###### Abstract  
The Industrial Internet of Things (IIoT), a key enabler of Industry 4.0, integrates advanced communication technologies with the industrial economy to enable intelligent manufacturing and interconnected systems. Secure and reliable identity authentication in the IIoT becomes essential as connectivity expands across devices, systems, and domains. Blockchain technology presents a promising solution due to its decentralized, tamper-resistant, and traceable characteristics, facilitating secure and transparent identity verification. However, current blockchain-based cross-domain authentication schemes often lack a lightweight design, rendering them unsuitable for latency-sensitive and resource-constrained industrial environments. This paper proposes a lightweight cross-domain authentication scheme that combines blockchain with Chebyshev chaotic mapping. Unlike existing schemes relying heavily on Elliptic Curve Cryptography or bilinear pairing, our design circumvents such computationally intensive primitives entirely through the algebraic structure of Chebyshev polynomials. A formal security analysis using the Real-Or-Random (ROR) model demonstrates the scheme's robustness. Furthermore, performance evaluations conducted with Hyperledger Fabric and the MIRACL cryptographic library validate the method's effectiveness and superiority over existing approaches in terms of both security and operational efficiency. L 22 May 202514 July 202522 July 20252 July 20252 July 20252 July 20252 May 20252 May 202522 May  
In the collaborative process of the IIoT, ensuring the trusted identity of devices is crucial [3]. Malicious devices can fake their identity to join the collaboration, steal sensitive data, or disrupt tasks. Without a unified identity authentication mechanism, devices cannot establish mutual trust, which prevents effective collaboration across the domains. Currently, networks in different management domains face identity isolation. They use separate identity management systems, with inconsistent standards for identity formats and authentication policies. This makes it difficult for devices to exchange and verify credentials across domains. As a result, trust cannot be easily established, leading to significant identity fragmentation. In IIoT, devices often interact across different management domains, making secure cross-domain authentication essential. Traditional centralized methods face challenges such as single points of failure, poor scalability, and limited trust interoperability [3]. To address this, a distributed identity authentication mechanism across management domains is needed. This will enable trusted authentication and identity management for cross-domain devices, allowing seamless collaboration between networks [4]. The decentralized, tamper-resistant, and traceable characteristics of blockchain make it particularly suitable for identity authentication in cross-domain collaboration within the IIoT [5]. It enables secure, transparent, and efficient authentication while addressing trust and efficiency issues in traditional authentication methods. Blockchain's decentralization allows different administrative domains to reach consensus on a unified identity authentication mechanism without relying on a single centralized certification authority. This enables cross-domain identity information sharing and authentication. Its tamper-resistant property ensures that once identity information is recorded on-chain during cross-domain collaboration, it cannot be maliciously altered, thus guaranteeing the integrity and authenticity of the shared identity data. The traceability feature of blockchain enables the recording of all authentication operations in chronological order, allowing identity verification and access history to be traced at any time. This is particularly important for multi-party collaboration and security auditing.