Abstract
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.
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References
Garlinski, J.,Intercept, the Enigma War, Dent, London, 1979.
Hellman, M. E., An extension of the Shannon theory approach to cryptography,IEEE Transactions on Information Theory, vol. IT-23, 1977, pp. 289–294.
Shannon, C. E., Communication Theory of Secrecy Systems,Bell System Technical Journal, vol. 28, 1949, pp. 656–715.
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This work was first reported at the CRYPTO 87 workshop, Santa Barbara, CA, August 1987.
Supported in part by Canada NSERC Grant A4107.
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Beauchemin, P., Brassard, G. A generalization of Hellman's extension to Shannon's approach to cryptography. J. Cryptology 1, 129–131 (1989). https://doi.org/10.1007/BF02252870
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DOI: https://doi.org/10.1007/BF02252870