Privacy-Preserving Distributed Processing: Metrics, Bounds, and Algorithms
This work addresses the need for systematic evaluation and design principles in privacy-preserving distributed processing, which is incremental as it builds on existing algorithms like differential privacy and secure multiparty computation.
The paper tackles the problem of comparing and relating privacy-preserving distributed processing algorithms by proposing information-theoretic metrics based on mutual information, deriving a lower bound on individual privacy, and validating claims through theoretical and numerical analysis of state-of-the-art approaches.
Privacy-preserving distributed processing has recently attracted considerable attention. It aims to design solutions for conducting signal processing tasks over networks in a decentralized fashion without violating privacy. Many algorithms can be adopted to solve this problem such as differential privacy, secure multiparty computation, and the recently proposed distributed optimization based subspace perturbation. However, how these algorithms relate to each other is not fully explored yet. In this paper, we therefore first propose information-theoretic metrics based on mutual information. Using the proposed metrics, we are able to compare and relate a number of existing well-known algorithms. We then derive a lower bound on individual privacy that gives insights on the nature of the problem. To validate the above claims, we investigate a concrete example and compare a number of state-of-the-art approaches in terms of different aspects such as output utility, individual privacy and algorithm robustness against the number of corrupted parties, using not only theoretical analysis but also numerical validation. Finally, we discuss and provide principles for designing appropriate algorithms for different applications.