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2008
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The trace of an optimal normal element and low complexity normal bases

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The trace of an optimal normal element and low complexity normal bases
Let Fq be a finite field and consider an extension Fqn where an optimal normal element exists. Using the trace of an optimal normal element in Fqn , we provide low complexity normal elements in Fqm , with m = n/k. We give theorems for Type I and Type II optimal normal elements. When Type I normal elements are used with m = n/2, m odd and q even, our construction gives Type II optimal normal elements in Fqm ; otherwise we give low complexity normal elements. Since optimal normal elements do not exist for every extension degree m of every finite field Fq, our results could have a practical impact in expanding the available extension degrees for fast arithmetic using normal bases. Keywords Finite fields ? low complexity ? normal basis ? dual basis. Mathematics Subject Classification (2000) 12E30
Maria Christopoulou, Theodoulos Garefalakis, Danie
Added 25 Dec 2009
Updated 25 Dec 2009
Type Conference
Year 2008
Where DCC
Authors Maria Christopoulou, Theodoulos Garefalakis, Daniel Panario, David Thomson
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