Statistical Privacy in Distributed Average Consensus on Bounded Real Inputs
This work addresses privacy concerns in distributed control or state estimation applications that involve real-valued data, but it is incremental as it extends a previous protocol from integral to real inputs.
The paper tackles the problem of ensuring statistical privacy for honest agents' bounded real-valued inputs in distributed average consensus against colluding adversaries, provided the colluding set is not a vertex cut in the network, which translates to a connectivity requirement of at least (t+1) for privacy against t colluding agents.
This paper proposes a privacy protocol for distributed average consensus algorithms on bounded real-valued inputs that guarantees statistical privacy of honest agents' inputs against colluding (passive adversarial) agents, if the set of colluding agents is not a vertex cut in the underlying communication network. This implies that privacy of agents' inputs is preserved against $t$ number of arbitrary colluding agents if the connectivity of the communication network is at least $(t+1)$. A similar privacy protocol has been proposed for the case of bounded integral inputs in our previous paper~\cite{gupta2018information}. However, many applications of distributed consensus concerning distributed control or state estimation deal with real-valued inputs. Thus, in this paper we propose an extension of the privacy protocol in~\cite{gupta2018information}, for bounded real-valued agents' inputs, where bounds are known apriori to all the agents.