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
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