Geodesic
Asymptotic estimates for numbers of Boolean mappings with given cryptographic properties
Matematičeskie voprosy kriptografii, Tome 5 (2014), pp. 73-97.

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

For linear combinations of coordinate functions of random Boolean mapping a local limit theorem for the distribution of subsets of weights of submappings is improved. Also a local limit theorem for subsets of their spectral coefficients is proved. By means of these theorems we obtain upper and lower asymptotic estimates for numbers of correlation-immune and ($n,m,k$)-resilient Boolean mappings. Also we obtain an upper asymptotic estimate of the number of plateaued Boolean mappings. 
@article{MVK_2014_5_a4,
     author = {K. N. Pankov},
     title = {Asymptotic estimates for numbers of {Boolean} mappings with given cryptographic properties},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {73--97},
     publisher = {mathdoc},
     volume = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2014_5_a4/}
}
TY  - JOUR
AU  - K. N. Pankov
TI  - Asymptotic estimates for numbers of Boolean mappings with given cryptographic properties
JO  - Matematičeskie voprosy kriptografii
PY  - 2014
SP  - 73
EP  - 97
VL  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MVK_2014_5_a4/
LA  - ru
ID  - MVK_2014_5_a4
ER  - 
%0 Journal Article
%A K. N. Pankov
%T Asymptotic estimates for numbers of Boolean mappings with given cryptographic properties
%J Matematičeskie voprosy kriptografii
%D 2014
%P 73-97
%V 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MVK_2014_5_a4/
%G ru
%F MVK_2014_5_a4
K. N. Pankov. Asymptotic estimates for numbers of Boolean mappings with given cryptographic properties. Matematičeskie voprosy kriptografii, Tome 5 (2014), pp. 73-97. http://geodesic.mathdoc.fr/item/MVK_2014_5_a4/

[1] Denisov O. V., “Asimptoticheskaya formula dlya chisla korrelyatsionno-immunnykh poryadka $k$ bulevykh funktsii”, Diskretnaya matematika, 3:2 (1991), 25–46 | MR | Zbl

[2] Denisov O. V., “Lokalnaya predelnaya teorema dlya raspredeleniya chasti spektra sluchainoi dvoichnoi funktsii”, Diskretnaya matematika, 12:1 (2000), 82–95 | DOI | MR | Zbl

[3] Zubov A. Yu., Matematika kodov autentifikatsii, Gelios ARV, M., 2007, 480 pp.

[4] Ivanov A. V., “Monomialnye priblizheniya platovidnykh funktsii”, Prikl. diskr. matem., 2008, no. 1(1), 10–14

[5] Kuznetsov Yu. V., Shkarin S. A., “Kody Rida–Mallera”, Matem. vopr. kibern., 6, 1996, 5–50 | MR | Zbl

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

[7] Pankov K. N., “Lokalnaya predelnaya teorema dlya raspredeleniya chasti vektora vesov podfunktsii komponent sluchainogo dvoichnogo otobrazheniya”, Matematicheskie voprosy kriptografii, 5:3 (2014), 49–80

[8] Pankov K. N., “Otsenki skorosti skhodimosti v predelnykh teoremakh dlya sovmestnykh raspredelenii chasti kharakteristik sluchainykh dvoichnykh otobrazhenii”, Prikl. diskr. matem., 2012, no. 4(18), 14–30

[9] Sachkov V. N., Kurs kombinatornogo analiza, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2013, 336 pp.

[10] Slovar kriptograficheskikh terminov, MTsNMO, M., 2006, 94 pp.

[11] Tarannikov Yu. V., Kombinatornye svoistva diskretnykh struktur i prilozheniya k kriptologii, MTsNMO, M., 2011, 152 pp.

[12] Tarannikov Yu. V., “O korrelyatsionno-immunnykh i ustoichivykh bulevykh funktsiyakh”, Matem. vopr. kibern., 11, 2002, 91–148 | MR | Zbl

[13] Yaschenko V. V., “Svoistva bulevykh otobrazhenii, svodimye k svoistvam ikh koordinatnykh funktsii”, Vestnik MGU, ser. Matem., 1997, no. 4, 11–13

[14] Bach E., “Improved asymptotic formulas for counting correlation immune Boolean functions”, SIAM J. Discrete Math., 23 (2009), 1525–1538 | DOI | MR | Zbl

[15] Bennett C., Brassard G., Robert J., “Privacy amplification by public discussion”, SIAM J. Comput., 17 (1988), 210–229 | DOI | MR

[16] Carlet C., “Vectorial Boolean functions for cryptography”, Encycl. Math. and its Appl., 134, Cambridge Univ. Press, New York, 2010, 398–469 | Zbl

[17] Cheon J., Chee S., “Elliptic curves and resilient function”, Information Security and Cryptology, ICISC 2000, Lect. Notes Comput. Sci., 2015, 2001, 64–72 | DOI | MR | Zbl

[18] Canfield E. R., Gao Z., Greenhill C., McKay B. D., Robinson R. W., “Asymptotic enumeration of correlation-immune Boolean functions”, Cryptography and Commun., 2:1 (2010), 111–126 | DOI | MR | Zbl

[19] Chor B., Goldreich O., Hastad J., Friedman J., Rudich S., Smolensky R., “The bit extraction problem or $t$-resilent functions”, IEEE Symp. Found. Comput. Sci., 26 (1985), 396–407

[20] Gopalakrishnan K., Stinson D. R., “Three characterizations of non-binary correlation-immune and resilient functions”, Des., Codes and Cryptogr., 5 (1995), 241–251 | DOI | MR | Zbl

[21] Siegenthaler T., “Correlation-immunity of nonlinear combining functions for cryptographic applications”, IEEE Trans. Inf. Theory, 30:5 (1984), 776–780 | DOI | MR | Zbl

[22] Stinson D., Massey J., “An infinite class of counterexamples to a conjecture concerning non-linear resilient functions”, J. Cryptology, 8:3 (1995), 167–173 | DOI | MR | Zbl

[23] Zhang X., Zheng Y., “Cryptographically resilient functions”, IEEE Trans. Inf. Theory, 43:5 (1997), 1740–1747 | DOI | MR | Zbl