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

This paper investigates the number of trace-one elements in a polynomial basis for . 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