Geodesic
On constructing special APN functions and their link with APN permutations
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 36-38

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The existence of APN permutation in even dimension is an important open problem on cryptographic Boolean functions. In this paper, we consider an algorithm for constructing $2$-to-$1$ APN functions and searching the corresponding affine functions such that their sum is an APN permutation. As a result, $2$-to-$1$ APN functions in 5 and 6 variables are found. These functions are APN permutations.
Keywords: vector Boolean function, APN function, bijective function, $2$-to-$1$ function
Mots-clés : permutation. 
@article{PDMA_2017_10_a13,
     author = {V. A. Idrisova},
     title = {On constructing special {APN} functions and their link with {APN} permutations},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {36--38},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a13/}
}
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V. A. Idrisova. On constructing special APN functions and their link with APN permutations. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 36-38. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a13/