods for finite fields
%A Jean-Marc Couveignes
%A Reynald Lercier
%J Mathematics
%D 2008
%I arXiv
%R 10.1016/j.ffa.2008.07.004
%X 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.
%U http://arxiv.org/abs/0802.0165v2