The breakthrough of fully homomorphic encryption (FHE) enables privacy-preserving arbitrary computation in the cloud, supporting both addition and multiplication over encrypted data. Current FHE implementations, however, suffer from high performance overheads and require expensive boot-strapping operations to decrease ciphertext noise. In this work, we discuss how homomorphic encryption primitives can implement a functionally complete set of homomorphic operations and enable arbitrary computation that is outsourced by a single party. We focus on obfuscated computation with or without special look-up tables, to enable branch decisions over encrypted values while preserving privacy. Since partial homomorphic encryption is orders of magnitude less expensive than FHE, it can be more practical for privacy-preserving applications in the cloud.