Paper 2005/332

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 $n-6$.

Metadata
Available format(s)
PDF PS
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
2005-09-25: received
Short URL
https://ia.cr/2005/332
License
Creative Commons Attribution
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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