4-Nonlinearity of a Constructed Quaternary Cryptographic Functions Class

  • Zoubida Jadda
  • Patrice Parraud
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6338)


New results on quaternary (ℤ4 = {0,1,2,3}-valued) cryptographic functions are presented. We define and characterize completely the ℤ4-balancedness and the ℤ4-nonlinearity according the Hamming metric and the Lee metric. In the particular case of quaternary Bent functions we show that the maximal nonlinearity of these functions is bounded for the Hamming metric and we give the exact value of the maximal nonlinearity of these functions for the Lee metric. A general construction, based on Galois ring is detailed and applied to obtain a class of balanced and high nonlinearity quaternary cryptographic functions. We use Gray map to derive these constructed quaternary functions to obtain balanced boolean functions having high nonlinearity.


quaternary functions boolean functions cryptographic functions nonlinearity balancedness quaternary algebra Gray map  Galois ring 


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Zoubida Jadda
    • 1
    • 2
  • Patrice Parraud
    • 3
  1. 1.IRMARINSA de RennesFrance
  2. 2.UMR 6625CNRSFrance
  3. 3.MACCLIA-CRECSaint Cyr-Coëtquidan 

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