Geodesic
Statistical independence of the Boolean function superposition
Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 11-12.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved here that if a Boolean function $f(x,y)$ is statistically independent on the variables in $x$, then the same is true for any Boolean function $g(f(x,y),z)$, but this may not be so for a superposition $g(f_1(x,y),\dots,f_s(x,y),z)$ where $s\geq2$ and every function $f_1(x,y),\dots,f_s(x,y)$ is statistically independent on $x$. 
@article{PDM_2011_13_a3,
     author = {O. L. Kolcheva and I. A. Pankratova},
     title = {Statistical independence of the {Boolean} function superposition},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {11--12},
     publisher = {mathdoc},
     number = {13},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2011_13_a3/}
}
TY  - JOUR
AU  - O. L. Kolcheva
AU  - I. A. Pankratova
TI  - Statistical independence of the Boolean function superposition
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2011
SP  - 11
EP  - 12
IS  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2011_13_a3/
LA  - ru
ID  - PDM_2011_13_a3
ER  - 
%0 Journal Article
%A O. L. Kolcheva
%A I. A. Pankratova
%T Statistical independence of the Boolean function superposition
%J Prikladnaâ diskretnaâ matematika
%D 2011
%P 11-12
%N 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2011_13_a3/
%G ru
%F PDM_2011_13_a3
O. L. Kolcheva; I. A. Pankratova. Statistical independence of the Boolean function superposition. Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 11-12. http://geodesic.mathdoc.fr/item/PDM_2011_13_a3/

[1] Agibalov G. P., Pankratova I. A., “Elementy teorii statisticheskikh analogov diskretnykh funktsii s primeneniem v kriptoanalize iterativnykh blochnykh shifrov”, Prikladnaya diskretnaya matematika, 2010, no. 3(9), 51–68

[2] Matsui M., “Linear Cryptanalysis Method for DES Cipher”, LNCS, 765, 1993, 386–397

[3] Matsui M., “The First Experimental Cryptanalysis of the Data Encryption Standard”, LNCS, 839, 1994, 1–11 | Zbl

[4] Logachev O. A., Salnikov A. A., Yaschenko V. V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MTsNMO, M., 2004