On Cryptographic Complexity of Boolean Functions

Claude Carlet
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Claude Carlet: University of Paris 8 and INRIA, GREYC

A chapter in Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, 2002, pp 53-69 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-59435-9_4

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DOI: 10.1007/978-3-642-59435-9_4

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