  In this paper we study a cybersecurity problem of protecting system's secrets
with multiple protections and a required security level, while minimizing the
associated cost due to implementation/maintenance of these protections as well
as the affected system usability. The target system is modeled as a
discrete-event system (DES) in which there are a subset of marker states
denoting the services/functions provided to regular users, a subset of secret
states, and multiple subsets of protectable events with different security
levels. We first introduce usability-aware cost levels for the protectable
events, and then formulate the security problem as to ensure that every system
trajectory that reaches a secret state contains a specified number of
protectable events with at least a certain security level, and the highest
usability-aware cost level of these events is minimum. We first provide a
necessary and sufficient condition under which this security problem is
solvable, and when this condition holds we propose an algorithm to solve the
problem based on the supervisory control theory of DES. Moreover, we extend the
problem to the case of heterogeneous secrets with different levels of
importance, and develop an algorithm to solve this extended problem. Finally,
we demonstrate the effectiveness of our solutions with a network security
example.
