Low complexity normal bases in F2n

Authors:
Benjamin Young;Daniel Panario
Affiliations:
School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ont., Canada K1S 5B6;School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ont., Canada K1S 5B6
Venue:
Finite Fields and Their Applications
Year:
2004

Citing 3
Cited 3

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On the complexity of the dual basis of a type I optimal normal basis

Finite Fields and Their Applications

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Abstract

We investigate low complexity normal bases in finite fields of the form F"2"^"n. First, we prove that if two normal elements have the same multiplication table, then they are conjugates. Then, we provide a partial converse to the known fact that if @a generates a Type I optimal normal basis in F"2"^"n, then its dual basis has complexity 3n-3. Finally, we determine the multiplication tables of low complexity normal elements that arise from products of normal elements in subfields of F"2"^"n.