  Prior work has shown that multibiometric systems are vulnerable to
presentation attacks, assuming that their matching score distribution is
identical to that of genuine users, without fabricating any fake trait. We have
recently shown that this assumption is not representative of current
fingerprint and face presentation attacks, leading one to overestimate the
vulnerability of multibiometric systems, and to design less effective fusion
rules. In this paper, we overcome these limitations by proposing a statistical
meta-model of face and fingerprint presentation attacks that characterizes a
wider family of fake score distributions, including distributions of known and,
potentially, unknown attacks. This allows us to perform a thorough security
evaluation of multibiometric systems against presentation attacks, quantifying
how their vulnerability may vary also under attacks that are different from
those considered during design, through an uncertainty analysis. We empirically
show that our approach can reliably predict the performance of multibiometric
systems even under never-before-seen face and fingerprint presentation attacks,
and that the secure fusion rules designed using our approach can exhibit an
improved trade-off between the performance in the absence and in the presence
of attack. We finally argue that our method can be extended to other biometrics
besides faces and fingerprints.
