On the message complexity of secure multiparty computation

Abstract

We study the minimal number of point-to-point messages required for general secure multiparty computation (MPC) in the setting of computational security against semi-honest, static adversaries who may corrupt an arbitrary number of parties. We show that for functionalities that take inputs from n parties and deliver outputs to k parties, 2n+k-3 messages are necessary and sufficient. The negative result holds even when given access to an arbitrary correlated randomness setup. The positive result can be based on any 2-round MPC protocol (which can in turn can be based on 2-message oblivious transfer), or on a one-way function given a correlated randomness setup.