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 “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 “zero-sum” obfuscation protocol preserves the sum of the agents' local cost functions and therefore ensures accuracy of the computed solution.