Heuristic Search in Encrypted Graphs

In this paper, we consider a scenario in which two parties are interested to find, in secure multiparty computation, the shortest path in a public graph. In particular, we consider the case in which, Alice knows the weights on the edges of the graph, Bob knows an heuristic to find the best path and together they want to discover the walk between two given nodes in privacy preserving way. We present a novel technique to enforce a version of the A* algorithm that is able to work on encrypted data in the above setting and we prove it to be secure in the honest but curious model. Our protocol achieves the goal of finding the shortest path in a public graph protecting respectively: the weights and the heuristic when those own to different parties.