Peer-to-peer (P2P) systems such as BitTorrent and Bitcoin are susceptible to serious attacks from byzantine nodes that join as peers. Due to well-known impossibility results for designing P2P primitives in unrestricted byzantine settings, research has explored many adversarial models with additional assumptions, ranging from mild (such as preestablished PKI) to strong (such as the existence of common random coins). One such widely-studied model is the generalomission model, which yields simple protocols with good efficiency, but has been considered impractical or unrealizable since it artificially limits the adversary only to omitting messages. In this work, we study the setting of a synchronous network wherein peer nodes have CPUs equipped with a recent trusted computing mechanism called Intel SGX. In this model, we observe that the byzantine adversary reduces to the adversary in the general-omission model. As a first result, we show that by leveraging SGX features, we eliminate any source of advantage for a byzantine adversary beyond that gained by omitting messages, making the general-omission model realizable. Second, we present new protocols that improve the communication complexity of two fundamental primitives — reliable broadcast and common random coins (or beacons) — in the synchronous setting, by utilizing SGX features. Our evaluation of 1000 nodes running on 40 DeterLab machines confirms theoretical efficiency claim.