Round-Efficient Byzantine Agreement and Multi-party Computation with Asynchronous Fallback

Protocols for Byzantine agreement (BA) and secure multi-party computation (MPC) can be classified according to the underlying communication model. The two most commonly considered models are synchronous one asynchronous one. Synchronous protocols typically lose their security guarantees as soon network violates synchrony assumptions. Asynchronous remain regardless of conditions, but achieve weaker even when is synchronous.Recent works by Blum, Katz Loss [TCC’19], Liu-Zhang [CRYPTO’20] introduced BA MPC achieving in both settings: up \(t_s\) corruptions a network, \(t_a\) an under provably optimal threshold trade-offs \(t_a \le t_s\) + 2t_s < n\). However, current solutions incur high round complexity compared state-of-the-art purely protocols. When synchronous, linear number parties, also depends linearly on depth circuit evaluate.In this work, we provide round-efficient constructions primitives with resilience: fixed-round expected constant-round protocols, protocol whose independent depth.