Geodesic
Classification of correlation-immune and minimal correlation-immune Boolean functions of 4 and 5 variables
Diskretnaya Matematika, Tome 27 (2015) no. 1, pp. 22-33.

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

A classification of correlation-immune and minimal corelation-immune Boolean function of $4$ and $5$ variables with respect to the Jevons group is given. Representatives of the equivalence classes of correlation-immune functions of 4 and 5 variables are decomposed into minimal correlation-immune functions. Characteristics of various decompositions of the constant function $\mathbf 1$ into minimal correlation-immune functions are presented.
Keywords: cryptography, correlation-immune functions, minimal correlation-immune functions, classification. 
@article{DM_2015_27_1_a1,
     author = {E. K. Alekseev and E. K. Karelina},
     title = {Classification of correlation-immune and minimal correlation-immune {Boolean} functions of 4 and 5 variables},
     journal = {Diskretnaya Matematika},
     pages = {22--33},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_1_a1/}
}
TY  - JOUR
AU  - E. K. Alekseev
AU  - E. K. Karelina
TI  - Classification of correlation-immune and minimal correlation-immune Boolean functions of 4 and 5 variables
JO  - Diskretnaya Matematika
PY  - 2015
SP  - 22
EP  - 33
VL  - 27
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2015_27_1_a1/
LA  - ru
ID  - DM_2015_27_1_a1
ER  - 
%0 Journal Article
%A E. K. Alekseev
%A E. K. Karelina
%T Classification of correlation-immune and minimal correlation-immune Boolean functions of 4 and 5 variables
%J Diskretnaya Matematika
%D 2015
%P 22-33
%V 27
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2015_27_1_a1/
%G ru
%F DM_2015_27_1_a1
E. K. Alekseev; E. K. Karelina. Classification of correlation-immune and minimal correlation-immune Boolean functions of 4 and 5 variables. Diskretnaya Matematika, Tome 27 (2015) no. 1, pp. 22-33. http://geodesic.mathdoc.fr/item/DM_2015_27_1_a1/

[1] Logachev O.A., Salnikov A.A., Smyshlyaev S.V., Yaschenko V.V., Bulevy funktsii v teorii kodirovaniya i kriptologii, 2-e izd., MTsNMO, M., 2012, 584 pp.

[2] Alekseev E.K., “O nekotorykh merakh nelineinosti bulevykh funktsii”, Prikladnaya diskretnaya matematika, 2 (2011), 5-16

[3] Alekseev E.K., “O nekotorykh algebraicheskikh i kombinatornykh svoistvakh korrelyatsionno-immunnykh bulevykh funktsii”, Diskretnaya matematika, 22 (2010), 110-126 | DOI | MR | Zbl

[4] Alekseev E.K., Approksimatsiya diskretnykh funktsii algebraicheski vyrozhdennymi funktsiyami v analize sistem zaschity informatsii, diss. kand. fiz.-matem. nauk, 2011

[5] Meier W., Staffelbach O., “Nonlinearity criteria for cryptographic functions”, EUROCRYPT'89, Springer Verlag, 1989, 549-562 | MR

[6] Siegenthaler T., “Decrypting a class of stream cipher using ciphertext only”, IEEE Trans. Computers, C-34:1 (1985), 81–85 | DOI

[7] Siegenthaler T., “Correlation-immunity of nonlinear combining functions for cryptographic applications”, IEEE Trans. Inf. Theory, IT-30 (1984), 776–780 | DOI | MR | Zbl

[8] Shestakov V.I. (red. perevoda), Sintez elektronnykh vychislitelnykh i upravlyayuschikh sistem, IL, M., 1954

[9] Braeken A., Borissov Y., Nikova S., Preneel B., Classification of boolean functions of 6 variables or less with respect to cryptographic properties, Cryptology ePrint Archive, Report 2004/248 | MR

[10] Brier E., Langevin P., “Classification of boolean cubic forms of nine variables”, IEEE Inf. Theory Workshop (ITW 2003), IEEE Press, 2002, 179–182

[11] Maiorana J., “A classification of the cosets of the Reed–Muller code R(1,6)”, Math. Comput., 57:195 (1991), 403–414 | MR | Zbl

[12] Harrison M.A., “On the classification of boolean functions by the general linear and affine group”, J. SIAM, 12 (1964), 284–299 | MR