Ridesharing is revolutionizing the transportation industry in many countries. Yet, the state of the art is based on heavily centralized services and platforms, where the service providers have full possession of the users’ location data. Recently, researchers have started addressing the challenge of enabling privacy-preserving ridesharing. The initial proposals, however, have shortcomings, as some rely on a central party, some incur high performance penalties, and most do not consider time preferences for ridesharing. TOPPool encompasses ridesharing based on the proximity of end-points of a ride as well as partial itinerary overlaps. To achieve the latter, we propose a simple yet powerful reduction to a private set intersection on trips represented as sets of consecutive road segments. We show that TOPPool includes time preferences while preserving privacy and without relying on a third party. We evaluate our approach on real-world data from the New York’s Taxi & Limousine Commission. Our experiments demonstrate that TOPPool is superior in performance over the prior work: our intersection-based itinerary matching runs in less than 0.3 seconds for reasonable trip length, in contrast, on the same set of trips prior work takes up to 10 hours.