Open Questions on Nonlinearity and on APN Functions

  • Claude CarletEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9061)


In a first part of the paper, we recall some known open questions on the nonlinearity of Boolean and vectorial functions and on the APN-ness of vectorial functions. All of them have been extensively searched and seem quite difficult. We also indicate related less well-known open questions. In the second part of the paper, we introduce four new open problems (leading to several related sub-problems) and the results which lead to them. Addressing these problems may be less difficult since they have not been much worked on.


Cryptography Boolean function Nonlinearity Almost Perfect Nonlinear Almost Bent 



We wish to thank Lilya Budaghyan, Faruk Gologlu and Sihem Mesnager for useful information.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LAGAUniversities of Paris 8 and Paris 13; CNRS, UMR 7539Saint-Denis Cedex 02France
  2. 2.Department of MathematicsUniversity of Paris 8Saint-Denis Cedex 02France

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