On linear equivalence of piecewise-linear permutations of the field 𝔽_2ⁿ

References

[1] Anashkin A. V., “On the number of CCZ classes of equivalent permutations on V₄”, Obozr. prikl. i promyshl. matem., 26:2 (2019), 138–139 (in Russian).Search in Google Scholar

[2] Bugrov A. D., “Piecewise-affine permutations of finite fields”, Prikl. diskretn. matem., 4:30 (2015), 5–23 (in Russian).10.17223/20710410/30/1Search in Google Scholar

[3] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, 2nd ed., SPb.: Lan, 2015 (in Russian), 608 pp.Search in Google Scholar

[4] Menyachikhin A. V., “Adapted spectral-differential method for constructing differentially 4-uniform piecewise-linear substitutions, orthomorphisms, involutions over the field 𝔽_2ⁿ”, Diskretnaya matematika, 35:2 (2023), 42–77 (in Russian).10.4213/dm1757Search in Google Scholar

[5] Pogorelov B. A., Pudovkina M. A., “Classes of piecewise-quasiaffine transformations on the generalized 2-group of quaternions”, Discrete Math. Appl., 33:5 (2023), 299–316.10.1515/dma-2023-0028Search in Google Scholar

[6] Pogorelov B. A., Pudovkina M. A., “Classes of piecewise quasiaffine transformations on dihedral, quasidihedral and modular maximal-cyclic 2-groups”, Discrete Math. Appl., 34:1 (2024), 15–27.Search in Google Scholar

[7] Sachkov V. N., “Combinatorial properties of differentially 2-uniform substitutions”, Matematicheskie voprosy kriptografii, 6:1 (2015), 159–179 (in Russian).10.4213/mvk156Search in Google Scholar

[8] Trishin A. E., “The nonlinearity index for a piecewise-linear substitution of the additive group of the field 𝔽_2ⁿ”, Prikl. diskretn. matem., 4:30 (2015), 32–42 (in Russian).10.17223/20710410/30/3Search in Google Scholar

[9] Biryukov A., De Canniere C., Braeken A., Preneel B., “A toolbox for cryptanalysis: linear and affine equivalence algorithms”, EUROCRYPT 2003, Lect. Notes Comput. Sci., 2656, 2003, 33–50.10.1007/3-540-39200-9_3Search in Google Scholar

[10] Brinkmann M., Leander G., “On the classification of APN functions up to dimension five”, Des., Codes Cryptogr., 49:1–3 (2008), 273–288.10.1007/s10623-008-9194-6Search in Google Scholar

[11] Browning K. A., Dillon J. F., McQuistan M. T., Wolfe A. J., “An APN permutation in dimension six”, Finite Fields Theory Appl., 518 (2010), 33–42.10.1090/conm/518/10194Search in Google Scholar

[12] Carlet C., Charpin P., Zinoviev V., “Codes, bent functions, and permutations suitable for DES-like cryptosystems”, Des., Codes Cryptogr., 15:2 (1998), 125–156.10.1023/A:1008344232130Search in Google Scholar

[13] Evans A. B., Orthomorphism Graphs of Groups, Lect. Notes Math., 1535, Springer, 1992, 116 pp.10.1007/BFb0092363Search in Google Scholar

[14] Lambin B., Derbez P., Fouque P.-A., “Linearly equivalent s-boxes and the division property”, Des., Codes Cryptogr., 88:10 (2020), 2207–2231.10.1007/s10623-020-00773-4Search in Google Scholar

[15] Leander G., Poschmann A., “On the classification of4 bit s-boxes”, Lect. Notes Comput. Sci., 4547, 2007, 159–176.10.1007/978-3-540-73074-3_13Search in Google Scholar

[16] Li Y., Wang M., “Permutation polynomials EA-equivalent to the inverse function over GF(2ⁿ)”, Cryptogr. Commun., 3:3 (2011), 175–186.10.1007/s12095-011-0045-3Search in Google Scholar

[17] Menyachikhin A.V., “Spectral-linear and spectral-differential methods for generating s-boxes having almost optimal cryptographic parameters”, Matematicheskie voprosy kriptografii, 8:2 (2017), 97–116.10.4213/mvk227Search in Google Scholar

[18] Niederreiter H., Winterhof A., “Cyclotomic R-orthomorphisms of finite fields”, Discrete Math., 295:1–3 (2005), 161–171.10.1016/j.disc.2004.12.011Search in Google Scholar

[19] Saarinen M.-J. O., “Cryptographic analysis of all 4x4-bit s-boxes”, Lect. Notes Comput. Sci., 7118, 2012, 118–133.10.1007/978-3-642-28496-0_7Search in Google Scholar

[20] Wan D., Lidl R., “Permutation polynomials of the form x^rf(x^q–1/d) and their group structure”, Monatsh. Math., 112:2 (1991), 149–163.10.1007/BF01525801Search in Google Scholar

[21] Wells C., “Groups of permutation polynomials”, Monatsh. Math., 71:3 (1967), 248–262.10.1007/BF01298331Search in Google Scholar

[22] Zhang W., Bao Z., Rijmen V., Liu M., “A new classification of 4-bit optimal s-boxes and its application to PRESENT, RECTANGLE and SPONGENT”, FSE 2015, Lect. Notes Comput. Sci., 9054, 2015, 494–515.10.1007/978-3-662-48116-5_24Search in Google Scholar