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

Ostafe, Alina; Shparlinski, Igor

doi:10.1090/S0025-5718-09-02271-6

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

Authors: Alina Ostafe and Igor E. Shparlinski
Journal: Math. Comp. 79 (2010), 501-511
MSC (2000): Primary 11K45, 11T23, 37A45, 37F10
DOI: https://doi.org/10.1090/S0025-5718-09-02271-6
Published electronically: July 7, 2009
MathSciNet review: 2552237
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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.

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