On Designs and Multiplier Groups Constructed from Almost Perfect Nonlinear Functions

  • Authors:
  • Yves Edel;Alexander Pott

  • Affiliations:
  • Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium B-9000;Department of Mathematics, Otto-von-Guericke-University, Magdeburg, Germany D-39016

  • Venue:
  • Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
  • Year:
  • 2009

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Abstract

Let $f:{\mathbb{F}_2^{n}}\to {\mathbb{F}_2^{n}}$ be an almost perfect nonlinear function (APN). The set $D_f:=\{(a,b)\: :\: f(x+a)-f(x)=b\mbox{\ has two solutions}\}$ can be used to distinguish APN functions up to equivalence. We investigate the multiplier groups of theses sets D f . This extends earlier work done by the authors [1].