Designs, Codes and Cryptography

, Volume 49, Issue 1–3, pp 273–288 | Cite as

On the classification of APN functions up to dimension five

  • Marcus BrinkmannEmail author
  • Gregor Leander


We classify the almost perfect nonlinear (APN) functions in dimensions 4 and 5 up to affine and CCZ equivalence using backtrack programming and give a partial model for the complexity of such a search. In particular, we demonstrate that up to dimension 5 any APN function is CCZ equivalent to a power function, while it is well known that in dimensions 4 and 5 there exist APN functions which are not extended affine (EA) equivalent to any power function. We further calculate the total number of APN functions up to dimension 5 and present a new CCZ equivalence class of APN functions in dimension 6.


APN functions Backtrack Affine equivalence CCZ equivalence Affine subspaces 

AMS Classification



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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Ruhr-Universität BochumBochumGermany
  2. 2.University of ToulonLa GardeFrance

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