Two fundamental tasks of mobility modeling are (1) to track the number of distinct persons that are present at a location of interest and (2) to reconstruct flows of persons between two or more different locations. Stationary sensors, such as Bluetooth scanners, have been applied to both tasks with remarkable success. However, this approach has privacy problems. For instance, Bluetooth scanners store the MAC address of a device that can in principle be linked to a single person. Unique hashing of the address only partially solves the problem because such a pseudonym is still vulnerable to various linking attacks. In this paper we propose a solution to both tasks using an extension of linear counting sketches. The idea is to map several individuals to the same position in a sketch, while at the same time the inaccuracies introduced by this overloading are compensated by using several independent sketches. This idea provides, for the first time, a general set of primitives for privacy preserving mobility modeling from Bluetooth and similar address-based devices.
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