## 4 System Model  
In the system model of our authentication method, there are four kinds of entities, as shown in Figure 1: _industrial device, edge gateway, blockchain anchor node,_ and _consortium blockchain network._  
* _Industrial devices_ refer to smart machines, sensors, actuators, and control systems deployed within manufacturing or operational environments. Each device is uniquely identifiable and equipped with a digital identity. These devices typically possess limited computational resources and are often constrained in terms of connectivity. As such, they rely on nearby infrastructure, the edge gateways, for identity verification and secure network onboarding. * _Edge gateways_ act as intermediaries between industrial devices. Positioned close to the devices at the network edge, an edge gateway performs initial identity verification for devices within its administrative domain. It maintains local access control policies and authentication protocols. The edge gateway collaborates with blockchain anchor nodes in cross-domain scenarios to validate device identities from other domains. Figure 1: The system model of the proposed method. * _Blockchain anchor nodes_ are specialized entities participating directly in the consortium blockchain network. They are responsible for maintaining a synchronized ledger of authenticated device identities across different domains. Each anchor node represents a local domain or administrative zone and communicates with peer anchor nodes to exchange identity verification records. When a device seeks access in a foreign domain, the local edge gateway can query its associated anchor node, which in turn consults the blockchain to verify the authenticity of the device's identity as issued by another domain's anchor node. In the context of the Industrial Internet, a domain refers to a logical segment where devices, data, networks, applications, and services are managed in a distributed manner. The division of domains is typically based on functionality, geographic location, permissions, or management requirements. It aims to enhance the system's management efficiency, security, and controllability. The domain serves as a boundary for administrative tasks and resource management. Typically, different domains are independent of each other, especially the authentication service. * _The consortium blockchain_ network is a permissioned ledger infrastructure where only authorized anchor nodes are allowed to validate transactions and contribute to consensus. This network ensures decentralized trust and provides tamper-evident storage for device identity credentials. It supports smart contracts that encode identity registration, revocation, and cross-domain verification logic. The use of a consortium model balances scalability with security, avoiding the performance drawbacks of fully public chains while still achieving distributed consensus. The authentication workflow is orchestrated through a multi-entity collaboration: (1) Industrial devices request authentication from the local edge gateway. (2) The edge gateway forwards the request to the anchor node for cross-domain verification. (3) The anchor node queries the consortium blockchain network to check the validity of the device identity as registered by a remote anchor node. This layered and federated architecture ensures that device identity is managed in a secure, decentralized, and scalable manner across the IIoT ecosystem. The primary role of blockchain is to replace traditional trusted authorities in storing and managing identity information, thereby enabling a decentralized identity authentication mechanism. Unlike conventional identity systems that rely on centralized Certificate Authorities (CAs) or Key Generation Centers (KGCs), blockchain leverages consensus protocols and tamper-resistant ledger structures to enhance the security, transparency, and auditability of identity data.