Reynald Lercier

J.-M. Couveignes and R. Lercier. Elliptic periods for finite fields. Finite Fields and their Applications, 15(1):1-22, January 2009.

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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