On the relationship between local affinities of a Boolean function and some types of its degeneracy

References

[1] Alekseev E.K., “On some measures of nonlinearity for Boolean functions”, Prikl. Diskr.Matem., 2:12 (2011), 5-16 (in Russian).10.17223/20710410/12/1Suche in Google Scholar

[2] Alekseev E.K., Kuschinskaya L.A., “Generalization of one method of a filter generator key recovery”, Discrete Math. Appl., 29:2 (2019), 69-87.10.1515/dma-2019-0008Suche in Google Scholar

[3] Alferov A.P., Zubov A.Yu., Kuzmin A.S., Cheremushkin A.V., Fundamentals of Cryptography, M.: Gelios, 2001 (in Russian), 480 pp.Suche in Google Scholar

[4] Gorshkov S.P., Tarasov A.V., “Maximal groups of invariant transformations of multiaffine, bijunctive, weakly positive, and weakly negative Boolean functions”, Discrete Math. Appl., 19:3 (2009), 283-291.10.1515/DMA.2009.017Suche in Google Scholar

[5] Kolomeets N.A., “An upper bound for the number of bent functions at the distance 2k from an arbitrary bent function in 2k variables”, Prikladnaya Diskretnaya Matematika, 2014, №3, 28-39 (in Russian).10.17223/20710410/25/3Suche in Google Scholar

[6] Logachev O.A., Salnikov A.A., Smyshlyaev S.V., Yashchenko V.V., Boolean functions in coding theory and cryptology, M.: LENAND, 2015 (in Russian), 573 pp.Suche in Google Scholar

[7] Logachev O.A., Salnikov A.A., Yashchenko V.V., “Nondegenerate normal forms of Boolean functions”, Doklady Mathematics, 62:1 (2000), 35-38.Suche in Google Scholar

[8] Logachev O.A., Salnikov A.A., Yashchenko V.V., “Some characteristics of “nonlinearity” of group mappings”, Diskretn. Anal. Issled. Oper., Ser. 1, 8:1 (2001), 40-54.Suche in Google Scholar

[9] Logachev O.A., Fedorov S.N., Yashchenko V.V., “On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions”, Discrete Math. Appl., 32:3 (2022), 177-192.10.1515/dma-2022-0016Suche in Google Scholar

[10] Bernasconi A., Codenotti B., “Spectral analysis of Boolean functions as a graph eigenvalue problem”, IEEE Trans. Comput., 48 3 (1999), 345-351.10.1109/12.755000Suche in Google Scholar

[11] Boyar J., Find M.G., “Constructive relationships between algebraic thickness and normality”, Int. Symp. Fundam. Comput. Theory, Lect. Notes Comput. Sci., 9210,2015,106-117.10.1007/978-3-319-22177-9_9Suche in Google Scholar

[12] Boyar J., FindM.G., Peralta R., “On various nonlinearity measures for Boolean functions”, Cryptogr. and Commun., 8:3 (2016), 313-330.10.1007/s12095-015-0150-9Suche in Google Scholar PubMed PubMed Central

[13] Canteaut A., Daum M., Dobbertin H., Leandr G., “Finding normal bent-functions”, Discr. Appl. Math., 154 (2006), 202-218.10.1016/j.dam.2005.03.027Suche in Google Scholar

[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), 2178-2185.10.1109/TIT.2004.833361Suche in Google Scholar

[15] Carlet C., Charpin P., “Cubic Boolean functions with highest resiliency”, IEEE Trans. Inf. Theory, 512 (2005), 562-571.10.1109/TIT.2004.840902Suche in Google Scholar

[16] Carlet C., Boolean Functions for Cryptography and Coding Theory, Cambridge Univ. Press, 2020, 574 pp.10.1017/9781108606806Suche in Google Scholar

[17] Dawson E., Wu C. K., “Construction of correlation immune Boolean functions”, Australasian J. Combinatorics, 21 (1997), 170-180.10.1007/BFb0028473Suche in Google Scholar

[18] Dickson L. E., Linear groups, Leipzig: B. G. Teubner, 1901.Suche in Google Scholar

[19] Lechner R. J., “Harmonic analysis of switching functions”, Developments in switching theory, Academic Press, 1971,121-228.10.1016/B978-0-12-509850-2.50010-5Suche in Google Scholar

[20] Matsui M., “Linear cryptanalysis method for DES cipher”, EUROCRYPT 1993, Lect. Notes Comput. Sci., 765,1993,386-397.10.1007/3-540-48285-7_33Suche in Google Scholar

[21] Rothaus O. S., “On bent functions”, J. Comb. Theory, Ser. A., 20 3 (1976), 300-305.10.1016/0097-3165(76)90024-8Suche in Google Scholar

[22] Sanyal S., “Sub-linear upper bounds on Fourier dimension of Boolean functions in terms of Fourier sparsity”, arXiv:14073500, 2014.10.1007/978-3-662-47672-7_84Suche in Google Scholar

[23] Shannon C. E., “The synthesis of two-terminal switching circuits”, The Bell System Technical J., 281 (1949), 59-98.10.1002/j.1538-7305.1949.tb03624.xSuche in Google Scholar

[24] Siegenthaler T., “Decrypting a class of stream ciphers using ciphertext only”, IEEE Trans. on Computers, 34:1 (1985), 81-85.10.1109/TC.1985.1676518Suche in Google Scholar