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Abstract

Cryptographic Boolean functions must be complex to satisfy Shannon’s principle of confusion. Two main criteria evaluating, from crytpographic viewpoint, the complexity of Boolean functions on F 2 n have been studied in the literature: the nonlinearity (the minimum Hamming distance to affine functions) and the algebraic degree. We consider two other criteria: the minimum number of terms in the algebraic normal forms of all affinely equivalent functions (we call it the algebraic thickness) and the non-normality. We show that, asymptotically, almost all Boolean functions have high algebraic degrees, high nonlinearities, high algebraic thicknesses and are highly non-normal.

Keywords

Boolean Function Block Cipher Stream Cipher Affine Function Bend Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Claude Carlet
    • 1
    • 2
  1. 1.GREYCUniversity of Paris 8 and INRIAFrance
  2. 2.INRIA Projet CODES, Domaine de VohlceauLe Chesnay CedexFrance

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