In this paper, we propose a toolkit for efficient and privacy-preserving outsourced calculation under multiple encrypted keys (EPOM). Using EPOM, a large scale of users can securely outsource their data to a cloud server for storage. Moreover, encrypted data belonging to multiple users can be processed without compromising on the security of the individual user's (original) data and the final computed results. To reduce the associated key management cost and private key exposure risk in EPOM, we present a distributed two-trapdoor public-key cryptosystem, the core cryptographic primitive. We also present the toolkit to ensure that the commonly used integer operations can be securely handled across different encrypted domains. We then prove that the proposed EPOM achieves the goal of secure integer number processing without resulting in privacy leakage of data to unauthorized parties. Last, we demonstrate the utility and the efficiency of EPOM using simulations.