Geodesic
On the invertibility of vector Boolean functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 35-37.

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The class $\mathcal F_{n,m,k}$ of invertible vector Boolean functions $F\colon\mathbb F_2^n\to\mathbb F_2^m$ with coordinate functions depending on the given number $k$ variables is considered. It is proved that 1) these functions do not exist for any $n=m$ and $k=2$; 2) the functions of the class $\mathcal F_{n,n,n-1}$ can (can not) be built from affine coordinate functions for even (odd) $n$; 3) if $\mathcal F_{n,m,k}\neq\varnothing$ then $\mathcal F_{n+1,m+1,k}\neq\varnothing$.
Keywords: vector Boolean functions, invertible function. 
@article{PDMA_2015_8_a13,
     author = {I. A. Pankratova},
     title = {On the invertibility of vector {Boolean} functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {35--37},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2015_8_a13/}
}
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I. A. Pankratova. On the invertibility of vector Boolean functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 35-37. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a13/

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