On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators

TL;DR

This paper investigates polynomial dynamical systems, providing degree growth estimates and exponential sum bounds, demonstrating their potential for improved pseudorandom number generation.

Contribution

It introduces new degree growth bounds for polynomial iterations and applies these to enhance pseudorandom number generator analysis.

Findings

Degree growth estimates for polynomial iterations

Stronger exponential sum bounds along orbits

Potential applications in pseudorandom number generation

Abstract

In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degreegrowth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates than in the general case and thus can be of use for pseudorandom number generation.