# Leveraging Digital Twin Technology for Enhanced Cybersecurity in Cyber-Physical Production Systems
## 3 Digital Twin-Based Security Assessment for CPPS
### Dependency Analysis and Criticality Calculation  
In the proposed CPPS architecture, we pinpoint critical components integral to the organization's operational continuity and mission fulfillment. Our focus lies on data and information components involved in production processes. This includes data stored on memory and hardware disks, as well as data in transit between computing nodes. For instance, programming instructions (e.g., G-code or M-code files) are transmitted from the CAM server to the control server within the control center. Machining data are relayed to the controllers such as the PLC controller for production execution. Simultaneously, processed data and a copy of the machining data are stored in the historian server, which maintains a time-tagged database of the production system's data points. The PLC controller is directly linked to the PLC gripper. Additionally, datasets such as product and manufacturing information, tool condition data, and product inspection data are both critical and confidential, essential for ensuring the system's functionality. To refine the criticality analysis process, we elaborated on the concept of functional dependencies (FD), as Definition 1, builds upon our previous works [55; 56]. **Definition 1** (Function Dependence). : _If component \(C_{i}\) requires component \(C_{j}\) for its functional operations, then \(C_{i}\) has a functional dependence on \(C_{j}\), denoted as \(FD_{(i,j)}\)._  
We introduce seven FD rules to elucidate the complexity of software component interactions, utilizing these for system dependency mapping based on static configuration data. Here, the embedding rule describes dependency arising from one component embedded within another, which is a vertical relationship in the system's architecture. The interaction rule indicates that the dependency is based on the interaction or data exchange between components, reflecting a horizontal relationship. Consider a cyber component, such as \(C_{i}\), an \(\Pi\) or OT component, such as \(C_{j}\), a hypervisor or operating system component, such as \(C_{i}\), and a physical component, such as \(C_{j}\). The functional dependency of one component on another is represented by \(FD_{(i,j)}\)  
Figure 6: Cyber layer of the CPPS reference model. indicating that component \(C_{i}\) is functionally dependent on component \(C_{j}\). The rules can then be formalized as follows:  
1. **FD Embedding Rule (ER):** * **ER-1:**\(FD_{(i,j)}\gets C_{i}\subseteq C_{j}\), for \(C_{i}\) embedded in \(C_{j}\). * **ER-2:**\(FD_{(j,i)}\gets C_{j}\subseteq C_{i}\), for \(C_{j}\) contained in \(C_{i}\). 2. **FD Interaction Rule (IR):** * **IR-1:**\(FD_{(k,j)}\gets C_{k}\xleftarrow{\text{data}}C_{j}\), for \(C_{k}\) receiving process data from \(C_{j}\). * **IR-2:**\(FD_{(j,i)}\gets C_{j}\xleftarrow{\text{control}}C_{i}\), for \(C_{j}\) receiving control data from \(C_{i}\). 3. **FD Data Rule (DR):** * **DR-1:**\(FD_{(i,j)}\gets C_{i}\xleftarrow{\text{stream}}C_{j}\), for \(C_{i}\) as data stream recipient from \(C_{j}\). * **DR-2:**\(FD_{(i,j)}\leftarrow C_{i}\xleftarrow{\text{listen}}C_{j}\), for \(C_{i}\) listening to the data stream from \(C_{j}\). 4. **FD Network Rule (NR):** * **NR-1:**\(FD_{(i,j)}\gets C_{i}\xleftarrow{\text{[network]}}C_{j}\), for \(C_{i}\) connected to the network via \(C_{j}\). \(\subseteq\) denotes an embedding relationship, \(\xleftarrow{\text{data}}\) and \(\xleftarrow{\text{control}}\) represent data and control flow dependencies, respectively, \(\xleftarrow{\text{stream}}\) and \(\xleftarrow{\text{listen}}\) indicate data stream relationships, and \(\xleftarrow{\text{[network]}}\) symbolizes network connectivity. These refined FD rules provide a structured framework for identifying and analyzing functional dependencies within a system, thereby enhancing the accuracy and comprehensiveness of vulnerability assessments. In doing so, we establish dependency matrices \(FD_{(i,j)}\) between component nodes \(C_{i}\) and \(C_{j}\).