Geodesic
Analysis of the spectrum of random symmetric Boolean functions
Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 1, pp. 59-76 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

General probabilistic model of a random symmetric Boolean function of $n$ variables is proposed. The characteristic function of the Walsh spectrum of a random symmetric Boolean function is defined; exact and asymptotic distributions of some spectrum characteristics as $n\to\infty$ are obtained in the case of the parametric measure. The basic properties of the Krawtchouk's polynomials (which are used in proofs) are reviewed. 
@article{MVK_2013_4_1_a2,
     author = {G. I. Ivchenko and Yu. I. Medvedev and V. A. Mironova},
     title = {Analysis of the spectrum of random symmetric {Boolean} functions},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {59--76},
     year = {2013},
     volume = {4},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2013_4_1_a2/}
}
TY  - JOUR
AU  - G. I. Ivchenko
AU  - Yu. I. Medvedev
AU  - V. A. Mironova
TI  - Analysis of the spectrum of random symmetric Boolean functions
JO  - Matematičeskie voprosy kriptografii
PY  - 2013
SP  - 59
EP  - 76
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MVK_2013_4_1_a2/
LA  - ru
ID  - MVK_2013_4_1_a2
ER  - 
%0 Journal Article
%A G. I. Ivchenko
%A Yu. I. Medvedev
%A V. A. Mironova
%T Analysis of the spectrum of random symmetric Boolean functions
%J Matematičeskie voprosy kriptografii
%D 2013
%P 59-76
%V 4
%N 1
%U http://geodesic.mathdoc.fr/item/MVK_2013_4_1_a2/
%G ru
%F MVK_2013_4_1_a2
G. I. Ivchenko; Yu. I. Medvedev; V. A. Mironova. Analysis of the spectrum of random symmetric Boolean functions. Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 1, pp. 59-76. http://geodesic.mathdoc.fr/item/MVK_2013_4_1_a2/

[1] Canteaut A., Videau M., “Symmetric Boolean Function”, IEEE Trans. Inf. Theory, 51:8 (2005), 2791–2811 | DOI | MR

[2] Sarkar S., Maitra S., “Efficient search for symmetric Boolean functions under constraints on Walsh spectra values”, J. Comb. Math. and Comb. Comput., 68 (2009), 163–191 | MR | Zbl

[3] Mouffron M., “Balanced alternating and symmetric functions over finite sets”, Workshop on Boolean Functions: Cryptography and Applications (BFCA' 08), Copenhagen, Denmark, 2008, 27–44 | MR

[4] Segë G., Ortogonalnye mnogochleny, FIZMATLIT, M., 1962

[5] Mak-Vilyams F. Dzh., Sloen N. Dzh. A., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1979

[6] Sidelnikov V. M., Teoriya kodirovaniya, FIZMATLIT, M., 2008

[7] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, Nauka, M., 1965

[8] Cusick Th. W., Stanica P., Cryptographic Boolean Functions and Applications, Elsevier/AP, Amsterdam etc., 2009 | MR | Zbl

[9] Savicky P., “On the bent Boolean functions that are symmetric”, European J. Comb., 15 (1994), 407–410 | DOI | MR | Zbl

[10] Khokhlov V. I., “Mnogochleny, ortogonalnye otnositelno polinomialnogo raspredeleniya, i faktorialno-stepennoi formalizm”, Teoriya veroyatnosti i eë primenenie, 46:3 (2001), 585–594 | DOI | MR | Zbl

[11] Khokhlov V. I., “Mnogochleny Ermita i mnogochleny Puassona–Sharle kak klassicheskie predely mnogochlenov Kravchuka”, Obozr. prikl. i promyshl. matem., 16:5 (2005), 937–940