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arXiv · 0802.0165

Elliptic periods for finite fields

Jean-Marc Couveignes·Reynald Lercier
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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.

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BibTeXRIS

Jean-Marc Couveignes, Reynald Lercier. 2008-06-17. Elliptic periods for finite fields. https://doi.org/10.1016/j.ffa.2008.07.004

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