
This article is cited in 2 scientific papers (total in 2 papers)
Decoding the tensor product of $ \mathrm{MLD} $ codes and applications for code cryptosystems
V. M. Deundyak^{ab}, Yu. V. Kosolapov^{b}, E. A. Lelyuk^{b} ^{a} FGNU NII "Specvuzavtomatika",
51 Gazetniy lane, RostovonDon 344002, Russia
^{b} South Federal University, 105/42 Bolshaya Sadovaya Str., RostovonDon 344006, Russia
Abstract:
For the practical application of code cryptosystems such as McEliece, it is necessary that the code used in the cryptosystem should have a fast decoding algorithm. On the other hand, the code used must be such that finding a secret key from a known public key would be impractical with a relatively small key size. In this connection, in the present paper it is proposed to use the tensor product $ C_1 \otimes C_2 $ of group $\mathrm{MLD}$ codes $ C_1 $ and $ C_2 $ in a McEliecetype cryptosystem. The algebraic structure of the code $ C_1 \otimes C_2 $ in the general case differs from the structure of the codes $ C_1 $ and $ C_2 $, so it is possible to build stable cryptosystems of the McEliece type even on the basis of codes $ C_i $ for which successful attacks on the key are known. However, in this way there is a problem of decoding the code $ C_1 \otimes C_2 $. The main result of this paper is the construction and justification of a set of fast algorithms needed for decoding this code. The process of constructing the decoder relies heavily on the group properties of the code $ C_1 \otimes C_2 $. As an application, the McEliecetype cryptosystem is constructed on the code $ C_1 \otimes C_2 $ and an estimate is given of its resistance to attack on the key under the assumption that for code cryptosystems on codes $ C_i $ an effective attack on the key is possible. The results obtained are numerically illustrated in the case when $ C_1 $, $ C_2 $ are Reed–Muller–Berman codes for which the corresponding code cryptosystem was hacked by L. Minder and A. Shokrollahi (2007).
Keywords:
majority decoder, Reed–Muller–Berman codes, tensor product codes.
DOI:
https://doi.org/10.18255/1818101520172239252
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UDC:
517.9 Received: 07.04.2017
Citation:
V. M. Deundyak, Yu. V. Kosolapov, E. A. Lelyuk, “Decoding the tensor product of $ \mathrm{MLD} $ codes and applications for code cryptosystems”, Model. Anal. Inform. Sist., 24:2 (2017), 239–252
Citation in format AMSBIB
\Bibitem{DeuKosLel17}
\by V.~M.~Deundyak, Yu.~V.~Kosolapov, E.~A.~Lelyuk
\paper Decoding the tensor product of $ \mathrm{MLD} $ codes and applications for code cryptosystems
\jour Model. Anal. Inform. Sist.
\yr 2017
\vol 24
\issue 2
\pages 239252
\mathnet{http://mi.mathnet.ru/mais561}
\crossref{https://doi.org/10.18255/1818101520172239252}
\elib{http://elibrary.ru/item.asp?id=29064007}
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http://mi.mathnet.ru/eng/mais561 http://mi.mathnet.ru/eng/mais/v24/i2/p239
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This publication is cited in the following articles:

V. M. Deundyak, Yu. V. Kosolapov, “On the Berger–Loidreau cryptosystem on the tensor product of codes”, J. Comp. Eng. Math., 5:2 (2018), 16–33

K. V. Vedenev, V. M. Deundyak, “Kody v diedralnoi gruppovoi algebre”, Model. i analiz inform. sistem, 25:2 (2018), 232–245

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