Geodesic
Characterization of almost perfect nonlinear functions in terms of subfunctions
Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 3-16.

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The paper is concerned with combinatorial description of almost perfect nonlinear functions (APN-functions). A complete characterization of $n$-place APN-functions in terms of $(n-1)$-place subfunctions is obtained. An $n$-place function is shown to be an APN-function if and only if each of its $(n-1)$-place subfunctions is either an APN-function or has the differential uniformity $4$ and the admissibility conditions hold. A detailed characterization of 2, 3 or 4-place APN-functions is presented.
Keywords: vectorial Boolean function, differential uniformity, APN-function, characterization. 
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A. A. Gorodilova. Characterization of almost perfect nonlinear functions in terms of subfunctions. Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 3-16. http://geodesic.mathdoc.fr/item/DM_2015_27_3_a0/

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