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.
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Communicated by: P. Wild
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Ahmadi, O., Menezes, A. On the Number of Trace-One Elements in Polynomial Bases for \(\mathbb{F}_{2^n}\). Des Codes Crypt 37, 493–507 (2005). https://doi.org/10.1007/s10623-004-4039-4
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DOI: https://doi.org/10.1007/s10623-004-4039-4