Convex Optimisation-Based Privacy-Preserving Distributed Average Consensus in Wireless Sensor Networks

Abstract

In many applications of wireless sensor networks, it is important that the privacy of the nodes of the network be protected. Therefore, privacy-preserving algorithms have received quite some attention recently. In this paper, we propose a novel convex optimizationbased solution to the problem of privacy-preserving distributed average consensus. The proposed method is based on the primal-dual method of multipliers (PDMM), and we show that the introduced dual variables of the PDMM will only converge in a certain subspace determined by the graph topology and will not converge in the orthogonal complement. These properties are exploited to protect the private data from being revealed to others. More specifically, the proposed algorithm is proven to be secure for both passive and eavesdropping adversary models. Finally, the convergence properties and accuracy of the proposed approach are demonstrated by simulations which show that the method is superior to the state-of-the-art.

Privacy-Preserving Distributed Graph Filtering

“…2, we compare the normalized error as a function of iteration number between desired filter output y = Hx and the approximated one y fit = H fit x of the proposed p-CEV graph filter and the privacy-preserving alternative using distributed optimization in the average consensus application. In particular, we choose to compare with the privacy-preserving primal-dual method of multipliers (p-PDMM) proposed in [15] as it also achieves information-theoretical security by noise insertion. In both algorithms, we set the noise variance as 100 times the variance of the associated private data, thereby guaranteeing a similar amount of noise perturbation.…”

“…Distinctly from the computational hardness assumption, it assumes a computationally unlimited adversary and that privacy is achieved only if the information obtained by the adversary just leads to a slightly better (or the same) posterior guess of the private data compared to the prior. Information-theoretical security is usually achieved by obfuscating the private data through noise insertion, it is thus computationally lightweight and has been used in various fields through different noise insertion methods, e.g., zerosum noise insertion for distributed average consensus [10]- [12]; differentially private Kalman filtering [13]; secret sharing based recursive least squares [14]; subspace noise insertion using distributed optimization [15], [16]. However, these algorithms suffer from a heavy communication overhead as a large number of iterations is required for convergence.…”

Communication efficient privacy-preserving distributed optimization using adaptive differential quantization

“…We use two applications to test the performance of the proposed approach: distributed average consensus and distributed least squares. The main reason for choosing these two applications is that they are intensively investigated in the literature [11], [14], [15], [24], [43]- [49]. The detailed problem formulation of distributed average consensus is already introduced in (2).…”

“…This, however, comes with additional communication costs as the distribution of shares requires extra communication. The third class is the class of subspace perturbation based distributed optimization approaches [14]- [16] which, by inserting noise in a subspace determined by the graph topology, alleviates the privacy-accuracy trade-off without severely increasing the communication costs.…”

Privacy-Preserving Distributed Processing: Metrics, Bounds, and Algorithms

“…The first two classes combine distributed signal processing with commonly used cryptographic tools, such as secure multiparty computation (SMPC) [29], [30], and privacy primitives, such as differential privacy (DP) [31], [32], respectively. The third class directly explores the potential of existing distributed signal processing tools for privacy preservation, such as distributed optimization based subspace perturbation (DOSP) [7], [18], [27]. Among these approaches, SMPC aims to securely compute a function over a number of parties' private data without revealing it.…”