Secure reachability query on private shared graphs

Reachability refers to the ability to get from one vertex to another within a graph. In this paper, we investigate the reachability problem on a distributed graph. We consider the scenario where there are two parties, each in possession of a private set of edges, while the vertices are public. The two parties wish to securely determine whether two particular vertices are connected but do not want to reveal any graph information except the result to the other party. Our proposed solution is secure in semi-honest model where each party correctly follows the protocol specification, yet attempts to learn additional information by analyzing the data flow. We discuss the solution for both undirected and directed graph. The experimental result shows that the protocols are efficient and scalable for small and medium size data.