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Privacy-preserving distributed average consensus has received significantattention recently due to its wide applicability. Based on the achievedperformances, existing approaches can be broadly classified into perfectaccuracy-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 revealsome private information, while methods from the second class provide privacyagainst the strongest adversary at the cost of a loss of accuracy. In thispaper, we propose a general approach named adaptive differentially quantizedsubspace perturbation (ADQSP) which combines quantization schemes withso-called subspace perturbation. Although not relying on cryptographicprimitives, the proposed approach enjoys the benefits of bothaccuracy-prioritized and privacy-prioritized methods and is able to unify them.More specifically, we show that by varying a single quantization parameter theproposed method can vary between SMPC-type performances and DP-typeperformances. Our results show the potential of exploiting traditionaldistributed signal processing tools for providing cryptographic guarantees. Inaddition to a comprehensive theoretical analysis, numerical validations areconducted to substantiate our results.

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