V. M. Fomichev, Ya. E. Avezova, A. M. Koreneva, S. N. Kyazhin, “Primitivity and local primitivity of digraphs and nonnegative matrices”, Diskretn. Anal. Issled. Oper., 25:3 (2018), 95–125; J. Appl. Industr. Math., 12:3 (2018), 453

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Diskretnyi Analiz i Issledovanie Operatsii, 2018, Volume 25, Issue 3, Pages 95–125
DOI: https://doi.org/10.17377/daio.2018.25.595 (Mi da903)

This article is cited in 15 scientific papers (total in 15 papers)

Primitivity and local primitivity of digraphs and nonnegative matrices

V. M. Fomichev^abc, Ya. E. Avezova^b, A. M. Koreneva^b, S. N. Kyazhin^b

^a Financial University under the Government of the Russian Federation, 49 Leningradsky Ave., 125993 Moscow, Russia
^b National Research Nuclear University MEPhI, 31 Kashirskoe Highway, 115409 Moscow, Russia
^c Institute of Informatics Problems of FRC CSC RAS, 44/2 Vavilova St., 119333 Moscow, Russia

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DOI: https://doi.org/10.17377/daio.2018.25.595

Abstract: The article surveys the main results on the primitivity and local primitivity of digraphs and matrices from the inception of this research area in 1912 by now. We review the universal and special criteria for primitivity and local primitivity as well as universal and special bounds on the exponents and local exponents of digraphs and matrices. We describe some cryptographic applications of this mathematical apparatus for analyzing the mixing properties of block ciphers and keystream generators. The new promising research directions are formulated in the study of primitivity and local primitivity of digraphs and matrices. Bibliogr. 47.

Keywords: primitive digraph, primitive matrix, local primitivity, primitive set, exponent, local exponent.

Funding agency	Grant number
Russian Foundation for Basic Research	16-01-00226
The first author was supported by the Russian Foundation for Basic Research (project no. 16-01-00226).

Received: 16.10.2017
Revised: 23.03.2018

English version:
Journal of Applied and Industrial Mathematics, 2018, Volume 12, Issue 3, Pages 453–469
DOI: https://doi.org/10.1134/S1990478918030067

Bibliographic databases:

Document Type: Article

UDC: 519.17

Language: Russian

Citation: V. M. Fomichev, Ya. E. Avezova, A. M. Koreneva, S. N. Kyazhin, “Primitivity and local primitivity of digraphs and nonnegative matrices”, Diskretn. Anal. Issled. Oper., 25:3 (2018), 95–125; J. Appl. Industr. Math., 12:3 (2018), 453–469

Citation in format AMSBIB

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\paper Primitivity and local primitivity of digraphs and nonnegative matrices

\jour Diskretn. Anal. Issled. Oper.

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\pages 95--125

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\crossref{https://doi.org/10.17377/daio.2018.25.595}

\elib{https://elibrary.ru/item.asp?id=35448327}

\transl

\jour J. Appl. Industr. Math.

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\crossref{https://doi.org/10.1134/S1990478918030067}

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Linking options:

https://www.mathnet.ru/eng/da903

https://www.mathnet.ru/eng/da/v25/i3/p95

This publication is cited in the following 15 articles:

P. A. Chezhegova, A. M. Koreneva, M. V. Polyakov, G. V. Firsov, “O peremeshivayuschikh svoistvakh registrovykh preobrazovanii algoritmov shifrovaniya TEA1 i TEA2”, PDM. Prilozhenie, 2024, no. 17, 120–122
Fomichev V. Bobrovskiy D. Koreneva A. Nabiev T. Zadorozhny D., “Data Integrity Algorithm Based on Additive Generators and Hash Function”, J. Comput. Virol. Hacking Tech., 18:1, SI (2022), 31–41
V. M. Fomichev, V. M. Bobrov, “O $\langle 2\rangle$-eksponentakh orgrafov nelineinosti registrovykh preobrazovanii”, PDM, 2022, no. 55, 77–87
Ramos G., Pequito S., Caleiro C., “on the Index of Convergence of a Class of Boolean Matrices With Structural Properties”, Int. J. Control, 94:6 (2021), 1475–1483
V. M. Fomichev, “On degree of nonlinearity of the coordinate polynomials for a product of transformations of a binary vector space”, J. Appl. Industr. Math., 15:2 (2021), 212–222
M. B. Abrosimov, I. V. Los, S. V. Kostin, “Primitivnye odnorodnye grafy s eksponentom 2 i chislom vershin do 16”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 21:2 (2021), 238–245
C. Catalano, U. Azfar, L. Charlier, R. M. Jungers, “A linear bound on the k-rendezvous time for primitive sets of NZ matrices”, Fundam. Inform., 180:4, SI (2021), 289–314
E. K. Egorova, A. V. Mokryakov, A. A. Suvorova, V. I. Tsurkov, “Algorithm of multidimensional data transmission using extremal uniform hypergraphs”, J. Comput. Syst. Sci. Int., 60:1 (2021), 69–74
V. M. Fomichev, Ya. E. Avezova, “Exact formula for exponents of mixing digraphs for register transformations”, J. Appl. Industr. Math., 14:2 (2020), 308–319
V. M. Fomichev, “Estimating nonlinearity characteristics for iterative transformations of a vector space”, J. Appl. Industr. Math., 14:4 (2020), 610–622
C. Catalano, R. M. Jungers, “The synchronizing probability function for primitive sets of matrices”, Int. J. Found. Comput. Sci., 31:6, SI (2020), 777–803
V. Fomichev, A. Koreneva, “Encryption performance and security of certain wide block ciphers”, J. Comput. Virol. Hacking Tech., 16:3 (2020), 197–216
V. M. Fomichev, “Ob uluchshennoi universalnoi otsenke eksponentov orgrafov”, PDM, 2019, no. 43, 115–123
Umer Azfar, Costanza Catalano, Ludovic Charlier, Raphaël M. Jungers, Lecture Notes in Computer Science, 11647, Developments in Language Theory, 2019, 59
V. M. Fomichev, A. M. Koreneva, A. R. Miftakhutdinova, D. I. Zadorozhny, “Otsenki predelnoi proizvoditelnosti algoritmov blochnogo shifrovaniya”, Matem. vopr. kriptogr., 10:2 (2019), 181–191

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

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