Approximating Quantified Information Leakage in Cyber-Physical Systems Through Their Digital Twins

Quantitative information flow analysis provides a systematic approach to evaluating the security of a system by measuring the amount of secret information exposed through public outputs. In this paper, we develop a formal framework for quantifying information leakage in cyber-physical systems by modeling their digital twins. We define a process-algebraic calculus for digital twins and specify their semantics using Markovian models, enabling rigorous information flow analysis. Cyber-physical systems operate in an uncountably infinite state space due to their continuous physical behaviors. In contrast, digital twins—through digitization—evolve in a finite space, enabling the feasibility of quantitative information flow analysis using Markovian models. This formulation captures the inherent nondeterminism and probabilistic transitions in cyber-physical systems arising from evolution uncertainties, sensor measurement errors, and concurrent control logic. Leveraging back-bisimulation, we systematically compare an attacker’s knowledge of system secrets before and after execution to quantify leakage, relying on Renyi’s min-entropy. This approach provides a structured methodology for assessing confidentiality risks in cyber-physical systems and demonstrates the role of digital twins in advancing security analysis.