@inproceedings{Gathen1990ConstructingNB,
title={Constructing Normal Bases in Nite Elds},
author={Joachim von zur Gathen and Mark Giesbrecht},
year={1990}
}

An eecient probabilistic algorithm to nd a normal basis in a nite eld is presented. It can, in fact, nd an element of arbitrary prescribed additive order. It is based on a density estimate for normal elements. A similar estimate yields a probabilistic polynomial-time reduction from nding primitive normal elements to nding primitive elements.