  This paper studies the impact of side initial state information on the
detectability of data deception attacks against cyber-physical systems. We
assume the attack detector has access to a linear function of the initial
system state that cannot be altered by an attacker. First, we provide a
necessary and sufficient condition for an attack to be undetectable by any
dynamic attack detector under each specific side information pattern. Second,
we characterize attacks that can be sustained for arbitrarily long periods
without being detected. Third, we define the zero state inducing attack, the
only type of attack that remains dynamically undetectable regardless of the
side initial state information available to the attack detector. Finally, we
design a dynamic attack detector that detects detectable attacks.
