The Fourier Entrophy-Influence Conjecture Holds for a Log-Density 1 Class of Cryptographic Boolean Functions
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Authors
Gangopadhyay, Sugata
Stănică, Pantelimon
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2014
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Abstract
We consider the Fourier Entropy-Infuence (FEI) conjecture in the context of cryptographic Boolean functions. We show that the FEI conjecture is true for the functions satisfying the strict avalanche criterion, which forms a subset of asymptotic log-density 1 in the set of all Boolean functions. Further, we prove that the FEI conjecture is satisfied for plateaued Boolean
functions, monomial algebraic normal form (with the best involved constant),
direct sums, as well as concatenations of Boolean functions. As a simple con-
sequence of these general results we fi nd that each affine equivalence class of
quadratic Boolean functions contains at least one function satisfying the FEI
conjecture. Further, we propose some leveled" FEI conjectures.
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This paper was written during an enjoyable visit of S. G. at the Applied Mathematics Department of Naval Postgraduate School in December, 2013.
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Applied Mathematics
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Naval Postgraduate School (U.S.)
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.