English version:
Journal of Applied and Industrial Mathematics, 2016, 10:1, 126-135

Volume 23, No 1, 2016, P. 65-81

UDC 519.7
V. A. Vitkup
On symmetric properties of APN-functions

We study symmetric properties of APN functions and the structure of their images. It is proven that there is no permutation of variables which keeps an APN function values. Upper bounds for the number of symmetric coordinate Boolean functions in APN function are obtained. Also, there are proven upper bounds for the number of coordinate Boolean functions of an APN function which are invariant under circular translation of indices. Upper bounds for the maximal number of coincidental values are obtained for n ≤ 6. A lower bound for the number of different values of an arbitrary APN function is proven.
Bibliogr. 14.

Keywords: vectorial Boolean function, APN function, symmetric function.

DOI: 10.17377/daio.2016.23.498

Valeriya A. Vitkup 1,2
1. Sobolev Institute of Mathematics,
4 Koptyug Ave., 630090 Novosibirsk, Russia
2. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
e-mail: vvitkup@yandex.ru

Received 11 April 2015
Revised 16 August 2015


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 © Sobolev Institute of Mathematics, 2015