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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
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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Additional Information

Alina Ostafe
Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190 CH-8057, Zürich, Switzerland
Email: alina.ostafe@math.uzh.ch

Igor E. Shparlinski
Affiliation: Department of Computing, Macquarie University, NSW 2109, Australia
Email: igor@ics.mq.edu.au

DOI: http://dx.doi.org/10.1090/S0025-5718-09-02271-6
PII: S 0025-5718(09)02271-6
Received by editor(s): February 23, 2009
Received by editor(s) in revised form: March 9, 2009
Published electronically: July 7, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.