Secure message transmission and Byzantine agreement have been studied extensively in incomplete networks. However, information theoretically secure multiparty computation (MPC) in incomplete networks is less well understood. In this paper, we characterize the conditions under which a pair of parties can compute oblivious transfer (OT) information theoretically securely against a general adversary structure in an incomplete network of reliable, private channels. We provide characterization for semi-honest model of corruption. A consequence of our results is a complete characterization of networks in which a given subset of parties can compute any functionality securely with respect to an adversary structure in the semi-honest case.
