Shortest path computation in presence of obstacles has been a subject of study since long and so has been the study of privacy preserving algorithms. In this paper we design efficient privacy preserving algorithms for computing the shortest path circumventing convex polygonal obstacles. Specifically, we assume that a party A has source sand destination d while another party B has the list of convex polygonal obstacles and A wishes to find the shortest path from s to d without compromising each others’ privacy. That is, at the end of the protocol, A must not know anything else about the obstacles other that what may be revealed by the shortest path that is output and B must not know anything about A’s source/destination.