Geodesic
On some open questions about APN functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 11-13.

Voir la notice de l'article provenant de la source Math-Net.Ru

Some open questions in the theory of APN functions are stated. Few results obtained in this direction are listed. For the sum of two APN functions of dimension 2, a necessary and sufficient condition to be an APN function is proved.
Keywords: vectorial Boolean function, APN function. 
@article{PDMA_2014_7_a2,
     author = {V. A. Vitkup},
     title = {On some open questions about {APN} functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {11--13},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2014_7_a2/}
}
TY  - JOUR
AU  - V. A. Vitkup
TI  - On some open questions about APN functions
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2014
SP  - 11
EP  - 13
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2014_7_a2/
LA  - ru
ID  - PDMA_2014_7_a2
ER  - 
%0 Journal Article
%A V. A. Vitkup
%T On some open questions about APN functions
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2014
%P 11-13
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2014_7_a2/
%G ru
%F PDMA_2014_7_a2
V. A. Vitkup. On some open questions about APN functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 11-13. http://geodesic.mathdoc.fr/item/PDMA_2014_7_a2/

[1] Nyberg K., “Perfect nonlinear S-boxes”, LNCS, 547, 1991, 378–386 | MR | Zbl

[2] Budaghyan L., Construction and Analysis of Cryptographic Functions, Habilitation Thesis, University of Paris, 8 Sept. 2013

[3] Tuzhilin M. E., “Pochti sovershennye nelineinye funktsii”, Prikladnaya diskretnaya matematika, 2009, no. 3, 14–20

[4] Gorodilova A. A., “Kharakterizatsiya APN-funktsii cherez podfunktsii”, Prikladnaya diskretnaya matematika. Prilozhenie, 2014, no. 7, 15–16

[5] McQuistan M. T., Wolfe A. J., Browning K. A., Dillon J. F., “An APN permutation in dimension six”, Finite fields: theory and applications, Contemp. Math., 518, Amer. Math. Soc., 2010, 33–42 | MR | Zbl

[6] Shushuev G. I., “Vektornye bulevy funktsii na rasstoyanii odin ot APN-funktsii”, Prikladnaya diskretnaya matematika. Prilozhenie, 2014, no. 7, 36–37