  We consider multi-agent systems interacting over directed network topologies
where a subset of agents is adversary/faulty and where the non-faulty agents
have the goal of reaching consensus, while fulfilling a differential privacy
requirement on their initial conditions. To address this problem, we develop an
update law for the non-faulty agents. Specifically, we propose a modification
of the so-called Mean-Subsequence-Reduced (MSR) algorithm, the Differentially
Private MSR (DP-MSR) algorithm, and characterize three important properties of
the algorithm: correctness, accuracy and differential privacy. We show that if
the network topology is $(2f +1)$-robust, then the algorithm allows the
non-faulty agents to reach consensus despite the presence of up to $f$ faulty
agents and we characterize the accuracy of the algorithm. Furthermore, we also
show in two important cases that our distributed algorithm can be tuned to
guarantees differential privacy of the initial conditions and the differential
privacy requirement is related to the maximum network degree. The results are
illustrated via simulations.
