Cyber-physical systems, such as self-driving cars or autonomous aircraft, must defend against attacks that target sensor hardware. Analyzing system design can help engineers understand how a compromised sensor could impact the systems behavior; however, designing security analyses for cyber-physical systems is difficult due to their combination of discrete dynamics, continuous dynamics, and nondeterminism. This paper contributes a framework for modeling and analyzing sensor attacks on cyber-physical systems, using the formalism of hybrid programs. We formalize and analyze two relational properties of a systems robustness. These relational properties respectively express (1) whether a systems safety property can be influenced by sensor attacks, and (2) whether a systems high-integrity state can be affected by sensor attacks. We characterize these relational properties by defining an equivalence relation between a system under attack and the original unattacked system. That is, the system satisfies the robustness properties if executions of the attacked system are appropriately related to executions of the unattacked system. We present two techniques for reasoning about the equivalence relation and thus proving the relational properties for a system. One proof technique decomposes large proof obligations to smaller proof obligations. The other proof technique adapts the self-composition technique from the literature on secure information-flow, allowing us to reduce reasoning about the equivalence of two systems to reasoning about properties of a single system. This technique allows us to reuse existing tools for reasoning about properties of hybrid programs, but is challenging due to the combination of discrete dynamics, continuous dynamics, and nondeterminism. To evaluate, we present three case studies motivated by real design flaws in existing cyber-physical systems.
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