Information-Theoretic Privacy in Distributed Average Consensus

We present a distributed average consensus protocol that preserves the privacy of agents' inputs. Unlike the differential privacy mechanisms, the presented protocol does not affect the accuracy of the output. It is shown that the protocol preserves the information-theoretic privacy of the agents' inputs against colluding passive adversarial (or honest-but-curious) agents in the network, if the adversarial agents do not constitute a vertex cut in the underlying communication network. This implies that we can guarantee information-theoretic privacy of all the honest agents' inputs against $t$ arbitrary colluding passive adversarial agents if the network is $(t+1)$-connected. The protocol is constructed by composing a distributed privacy mechanism that we propose with any (non-private) distributed average consensus algorithm.
Comment: Related to the prior work (1) Gupta, Nirupam, Jonathan Kat, and Nikhil Chopra. "Statistical Privacy in Distributed Average Consensus on Bounded Real Inputs." 2019 IEEE American Control Conference, and (2) Gupta, Nirupam, Jonathan Katz, and Nikhil Chopra. "Privacy in distributed average consensus." IFAC-PapersOnLine 2017. Comprises 7 pages (two-column format), and 3 figures