Theoretical and Experimental Comparison of Efficiency of Finite Field Extensions

An extension of composite degree over a finite field may be implemented in one or more steps, involving the implementation of zero or more intermediate fields. A comparison of the expected efficiency of different field extensions is made, using a known probabilistic algorithm to form each extension. A new algorithm is described which provides a different method for forming single extensions of composite degree. It is shown that this method is expected to be more efficient than the previously used algorithm. Results of test runs of implementations of these algorithms are presented which support the theoretical claims.