Journal of Cryptology

, Volume 1, Issue 3, pp 129–131 | Cite as

A generalization of Hellman's extension to Shannon's approach to cryptography

  • Pierre Beauchemin
  • Gilles Brassard


In his landmark 1977 paper [2], Hellman extends the Shannon theory approach to cryptography [3]. In particular, he shows that the expected number of spurious key decipherments on lengthn messages is at least 2H(K)−nD−1 forany uniquely encipherable, uniquely decipherable cipher, as long as each key is equally likely and the set of meaningful cleartext messages follows a uniform distribution (whereH(K) is the key entropy andD is the redundancy of the source language). Here we show that Hellman's result holds with no restrictions on the distribution of keys and messages. We also bound from above and below the key equivocation upon seeing the ciphertext. The results are obtained through very simple purely information theoretic arguments, with no need for (explicit) counting arguments.

Key words

Cryptography Information theory Key equivocation Shannon theory Spurious decipherments 


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  1. [1]
    Garlinski, J.,Intercept, the Enigma War, Dent, London, 1979.Google Scholar
  2. [2]
    Hellman, M. E., An extension of the Shannon theory approach to cryptography,IEEE Transactions on Information Theory, vol. IT-23, 1977, pp. 289–294.Google Scholar
  3. [3]
    Shannon, C. E., Communication Theory of Secrecy Systems,Bell System Technical Journal, vol. 28, 1949, pp. 656–715.Google Scholar

Copyright information

© International Association for Cryptologic Research 1988

Authors and Affiliations

  • Pierre Beauchemin
    • 1
  • Gilles Brassard
    • 1
  1. 1.Département IROUniversité de MontréalMontréalCanada

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