Elliptic periods for finite fields

Authors:
Jean-Marc Couveignes;Reynald Lercier
Affiliations:
Institut de Mathématiques de Toulouse, Université de Toulouse et CNRS, Département de Mathématiques et Informatique, Université Toulouse 2, 5 allées Antonio Machado, ...;DGA/CÉLAR, La Roche Marguerite, F-35174 Bruz, France and IRMAR, Université de Rennes 1, Campus de Beaulieu, F-35042 Rennes, France
Venue:
Finite Fields and Their Applications
Year:
2009

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Abstract

We construct two new families of basis for finite field extensions. Bases in the first family, the so-called elliptic bases, are not quite normal bases, but they allow very fast Frobenius exponentiation while preserving sparse multiplication formulas. Bases in the second family, the so-called normal elliptic bases are normal bases and allow fast (quasi-linear) arithmetic. We prove that all extensions admit models of this kind.