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.

翻译：近年来，隐私保护的分布式平均一致性因其广泛适用性而受到高度关注。根据已实现性能，现有方法大致可分为两类：以完美精度优先的方法（如安全多方计算，SMPC）和以最坏情况隐私优先的方法（如差分隐私，DP）。第一类方法可实现完美的输出精度，但会泄露部分隐私信息；第二类方法在牺牲精度的代价下，能针对最强攻击者提供隐私保护。本文提出一种名为自适应差分量子化子空间扰动（ADQSP）的通用方法，该方法将量子化方案与所谓的子空间扰动相结合。尽管不依赖密码学原语，所提出的方法兼具精度优先与隐私优先两类方法的优势，并能实现二者的统一。具体而言，我们证明通过调节单个量子化参数，该方法可在SMPC型与DP型性能之间连续变化。研究结果表明，利用传统分布式信号处理工具提供密码学级别的保障具有潜力。除全面的理论分析外，本文还通过数值验证进一步佐证了研究结果。