Designs, Codes and Cryptography

, Volume 37, Issue 3, pp 493–507

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


DOI: 10.1007/s10623-004-4039-4

Cite this article as:
Ahmadi, O. & Menezes, A. Des Codes Crypt (2005) 37: 493. doi:10.1007/s10623-004-4039-4


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.


finite fields trace function polynomial bases 

AMS Classification

11T06 11T71 

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Combinatorics & OptimizationUniversity of WaterlooCanada

Personalised recommendations