A Generalization of Hellman’s Extension of Shannon’s Approach to Cryptography (Abstract)

  • Pierre Beauchemin
  • Gilles Brassard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 293)


In his landmark 1977 paper [Hell77], Hellman extends the Shannon theory approach to cryptography [Shan49]. In particular, he shows that the expected number of spurious key decipherements on length n messages is at least 2H(K)-nD - 1 for any uniquely enci- pherable, uniquely decipherable cipher, as long as each key is equally likely and the set of meaningful cleartext messages follows a uniform distribution (where H(K) is the key entropy and D is the redundancy of the source language). In this paper, 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. Sufficient conditions for these bounds to be tight are given. The results are obtained through very simple purely information theoretic arguments, with no needs for (explicit) counting arguments.


Uniform Distribution IEEE Transaction Information Theory Formal Statement Theory Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [BB88]
    Beauchemin, P. and G. Brassard, “A generalization of Hellman’s extension of Shannon’s approach to cryptography”, to appear in Joumal of Ctyptology, 1988.Google Scholar
  2. [Hell77]
    Hellman, M. E., “An extension of the Shannon theory approach to cryptography”, IEEE Transactions on Information Theory, vol. IT-23, 1977, pp. 289–294.MathSciNetCrossRefGoogle Scholar
  3. [Shan49]
    Shannon, C. E., “Communication theory of secrecy systems”, Bell System Technical Journal, vol. 28, 1949, pp. 656–715.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Pierre Beauchemin
    • 1
  • Gilles Brassard
    • 1
  1. 1.Département d’informatique et de recherche opérationnelleUniversité de MontréalMontréalCanada

Personalised recommendations