A Design Framework for Strongly ${\chi }^2$-Private Data Disclosure

Abstract

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 ${\chi }^2$-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 $(Z,Y)-X-U$.

16 pages, 2 figures

Cited by in corpus (3)

• On the Lift, Related Privacy Measures, and Applications to Privacy-Utility Tradeoffs
• Private Variable-Length Coding with Zero Leakage
• Information Density Bounds for Privacy