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

An Braeken, Yuri Borissov, 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 $n-6$.

Available format(s)
Category
Secret-key cryptography
Publication info
Published elsewhere. submitted to IEEE transactions on information theory
Keywords
resilient cubic functionWalsh spectrumlinear space
Contact author(s)
An Braeken @ esat kuleuven ac be
History
Short URL
https://ia.cr/2005/332

CC BY

BibTeX

@misc{cryptoeprint:2005/332,
author = {An Braeken and Yuri Borissov and Svetla Nikova and Bart Preneel},
title = {Classification of Cubic $(n-4)$-resilient Boolean Functions},
howpublished = {Cryptology ePrint Archive, Paper 2005/332},
year = {2005},
note = {\url{https://eprint.iacr.org/2005/332}},
url = {https://eprint.iacr.org/2005/332}
}

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