Involutions, Trace Maps, and Pseudorandom Numbers

Abstract

Interesting properties of the partitions of a finite field ${\mathbb{F}}_q$ induced by the combination of involutions and trace maps are studied. The special features of involutions of the form $\frac{u}{z}$, $u$ being a fixed element of ${\mathbb{F}}_q$, 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 ${\mathbb{F}}_q$.

minor changes