International Association for Cryptologic Research

International Association
for Cryptologic Research


Classification of Cubic $(n-4)$-resilient Boolean Functions

An Braeken
Yuri Borissov
Svetla Nikova
Bart Preneel
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Abstract: Carlet and Charpin classified in \cite{CC04} the set of cubic $(n-4)$-resilient Boolean functions into four different types with respect to the Walsh spectrum and the dimension of the linear space. Based on the classification of $RM(3,6)/RM(1,6)$, we completed the classification of the cubic $(n-4)$-resilient Boolean function by deriving the corresponding ANF and autocorrelation spectrum for each of the four types. In the same time, we solved an open problem of \cite{CC04} by proving that all plateaued cubic $(n-4)$-resilient Boolean functions have dimension of the linear space equal either to $n-5$ or $n-6$.
  title={Classification of Cubic $(n-4)$-resilient Boolean Functions},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / resilient cubic function, Walsh spectrum, linear space},
  note={submitted to IEEE transactions on information theory 13048 received 22 Sep 2005},
  author={An Braeken and Yuri Borissov and Svetla Nikova and Bart Preneel},