  Estimation of an unknown deterministic vector from quantized sensor data is
considered in the presence of spoofing attacks which alter the data presented
to several sensors. Contrary to previous work, a generalized attack model is
employed which manipulates the data using transformations with arbitrary
functional forms determined by some attack parameters whose values are unknown
to the attacked system. For the first time, necessary and sufficient conditions
are provided under which the transformations provide a guaranteed attack
performance in terms of Cramer-Rao Bound (CRB) regardless of the processing the
estimation system employs, thus defining a highly desirable attack.
Interestingly, these conditions imply that, for any such attack when the
attacked sensors can be perfectly identified by the estimation system, either
the Fisher Information Matrix (FIM) for jointly estimating the desired and
attack parameters is singular or that the attacked system is unable to improve
the CRB for the desired vector parameter through this joint estimation even
though the joint FIM is nonsingular. It is shown that it is always possible to
construct such a highly desirable attack by properly employing a sufficiently
large dimension attack vector parameter relative to the number of quantization
levels employed, which was not observed previously. To illustrate the theory in
a concrete way, we also provide some numerical results which corroborate that
under the highly desirable attack, attacked data is not useful in reducing the
CRB.
