  We study a security problem for interconnected systems, where each subsystem
aims to detect local attacks using local measurements and information exchanged
with neighboring subsystems. The subsystems also wish to maintain the privacy
of their states and, therefore, use privacy mechanisms that share limited or
noisy information with other subsystems. We quantify the privacy level based on
the estimation error of a subsystem's state and propose a novel framework to
compare different mechanisms based on their privacy guarantees. We develop a
local attack detection scheme without assuming the knowledge of the global
dynamics, which uses local and shared information to detect attacks with
provable guarantees. Additionally, we quantify a trade-off between security and
privacy of the local subsystems. Interestingly, we show that, for some
instances of the attack, the subsystems can achieve a better detection
performance by being more private. We provide an explanation for this
counter-intuitive behavior and illustrate our results through numerical
examples.
