Fast Deterministic Normal Bases and Circulant Polynomial Determinants

Mark Giesbrecht, Armin Jamshidpey, Éric Schost

Let $\mathsf{E}={\mathbb{F}}_q[x]/(\hat{I}“)$ be an algebraic extension of degree $n$ over the finite field ${\mathbb{F}}_q$, given by a $\hat{I}“\in {\mathbb{F}}_q[x]$ monic and irreducible. It is clas…