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Model. Anal. Inform. Sist., 2017, Volume 24, Number 2, Pages 239–252 (Mi mais561)  

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. Deundyakab, Yu. V. Kosolapovb, E. A. Lelyukb

a FGNU NII "Specvuzavtomatika", 51 Gazetniy lane, Rostov-on-Don 344002, Russia
b South Federal University, 105/42 Bolshaya Sadovaya Str., Rostov-on-Don 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 McEliece-type 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 McEliece-type 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.


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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
\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 239--252

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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  elib
    2. K. V. Vedenev, V. M. Deundyak, “Kody v diedralnoi gruppovoi algebre”, Model. i analiz inform. sistem, 25:2 (2018), 232–245  mathnet  crossref  elib
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