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Byzantine fault-tolerant agreement (BFT) in a partially synchronous system usually requires 3f + 1 nodes to tolerate f faulty replicas. Due to their high throughput and finality property BFT algorithms build the core of recent permissioned blockchains. As a complex and resource-demanding infrastructure, multiple cloud providers have started offering Blockchain-as-a-Service. This eases the deployment of permissioned blockchains but places the cloud provider in a central controlling position, thereby questioning blockchains' fault tolerance and decentralization properties and their underlying BFT algorithm. This paper presents SplitBFT, a new way to utilize trusted execution technology (TEEs), such as Intel SGX, to harden the safety and confidentiality guarantees of BFT systems thereby strengthening the trust in could-based deployments of permissioned blockchains. Deviating from standard assumptions, SplitBFT acknowledges that code protected by trusted execution may fail. We address this by splitting and isolating the core logic of BFT protocols into multiple compartments resulting in a more resilient architecture. We apply SplitBFT to the traditional practical byzantine fault tolerance algorithm (PBFT) and evaluate it using SGX. Our results show that SplitBFT adds only a reasonable overhead compared to the non-compartmentalized variant.