Geodesic
On the decomposition of a vectorial Boolean function into a composition of two functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 31-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the paper, we prove that if a vectorial Boolean function $F$ in $n$ variables, $\deg(F)=d>2$, is decomposable, then the function $ F '= A_2 \circ F \circ A_1 $, where $ A_1, A_2 $ are arbitrary affine $ (n, n) $-permutations, is also decomposable; and if $F(x)=G(H(x))$, $\max\{\deg(F),\deg(H)\}=d'$, function $H$ is invertible and $ \deg (H ^ {- 1}) \leq d'$, then the function $ F^{''} = F + A_0 $ is decomposable for any affine function $A_0$. The construction of a decomposable vectorial Boolean function of the third degree in an arbitrary number of variables is presented. A computational experiment showed that all vectorial Boolean functions of the third degree in three variables are decomposable.
Keywords: vectorial Boolean function, threshold implementation.
Mots-clés : decomposition 
@article{PDMA_2020_13_a7,
     author = {G. M. Pintus},
     title = {On the decomposition of a vectorial {Boolean} function into a composition of two functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {31--32},
     year = {2020},
     number = {13},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2020_13_a7/}
}
TY  - JOUR
AU  - G. M. Pintus
TI  - On the decomposition of a vectorial Boolean function into a composition of two functions
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2020
SP  - 31
EP  - 32
IS  - 13
UR  - http://geodesic.mathdoc.fr/item/PDMA_2020_13_a7/
LA  - ru
ID  - PDMA_2020_13_a7
ER  - 
%0 Journal Article
%A G. M. Pintus
%T On the decomposition of a vectorial Boolean function into a composition of two functions
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2020
%P 31-32
%N 13
%U http://geodesic.mathdoc.fr/item/PDMA_2020_13_a7/
%G ru
%F PDMA_2020_13_a7
G. M. Pintus. On the decomposition of a vectorial Boolean function into a composition of two functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 31-32. http://geodesic.mathdoc.fr/item/PDMA_2020_13_a7/

[1] Bhunia S., Tehranipoor M., Hardware Security. A Hands-On Learning Approach, Elsevier Inc., 2019, 526 pp.

[2] Nikova S., Rechberger C., Rijmen V., “Threshold implementations against side-channel attacks and glitches”, Inform. Commun. Technol., 4307 (2006), 529–546 | MR