1970-01-01

(2025-12) A New Approach to Large Party Beaver-Style MPC with Small Computational Overhead

[[Aayush Jain]]
[[Huijia Lin]]
[[Nuozhou Sun]]

2025-12-22

Abstract

Secure multi-party computation (MPC) enables $N$ parties to jointly evaluate any function over their private inputs while preserving confidentiality. While decades of research have produced concretely efficient protocols for small to moderate numbers of participants, scaling MPC to thousands of parties remains a central challenge. Most of the existing approaches either incur per-party costs linear in $N$ , due to pairwise computations, or rely on heavy cryptographic tools such as homomorphic encryption, which introduces prohibitive overheads when evaluating Boolean circuits.

In this work, we introduce a new lightweight approach to designing semi-honest MPC protocols with per-party, per-gate computation and communication costs that are independent of $N$ . Our construction leverages the Sparse Learning Parity with Noise (Sparse LPN) assumption in the random oracle model to achieve per-gate costs of $O(k^2 \cdot c(\lambda))$ computation and $O(c(\lambda))$ communication, where $k$ is the sparsity parameter for the Sparse LPN assumption and $c(\lambda)$ is an arbitrarily small super-constant in the security parameter $\lambda$ . Assuming Sparse LPN remains hard for any super-constant sparsity, this yields the first semi-honest MPC protocol in the dishonest-majority setting with per-party per-gate costs bounded by an arbitrarily small super-constant overhead in $\lambda$ .

Structurally, our MPC instantiates a Beaver style MPC with the required correlations generated efficiently. Departing from prior approaches that generate Beaver triples silently (Boyle et al., 2019; 2020; 2022) or using homomorphic computation (Damgård et al., 2012) for Beaver style MPC, the focus of this work rests on efficiently generating a weaker correlation. In particular, using Sparse LPN we show that if we relax the correctness requirement in generating random Beaver triples to permit a tunably small inverse-polynomial error probability, such triples can be silently generated with arbitrarily small super-constant per-party computation. We then show that such correlations can be used in an efficient online phase similar to Beaver's protocol (with a tiny super-constant factor blow-up in communication).