As one of the fundamental primitive operations, querying shortest distance between node pairs in a graph has gradually attracted great attention in both academia and industry. In recent years, with the rapid development of cloud computing, it allows clients to outsource their data to cloud servers. In this way, users can outsource large volumes of data which were difficult to store and compute on their own clients. However, it worth noting that for privacy and security reasons, user data needs to be encrypted before being transmission to the server. Meanwhile, it is crucial for the encrypted data transmitted to server to maintain availability in order to enable users' operations searching and querying. To preserve data privacy while enabling querying, clients must construct and transmit a secure index to the server for subsequent querying. When performing shortest distance queries on encrypted graph data outsourced in external storage, a significant challenge is computing the shortest distance in an efficient, accurate and secure manner. Furthermore, the challenge becomes more pronounced as the scale of the graph increases. In this paper, we propose a novel approach to address this issue by splitting the graph data into multiple segments and constructing 2HCL index LID within each subgraphs, as well as establishing an index LBD among these subgraphs. We also provide a comprehensive analysis of complexity and security of SSDAQ and present conclusion at the end of this paper. Compared to 2HCL, which is a classical and widely used algorithm, we reduce the time and space complexity from O(N 2 ) time and O(kn|L max (s N )|) space to O(kn 2 ) time and O(kn|L max (s n )|) space in setup phase.