  With the increasing popularity of hand-held devices, location-based
applications and services have access to accurate and real-time location
information, raising serious privacy concerns for their users. The recently
introduced notion of geo-indistinguishability tries to address this problem by
adapting the well-known concept of differential privacy to the area of
location-based systems. Although geo-indistinguishability presents various
appealing aspects, it has the problem of treating space in a uniform way,
imposing the addition of the same amount of noise everywhere on the map. In
this paper we propose a novel elastic distinguishability metric that warps the
geometrical distance, capturing the different degrees of density of each area.
As a consequence, the obtained mechanism adapts the level of noise while
achieving the same degree of privacy everywhere. We also show how such an
elastic metric can easily incorporate the concept of a "geographic fence" that
is commonly employed to protect the highly recurrent locations of a user, such
as his home or work. We perform an extensive evaluation of our technique by
building an elastic metric for Paris' wide metropolitan area, using semantic
information from the OpenStreetMap database. We compare the resulting mechanism
against the Planar Laplace mechanism satisfying standard
geo-indistinguishability, using two real-world datasets from the Gowalla and
Brightkite location-based social networks. The results show that the elastic
mechanism adapts well to the semantics of each area, adjusting the noise as we
move outside the city center, hence offering better overall privacy.
