Perfect nonlinear S-boxes

  • Kaisa Nyberg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 547)


A perfect nonlinear S-box is a substitution transformation with evenly distributed directional derivatives. Since the method of differential cryptanalysis presented by E. Biham and A. Shamir makes use of nonbalanced directional derivatives, the perfect nonlinear S-boxes are immune to this attack. The main result is that for a perfect nonlinear S-box the number of input variables is at least twice the number of output variables. Also two different construction methods are given. The first one is based on the Maiorana-McFarland construction of bent functions and is easy and efficient to implement. The second method generalizes Dillon’s construction of difference sets.


Directional Derivative Bend Function Linear Feedback Shift Register Bent Function Differential Cryptanalysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Kaisa Nyberg
    • 1
  1. 1.Finnish Defense Forces and University of HelsinkiHelsinki

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