Efficient Computation of the Mean Time to Security Failure in Cyber Physical Systems

In this paper, we present a computationally efficient technique for calculating the mean time to security failure (MTTSF) of a mobile cyber physical system (CPS). The CPS analyzed here has been comprehensively studied by other authors using stochastic reward nets (SRN). In simple terms, the CPS is composed of a collection of communicating nodes, which are subject to security attacks. An intrusion detection mechanism is used to detect such attacks based on a voting scheme of some selected nodes. Three sources of failure are considered: successful inside attacks, Byzantine failure condition and energy exhaustion. The numerical solution technique proposed here takes advantage of the acyclic structure of the underlying Markov chain (MC) that captures the CPS dynamics. The proposed approach avoids the generation of the actual state-space of the MC, by performing a direct recursive computation with a space complexity proportional to a fraction of the number of nodes considered, which is orders of magnitude smaller than in previous works. This enables the calculation of the MTTSF for systems composed of several thousands of nodes without using parallelism.