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

An Braeken; Yuri Borissov; Svetla Nikova; Bart Preneel

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

An Braeken, Yuri Borissov, Svetla Nikova, Bart Preneel

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Carlet and Charpin classified 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 have completed this classification of cubic (n - 4)-resilient Boolean functions by deriving the corresponding algebraic normal form (ANF) and autocorrelation spectrum for each of the four types. At the same time, we have solved an open problem 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.

Original language	English
Pages (from-to)	1670-1676
Number of pages	6
Journal	IEEE Transactions on Information Theory
Volume	52
Issue number	4
Publication status	Published - Jan 2006

Keywords

Walsh spectrum, linear space, Boolean function

Cite this

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title = "Classification of Cubic (n-4)-resilient Boolean Functions",

abstract = "Carlet and Charpin classified 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 have completed this classification of cubic (n - 4)-resilient Boolean functions by deriving the corresponding algebraic normal form (ANF) and autocorrelation spectrum for each of the four types. At the same time, we have solved an open problem 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.",

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author = "An Braeken and Yuri Borissov and Svetla Nikova and Bart Preneel",

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language = "English",

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T1 - Classification of Cubic (n-4)-resilient Boolean Functions

AU - Braeken, An

AU - Borissov, Yuri

AU - Nikova, Svetla

AU - Preneel, Bart

PY - 2006/1

Y1 - 2006/1

N2 - Carlet and Charpin classified 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 have completed this classification of cubic (n - 4)-resilient Boolean functions by deriving the corresponding algebraic normal form (ANF) and autocorrelation spectrum for each of the four types. At the same time, we have solved an open problem 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.

AB - Carlet and Charpin classified 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 have completed this classification of cubic (n - 4)-resilient Boolean functions by deriving the corresponding algebraic normal form (ANF) and autocorrelation spectrum for each of the four types. At the same time, we have solved an open problem 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.

KW - Walsh spectrum, linear space, Boolean function

M3 - Article

VL - 52

SP - 1670

EP - 1676

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 4

ER -

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

Abstract

Keywords

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