Pseudorandomness and Dynamics of Fermat Quotients

TL;DR

This paper investigates the properties and pseudorandom characteristics of Fermat quotients, including fixed points, distribution, cycle lengths, and linear complexity, through theoretical analysis and experiments.

Contribution

It provides new theoretical insights and experimental data on the dynamical behavior and pseudorandomness of Fermat quotients.

Findings

Analysis of fixed points and cycle lengths of Fermat quotient dynamics

Experimental results on distribution and pseudorandom properties

Assessment of linear complexity and joint distribution patterns

Abstract

We obtain some theoretic and experimental results concerning various properties (the number of fixed points, image distribution, cycle lengths) of the dynamical system naturally associated with Fermat quotients acting on the set $\{0, ..., p-1\}$. We also consider pseudorandom properties of Fermat quotients such as joint distribution and linear complexity.