Sentence:  When using <WSD>polynomial bases</WSD>, the first stage in computing the product of two elements of \mathbb F_{2^n} is the multiplication of two polynomials of degree at most n-1 in \mathbb F_2[x]. 
Meaning of the word marked with <WSD> tags:  "Specifically", a basis, of the form <big>{</big>1, "α", ..., "α''''n"-1<big>}</big>, of a finite extension '''F'''<sub>"qn"</sub> of a Galois field '''F'''<sub>"q"</sub>, where "α" is a primitive element of '''F'''<sub>"qn"</sub> (i.e., a root of a degree-"n" primitive polynomial over '''F'''<sub>"q"</sub>).