Key Agreement over an Interference Channel with Noiseless Feedback: Achievable Region & Distributed Allocation

Secret key establishment leveraging the physical layer as a source of common randomness has been investigated in a range of settings. We investigate the problem of establishing, in an information-theoretic sense, a secret key between a user and a base-station (BS) (more generally, part of a wireless infrastructure), but for two such user-BS pairs attempting the key establishment simultaneously. The challenge in this novel setting lies in that a user can eavesdrop another BS-user communications. It is thus paramount to ensure the two keys are established with no leakage to the other user, in spite the interference across neighboring cells. We model the system with BS-user communication through an interference channel and user-BS communication through a public channel. We find the region including achievable secret key rates for the general case that the interference channel (IC) is discrete and memoryless. Our results are examined for a Gaussian IC. In this setup, we investigate the performance of different transmission schemes for power allocation. The chosen transmission scheme by each BS essentially affects the secret key rate of the other BS-user. Assuming base stations are trustworthy but that they seek to maximize the corresponding secret key rate, a game-theoretic setting arises to analyze the interaction between the base stations.We model our key agreement scenario in normal form for different power allocation schemes to understand performance without cooperation. Numerical simulations illustrate the inefficiency of the Nash equilibrium outcome and motivate further research on cooperative or coordinated schemes.Comment: A shorter version of this paper was presented at CNS 201

Strong Secrecy in Pairwise Key Agreement over a Generalized Multiple Access Channel

This paper considers the problem of pairwise key agreement without public communication between three users connected through a generalized multiple access channel (MAC). While two users control the channel inputs, all three users observe noisy outputs from the channel and each pair of users wishes to agree on a secret key hidden from the remaining user. We first develop a "pre-generated" key-agreement scheme based on secrecy codes for the generalized MAC, in which the channel is only used to distribute pre-generated secret keys. We then extend this scheme to include an additional layer of rate-limited secret-key generation by treating the observed channel outputs as induced sources. We characterize inner and outer bounds on the strong secret-key capacity region for both schemes. For a special case of the "pre-generated" scheme, we obtain an exact characterization. We also illustrate with some binary examples that exploiting the generalized nature of the generalized MAC may lead to significantly larger key-agreement rates.Comment: 45 pages, 11 figures, Submitted to the IEEE Transactions on Information Theor