Geodesic
Properties of coordinate functions for a~class of permutations on~$\mathbb F_2^n$
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 38-40.

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In the class $\mathcal F_n$ of permutations on $\mathbb F_2^n$ with coordinate functions depending on all variables, we consider the subclass $\mathcal K_n$, where each permutation is obtained from the identity by $n$ independent transpositions. For permutations in $\mathcal K_n$, some cryptographic properties of coordinate functions $f_i$ are given, namely, $\operatorname{deg}f_i=n-1$, non-linearity $N_{f_i}=2$, correlation immunity order $\operatorname{cor}(f_i)=0$, algebraic immunity $\operatorname{AI}(f_i)=2$. The cardinalities $|\mathcal K_n|$ for $n=3,\dots,6$ has been presented.
Keywords: vector Boolean functions, invertible functions, non-linearity, correlation immunity, algebraic immunity. 
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L. A. Karpova; I. A. Pankratova. Properties of coordinate functions for a~class of permutations on~$\mathbb F_2^n$. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 38-40. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a14/

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

[2] Tarannikov Yu. V., “O korrelyatsionno-immunnykh i ustoichivykh bulevykh funktsiyakh”, Matem. voprosy kibernetiki, 11, 2002, 91–148 | MR | Zbl

[3] Lobanov M. S., “Tochnoe sootnoshenie mezhdu nelineinostyu i algebraicheskoi immunnostyu”, Diskretnaya matematika, 18:3 (2006), 152–159 | DOI | MR | Zbl

[4] Agibalov G. P., “SIBCiphers – simmetrichnye iterativnye blochnye shifry iz bulevykh funktsii s klyuchevymi argumentami”, Prikladnaya diskretnaya matematika. Prilozhenie, 2014, no. 7, 43–48

[5] Agibalov G. P., “Kriptoavtomaty s funktsionalnymi klyuchami”, Prikladnaya diskretnaya matematika, 2017, no. 36, 59–72

[6] Pankratova I. A., “Ob obratimosti vektornykh bulevykh funktsii”, Prikladnaya diskretnaya matematika. Prilozhenie, 2015, no. 8, 35–37