  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.
