Geodesic
An iterative construction of almost perfect nonlinear functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 24-25

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Vectorial Boolean functions $F$ and $G$ are equivalent if $\forall a\neq 0\,\forall b\,[\exists x(F(x)\oplus F(x\oplus a)=b)\Leftrightarrow\exists x(G(x)\oplus G(x\oplus a)=b)]$. It is proved that every class of equivalent almost perfect nonlinear (APN) functions in $n$ variables contains $2^{2n}$ different functions. An iterative procedure is proposed for constructing APN functions in $n+1$ variables from two APN and two Boolean functions in $n$ variables satisfying some conditions. Computer experiment show that among functions in small variables there are many functions satisfying these conditions.
Keywords: vectorial Boolean function, APN function, iterative construction.
Mots-clés : $\gamma$-equivalence 
@article{PDMA_2013_6_a11,
     author = {A. A. Frolova},
     title = {An iterative construction of almost perfect nonlinear functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {24--25},
     publisher = {mathdoc},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2013_6_a11/}
}
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A. A. Frolova. An iterative construction of almost perfect nonlinear functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 24-25. http://geodesic.mathdoc.fr/item/PDMA_2013_6_a11/