  Location trajectories collected by smartphones and other devices represent a
valuable data source for applications such as location-based services.
Likewise, trajectories have the potential to reveal sensitive information about
individuals, e.g., religious beliefs or sexual orientations. Accordingly,
trajectory datasets require appropriate sanitization. Due to their strong
theoretical privacy guarantees, differential private publication mechanisms
receive much attention. However, the large amount of noise required to achieve
differential privacy yields structural differences, e.g., ship trajectories
passing over land. We propose a deep learning-based Reconstruction Attack on
Protected Trajectories (RAoPT), that leverages the mentioned differences to
partly reconstruct the original trajectory from a differential private release.
The evaluation shows that our RAoPT model can reduce the Euclidean and
Hausdorff distances between the released and original trajectories by over 68%
on two real-world datasets under protection with $\varepsilon \leq 1$. In this
setting, the attack increases the average Jaccard index of the trajectories'
convex hulls, representing a user's activity space, by over 180%. Trained on
the GeoLife dataset, the model still reduces the Euclidean and Hausdorff
distances by over 60% for T-Drive trajectories protected with a
state-of-the-art mechanism ($\varepsilon = 0.1$). This work highlights
shortcomings of current trajectory publication mechanisms, and thus motivates
further research on privacy-preserving publication schemes.
