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Elliptic periods for finite fields. (English) Zbl 1216.11106
Summary: We construct two new families of bases 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.

MSC:
11T30 Structure theory for finite fields and commutative rings (number-theoretic aspects)
12E20 Finite fields (field-theoretic aspects)
Software:
Magma
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References:
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