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

Alina Ostafe; Igor E. Shparlinski

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

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

Alina Ostafe^*
, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

39 Downloads (Pure)

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.

Original language	English
Pages (from-to)	501-511
Number of pages	11
Journal	Mathematics of Computation
Volume	79
Issue number	269
DOIs	https://doi.org/10.1090/S0025-5718-09-02271-6
Publication status	Published - 2010

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title = "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.",

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AU - Ostafe, Alina

AU - Shparlinski, Igor E.

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/77950865435

U2 - 10.1090/S0025-5718-09-02271-6

DO - 10.1090/S0025-5718-09-02271-6

M3 - Article

AN - SCOPUS:77950865435

SN - 0025-5718

VL - 79

SP - 501

EP - 511

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 269

ER -

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

Abstract

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