Privacy-Constrained Lossy Function Computation in Distributed Databases

Consider lossy function computation in distributed databases that contain both sensitive (private) and non-sensitive (public) attributes. A user aims to compute a function of the public attributes and side information and interacts with the databases to download a response from each for computing the function. In this paper, we are interested in quantifying the optimal download cost and the minimum information leakage about the private attributes that the user can learn. Our main contributions include complete characterizations of the optimal trade-offs among download cost, leakage, and distortion in a single database for both discrete and Gaussian sources, as well as inner and outer bounds of the tradeoffs for distributed databases.