Geodesic
Statistical estimation of the significant arguments set of the binary vector-function with corrupted values
Matematičeskie voprosy kriptografii, Tome 5 (2014), pp. 41-61.

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

Let $\Theta$ be the set of significant arguments of the unknown binary vector-function with the random uniformly distributed arguments and corrupted values. Algorithm for constructing the estimate $\Theta^*$ of $\Theta$ based on statistical estimates of function spectrum is proposed. For some function classes (particularly, for vectorial bent-functions and bijective mappings) we get asymptotic bounds of the data size sufficient for the successful work of the algorithm, i.e. $\mathbf P\{\Theta^*=\Theta\}\to1$. 
@article{MVK_2014_5_a2,
     author = {O. V. Denisov},
     title = {Statistical estimation of the significant arguments set of the binary vector-function with corrupted values},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {41--61},
     publisher = {mathdoc},
     volume = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2014_5_a2/}
}
TY  - JOUR
AU  - O. V. Denisov
TI  - Statistical estimation of the significant arguments set of the binary vector-function with corrupted values
JO  - Matematičeskie voprosy kriptografii
PY  - 2014
SP  - 41
EP  - 61
VL  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MVK_2014_5_a2/
LA  - ru
ID  - MVK_2014_5_a2
ER  - 
%0 Journal Article
%A O. V. Denisov
%T Statistical estimation of the significant arguments set of the binary vector-function with corrupted values
%J Matematičeskie voprosy kriptografii
%D 2014
%P 41-61
%V 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MVK_2014_5_a2/
%G ru
%F MVK_2014_5_a2
O. V. Denisov. Statistical estimation of the significant arguments set of the binary vector-function with corrupted values. Matematičeskie voprosy kriptografii, Tome 5 (2014), pp. 41-61. http://geodesic.mathdoc.fr/item/MVK_2014_5_a2/

[1] Ambrosimov A. S., “Svoistva bent-funktsii $q$-znachnoi logiki nad konechnymi polyami”, Diskretnaya matematika, 6:3 (1994), 50–60 | MR | Zbl

[2] Arenbaev N. K., “O neravenstvakh dlya sluchainykh vektorov”, Teoriya veroyatn. i primen., 22:3 (1977), 585–589 | MR | Zbl

[3] Borovkov A. A., Teoriya veroyatnostei, Editorial URSS, M., 1999, 472 pp. | MR

[4] Prokhorov Yu. V., “O rasprostranenii neravenstv S. N. Bernshteina na mnogomernyi sluchai”, Teoriya veroyatn. i primen., 13:2 (1968), 266–274 | MR | Zbl

[5] Tokareva N. N., “Bent-funktsii: rezultaty i prilozheniya. Obzor rabot”, Prikladnaya diskretnaya matematika, 2009, no. 1(3), 15–37

[6] Nyberg K., “Perfect nonlinear $S$-boxes”, Advances in cryptology Eurocrypt-1991, LNCS, 547, 1991, 378–386 | MR | Zbl

[7] Titsworth R. C., Correlation properties of cyclic sequences, Thesis for the degree of doctor of Philosophy, California Institute of Technology, 1962, 244 pp. available at http://thesis.library.caltech.edu