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Mission critical systems deployed in data centers today are facing more sophisticated failures. Byzantine fault tolerant (BFT) protocols are capable of masking these types of failures, but are rarely deployed due to their performance cost and complexity. In this work, we propose a new approach to designing high performance BFT protocols in data centers. By re-examining the ordering responsibility between the network and the BFT protocol, we advocate a new abstraction offered by the data center network infrastructure. Concretely, we design a new authenticated ordered multicast primitive (AOM) that provides transferable authentication and non-equivocation guarantees. Feasibility of the design is demonstrated by two hardware implementations of AOM -- one using HMAC and the other using public key cryptography for authentication -- on new-generation programmable switches. We then co-design a new BFT protocol, Matrix, that leverages the guarantees of AOM to eliminate cross-replica coordination and authentication in the common case. Evaluation results show that Matrix outperforms state-of-the-art protocols on both latency and throughput metrics by a wide margin, demonstrating the benefit of our new network ordering abstraction for BFT systems.