# Statistical Privacy in Distributed Average Consensus on Bounded Real Inputs

## TL;DR

This paper introduces a privacy-preserving protocol for distributed average consensus on bounded real inputs, ensuring input privacy against colluding agents in networks with sufficient connectivity, extending previous work on integral inputs.

## Contribution

It extends a prior privacy protocol to real-valued inputs with known bounds, applicable to distributed control and state estimation scenarios.

## Key findings

- Guarantees privacy against colluding agents if network connectivity is sufficient.
- Extends previous protocol from integral to real-valued inputs.
- Ensures privacy preservation in distributed consensus with bounded real inputs.

## Abstract

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.