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Some Theorems on Planar Mappings

  • Gohar M. Kyureghyan
  • Alexander Pott
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5130)

Abstract

A mapping \(f:{\mathbb{F}}_p^n\to {\mathbb{F}}_p^n\) is called planar if for every nonzero \(a \in {\mathbb{F}}_p^n\) the difference mapping D f,a: xf(x + a) − f(x) is a permutation of \({\mathbb{F}}_p^n\). In this note we prove that two planar functions are CCZ-equivalent exactly when they are EA-equivalent. We give a sharp lower bound on the size of the image set of a planar function. Further we observe that all currently known main examples of planar functions have image sets of that minimal size.

Keywords

Planar mapping Perfect nonlinear mapping CCZ- equivalence Image set 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Gohar M. Kyureghyan
    • 1
  • Alexander Pott
    • 1
  1. 1.Department of MathematicsOtto-von-Guericke University of MagdeburgMagdeburgGermany

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