Fast and Efficient Perfectly Secure Network-Agnostic Secure Computation

Secure multiparty computation (MPC) enables mutually distrustful parties to jointly compute over private data without revealing their inputs. While protocols in both synchronous and asynchronous settings have achieved impressive efficiency in either communication or round complexity, combining the two has remained challenging. Only recently, Abraham, Asharov, Patil, and Patra (Eurocrypt’23, Eurocrypt’24) achieved protocols that combine low communication complexity ($O((Cn + Dn^2 + n^4)\log n)$) with fast execution ($O(D)$ rounds) in both synchronous and asynchronous models, for circuits of size $C$ and depth $D$, in the perfect setting with optimal resilience. However, both protocols crucially assume advanced knowledge of the network type and are fragile under mismatched or varying network conditions.

The fragility of protocols under mismatched network assumptions highlights the need for network-agnostic MPC, where security and correctness are preserved in both synchronous and asynchronous settings. Yet, all known perfect network-agnostic protocols incur $\Omega(D+n)$ rounds and communication complexity in the order of $n^3$ or higher, far worse than their network-specific counterparts.

In this work, we present the first network-agnostic MPC protocol in the perfect security setting, achieving expected round complexity $O(D)$. Our protocol has expected communication complexity $O((Cn^2 + Dn^2 + n^4)\log n)$, improving on the state of the art by a factor of $n^3$ for small circuits and $n^2$ for large circuits in communication, in addition to an additive $O(n)$ improvement in round complexity. Our design departs from the structure of prior network-agnostic protocols and introduces several new technical ideas that enable both round and communication efficiency.