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You Don't Know What I Know: On Notion of High-Order Opacity in Discrete-Event Systems
In this paper, we investigate a class of information-flow security properties
called opacity in partial-observed discrete-event systems. Roughly speaking, a
system is said to be opaque if the intruder, which is modeled by a passive
observer, can never determine the "secret" of the system for sure. Most of the
existing notions of opacity consider secrets related to the actual behaviors of
the system. In this paper, we consider a new type of secret related to the
knowledge of the system user. Specifically, we assume that the system user also
only has partial observation of the system and has to reason the actual
behavior of the system. We say a system is high-order opaque if the intruder
can never determine that the system user knows some information of importance
based on its own incomparable information. We provide the formal definition of
high-order opacity. Two algorithms are provided for the verification of this
new notion: one with doubly-exponential complexity for the worst case and the
other with single-exponential complexity. Illustrative examples are provided
for the new notion of high-order opacity