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Licensed Unlicensed Requires Authentication Published by De Gruyter 2019

8. A survey on iterations of mappings over finite fields

From the book Combinatorics and Finite Fields

  • Rodrigo Martins , Daniel Panario and Claudio Qureshi
https://doi.org/10.1515/9783110642094-008

Abstract

We survey iterations of polynomials and rational functions over finite fields. We show precise information on periodicity and permutational properties for some classical functions over finite fields including some quadratic polynomials, Chebyshev, Rédei, linearized and power maps. It seems hard to predict the periodicity behavior of functions over a finite field, so we provide heuristic arguments aiming at understanding their behavior in comparison to random uniform mappings over a finite field. We conclude showing a well-known methodology that provides many results about uniform random mappings.

© 2019 Walter de Gruyter GmbH, Berlin/Munich/Boston
From the book
Combinatorics and Finite Fields
Combinatorics and Finite Fields

Chapters in this book (18)

Frontmatter
Introduction
Contents
1. Tiling rings with “precious” differences
2. q-analogs of group divisible designs
3. A survey on bent functions and their duals
4. Construction of Bent functions using covering extended building sets
5. Results on permutation polynomials of shape xt + γTrqn/q(xd)
6. A new structure for difference matrices over abelian p-groups
7. Weil sums of binomials: properties, applications and open problems
8. A survey on iterations of mappings over finite fields
9. Cyclotomy, difference sets, sequences with low correlation, strongly regular graphs and related geometric substructures
10. Pseudorandomness of large sets in finite fields
11. Point-plane incidences and some applications in positive characteristic
12. A survey of group invariant Butson matrices and their relation to generalized bent functions and various other objects
13. MRD codes: constructions and connections
14. Differential fault attack on hardware stream ciphers—a technical survey
15. Polynomials over finite fields: an index approach
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