A Separation Result for Secure Communication

Alice wants to communicate securely to Bob in the presence of an eavesdropper Eve. There are two resources available to facilitate this. First, Alice, Bob (and Eve) have access to dependent source observations. Secondly, there is a noisy broadcast channel from Alice to Bob and Eve. Under this general source and channel setup, we are interested in three classes of problems. First, what is the secret key generation capacity, where Alice and Bob agree on a secret key to the exclusion of Eve? Secondly, what is the secure communication capacity where Alice wants to convey an independent secret message to Bob? Thirdly, what is the optimal joint secure communication capacity and attainable state distortion, where Alice wants to convey to Bob both her state (source) observation unsecurely, under a distortion constraint, and an independent secure message? While a complete characterization of these problems under general source and channel models remains open, we can fully characterize several interesting special cases. In a nutshell, these special cases involve those where either the sources or the channel are individually incapable of generating useful secret common randomness between Alice and Bob in the presence of Eve; i.e., one of the resources by itself is useless in generating a secret key. Interestingly, the solutions for these cases expose the optimality of a separation architecture at multiple scales. First, there is an optimal decoupling between the use of the correlated sources from the use of the noisy channel. Thus, when the latter is the useless resource, this separation implies that it can be abstracted away as a noiseless public bit-pipe of capacity equal to the capacity of the channel from Alice to Bob. Secondly, in this situation, for the secure communication problem, there is a separation in the use of this finite rate public bit-pipe between a key generation first-phase and a secure message transmission second-phase that uses the first-phase key as a one-time pad.