Paper 2025/1555 Original: eprint.iacr.org/2025/1555 ↗

Statistical MPC with a Constant Communication Overhead

Abstract

We study the feasibility of constant communication-overhead statistically-secure MPC tolerating malicious adversaries in the synchronous setting and guaranteed output delivery (GOD). We propose a protocol with $n = 3t + 1$ for SIMD circuits with a communication overhead of ${\cal O}(1)$ and round complexity ${\cal O}(D)$ for circuit depth $D$, where $n$ is the number of parties and $t$ is the maximum number of corruptions. Moreover, our protocol achieves GOD. This is the first MPC protocol with above characteristics. To design our protocol, we give two major contributions. Our first technical contribution is a verifiable secret sharing (VSS) protocol that achieves constant per-secret overhead via two-dimensional packing. Our second contribution is a constant-overhead degree-reduction protocol that converts a high-degree packed sharing into a lower-degree packed sharing.