Open Questions on Nonlinearity and on APN Functions

Conference paper

DOI: 10.1007/978-3-319-16277-5_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9061)
Cite this paper as:
Carlet C. (2015) Open Questions on Nonlinearity and on APN Functions. In: Koç Ç., Mesnager S., Savaş E. (eds) Arithmetic of Finite Fields. WAIFI 2014. Lecture Notes in Computer Science, vol 9061. Springer, Cham


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 

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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