Document storage in the cloud infrastructure is rapidly gaining popularity throughout the world. However, it poses risks to consumers unless the data are encrypted for security. Encrypted data should be effectively searchable and retrievable without any privacy leaks, particularly for the mobile client. Although recent research has solved many security issues, the architecture cannot be applied on mobile devices directly under the mobile cloud environment. This is due to the challenges imposed by wireless networks, such as latency sensitivity, poor connectivity, and low transmission rates. This leads to a long search time and extra network traffic costs when using the traditional search schemes. This paper addresses these issues by proposing an efficient encrypted data search (EnDAS) scheme as a mobile cloud service. This innovative scheme uses a lightweight trapdoor (encrypted keyword) compression method, which optimizes the data communication process by reducing the trapdoor's size for traffic efficiency. In this paper, we also propose two optimization methods for document search, called the trapdoor mapping table module and ranked serial binary search algorithm, to speed the search time. Results show that EnDAS reduces search time by 34% to 47% as well as network traffic by 17% to 41%.