Elliptic periods for finite fields

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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https://hal.archives-ouvertes.fr/hal-00630391
Contributor : Jean-Marc Couveignes <>
Submitted on : Sunday, October 9, 2011 - 6:58:17 PM
Last modification on : Thursday, October 17, 2019 - 8:57:41 AM

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Jean-Marc Couveignes, Reynald Lercier. Elliptic periods for finite fields. Finite Fields and Their Applications, Elsevier, 2009, 15 (1), pp.1-22. ⟨10.1016/j.ffa.2008.07.004⟩. ⟨hal-00630391⟩

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