There have been works considering protocols for accessing partitioned data. Most of these works assume the local cluster based environment and their designs target atomic semantics. However, when considering widely distributed cloud storage systems, these existing protocols may not scale well. In this paper, we analyze the requirements of access protocols for storage systems based on data partitioning schemes in widely distributed cloud environments. We consider the regular semantics instead of atomic semantics to improve access efficiency. Then, we develop an access protocol following the requirements to achieve correct and efficient data accesses. Various protocols are compared experimentally and the results show that our protocol yields much better performance than the existing ones.