Adaptive Differentially Quantized Subspace Perturbation (ADQSP): A Unified Framework for Privacy-Preserving Distributed Average Consensus

TL;DR

This paper proposes a general approach named adaptive differentially quantized subspace perturbation (ADQSP) which combines quantization schemes with so-called subspaceperturbation and shows the potential of exploiting traditional distributed signal processing tools for providing cryptographic guarantees.

Abstract

Privacy-preserving distributed average consensus has received significant attention recently due to its wide applicability. Based on the achieved performances, existing approaches can be broadly classified into perfect accuracy-prioritized approaches such as secure multiparty computation (SMPC), and worst-case privacy-prioritized approaches such as differential privacy (DP). Methods of the first class achieve perfect output accuracy but reveal some private information, while methods from the second class provide privacy against the strongest adversary at the cost of a loss of accuracy. In this paper, we propose a general approach named adaptive differentially quantized subspace perturbation (ADQSP) which combines quantization schemes with so-called subspace perturbation. Although not relying on cryptographic primitives, the proposed approach enjoys the benefits of both accuracy-prioritized and privacy-prioritized methods and is able to unify them. More specifically, we show that by varying a single quantization parameter the proposed method can vary between SMPC-type performances and DP-type performances. Our results show the potential of exploiting traditional distributed signal processing tools for providing cryptographic guarantees. In addition to a comprehensive theoretical analysis, numerical validations are conducted to substantiate our results.

Figures (5)

• Figure 1: Convergence of the optimization variable in terms of three different variances of the auxiliary variable, i.e., $\sigma_z=10^3$, $\sigma_z=10^2$ and $\sigma_z=10^1$ given three different distributed optimizers: (a) $\theta=0$ (PDMM), (b) $\theta=0.2$ and (c) $\theta=0.5$ (ADMM), wherein $\Delta_{ \mathrm{min}}=0$.
• Figure 2: Convergence of the optimization variable in terms of three different quantization parameter setting, i.e., $\Delta_{ \mathrm{min}}=10^{-3}$, $\Delta_{ \mathrm{min}}=10^{-2}$ and $\Delta_{ \mathrm{min}}=10^{-1}$ given three different distributed optimizers: (a) $\theta=0$ (PDMM), (b) $\theta=0.2$ and (c) $\theta=0.5$ (ADMM), wherein $\sigma_z=10^3$.
• Figure 3: Individual privacy: normalized mutual information (RHS of \ref{['eq:spUpper1']}) as a function of $\sigma_z$ using the proposed approach; NMI of ${\rm I}(S_i;\mathop{\mathrm{\sum}}\limits_{ j\in {\cal V}_{ h,1}}S_j)$ using the existing SMPC approach.
• Figure 4: Output accuracy: MSE of the optimization variable in terms of iteration numbers using the proposed approach and DP approach under two different sets of parameter.
• Figure 5: Individual privacy: NMI as a function of iteration numbers using the proposed approach and DP approach under two different set of parameters.

Theorems & Definitions (24)

• Lemma 1
• Proposition 1
• proof
• Proposition 2
• proof
• Theorem 1
• proof
• Proposition 3
• proof
• Theorem 2