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@article{DM_2022_34_2_a1, author = {A. A. Babueva and O. A. Logachev and V. V. Yashchenko}, title = {On the relationship between local affinities of a {Boolean} function and some types of its degeneracy}, journal = {Diskretnaya Matematika}, pages = {7--25}, publisher = {mathdoc}, volume = {34}, number = {2}, year = {2022}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/DM_2022_34_2_a1/} }
TY - JOUR AU - A. A. Babueva AU - O. A. Logachev AU - V. V. Yashchenko TI - On the relationship between local affinities of a Boolean function and some types of its degeneracy JO - Diskretnaya Matematika PY - 2022 SP - 7 EP - 25 VL - 34 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DM_2022_34_2_a1/ LA - ru ID - DM_2022_34_2_a1 ER -
%0 Journal Article %A A. A. Babueva %A O. A. Logachev %A V. V. Yashchenko %T On the relationship between local affinities of a Boolean function and some types of its degeneracy %J Diskretnaya Matematika %D 2022 %P 7-25 %V 34 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/DM_2022_34_2_a1/ %G ru %F DM_2022_34_2_a1
A. A. Babueva; O. A. Logachev; V. V. Yashchenko. On the relationship between local affinities of a Boolean function and some types of its degeneracy. Diskretnaya Matematika, Tome 34 (2022) no. 2, pp. 7-25. http://geodesic.mathdoc.fr/item/DM_2022_34_2_a1/
[1] Alekseev E.K., “O nekotorykh merakh nelineinosti bulevykh funktsii”, Prikl. diskr. matem., 2:12 (2011), 5–16 | Zbl
[2] Alekseev E. K., Kuschinskaya L. A., “Obobschenie odnogo metoda vosstanovleniya klyucha filtruyuschego generatora”, Diskretnaya matematika, 29:4 (2017), 3–27
[3] Alferov A.P., Zubov A.Yu., Kuzmin A.S., Cheremushkin A.V., Osnovy kriptografii, Gelios, M., 2001, 480 pp.
[4] Gorshkov S.P., Tarasov A.V., “O maksimalnykh gruppakh invariantnykh preobrazovanii multiaffinnykh, biyunktivnykh, slabo polozhitelnykh i slabo otritsatelnykh bulevykh funktsii”, Diskretnaya matematika, 21:2 (2009), 94–101 | Zbl
[5] Kolomeets N.A., “Verkhnyaya otsenka chisla bent-funktsii na rasstoyanii $2^k$ ot proizvolnoi bent-funktsii ot $2k$ peremennykh”, Prikl. diskr. matem., 2014, no. 3, 28–39 | Zbl
[6] Logachev O.A., Salnikov A.A., Smyshlyaev S.V., Yaschenko V.V., Bulevy funktsii v teorii kodirovaniya i kriptologii, LENAND, M., 2015, 573 pp.
[7] Logachev O.A., Salnikov A.A., Yaschenko V.V., “Nevyrozhdennaya normalnaya forma bulevykh funktsii”, Dokl. Akademii nauk, 373:2 (2000), 164–167 | MR | Zbl
[8] Logachev O.A., Salnikov A.A., Yaschenko V.V., “Nekotorye kharakteristiki «nelineinosti» gruppovykh otobrazhenii”, Diskretn. analiz i issled. oper., ser. 1, 8:1 (2001), 40–54 | MR | Zbl
[9] Logachev O.A., Fedorov S.N., Yaschenko V.V., “O nekotorykh invariantakh deistviya $GA(n, 2)$ na mnozhestve bulevykh funktsii”, Diskretnaya matematika, 33:2 (2021), 66–85
[10] Bernasconi A., Codenotti B., “Spectral analysis of Boolean functions as a graph eigenvalue problem”, IEEE Trans. Comput., 48:3 (1999), 345–351, IEEE | DOI | MR | Zbl
[11] Boyar J., Find M.G., “Constructive relationships between algebraic thickness and normality”, Int. Symp. Fundam. Comput. Theory, Lect. Notes Comput. Sci., 9210, 2015, 106–117 | DOI | MR | Zbl
[12] Boyar J., Find M.G., Peralta R., “On various nonlinearity measures for Boolean functions”, Cryptogr. and Commun., 8:3 (2016), 313–330 | DOI | MR | Zbl
[13] Canteaut A., Daum M., Dobbertin H., Leandr G., “Finding normal bent-functions”, Discr. Appl. Math., 154 (2006), 202–218 | DOI | MR | Zbl
[14] Carlet C., “On the degree, nonlinearity, algebraic thickness, and nonnormality of Boolean functions, with developments on symmetric functions”, IEEE Trans. Inf. Theory, 50:9 (2004), 2178–2185, IEEE | DOI | MR | Zbl
[15] Carlet C., Charpin P., “Cubic Boolean functions with highest resiliency”, IEEE Trans. Inf. Theory, 51:2 (2005), 562–571, IEEE | DOI | MR | Zbl
[16] Carlet C., Boolean Functions for Cryptography and Coding Theory, Cambridge Univ. Press, 2020, 574 pp. | Zbl
[17] Dawson E., Wu C. K., “Construction of correlation immune Boolean functions”, Australasian J. Combinatorics, 21 (1997), 170–180 | MR
[18] Dickson L. E., Linear groups, B. G. Teubner, Leipzig, 1901 | Zbl
[19] Lechner R. J., “Harmonic analysis of switching functions”, Developments in switching theory, Academic Press, 1971, 121–228 | DOI | MR
[20] Matsui M., “Linear cryptanalysis method for DES cipher”, EUROCRYPT 1993, Lect. Notes Comput. Sci., 765, 1993, 386–397 | DOI
[21] Rothaus O. S., “On bent functions”, J. Comb. Theory, Ser. A., 20:3 (1976), 300–305 | DOI | MR | Zbl
[22] Sanyal S., Sub-linear upper bounds on Fourier dimension of Boolean functions in terms of Fourier sparsity, 2014, arXiv: 1407.3500 | MR
[23] Shannon C. E., “The synthesis of two-terminal switching circuits”, The Bell System Technical J., 28:1 (1949), 59–98 | DOI | MR
[24] Siegenthaler T., “Decrypting a class of stream ciphers using ciphertext only”, IEEE Trans. on computers, 34:1 (1985), 81–85 | DOI