# Privacy of Agents' Costs in Peer-to-Peer Distributed Optimization

## TL;DR

This paper introduces a privacy-preserving protocol for peer-to-peer distributed optimization that protects agents' cost information against passive adversaries, leveraging network connectivity properties.

## Contribution

It presents a novel privacy protocol that guarantees the confidentiality of agents' cost components based on network topology and adversary model.

## Key findings

- Privacy of affine cost parts is maintained if corrupted agents do not form a vertex cut.
- The protocol works with any distributed optimization algorithm when combined with the proposed privacy mechanism.
- Privacy is guaranteed if the network has (t+1)-connectivity with up to t corrupted agents.

## Abstract

In this paper, we propose a protocol that preserves (statistical) privacy of agents' costs in peer-to-peer distributed optimization against a passive adversary that corrupts certain number of agents in the network. The proposed protocol guarantees privacy of the affine parts of the honest agents' costs (agents that are not corrupted by the adversary) if the corrupted agents do not form a vertex cut of the underlying communication topology. Therefore, if the (passive) adversary corrupts at most t arbitrary agents in the network then the proposed protocol can preserve the privacy of the affine parts of the remaining honest agents' costs if the communication topology has (t+1)-connectivity. The proposed privacy protocol is a composition of a privacy mechanism (we propose) with any (non-private) distributed optimization algorithm.