### The Fourier Entropy-Influence conjecture holds for a log-density 1 class of cryptographic Boolean functions

##### Abstract

We consider the Fourier Entropy-Influence (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 consequence of these general results we find 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.

Available format(s)
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
Contact author(s)
pstanica @ nps edu
History
Short URL
https://ia.cr/2014/054

CC BY

BibTeX

@misc{cryptoeprint:2014/054,
author = {Sugata Gangopadhyay and Pantelimon Stanica},
title = {The Fourier Entropy-Influence conjecture holds for a log-density 1 class of cryptographic Boolean functions},
howpublished = {Cryptology ePrint Archive, Paper 2014/054},
year = {2014},
note = {\url{https://eprint.iacr.org/2014/054}},
url = {https://eprint.iacr.org/2014/054}
}
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