Multivariate Permutation Polynomial Systems and Nonlinear Pseudorandom Number Generators

TL;DR

This paper investigates multivariate permutation polynomial systems that generate dynamical systems with polynomial degree growth, providing bounds on exponential sums and demonstrating their potential for improved pseudorandom number generation.

Contribution

It introduces a new class of dynamical systems based on multivariate permutation polynomials and establishes stronger average-case bounds for their exponential sums, enhancing pseudorandomness analysis.

Findings

Polynomial degree growth in the systems

Stronger average bounds on exponential sums

Potential application in pseudorandom number generators

Abstract

In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques studied previously for inversive generators, we bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates on average over all initial values than in the general case and thus can be of use for pseudorandom number generation.