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Graph databases have received increased interests as many applications are handled as graph problems. Shortest distance queries are one of the fundamental operations and have been studied for recent years. To ensure the data and query privacy, researchers have introduced some secure graph encryption schemes which support the shortest distance queries on a large-scale graph database. Unfortunately, most of them only provide an approximate result by pre-computing and storing a distance oracle. To provide the exact shortest path, our solution employs a distributed two-trapdoor public-key crypto-system to perform addition and comparison operations over ciphertexts. The detailed security analysis indicates that our scheme achieves semantically secure under DDH assumption and the experiments are performed on various real-world database and random database. The experimental result shows the feasibility of our scheme. [ABSTRACT FROM AUTHOR]