Involutions, trace maps, and pseudorandom numbers

Abstract

Interesting properties of the partitions of a finite field 𝔽q induced by the combination of involutions and trace maps are studied. The special features of involutions of the form , u being a fixed element of 𝔽q, are exploited to generate pseudorandom numbers, the randomness resting on the uniform distribution of the images of zero-trace elements among the sets of non-zero trace elements of 𝔽q.