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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2014, Volume 7, Issue 2, Pages 66–73
DOI: https://doi.org/10.14529/mmp140206
(Mi vyuru131)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical Modelling

On Perfect Ciphers Based on Orthogonal Tables

S. M. Ratseeva, O. I. Cherevatenkob

a Ulyanovsk State University, Ulyanovsk, Russian Federation
b Ulyanovsk State I. N. Ulyanov Pedagogical University, Ulyanovsk, Russian Federation
Full-text PDF (466 kB) Citations (1)
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Abstract: We study perfect imitation resistant ciphers, highlighting particularly the case in which the probabilities of successful imitation and substitution attain their lower limits. It is known that the Vernam cipher with equiprobable gamma is a perfect cipher, but it is maximally vulnerable to imitation attempts owing to its use of alphabets of the same size for plaintexts and ciphertexts. Since the limitation on the size of the sets of plaintexts and keys is a drawback of the mathematical model of the cipher, we begin by studying Zubov's mathematical model of substitution cipher with unbounded key. Basing on this model, we construct models of perfect imitation resistant ciphers. These ciphers use orthogonal tables and Latin rectangles. We study the case in which the generator of random key sequences need not have the uniform probability distribution. Since the keys of these ciphers are at least as long as the transmitted messages, substitution ciphers with unbounded key should be used in very important cases.
Keywords: cipher; perfect cipher; imitation of message.
Received: 24.01.2014
Document Type: Article
UDC: 519.7
MSC: 68P25, 94A60
Language: Russian
Citation: S. M. Ratseev, O. I. Cherevatenko, “On Perfect Ciphers Based on Orthogonal Tables”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:2 (2014), 66–73
Citation in format AMSBIB
\Bibitem{RatChe14}
\by S.~M.~Ratseev, O.~I.~Cherevatenko
\paper On Perfect Ciphers Based on Orthogonal Tables
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2014
\vol 7
\issue 2
\pages 66--73
\mathnet{http://mi.mathnet.ru/vyuru131}
\crossref{https://doi.org/10.14529/mmp140206}
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  • https://www.mathnet.ru/eng/vyuru/v7/i2/p66
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Full-text PDF :85
    References:39
     
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