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On Cryptographic Complexity of Boolean Functions

In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas

Author

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  • Claude Carlet

    (University of Paris 8 and INRIA, GREYC
    INRIA Projet CODES, Domaine de Vohlceau)

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.

Suggested Citation

  • Claude Carlet, 2002. "On Cryptographic Complexity of Boolean Functions," Springer Books, in: Gary L. Mullen & Henning Stichtenoth & Horacio Tapia-Recillas (ed.), Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pages 53-69, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59435-9_4
    DOI: 10.1007/978-3-642-59435-9_4
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