Geodesic
Locally invertible Boolean functions
Prikladnaâ diskretnaâ matematika, no. 4 (2011), pp. 11-21.

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

The property of local invertibility of Boolean functions is considered. A number of necessary conditions of local invertibility is proven; they can be used to construct functions that are not locally invertible. We prove a new criterion of local invertibility connecting this property with some properties of Boolean functions with barrier.
Keywords: perfectly balanced functions, barriers of Boolean functions, local invertibility, cryptography. 
@article{PDM_2011_4_a1,
     author = {S. V. Smyshlyaev},
     title = {Locally invertible {Boolean} functions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {11--21},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2011_4_a1/}
}
TY  - JOUR
AU  - S. V. Smyshlyaev
TI  - Locally invertible Boolean functions
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2011
SP  - 11
EP  - 21
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2011_4_a1/
LA  - ru
ID  - PDM_2011_4_a1
ER  - 
%0 Journal Article
%A S. V. Smyshlyaev
%T Locally invertible Boolean functions
%J Prikladnaâ diskretnaâ matematika
%D 2011
%P 11-21
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2011_4_a1/
%G ru
%F PDM_2011_4_a1
S. V. Smyshlyaev. Locally invertible Boolean functions. Prikladnaâ diskretnaâ matematika, no. 4 (2011), pp. 11-21. http://geodesic.mathdoc.fr/item/PDM_2011_4_a1/

[1] Preparata F. P., “Convolutional Transformations of Binary Sequences: Boolean Functions and Their Resynchronizing Properties”, IEEE Trans. Electron. Comput., 15:6 (1966), 898–909 | DOI

[2] Golic J. Dj., “On the Security of Nonlinear Filter Generators”, LNCS, 1039, 1996, 173–188

[3] Logachev O. A., “O lokalnoi obratimosti odnogo klassa bulevykh otobrazhenii”, Materialy IX Mezhdunar. seminara “Diskretnaya matematika i ee prilozheniya”, posvyaschennogo 75-letiyu so dnya rozhdeniya akad. O. B. Lupanova (Moskva, 18–23 iyunya 2007 goda), Izd-vo mekhaniko-matematicheskogo fakulteta MGU, M., 2007, 440–442

[4] Rystsov I. K., “Vozvratnye slova dlya razreshimykh avtomatov”, Kibernetika i sistemnyi analiz, 1994, no. 6, 21–26 | MR | Zbl

[5] Sumarokov S. N., “Zaprety dvoichnykh funktsii i obratimost dlya odnogo klassa kodiruyuschikh ustroistv”, Obozrenie prikladnoi i promyshlennoi matematiki, 1:1 (1994), 33–55 | MR | Zbl

[6] Logachev O. A., Smyshlyaev S. V., Yaschenko V. V., “Novye metody izucheniya sovershenno uravnoveshennykh bulevykh funktsii”, Diskretnaya matematika, 21:2 (2009), 51–74 | MR

[7] Smyshlyaev S. V., “Perfectly Balanced Boolean Functions and Golic Conjecture”, J. Cryptology (to appear) | DOI

[8] Smyshlyaev S. V., “Barery sovershenno uravnoveshennykh bulevykh funktsii”, Diskretnaya matematika, 22:2 (2010), 66–79 | MR | Zbl

[9] Smyshlyaev S. V., “O kriptograficheskikh slabostyakh nekotorykh klassov preobrazovanii dvoichnykh posledovatelnostei”, Prikladnaya diskretnaya matematika, 2010, no. 1(7), 5–15

[10] Smyshlyaev S. V., “Bulevy funktsii bez predskazyvaniya”, Diskretnaya matematika, 23:1 (2011), 102–118 | MR

[11] Smyshlyaev S. V., “Postroenie klassov sovershenno uravnoveshennykh bulevykh funktsii bez barera”, Prikladnaya diskretnaya matematika, 2010, no. 3(9), 41–50

[12] Hedlund G. A., “Endomorphisms and automorphisms of the shift dynamical system”, Math. Sys. Theory, 3:4 (1969), 320–375 | DOI | MR | Zbl