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 α generates a Type I optimal normal basis in F 2 n , then its dual basis has complexity 3 n−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 .
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