One of the key service of social networks is path discovery, in that release of a resource or delivering of a service is usually constrained by the existence of a path with given characteristics in the social network graph. One fundamental issue is that path discovery should preserve relationship privacy. In this paper, we address this issue by proposing a Privacy-Preserving Path Discovery protocol, called P3D. Relevant features of P3D are that: (1) it computes only aggregate information on the discovered paths, whereas details on single relationships are not revealed to anyone, (2) it is designed for a decentralized social network. Moreover, P3D is designed such to reduce the drawbacks that offline nodes may create to path discovery. In the paper, besides giving the details of the protocol, we provide an extensive performance study. We also present the security analysis of P3D, showing its robustness against the main security threats.