• 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