On the Design of Security-Guaranteeing Dynamic Watermarks

Dynamic watermarking is a defense mechanism to secure cyberphysical systems from arbitrary sensor attacks. The approach involves the actuators of a plant superimposing on the control policy-specified input a “small” random signal called the dynamic watermark (DW), and conducting certain carefully designed tests to detect the presence of adversarial sensors. Prior works on this topic have restricted attention to systems where the process and measurement noises affecting the system are Gaussian random processes. In this letter, we go beyond the class of Gaussian systems and address the problem of designing watermarks for linear systems affected by arbitrarily distributed noise. We first show how the fundamental security guarantee of DW can fail when the statistics of the watermark are not chosen appropriately taking into account the parameters of the noise process that affects the system. Subsequently, we address the problem of how security-guaranteeing DWs should be designed. Specifically, we consider the class of finite-dimensional, perfectly observed, linear stochastic systems with arbitrary process noise distributions, and derive for any such system the necessary and sufficient conditions that the statistics of the watermark should satisfy in order for the fundamental security guarantee to hold.