Multi-party garbled circuits employ distributed garbling strategy to achieve constant-round secure computation and authentication techniques to resist malicious adversaries. Implementations of these multi-party authenticated garbled circuits are used in constructing payment channels in blockchain and decentralized oracles for TLS. However, the high communication and computation costs limit their application in large-scale scenarios. In this paper, we propose an efficient, large-scale and constant-round multi-party computation protocol based on information-theoretic message authentication code and garbled circuit in the malicious model. Additionally, we propose a novel path-related optimization technique for multi-party authenticated garbled circuit, where parties generate a garbled circuit based on the related path in the circuit rather than the entire circuit. Through experimental evaluation and comparison with related work, the proposed scheme demonstrates dramatic improvement in computation and communication efficiency for each party when the number of parties increases.