Communication-Efficient Unconditional MPC with Guaranteed Output Delivery
We study the communication complexity of unconditionally secure MPC with guaranteed output delivery over point-to-point channels for corruption threshold $$t < n/3$$ . We ask the question: “is it possible to construct MPC in this setting s.t. the communication complexity per multiplication gate is linear in the number of parties?” While a number of works have focused on reducing the communication complexity in this setting, the answer to the above question has remained elusive for over a decade.We resolve the above question in the affirmative by providing an MPC with communication complexity $$O(Cn\kappa + n^3\kappa )$$ where $$\kappa $$ is the size of an element in the field, C is the size of the (arithmetic) circuit, and, n is the number of parties. This represents a strict improvement over the previously best known communication complexity of $$O(Cn\kappa +D_Mn^2\kappa +n^3\kappa )$$ where $$D_M$$ is the multiplicative depth of the circuit. To obtain this result, we introduce a novel technique called 4-consistent tuples of sharings which we believe to be of independent interest.