Primitive Normal Bases for Finite Fields

@inproceedings{Lenstra2010PrimitiveNB,
  title={Primitive Normal Bases for Finite Fields},
  author={Hendrik W. Lenstra and Ren{\'e} Schoof},
  year={2010}
}
It is proved that any finite extension of a finite field has a normal basis consisting of primitive roots. Introduction. Let q be a prime power, q > 1. We denote by Vq a finite field of q elements. It is well known that for every positive integer m there exists a normal basis of F ». over F?, i.e., a basis of the form (a,aq,aql,...,aq"'^) with a e F TM. It is also well known that the multiplicative group F*m of F^», is cyclic, i.e., that for some a G Fl we have ¥*,= {a": « e Z}. Such an element… CONTINUE READING
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