Cryptology ePrint Archive: Report 2002/021

Spectral Analysis of Boolean Functions under Non-uniformity of Arguments

Kanstantsin Miranovich

Abstract: For independent binary random variables x_1,...,x_n and a Boolean function f(x), x=(x_1,...,x_n), we suppose that |1/2 - P{x_i = 1}|<=e, 1<=i<=n. Under these conditions we present new characteristics D_F(f(),e) = max{|1/2 - P{y=1}|} of the probability properties of Boolean functions, where y = F(x), and F(x) being equal to 1) F(x)=f(x), 2) F(x)=f(x)+(a,x), 3) F(x)=f(x)+f(x+a), and investigate their properties. Special attention is paid to the classes of balanced and correlation immune functions, bent functions, and second order functions, for which upper estimates of D_F(f(),e) are found and statements on behaviour of sequences f^{(n)}(x) of functions of n arguments are made.

Category / Keywords: secret-key cryptography / Boolean functions, Walsh-Hadamard transform, correlation-immune functions, bent functions, second order functions

Date: received 18 Feb 2002

Contact author: Miranovich at yandex ru

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Version: 20020219:014430 (All versions of this report)

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