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Title:
Spectral Analysis of High Order Correlation Immune Functions
Authors: Yuriy Tarannikov, Denis Kirienko
Abstract:We use the recent results on the spectral structure of
correlation immune and resilient Boolean functions for the
investigations of high order correlation immune functions.
At first, we give simple proofs of some theorems where only
long proofs were known. Next, we introduce the matrix of
nonzero Walsh coefficients and establish important properties
of this matrix. We use these properties to prove the nonexistence
of some high order correlation immune functions. Finally, we
establish the order of magnitude for the number of (n-4)th
order correlation immune functions of n variables.
ePrint: https://eprint.iacr.org/2000/050
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