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

*An Braeken and Yuri Borissov and Svetla Nikova and Bart Preneel*

**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 $n-6$.

**Category / Keywords: **secret-key cryptography / resilient cubic function, Walsh spectrum, linear space

**Publication Info: **submitted to IEEE transactions on information theory

**Date: **received 22 Sep 2005

**Contact author: **An Braeken at esat kuleuven ac be

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**Version: **20050925:125207 (All versions of this report)

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