Abstract—With the growing popularity of mobile devices that have sophisticated localization capability, it becomes more con-venient and tempting to give away location data in exchange for recognition and status in the social networks. Geosocial networks, as an example, offer the ability to notify a user or trigger a service when a friend is within geographical proximity. To achieve this, users ’ devices need to periodically send location updates to the service provider, which then computes the geographical distance in an unencrypted form. Existing privacy preserving mechanisms focus on the storage or release of coordinate data by means of classical encryption and differential privacy. These techniques limit the utility of the encrypted or synthesized data if further computations are needed. In this paper, we present two methods to support secure distance computation on encrypted location data; that is, computing distance functions without knowing the actual coordinates of users. The underlying security is ensured by the homomorphic encryption scheme which supports computation on encrypted data. We demonstrate feasibility of the proposed approaches by conducting various performance evaluations on platforms with different specifications. We argue that the novelty of this work enables a new breed of pervasive and mobile computing concepts, which was previously not possible due to the lack of feasible mechanisms that support computation on encrypted location data. I.

Mellon’s Human-Computer Interaction Institute. Any findings, conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the above organizations or corporations.