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Simple method to find the trace of an arbitrary element of a finite field

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<mark>Journal publication date</mark>30/03/2006
<mark>Journal</mark>Electronics Letters
Issue number7
Volume42
Number of pages3
Pages (from-to)423-425
<mark>State</mark>Published
<mark>Original language</mark>English

Abstract

A novel technique is described for computing the trace over GF(2) of an element from a given finite field GF(2m). This technique requires a primitive polynomial of degree m and a division circuit only, i.e. the usual knowledge of a table of powers of a primitive element of GF(2m) is not required. The computation of the minimal polynomial of an element of GF(2m) is derived as a function of the trace and of a sub-trace function