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

Authors:
Omran Ahmadi;Alfred Menezes
Affiliations:
Department of Combinatorics & Optimization, University of Waterloo, Canada;Department of Combinatorics & Optimization, University of Waterloo, Canada
Venue:
Designs, Codes and Cryptography
Year:
2005

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Abstract

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.