On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators

Abstract

In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degree growth 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. © 2009 American Mathematical Society Reverts to public domain 28 years from publication. © 2009 American Mathematical Society.