  This paper considers a sensor attack and fault detection problem for linear
cyber-physical systems, which are subject to system noise that can obey an
unknown light-tailed distribution. We propose a new threshold-based detection
mechanism that employs the Wasserstein metric, and which guarantees system
performance with high confidence employing a finite number of measurements. The
proposed detector may generate false alarms with a rate $\Delta$ in normal
operation, where $\Delta$ can be tuned to be arbitrarily small by means of a
benchmark distribution which is part of our mechanism. Thus, the proposed
detector is sensitive to sensor attacks and faults which have a statistical
behavior that is different from that of the system's noise. We quantify the
impact of stealthy attacks---which aim to perturb the system operation while
producing false alarms that are consistent with the natural system's
noise---via a probabilistic reachable set. To enable tractable implementation
of our methods, we propose a linear optimization problem that computes the
proposed detection measure and a semidefinite program that produces the
proposed reachable set.
