Abstract: Cloud Computing enables customers with limited computational resources to outsource their large computation workloads to cloud, and economically enjoy the massive computational power, bandwidth, storage, and even appropriate software that can be shared in a pay-per-use manner. Security is the primary obstacle that prevents the wide adoption of this promising computing model, especially for customers when their confidential data are consumed and produced during the computation. Treating the cloud as an intrinsically insecure computing platform from the viewpoint of the cloud customers, we must design mechanisms that not only protect sensitive information by enabling computations with encrypted data, but also protect customers from malicious behaviors by enabling the validation of the computation result.