Paper 2026/1860

(Im)possibility of Asynchronous MPC with Honest Majority over Blockchains

Abstract

This work studies asynchronous verifiable secret sharing (AVSS) and asynchronous multi-party computation (AMPC) in the blockchain-hybrid model, where parties have black-box access to an ideal (asynchronous) blockchain functionality providing only persistence and eventual liveness. Motivated by the practical deployment of MPC in blockchain applications such as privacy-preserving payments and threshold wallets, we investigate whether blockchain access can improve the classical resilience bound of $n > 3t$, where $n$ is the total number of parties, and $t$ is the number of parties that can be compromised by an adversary. In particular, in the blockchain-hybrid model, we provide a comprehensive set of lower and upper bounds across three cryptographic settings: (i) no trusted setup, (ii) trusted setup with Minicrypt assumptions, (iii) trusted setup with public-key assumptions. 1. We show that without a trusted setup, or under Minicrypt assumptions, even with a setup, the classical resilience bound for AMPC is inherent: AMPC is impossible for $n \leq 3t$, even against weaker fail-stop or omission adversaries. 2. We establish separations between AVSS and AMPC in the intermediate regime $2t < n \leq 3t$: against a fail-stop adversary, unlike AMPC, AVSS is possible for $n>2t$ without any setup. Moreover, against a Byzantine adversary, again unlike AMPC, AVSS is possible for $n>2t$ under Minicrypt assumptions with a setup. 3. In contrast, under public-key assumptions with trusted setup, we construct an AMPC protocol tolerating Byzantine adversaries whenever $n>2t$. Our protocol leverages threshold homomorphic encryption, threshold signatures, commitments, and zero-knowledge proofs to minimize on-chain communication, achieving blockchain communication complexity independent of the circuit size. In the process, we define an efficient agreement on a common subset primitive for large messages in the blockchain-hybrid model, which can be of independent interest for secure distributed computing systems.