A Design Framework for Strongly χ²-Private Data Disclosure

In this paper, we study a stochastic disclosure control problem using information-theoretic methods. The useful data to be disclosed depend on private data that should be protected. Thus, we design a privacy mechanism to produce new data which maximizes the disclosed information about the useful data under a strong χ ² -privacy criterion. For sufficiently small leakage, the privacy mechanism design problem can be geometrically studied in the space of probability distributions by a local approximation of the mutual information. By using methods from Euclidean information geometry, the original highly challenging optimization problem can be reduced to a problem of finding the principal right-singular vector of a matrix, which characterizes the optimal privacy mechanism. In two extensions we first consider a scenario where an adversary receives a noisy version of the user's message and then we look for a mechanism which finds U based on observing X, maximizing the mutual information between U and Y while satisfying the privacy criterion on U and Z under the Markov chain (Z, Y)-X-U.