Geodesic
Vectorial $2$-to-$1$ functions as subfunctions of APN permutations
Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 39-41

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This work concerns the problem of APN permutations existence for even dimensions. We consider the differential properties of $(n-1)$-subfunctions of APN permutations. It is proved that every $(n-1)$-subfunction of an APN permutation can be derived using special symbol sequences. These results allow us to propose an algorithm for constructing APN permutations through $2$-to-$1$ functions and corresponding coordinate Boolean functions. A lower bound for the number of such Boolean functions is obtained.
Keywords: vectorial Boolean function, APN function, bijective function, $2$-to-$1$ function
Mots-clés : permutation. 
@article{PDMA_2018_11_a10,
     author = {V. A. Idrisova},
     title = {Vectorial $2$-to-$1$ functions as subfunctions of {APN} permutations},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {39--41},
     publisher = {mathdoc},
     number = {11},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2018_11_a10/}
}
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V. A. Idrisova. Vectorial $2$-to-$1$ functions as subfunctions of APN permutations. Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 39-41. http://geodesic.mathdoc.fr/item/PDMA_2018_11_a10/