Graph Encryption for Shortest Path Queries with k Unsorted Nodes

Shortest distance queries over large-scale graphs bring great benefits to various applications, i.e., save planning time and travelling expenses. To protect the sensitive nodes and edges in the graph, a user outsources an encrypted graph to an untrusted server without losing the query ability. However, no prior work has considered the user requirement of the shortest path with k unsorted nodes. In particular, we are concerned with how to securely find the shortest path by passing k nodes that do not have a fixed traverse order. To solve the problems, we propose Gespun (stands for Graph encryption for shortest path queries with k unordered nodes). It includes an oracle encryption scheme that is provably secure against the semi-honest server. Specifically, we compute the shortest paths and distances for all nodes locally to obtain path-distance oracles. We transform the shortest paths to a sequence of secure codes by using a pseudo-random permutation to protect the structure privacy. We encrypt the shortest distance by using additively homomorphic encryption. Second, we pack the oracles in link-list nodes and store them in an array-based dictionary after another permutation. Next, we construct a search graph to compute the shortest path while guaranteeing that the path passes the required k nodes. We formally prove that Gespun is adaptively semantically-secure in the random oracle. We implement a prototype of Gespun and evaluate its performance. Experiments results demonstrate that Gespun is efficient, e.g., a query over 6301 nodes, 20777 edges, and 5 unsorted nodes only needs 483 ms to get queried results. We believe that our research problem span new research that soon promotes a new line of graph encryption schemes.