Designs, Codes and Cryptography

, Volume 86, Issue 5, pp 989–995 | Cite as

Properties of two Shannon’s ciphers

  • Boris Ryabko


In 1949 Shannon published the famous paper “Communication theory of secrecy systems” where he briefly described two ciphers, but did not investigate their properties. In this note we carry out information-theoretical analysis of these ciphers. In particular, we propose estimations of the cipher equivocation and the probability of correct deciphering without key.


Shannon cipher Cryptography Entropy Information theory 

Mathematics Subject Classification

94A60 Cryptography 94A15 Information theory 



This research was supported by Russian Foundation for Basic Research (Grant No. 15-29-07932).


  1. 1.
    Calmon E.P., Medard M., Varia M., Duffy K.R., Christiansen M.M., Zeger L.M.: Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security. arxiv:1503.08515 (2015).
  2. 2.
    Cover T.M., Thomas J.A.: Elements of Information Theory. Wiley-Interscience, New York (2006).zbMATHGoogle Scholar
  3. 3.
    Diffie W., Hellman M.E.: Privacy and authentication: an introduction to cryptography. Proc. IEEE 67(3), 397–427 (1979).CrossRefGoogle Scholar
  4. 4.
    Hellman M.E.: An extension of the Shannon theory approach to cryptography. IEEE Trans. Inf. Theory 23(3), 289–294 (1977).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Lu S.-C.: The existence of good cryptosystems for key rates greater than the message redundancy. IEEE Trans. Inf. Theory 25(4), 475–477 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ryabko B.: The Vernam cipher is robust to small deviations from randomness. Probl. Inf. Transm. 51(1), 82–86 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Shannon C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Shannon C.E.: Prediction and entropy of printed English. Bell Syst. Tech. J. 30(1), 50–64 (1951).CrossRefzbMATHGoogle Scholar
  9. 9.
    Takahira R., Tanaka-Ishii K., Debowski L.: Entropy rate estimates for natural languagea new extrapolation of compressed large-scale corpora. Entropy 18(10), 364 (2016).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Institute of Computational Technologies SB RASNovosibirskRussian Federation
  2. 2.Novosibirsk State UniversityNovosibirskRussian Federation

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