Email this article Primitivity and Local Primitivity of Digraphs and Nonnegative Matrices
- Authors: Fomichev V.M.1,2,3, Avezova Y.E.2, Koreneva A.M.2, Kyazhin S.N.2
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Affiliations:
- Financial University under the Government of the Russian Federation
- National Research Nuclear University MEPhI
- Institute of Informatics Problems
- Issue: Vol 12, No 3 (2018)
- Pages: 453-469
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213085
- DOI: https://doi.org/10.1134/S1990478918030067
- ID: 213085
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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.
About the authors
V. M. Fomichev
Financial University under the Government of the Russian Federation; National Research Nuclear University MEPhI; Institute of Informatics Problems
Author for correspondence.
Email: fomichev@nm.ru
Russian Federation, Leningradskii pr. 49, Moscow, 125993; Kashirskoe sh. 31, Moscow, 115409; ul. Vavilova 44, korp. 2, Moscow, 119333
Ya. E. Avezova
National Research Nuclear University MEPhI
Email: fomichev@nm.ru
Russian Federation, Kashirskoe sh. 31, Moscow, 115409
A. M. Koreneva
National Research Nuclear University MEPhI
Email: fomichev@nm.ru
Russian Federation, Kashirskoe sh. 31, Moscow, 115409
S. N. Kyazhin
National Research Nuclear University MEPhI
Email: fomichev@nm.ru
Russian Federation, Kashirskoe sh. 31, Moscow, 115409
