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

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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

$n$ -place APN-functions in terms of

(n - 1)

$(n-1)$ -place subfunctions is obtained. An

n

$n$ -place function is shown to be an APN-function if and only if each of its

(n - 1)

$(n-1)$ -place subfunctions is either an APN-function or has the differential uniformity

4

$4$ 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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Linking options:

https://www.mathnet.ru/eng/dm1331

https://doi.org/10.4213/dm1331

https://www.mathnet.ru/eng/dm/v27/i3/p3

This publication is cited in the following 15 articles:

Yu. S. Kalinin, “Issledovanie bumerangovoi ravnomernosti kvadratichnykh vzaimno odnoznachnykh vektornykh bulevykh funktsii”, PDM. Prilozhenie, 2024, no. 17, 28–34
N. A. Kolomeets, “O podstanovkakh, razrushayuschikh strukturu podprostranstv opredelennykh razmernostei”, PDM, 2024, no. 65, 5–20
N. A. Kolomeets, “O sokhranenii struktury podprostranstv vektornymi bulevymi funktsiyami”, PDM. Prilozhenie, 2023, no. 16, 23–26
Konstantin Kalgin, Valeriya Idrisova, “The classification of quadratic APN functions in 7 variables and combinatorial approaches to search for APN functions”, Cryptogr. Commun., 15:2 (2023), 239
Beierle Ch., Leander G., Perrin L., “Trims and Extensions of Quadratic Apn Functions”, Designs Codes Cryptogr., 90:4 (2022), 1009–1036
A. E. Doronin, K. V. Kalgin, “Primenenie SAT-reshatelei k zadache poiska vektornykh bulevykh funktsii s trebuemymi kriptograficheskimi svoistvami”, Diskretn. analiz i issled. oper., 29:4 (2022), 38–58
A. E. Doronin, K. V. Kalgin, “Application of SAT-Solvers to the Problem of Finding Vectorial Boolean Functions with Required Cryptographic Properties”, J. Appl. Ind. Math., 16:4 (2022), 632
K. V. Kalgin, V. A. Idrisova, “On a secondary construction of quadratic APN functions”, PDM. Prilozhenie, 2020, no. 13, 37–39
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
A. Gorodilova, “On the differential equivalence of APN functions”, Cryptogr. Commun., 11:4 (2019), 793–813
V. A. Idrisova, “O postroenii APN-perestanovok s pomoschyu podfunktsii”, PDM, 2018, no. 41, 17–27
V. A. Vitkup, “On symmetric properties of APN functions”, J. Appl. Industr. Math., 10:1 (2016), 126–135
A. A. Gorodilova, “Ot kriptoanaliza shifra k kriptograficheskomu svoistvu bulevoi funktsii”, PDM, 2016, no. 3(33), 16–44
A. A. Gorodilova, “Lineinyi spektr kvadratichnykh APN-funktsii”, PDM, 2016, no. 4(34), 5–16
M. M. Glukhov, “O priblizhenii diskretnykh funktsii lineinymi funktsiyami”, Matem. vopr. kriptogr., 7:4 (2016), 29–50

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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