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Diskretnyi Analiz i Issledovanie Operatsii, 2023, Volume 30, Issue 4, Pages 46–90
DOI: https://doi.org/10.33048/daio.2023.30.771 (Mi da1334) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Post-quantum cryptosystems: open problems and solutions. Lattice-based cryptosystems

E. S. Malyginaab, A. V. Kutsenkob, S. A. Novoselova, N. S. Kolesnikova, A. O. Bakharevb, I. S. Khilchukb, A. S. Shaporenkob, N. N. Tokarevaba

a Immanuel Kant Baltic Federal University, 14 Aleksandr Nevskii Street, 236041 Kaliningrad, Russia
b Novosibirsk State University, 2 Pirogov Street, 630090 Novosibirsk, Russia
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DOI: https://doi.org/10.33048/daio.2023.30.771
Abstract: The paper provides an overview of the main approaches to the construction of post-quantum cryptographic systems that are currently used. The area of lattice-based cryptography is analyzed in detail. We give the description and characteristics of some known lattice-based cryptosystems whose security is based on the complexity of the shortest vector problem, learning with errors problem, and their variations. The main approaches to solving the problems from lattice theory, on which attacks on the corresponding cryptosystems are based, are analyzed. In particular, some known theoretical estimates of time and memory complexity of lattice basis reduction and lattice sieving algorithms are presented. Tab. 6, illustr. 1, biblogr. 93.
Keywords: post-quantum cryptography, quantum computer, integer lattice.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2023-934
075-15-2022-282
The work of the first, third, and fourth authors is supported by the Kovalevskaya North-Western Mathematical Center of Immanuel Kant Baltic Federal University under the agreement with the Ministry of Science and Higher Education of Russia (Agreement 075–02–2023–934). The work of the second, fifth, sixth, seventh, and eighth authors is supported by the Mathematical Center in Akademgorodok under agreement with the Ministry of Science and Higher Education of Russia (Agreement 075–15–2022–282).
Received: 04.05.2023
Revised: 28.07.2023
Accepted: 20.08.2023
English version:
Journal of Applied and Industrial Mathematics, 2023, Volume 17, Issue 4, Pages 767–790
DOI: https://doi.org/10.1134/S1990478923040087
Document Type: Article
UDC: 519.7
Language: Russian
Citation: E. S. Malygina, A. V. Kutsenko, S. A. Novoselov, N. S. Kolesnikov, A. O. Bakharev, I. S. Khilchuk, A. S. Shaporenko, N. N. Tokareva, “Post-quantum cryptosystems: open problems and solutions. Lattice-based cryptosystems”, Diskretn. Anal. Issled. Oper., 30:4 (2023), 46–90; J. Appl. Industr. Math., 17:4 (2023), 767–790
Citation in format AMSBIB
\Bibitem{MalKutNov23}
\by E.~S.~Malygina, A.~V.~Kutsenko, S.~A.~Novoselov, N.~S.~Kolesnikov, A.~O.~Bakharev, I.~S.~Khilchuk, A.~S.~Shaporenko, N.~N.~Tokareva
\paper Post-quantum cryptosystems: open problems and solutions. Lattice-based cryptosystems
\jour Diskretn. Anal. Issled. Oper.
\yr 2023
\vol 30
\issue 4
\pages 46--90
\mathnet{http://mi.mathnet.ru/da1334}
\crossref{https://doi.org/10.33048/daio.2023.30.771}
\transl
\jour J. Appl. Industr. Math.
\yr 2023
\vol 17
\issue 4
\pages 767--790
\crossref{https://doi.org/10.1134/S1990478923040087}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Дискретный анализ и исследование операций
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