The ever-growing of Internet of Things (IoT) data and the new spectrum of data applications have stimulated IoT clients to outsource their data to cloud servers or datacenters. Apart from storage service, the IoT clients also desires the servers to execute functional operations per client's request. In this paper, we aim to design the secure mechanisms that allow the IoT clients to outsource their encrypted data to geographically distributed servers while supporting homomorphic computation functions. We leverage the distributed index framework to disassemble and spread data evenly across geographically distributed servers while employing the key-value store as the underlying structure for fast data retrieval. To support computing over encrypted data, we customize Shamir's secret sharing into our mechanisms to design a tunable scheme for the adaption of different IoT application scenarios. In particular, we design three tunable protocols to achieve the effective additive homomorphic computations while approaching efficiency in terms of servers utilization, computation, and storage overhead. Even the designs focus on the additive computation, we show that it can be readily extended to other types of homomorphic computations as well as verifying the correctness of stored data. Based on the proposed protocols, we design system prototypes, deploy them in Amazon Web services, and evaluate our construction experimentally. Through experimental results, we show that our designs can achieve the efficiency in various perspectives.