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Diskretn. Anal. Issled. Oper., 2016, Volume 23, Number 1, Pages 65–81 (Mi da839)  
On symmetric properties of APN functions

V. A. Vitkupab

a Sobolev Institute of Mathematics, 4 Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia

Abstract: 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 $n\le6$. 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-31-20635


DOI: https://doi.org/10.17377/daio.2016.23.498

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

Bibliographic databases:

Document Type: Article
UDC: 519.7
Received: 11.06.2015
Revised: 27.08.2015

Citation: V. A. Vitkup, “On symmetric properties of APN functions”, Diskretn. Anal. Issled. Oper., 23:1 (2016), 65–81; J. Appl. Industr. Math., 10:1 (2016), 126–135

Citation in format AMSBIB
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\paper On symmetric properties of APN functions
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\pages 65--81
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\jour J. Appl. Industr. Math.
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\pages 126--135
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