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This article is cited in 1 scientific paper (total in 1 paper)
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.
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:
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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\jour J. Appl. Industr. Math.
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\pages 126--135
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http://mi.mathnet.ru/eng/da839 http://mi.mathnet.ru/eng/da/v23/i1/p65
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This publication is cited in the following articles:
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V. Idrisova, “On an algorithm generating 2-to-1 APN functions and its applications to “the big APN problem””, Cryptogr. Commun., 11:1, SI (2019), 21–39
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