Secret Key Generation for Correlated Gaussian Sources

Secret key generation by multiple terminals is considered based on their observations of jointly distributed Gaussian signals, followed by public communication among themselves. Exploiting an inherent connection between secrecy generation and lossy data compression, two main contributions are made. The first is a characterization of strong secret key capacity, and entails a converse proof technique that is valid for real-valued (and not necessarily Gaussian) as well as finite-valued signals. The capacity formula acquires a simple form when the terminals observe "symmetrically correlated" jointly Gaussian signals. For the latter setup with two terminals, considering schemes that involve quantization at one terminal, the best rate of an achievable secret key is characterized as a function of quantization rate; secret key capacity is attained as the quantization rate tends to infinity. Structured codes are shown to attain the optimum tradeoff between secret key rate and quantization rate, constituting our second main contribution.