Activity-based social networks, where people upload and share information about their location-based activities (e.g., the routes of their activities), are increasingly popular. Such systems, however, raise privacy and security issues: The service providers know the exact locations of their users; the users can report fake location information in order to, for example, unduly brag about their performance. In this paper, we propose a secure privacy-preserving system for reporting location-based activity summaries (e.g., the total distance covered and the elevation gain). Our solution is based on a combination of cryptographic techniques and geometric algorithms, and it relies on existing Wi-Fi access-point networks deployed in urban areas. We evaluate our solution by using real data sets from the FON community networks and from the Garmin Connect activity-based social network, and we show that it can achieve tight (up to a median accuracy of 76%) verifiable lower-bounds of the distance covered and of the elevation gain, while protecting the location privacy of the users with respect to both the social network operator and the access-point network operator(s).