, Volume 37, Issue 3, pp 493-507

On the Number of Trace-One Elements in Polynomial Bases for \(\mathbb{F}_{2^n}\)

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This paper investigates the number of trace-one elements in a polynomial basis for \(\mathbb{F}_{2^n}\) . A polynomial basis with a small number of trace-one elements is desirable because it results in an efficient and low cost implementation of the trace function. We focus on the case where the reduction polynomial is a trinomial or a pentanomial, in which case field multiplication can also be efficiently implemented.

Communicated by: P. Wild