With the rapid growth of big data, clients lack in storage and computational resources tend to outsource their data and computation tasks to cloud service providers. Due to concerns of privacy leakage in cloud, data owners encrypt the data via their own keys before outsourcing. However, it's rather difficult for cloud servers to perform computations over those encrypted data, since most of existing solutions are restricted to single key setting and may reveal the final output to adversary. In this paper, we propose two sets of privacy-preserving building blocks to support outsourced computation. Specifically, these schemes allow the cloud servers to evaluate basic arithmetic functions including addition, multiplication, and exponentiation over ciphertexts under different keys by utilizing the property of proxy re-encryption technique to transform ciphertexts. They are proven to be secure in the semi-honest model and secure against eavesdropping attacks. Experimental results on local testbed and real cloud environment demonstrate that the proposed solutions achieve great performance improvements with low overhead on data owners.