Among several proposed solutions for private processing in cloud computing, perhaps the most promising class of approaches is privacy-preserving computation. This thesis reviews existing approaches for private processing and demonstrates practical use of one such novel approach for privacy-preserving computation, fully homomorphic encryption (FHE). FHE allows arbitrary computations on ciphertexts and yields a result, which, when decrypted, is the same as if they were performed on corresponding plaintexts. We develop a simple web bank cloud application that uses FHE to preserve privacy of banking transactions. In order to support FHE client-side, we produce two architecturally different setups that can be used with the same web application. ...