Efficient algorithm for finding a primitive element of a finite field

Develop a polynomial-time algorithm for finding a primitive element (generator of the multiplicative group) of an arbitrary finite field F.

Background

The proposed approach to rank-1 wildcard decomposition over fixed finite fields relies on expressing values as powers of a primitive element to convert multiplicative equations into additive ones. This step hinges on the availability of an efficient method to find a primitive element, which is presently not known.