Geodesic
Construction of balanced functions with high nonlinearity and other cryptographic properties
Prikladnaâ diskretnaâ matematika, no. 1 (2024), pp. 8-23

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We present an iterative construction that can be used to construct balanced functions with high nonlinearity. Using this construction, we obtained Boolean functions in an even number $n\geqslant 18$ of variables which have no linear structures with nonlinearity $2^{n-1}-(2^{{n}/{2}-1}+2^{{n}/{2}-3}+2^{{n}/{2}-5}+2^{{n}/{2}-7})$. Additional conditions are given under which the functions obtained using the construction will be correlation immune. We also present results concerning “bent sum decomposition problem”.
Keywords: balanced Boolean functions, nonlinear Boolean functions, bent functions. 
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     author = {A. S. Shaporenko},
     title = {Construction of balanced functions with high nonlinearity and other cryptographic properties},
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     pages = {8--23},
     publisher = {mathdoc},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2024_1_a1/}
}
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A. S. Shaporenko. Construction of balanced functions with high nonlinearity and other cryptographic properties. Prikladnaâ diskretnaâ matematika, no. 1 (2024), pp. 8-23. http://geodesic.mathdoc.fr/item/PDM_2024_1_a1/