Geodesic
Local limit theorem for the distribution of incomplete vector formed by the weights of subfunctions of random binary mapping components
Matematičeskie voprosy kriptografii, Tome 5 (2014) no. 3, pp. 49-80 
K. N. Pankov. Local limit theorem for the distribution of incomplete vector formed by the weights of subfunctions of random binary mapping components. Matematičeskie voprosy kriptografii, Tome 5 (2014) no. 3, pp. 49-80. http://geodesic.mathdoc.fr/item/MVK_2014_5_3_a3/
@article{MVK_2014_5_3_a3,
     author = {K. N. Pankov},
     title = {Local limit theorem for the distribution of incomplete vector formed by the weights of subfunctions of random binary mapping components},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {49--80},
     year = {2014},
     volume = {5},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2014_5_3_a3/}
}
TY  - JOUR
AU  - K. N. Pankov
TI  - Local limit theorem for the distribution of incomplete vector formed by the weights of subfunctions of random binary mapping components
JO  - Matematičeskie voprosy kriptografii
PY  - 2014
SP  - 49
EP  - 80
VL  - 5
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MVK_2014_5_3_a3/
LA  - ru
ID  - MVK_2014_5_3_a3
ER  - 
%0 Journal Article
%A K. N. Pankov
%T Local limit theorem for the distribution of incomplete vector formed by the weights of subfunctions of random binary mapping components
%J Matematičeskie voprosy kriptografii
%D 2014
%P 49-80
%V 5
%N 3
%U http://geodesic.mathdoc.fr/item/MVK_2014_5_3_a3/
%G ru
%F MVK_2014_5_3_a3

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

For linear combinations of coordinate functions of random binary mapping a local limit theorem for the joint distribution of weights of some their subfunctions is proved. By means of this theorem we obtain asymptotic estimates for the number of $(n,m,k)$-resilient vectorial Boolean functions for $m=2,3,4$.

[1] Borovkov A. A., Teoriya veroyatnostei, URSS, M., 2009, 656 pp.

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

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

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

[5] Pankov K. N., “Otsenki skorosti skhodimosti v predelnykh teoremakh dlya sovmestnykh raspredelenii chasti kharakteristik sluchainykh dvoichnykh otobrazhenii”, Prikladnaya diskretnaya matematika, 2012, no. 4, 14–30 | MR

[6] Prokhorov Yu. V., “Predelnye teoremy dlya summ sluchainykh vektorov, razmernost kotorykh stremitsya k beskonechnosti”, Teoriya veroyatn. i ee primen., 35:4 (1990), 751–753 | MR | Zbl

[7] Sevastyanov B. A., Kurs teorii veroyatnostei i matematicheskoi statistiki, Nauka, M., 1982, 256 pp. | MR | Zbl

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

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

[10] Carlet C., “Vectorial Boolean functions for cryptography”, Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Encyclopedia of Mathematics and its Applications, 134, Cambridge University Press, New York, 2010, 398–469 | Zbl

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