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. 
@article{PDMA_2017_10_a14,
     author = {L. A. Karpova and I. A. Pankratova},
     title = {Properties of coordinate functions for a~class of permutations on~$\mathbb F_2^n$},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {38--40},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a14/}
}
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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/