As the practice of renting remote computing resources from a cloud computing platform becomes increasingly popular, the security of such systems is a subject of continued scrutiny. This thesis explores the current state of cloud computing security along with critical components of the cloud computing model. It identifies the need to trust a third party with sensitive information as a substantial obstacle for cloud computing customers. It then proposes a new model, Host-Obscure Computing, for a cloud computing service using secure enclaves and encryption that allows a customer to execute code remotely without exposing sensitive information, including program flow control logic. It presents a proof of concept for a secure cloud computing service using confidential computing technology, cryptography, and an emulator that runs in a secure memory space. It then provides an analysis of its effectiveness at reducing data exposure and its performance impact. Finally, it analyzes this model's advantages and its potential impact on the cloud computing industry.