Modified planar functions and their components

Nurdagül Anbar Meidl, Wilfried Meidl Meidl

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Zhou ([20]) introduced modified planar functions in order to describe (2n; 2n; 2n; 1) relative difference sets R as a graph of a function on the finite field F2n, and pointed out that projections of R are difference sets that can be described by negabent or bent4 functions, which are Boolean functions given in multivariate form. One of the objectives of this paper is to contribute to the understanding of these component functions of modified planar functions. Moreover, we obtain a description of modified planar functions by their components which is similar to that of the classical planar functions in odd characteristic as a vectorial bent function. We finally point out that though these components behave somewhat different than the multivariate bent4 functions, they are bent or semibent functions shifted by a certain quadratic term, a property which they share with their multivariate counterpart.
Original languageEnglish
JournalCryptography and Communications
Issue number2
Pages (from-to)235-249
Publication statusPublished - 2017


  • Bent4 (modified) planar function
  • Bent4 ·
  • Bent
  • Negabent ·
  • Difference set



Præstrud, M. R. & Brodersen, S. W.


Project: Research

Cite this

Anbar Meidl, N., & Meidl, W. M. (2017). Modified planar functions and their components. Cryptography and Communications, 10(2), 235-249.