A Design Framework for Strongly χ²-Private Data Disclosure

• Published in: IEEE transactions on information forensics and security 2021, Vol.16, p.2312-2325
• Main Authors: Zamani, Amirreza, Oechtering, Tobias J., Skoglund, Mikael
• Format: Article
• Language: English
• Subjects: <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">χ ²-privacy criterion; Data privacy; Euclidean information geometry; Information geometry; Markov processes; Mutual information; Optimization; Privacy; privacy mechanism design; Upper bound
• ISSN: 1556-6013; 1556-6021
• DOI: 10.1109/TIFS.2021.3053462

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 .