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Paper 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.
Metadata
- Available format(s)
- PS
- Category
- Secret-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Boolean functionsWalsh-Hadamard transformcorrelation-immune functionsbent functionssecond order functions
- Contact author(s)
- Miranovich @ yandex ru
- History
- 2002-02-19: received
- Short URL
- https://ia.cr/2002/021
- License
-
CC BY
