The proliferation of sensors in devices of frequent use, such as mobile phones, offers unprecedented opportunities for forming self-selected communities around shared sensory data pools that enable community specific applications of mutual interest. Such applications have recently been termed participatory sensing. An important category of participatory sensing applications is one that construct maps of different phenomena (e.g., traffic speed, pollution) using vehicular participatory sensing. An example is sharing data from GPS-enabled cell-phones to map traffic or noise patterns. Concerns with data privacy are a key impediment to the proliferation of such applications. This paper presents theoretical foundations, a system implementation, and an experimental evaluation of a perturbation-based mechanism for ensuring privacy of location-tagged participatory sensing data while allowing correct reconstruction of community statistics of interest (computed from shared perturbed data). The system is applied to construct accurate traffic speed maps in a small campus town from shared GPS data of participating vehicles, where the individual vehicles are allowed to "lie" about their actual location and speed at all times. An extensive evaluation demonstrates the efficacy of the approach in concealing multi-dimensional, correlated, time-series data while allowing for accurate reconstruction of spatial statistics.