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Diskretnaya Matematika, 2015, Volume 27, Issue 3, Pages 3–16
DOI: https://doi.org/10.4213/dm1331 (Mi dm1331) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Characterization of almost perfect nonlinear functions in terms of subfunctions

A. A. Gorodilova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (553 kB) Citations (15)
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DOI: https://doi.org/10.4213/dm1331
Abstract: 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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-1939.2014.1
Russian Foundation for Basic Research 15-07-01328
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 15-07-01328) and the Programme of Support of Leading Scientific Schools of the President of the Russian Federation (grant no. NSh-1939.2014.1).
Received: 28.08.2014
English version:
Discrete Mathematics and Applications, 2016, Volume 26, Issue 4, Pages 193–202
DOI: https://doi.org/10.1515/dma-2016-0017
Bibliographic databases:
Document Type: Article
UDC: 519.571
Language: Russian
Citation: A. A. Gorodilova, “Characterization of almost perfect nonlinear functions in terms of subfunctions”, Diskr. Mat., 27:3 (2015), 3–16; Discrete Math. Appl., 26:4 (2016), 193–202
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретная математика
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    Full-text PDF :235
    References:73
    First page:37
     
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