Unconditionally Secure MPC for Boolean Circuits with Constant Communication

The communication complexity of unconditionally Secure Multi-Party Computation (MPC) protocols has been studied by a series of works in the honest-majority setting. For evaluating an arbitrary Boolean circuit, the state-of-the-art MPC protocol by Goyal et al. (Crypto 2021 and Crypto 2022) achieves the total communication cost of $O(\log n)$ bits per gate, where $n$ is the number of parties. In this work, we present the first unconditional MPC protocol for any Boolean circuit with communication of $O(1)$ bits per gate. We first construct an unconditionally secure protocol in the presence of semi-honest adversaries, and then strengthen it to guarantee security against malicious adversaries with the same communication efficiency.