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Diskr. Mat., 1992, Volume 4, Issue 3, Pages 57–63 (Mi dm747)  

This article is cited in 9 scientific papers (total in 9 papers)

On an encoding system constructed on the basis of generalized Reed–Solomon codes

V. M. Sidel'nikov, S. O. Shestakov


Abstract: In earlier papers [1, 2], based on code-theoretic constructions, methods were presented for constructing an open encoding system. They are based on the well-known $\mathfrak B$ matrix of dimension $(s+1)\times N$ with elements from a finite field $\mathrm F_q$, of the form $\mathfrak B=H\cdot\mathfrak A$, where $\mathfrak A$ is some unknown matrix that is a test matrix of a $q$-valued generalized Reed–Solomon code, in particular of a Goppa code, and $H$ is an unknown nonsingular matrix with dimension $(s+1)\times(s+1)$.
In this paper we present a method for finding the unknown matrices $\mathfrak A$ and $H$ with elements from the field $\mathrm F_q$ that determine the matrix $\mathfrak B$ in $O(s^4+sN)$ operations. Thus, we establish the unreliability of the open encoding systems considered.

Full text: PDF file (580 kB)

English version:
Discrete Mathematics and Applications, 1992, 2:4, 439–444

Bibliographic databases:

UDC: 519.72
Received: 03.03.1992

Citation: V. M. Sidel'nikov, S. O. Shestakov, “On an encoding system constructed on the basis of generalized Reed–Solomon codes”, Diskr. Mat., 4:3 (1992), 57–63; Discrete Math. Appl., 2:4 (1992), 439–444

Citation in format AMSBIB
\Bibitem{SidShe92}
\by V.~M.~Sidel'nikov, S.~O.~Shestakov
\paper On an encoding system constructed on the basis of generalized Reed--Solomon codes
\jour Diskr. Mat.
\yr 1992
\vol 4
\issue 3
\pages 57--63
\mathnet{http://mi.mathnet.ru/dm747}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1220968}
\zmath{https://zbmath.org/?q=an:0796.94006}
\transl
\jour Discrete Math. Appl.
\yr 1992
\vol 2
\issue 4
\pages 439--444


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. È. M. Gabidulin, V. A. Obernikhin, “Codes in the Vandermonde $\mathcal F$-Metric and Their Applications”, Problems Inform. Transmission, 39:2 (2003), 159–169  mathnet  crossref  mathscinet  zmath
    2. I. V. Chizhov, “The key space of the McEliece–Sidelnikov cryptosystem”, Discrete Math. Appl., 19:5 (2009), 445–474  mathnet  crossref  crossref  mathscinet  elib
    3. I. V. Chizhov, “Obobschennye avtomorfizmy koda Rida–Mallera i kriptosistema Mak-Elisa–Sidelnikova”, PDM, 2009, prilozhenie № 1, 36–37  mathnet
    4. Terentev A.I., “Postroenie asimmetrichnykh kriptograficheskikh sistem na osnove chislovykh lineinykh blokovykh korrektiruyuschikh kodov”, Nauchn. vestn. Mosk. gos. tekhnich. un-ta grazhdanskoi aviatsii, 2009, no. 145, 82–88
    5. Samokhina M.A., “Primenenie modifikatsii kriptosistemy Niderraitera dlya zaschity informatsii pri peredache videoizobrazhenii”, Informatsionno-upravlyayuschie sistemy, 2009, no. 1, 41–46
    6. M. M. Glukhov-ml., “O sisteme Mak-Elisa na nekotorykh algebro-geometricheskikh kodakh”, PDM. Prilozhenie, 2012, no. 5, 39–41  mathnet
    7. V. M. Deundyak, Yu. V. Kosolapov, “Kriptosistema na indutsirovannykh gruppovykh kodakh”, Model. i analiz inform. sistem, 23:2 (2016), 137–152  mathnet  crossref  mathscinet  elib
    8. V. M. Deundyak, Yu. V. Kosolapov, E. A. Lelyuk, “Dekodirovanie tenzornogo proizvedeniya $\mathrm{MLD}$-kodov i prilozheniya k kodovym kriptosistemam”, Model. i analiz inform. sistem, 24:2 (2017), 239–252  mathnet  crossref  elib
    9. V. V. Vysotskaya, “Kvadrat koda Rida–Mallera i klassy ekvivalentnosti sekretnykh klyuchei kriptosistemy Mak-Elisa–Sidelnikova”, PDM. Prilozhenie, 2017, no. 10, 66–68  mathnet  crossref
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