Geodesic
On algebraic immunity of vector Boolean functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 37-39.

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

In the paper, the component algebraic immunity of vector Boolean functions is studied. A theorem on a correspondence between the maximum component algebraic immunity of a function and its balancedness is proven. A relationship between the maximum component algebraic immunity and matrices of a special form is obtained. For a small number of variables, some functions with maximum component algebraic immunity are constructed.
Keywords: component algebraic immunity, vector Boolean function, balancedness. 
@article{PDMA_2015_8_a14,
     author = {D. P. Pokrasenko},
     title = {On algebraic immunity of vector {Boolean} functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {37--39},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2015_8_a14/}
}
TY  - JOUR
AU  - D. P. Pokrasenko
TI  - On algebraic immunity of vector Boolean functions
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2015
SP  - 37
EP  - 39
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2015_8_a14/
LA  - ru
ID  - PDMA_2015_8_a14
ER  - 
%0 Journal Article
%A D. P. Pokrasenko
%T On algebraic immunity of vector Boolean functions
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2015
%P 37-39
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2015_8_a14/
%G ru
%F PDMA_2015_8_a14
D. P. Pokrasenko. On algebraic immunity of vector Boolean functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 37-39. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a14/

[1] Courtois N., Meier W., “Algebraic attacks on stream ciphers with linear feedback”, Eurocrypt'2003, LNCS, 2656, 2003, 345–359 | MR | Zbl

[2] Meier W., Pasalic E., Carlet C., “Algebraic attacks and decomposition of Boolean functions”, Eurocrypt'2004, LNCS, 3027, 2004, 474–491 | MR | Zbl

[3] Armknecht F., Krause M., “Constructing single- and multi-output Boolean functions with maximal immunity”, ICALP'2006, LNCS, 4052, 2006, 180–191 | MR | Zbl

[4] Ars G., Faugère J.-C., “Algebraic immunities of functions over finite fields”, Proc. Conf. BFCA, 2005, 21–38

[5] Carlet C., “On the algebraic immunities and higher order nonlinearities of vectorial Boolean functions”, Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes, IOS Press, Amsterdam, 2009, 104–116 | MR