Properties of two Shannon’s ciphers
Article
First Online:
Received:
Revised:
Accepted:
- 74 Downloads
Abstract
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.
Keywords
Shannon cipher Cryptography Entropy Information theoryMathematics Subject Classification
94A60 Cryptography 94A15 Information theoryNotes
Acknowledgements
This research was supported by Russian Foundation for Basic Research (Grant No. 15-29-07932).
References
- 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.Cover T.M., Thomas J.A.: Elements of Information Theory. Wiley-Interscience, New York (2006).MATHGoogle Scholar
- 3.Diffie W., Hellman M.E.: Privacy and authentication: an introduction to cryptography. Proc. IEEE 67(3), 397–427 (1979).CrossRefGoogle Scholar
- 4.Hellman M.E.: An extension of the Shannon theory approach to cryptography. IEEE Trans. Inf. Theory 23(3), 289–294 (1977).MathSciNetCrossRefMATHGoogle Scholar
- 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).MathSciNetCrossRefMATHGoogle Scholar
- 6.Ryabko B.: The Vernam cipher is robust to small deviations from randomness. Probl. Inf. Transm. 51(1), 82–86 (2015).MathSciNetCrossRefMATHGoogle Scholar
- 7.Shannon C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949).MathSciNetCrossRefMATHGoogle Scholar
- 8.Shannon C.E.: Prediction and entropy of printed English. Bell Syst. Tech. J. 30(1), 50–64 (1951).CrossRefMATHGoogle Scholar
- 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