2022/11/28 by Amirreza Zamani, Zamani, Amirreza, Tobias J. Oechtering +3 · 1 citation
Computer Science · Social Sciences · #Blockchain Technology Applications and Security #FOS: Computer and information sciences #Information Theory (cs.IT) #Privacy, Security, and Data Protection #Privacy-Preserving Technologies in Data
paper · pdf · doi:10.48550/arxiv.2211.15525
openalex publication_date 2022/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A privacy mechanism design problem is studied through the lens of information theory. In this work, an agent observes useful data Y=(Y1,...,YN) that is correlated with private data X=(X1,...,XN) which is assumed to be also accessible by the agent. Here, we consider K users where user i demands a sub-vector of Y, denoted by Ci. The agent wishes to disclose Ci to user i. Since Ci is correlated with X it can not be disclosed directly. A privacy mechanism is designed to generate disclosed data U which maximizes a linear combinations of the users utilities while satisfying a bounded privacy constraint in terms of mutual information. In a similar work it has been assumed that Xi is a deterministic function of Yi, however in this work we let Xi and Yi be arbitrarily correlated. First, an upper bound on the privacy-utility trade-off is obtained by using a specific transformation, Functional Representation Lemma and Strong Functional Representaion Lemma, then we show that the upper bound can be decomposed into N parallel problems. Next, lower bounds on privacy-utility trade-off are derived using Functional Representation Lemma and Strong Functional Representaion Lemma. The upper bound is tight within a constant and the lower bounds assert that the disclosed data is independent of all \Xj\i=1N except one which we allocate the maximum allowed leakage to it. Finally, the obtained bounds are studied in special cases.