Secrecy Codes for State Estimation of General Linear Systems

A typical cyber-physical system setup includes a local system sending measurements of its internal state to a remote state estimator. A form of attack consists of an eavesdropper observing this information exchange. Secrecy coding schemes have been recently proposed to achieve immunity to eavesdropping. The essential idea consists in coding the transmitting information in a way such that a single packet lost by the eavesdropper causes an irrecoverable error of its state estimation. Common limitations of the available methods are the assumptions that the local system can directly measure its internal state and that the system is unstable. In this work, we drop these assumptions and consider the general case in which measurements are noisy linear combinations of an inaccessible internal state and that the system is not necessarily unstable. To design the coding scheme, we introduce the concept of total secrecy, meaning that if the eavesdropper misses a packet that is available at the remote estimator, the former behaves as if no further packets were received. We derive a sufficient condition for total secrecy, as well as the code achieving this property. Also, for the case in which we cannot guarantee total secrecy, we address the problem of designing a code achieving maximum secrecy in some sense. We present numerical examples illustrating our claims.