Towards characterizing when information-theoretic secret key agreement is possible

Abstract

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.