  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.
