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Designs, Codes and Cryptography

, Volume 87, Issue 2–3, pp 393–416 | Cite as

The graph structure of Chebyshev polynomials over finite fields and applications

  • Claudio Qureshi
  • Daniel PanarioEmail author
Article
Part of the following topical collections:
  1. Special Issue: Coding and Cryptography

Abstract

We completely describe the functional graph associated to iterations of Chebyshev polynomials over finite fields. Then, we use our structural results to obtain estimates for the average rho length, average number of connected components and the expected value for the period and preperiod of iterating Chebyshev polynomials.

Keywords

Chebyshev polynomials Dynamical systems over finite fields Permutation polynomials over finite fields 

Mathematics Subject Classification

12E20 11T06 11T71 

Notes

Acknowledgements

Claudio Qureshi was supported by Fapesp grant 201526420-1 and the second author by NSERC of Canada. Most of this work was done while the Claudio Qureshi was visiting Carleton University. This author wishes to thank the Fields Institute for funding this visit.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematics, Statistics and Computing ScienceUnicampCampinasBrazil
  2. 2.School of Mathematics and StatisticsCarleton UniversityOttawaCanada

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