Towards characterizing when information-theoretic secret key agreement is possible
This paper is concerned with information-theoretically secure secret key agreement in the general scenario where three parties, Alice, Bob, and Eve, know random variables X, Y, and Z, respectively, with joint distribution P xyz , for instance resulting from receiving a sequence of random bits broadcast by a satellite. We consider the problem of determining for a given distribution P xyz whether Alice and Bob can in principle, by communicating over an insecure channel accessible to Eve, generate a secret key about which Eve's information is arbitrarily small. When X, Y, and Z are random variables that result from a binary random variable being sent through three arbitrary independent channels, it is shown that secret key agreement is possible if and only if I(X;Y¦Z) >0, i.e., under the sole condition that X and Y have some (arbitrarily weak) statistical dependence when given Z.
KeywordsCryptography Secret key agreement Unconditional security Information theory
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- 1.C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, Experimental quantum cryptography, Journal of Cryptology, Springer Verlag, Vol. 5, No. 1, pp. 3–28, 1992.Google Scholar
- 2.T. M. Cover and J. A. Thomas, Elements of information theory, Wiley Series in Telecommunications, 1992.Google Scholar
- 4.W. Feller, An introduction to probability theory and its applications, 3rd edition, Vol. 1, Wiley International, 1968.Google Scholar
- 5.M. J. Fischer and R. N. Wright, Bounds on secret key exchange using a random deal of cards, Journal of Cryptology, Springer Verlag, Vol. 9, No. 2, pp. 71–99, 1996.Google Scholar
- 6.U. M. Maurer, Protocols for secret key agreement based on common information, Advances in Cryptology — CRYPTO '92, Lecture Notes in Computer Science, Berlin: Springer-Verlag, Vol. 740, pp. 461–470, 1993.Google Scholar
- 8.C. E. Shannon, Communication theory of secrecy systems, Bell System Technical Journal, Vol. 28, pp. 656–715, Oct. 1949.Google Scholar
- 9.A. D. Wyner, The wire-tap channel, Bell System Technical Journal, Vol. 54, No. 8, pp. 1355–1387, 1975.Google Scholar