DocumentCode
890526
Title
Classification of cubic (n-4)-resilient Boolean functions
Author
Braeken, An ; Borissov, Yuri ; Nikova, Svetla ; Preneel, Bart
Author_Institution
Dept. of Electr. Eng.-ESAT/SCD/COSIC, Katholieke Univ. Leuven, Belgium
Volume
52
Issue
4
fYear
2006
fDate
4/1/2006 12:00:00 AM
Firstpage
1670
Lastpage
1676
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.
Keywords
Boolean functions; Reed-Muller codes; Walsh functions; correlation theory; ANF; Walsh spectrum; algebraic normal form; autocorrelation spectrum; cubic (n-4) classification; linear space dimension; resilient Boolean function; Boolean functions; Galois fields; Polynomials; Algebraic normal form (ANF); Boolean function; classification; cubic; linear space; resiliency;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.2006.871063
Filename
1614090
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