Hosting Services on an Untrusted Cloud.

We consider a scenario where a service provider has created a software service S and desires to outsource the execution of this service to an untrusted cloud. The software service contains secrets that the provider would like to keep hidden from the cloud. For example, the software might contain a secret database, and the service could allow users to make queries to different slices of this database depending on the user's identity. This setting presents significant challenges not present in previous works on outsourcing or secure computation. Because secrets in the software itself must be protected against an adversary that has full control over the cloud that is executing this software, our notion implies indistinguishability obfuscation. Furthermore, we seek to protect knowledge of the software S to the maximum extent possible even if the cloud can collude with several corrupted users. In this work, we provide the first formalizations of security for this setting, yielding our definition of a secure cloud service scheme. We provide constructions of secure cloud service schemes assuming indistinguishability obfuscation, one-way functions, and non-interactive zero-knowledge proofs. At the heart of our paper are novel techniques to allow parties to simultaneously authenticate and securely communicate with an obfuscated program, while hiding this authentication and communication from the entity in possession of the obfuscated program.