Preserving Privacy of the Influence Structure in Friedkin-Johnsen Systems

TL;DR

This paper introduces a local, time-varying masking technique to protect the influence structure in Friedkin-Johnsen systems from external eavesdroppers, ensuring privacy without compromising system stability.

Contribution

It proposes a novel, decentralized masking method that perturbs the influence structure with decaying pseudonoise, preserving stability and enhancing privacy in distributed consensus systems.

Findings

The mask effectively conceals the influence structure from eavesdroppers.

Stability of Friedkin-Johnsen systems is maintained under the proposed masking.

Simulations demonstrate the mask's robustness against various system parameters.

Abstract

The nature of information sharing in common distributed consensus algorithms permits network eavesdroppers to expose sensitive system information. An important parameter within distributed systems, often neglected under the scope of privacy preservation, is the influence structure - the weighting each agent places on the sources of their opinion pool. This paper proposes a local (i.e. computed individually by each agent), time varying mask to prevent the discovery of the influence structure by an external observer with access to the entire information flow, network knowledge and mask formulation. This result is produced through the auxiliary demonstration of the preserved stability of a Friedkin-Johnsen system under a set of generalised conditions. The mask is developed under these constraints and involves perturbing the influence structure by decaying pseudonoise. This paper provides the information matrix of the best influence structure estimate by an eavesdropper lacking a priori knowledge and uses stochastic simulations to analyse the performance of the mask against ranging system hyperparameters.