Constructing vector Boolean functions with non-degenerate coordinate functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 30-33.

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An algorithm for constructing a bijection on $\mathbb{Z}_2^n$ with coordinate functions depending essentially on all variables is proposed. The algorithm consists of three steps: generation of a random bijection $F:\mathbb{Z}_2^n\to\mathbb{Z}_2^n$, analysis of the degeneracy of its coordinates, and one transposition of the values of $F(x)$ and $F(y)$ such that they differ only in the positions corresponding to the degenerate coordinate functions.
Keywords: vector Boolean function, essential dependence of a function on a variable.
Mots-clés : bijection
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I. A. Pankratova; E. A. Ruban; S. V. Chikalova. Constructing vector Boolean functions with non-degenerate coordinate functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 30-33. http://geodesic.mathdoc.fr/item/PDMA_2022_15_a7/

[1] Agibalov G. P., “Substitution block ciphers with functional keys”, Prikladnaya diskretnaya matematika, 2017, no. 38, 57–65 | MR | Zbl

[2] Agibalov G. P. and Pankratova I. A., “Asymmetric cryptosystems on Boolean functions”, Prikladnaya diskretnaya matematika, 2018, no. 40, 23–33 | MR | Zbl

[3] Pankratova I. A., “Construction of invertible vectorial Boolean functions with coordinates depending on given number of variables”, Materialy Mezhdunar. nauch. kongressa po informatike: Informatsionnye sistemy i tekhnologii (Respublika Belarus, Minsk, 24–27 okt. 2016), BGU, Minsk, 2016, 519–521

[4] Karpova L. A., Pankratova I. A., “Svoistva koordinatnykh funktsii odnogo klassa podstanovok na $\mathbb{F}_2^n$”, Prikladnaya diskretnaya matematika. Prilozhenie, 2017, no. 10, 38–40

[5] Pankratova I. A., “Svoistva komponent nekotorykh klassov vektornykh bulevykh funktsii”, Prikladnaya diskretnaya matematika, 2019, no. 44, 5–11 | Zbl

[6] Pankratova I. A., Bulevy funktsii v kriptografii, Lan, SPb.–M.–Krasnodar, 2019

[7] Knut D. E., Iskusstvo programmirovaniya, v. 2, Poluchislennye algoritmy, 3-e izd., Vilyams, M., 2007 | MR