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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 1(34), Pages 192–199 (Mi vsgtu1271)  

This article is cited in 2 scientific papers (total in 2 papers)

Computer Science

On Construction of Perfect Ciphers

S. M. Ratseev

Ulyanovsk State University, Ulyanovsk, 432017, Russian Federation

Abstract: K. Shannon in the 40s of the 20th century introduced the concept of a perfect cipher, which provides the best protection of plaintexts. Perfect secrecy means that cryptanalyst can obtain no information about the plaintext by observing the ciphertext. In the paper we study the problem of construction of perfect ciphers on a given set of plaintexts $X$, a set of keys $K$ and a probability distribution $P(K)$. We give necessary and sufficient conditions for a perfect ciphers on given $X$, $K$ and $P(K)$. It is shown that this problem is reduced to construction of the set of partitions of the set $K$ with certain conditions. As one of the drawbacks of the probability model of cipher are limitations on the power of sets of plaintexts, keys and ciphertexts we also study the problem of construction of substitution cipher with unbounded key on a given set of ciphervalues, a set of keys and a probability distribution on the set of keys.

Keywords: cipher, perfect cipher, set of keys, probability distribution

DOI: https://doi.org/10.14498/vsgtu1271

Full text: PDF file (562 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 519.72
MSC: 68P25, 94A60
Original article submitted 22/X/2013
revision submitted – 27/I/2014

Citation: S. M. Ratseev, “On Construction of Perfect Ciphers”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(34) (2014), 192–199

Citation in format AMSBIB
\Bibitem{Rat14}
\by S.~M.~Ratseev
\paper On Construction of Perfect Ciphers
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 1(34)
\pages 192--199
\mathnet{http://mi.mathnet.ru/vsgtu1271}
\crossref{https://doi.org/10.14498/vsgtu1271}
\zmath{https://zbmath.org/?q=an:06968836}
\elib{http://elibrary.ru/item.asp?id=22813971}


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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. S. M. Ratseev, “Nekotorye obobscheniya teorii Shennona o sovershennykh shifrakh”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:1 (2015), 111–127  mathnet  crossref  zmath  elib  scopus
    2. S. M. Ratseev, V. M. Ratseev, “Postroenie sovershennykh imitostoikikh shifrov na osnove kombinatornykh ob'ektov”, Vestn. SamU. Estestvennonauchn. ser., 2016, no. 1-2, 46–50  mathnet  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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