Paper 2002/021
Spectral Analysis of Boolean Functions under Nonuniformity 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
 Secretkey cryptography
 Publication info
 Published elsewhere. Unknown where it was published
 Keywords
 Boolean functionsWalshHadamard transformcorrelationimmune functionsbent functionssecond order functions
 Contact author(s)
 Miranovich @ yandex ru
 History
 20020219: received
 Short URL
 https://ia.cr/2002/021
 License

CC BY
BibTeX
@misc{cryptoeprint:2002/021, author = {Kanstantsin Miranovich}, title = {Spectral Analysis of Boolean Functions under Nonuniformity of Arguments}, howpublished = {Cryptology ePrint Archive, Paper 2002/021}, year = {2002}, note = {\url{https://eprint.iacr.org/2002/021}}, url = {https://eprint.iacr.org/2002/021} }