Privacy Assessment for Linear Consensus using Constrained Convex Generators

The problem of designing privacy-preserving algorithms for multi-agent systems running distributed algorithms has attracted the attention of the Control community, especially for maintaining the privacy of the initial state. In this paper, we tackle the problem of checking the privacy of the algorithm itself in terms of the linear parameters used by each agent. We first start by introducing a metric of privacy that translates the uncertainty that an attacker has related to the parameters for the case that it can eavesdrop the state from other agents given the public nature of the network. We then propose to resort to techniques in the literature to compute such metric and show how these can be used by: i) the attacker to estimate the parameters from successive runs of the algorithm; ii) by a defender that can decide when to trigger a negotiation of new parameters to ensuse privacy of the overall system. The technique is illustrated in simulations for the specific example of a consensus protocol. The tools developed herein can complement resilient consensus algorithms based on reputation metrics in the sense that the defender triggering changes to the dynamics while maintaining the overall convergence value can render the calculations of the optimal attacks rather troublesome.