  We present a distributed optimization protocol that preserves statistical
privacy of agents' local cost functions against a passive adversary that
corrupts some agents in the network. The protocol is a composition of a
distributed ``{\em zero-sum}" obfuscation protocol that obfuscates the agents'
local cost functions, and a standard non-private distributed optimization
method. We show that our protocol protects the statistical privacy of the
agents' local cost functions against a passive adversary that corrupts up to
$t$ arbitrary agents as long as the communication network has $(t+1)$-vertex
connectivity. The ``{\em zero-sum}" obfuscation protocol preserves the sum of
the agents' local cost functions and therefore ensures accuracy of the computed
solution.
