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Diskretnyi Analiz i Issledovanie Operatsii, 2024, Volume 31, Issue 1, Pages 52–84
DOI: https://doi.org/10.33048/daio.2024.31.772 (Mi da1339) 		 
Post-quantum cryptosystems: open problems and current solutions. Isogeny-based and code-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.2024.31.772
Abstract: This paper is a survey of modern post-quantum cryptographic schemes based on codes and isogenies. Special attention is paid to cryptanalysis of these schemes. In particular, for code-based cryptosystems we describe the information set decoding and the support splitting algorithm as main attacks, and for cryptosystems based on isogenies we describe in detail the Castryck — Decru attack on SIDH/SIKE. Tab. 2, bibliogr. 43.
Keywords: post-quantum cryptography, error-correcting code, elliptic curve, isogeny.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075–02–2023–934
075–15–2022–282
Received: 11.05.2023
Revised: 07.08.2023
Accepted: 22.09.2023
English version:
Journal of Applied and Industrial Mathematics, 2024, Volume 18, Issue 1, Pages 103–121
DOI: https://doi.org/10.1134/S1990478924010101
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 current solutions. Isogeny-based and code-based cryptosystems”, Diskretn. Anal. Issled. Oper., 31:1 (2024), 52–84; J. Appl. Industr. Math., 18:1 (2024), 103–121
Citation in format AMSBIB
\Bibitem{MalKutNov24}
\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~current solutions. Isogeny-based~and~code-based~cryptosystems
\jour Diskretn. Anal. Issled. Oper.
\yr 2024
\vol 31
\issue 1
\pages 52--84
\mathnet{http://mi.mathnet.ru/da1339}
\crossref{https://doi.org/10.33048/daio.2024.31.772}
\transl
\jour J. Appl. Industr. Math.
\yr 2024
\vol 18
\issue 1
\pages 103--121
\crossref{https://doi.org/10.1134/S1990478924010101}
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