## 2 Related Work
### Cross-domain authentication Based on IBA and Blockchain  
Identity-Based Authentication (IBA) [18] is a method where a user's identity (e.g., email or username) serves as their public key, thereby eliminating the need for digital PKI certificates. In this approach, a trusted entity called the Key Generation Center (KGC) is responsible for generating the corresponding private keys of all users. During authentication, users demonstrate possession of their private keys by generating a valid cryptographic response, which can be verified by others using the public key derived from the user's identity. As a result, IBA significantly simplifies key management and reduces the overhead associated with certificate handling. Therefore, it is particularly suitable for distributed environments such as IoT and IIoT. However, since the KGC holds the power to generate any user's private key, IBA introduces potential key escrow and trust concerns. To address these concerns, researchers have turned to blockchain technology, leveraging its decentralized, tamper-resistant architecture to reconstruct IBA frameworks without the need for a centralized KGC. For instance, [PERSON] et al. [19] proposed DIBRS-CE, a blockchain-based distributed identity-based ring signature scheme with identity abort, tailored for consumer electronics. Their design features a decentralized threshold identity-based ring signature protocol that removes reliance on a Key Generation Center (KGC). [PERSON] et al. [20] presented an identity-based data rights governance (IDRG) framework designed for blockchain-enabled, human-centric metaverse communication. By integrating blockchain technology with polynomial functions, their scheme supports access policies involving multiple users, thereby addressing the constraint of conventional identity-based encryption methods, which typically allow only single-user policies. [PERSON] et al. [21] presented a blockchain-assisted distributed identity-based signature scheme designed to enhance security in resource-constrained IoT applications. By eliminating reliance on a centralized Key Generation Center (KGC), the scheme enables users to collaboratively generate master and signing keys through threshold protocols, addressing key escrow risks and single points of failure. [PERSON] et al. [22] introduced the Advanced Hierarchical Identity-Based Security Mechanism by Blockchain (AHISM-B) for Named Data Networking (NDN). Their approach leverages hierarchical identity-based cryptography to associate data names with public keys while utilizing blockchain to oversee public parameters, thereby mitigating the risk of single-point failures. [PERSON] et al. [23] proposed an efficient identity-based aggregate signcryption scheme with blockchain (B-ID-ASC) for IoT-enabled maritime transportation systems (IMTSs). They design decentralized device authentication and tamper-proof transaction logging to replace centralized authorities, mitigating single-point failures. [PERSON] et al. [24] introduced a decentralized Identity-Based Authentication framework for IoT devices, leveraging a permissioned blockchain. In their approach, the blockchain functions as a distributed Private Key Generator (PKG), effectively mitigating issues such as single points of failure and key escrow that are commonly associated with conventional Public Key Infrastructure (PKI) and IBA. Despite these advancements, blockchain-based IBA systems are not without challenges. First of all, resource-constrained devices in IIoT may struggle with blockchain's computational and storage requirements, particularly when managing extensive data. To reduce computational overhead, [PERSON] et al. [25] proposed a provably secure multivariate identity-based multi-signature scheme (MV-MSS) for the Internet of Vehicles (IoV) environment. The MV-MSS produces a single compact signature for multiple signers, reducing communication overhead. [PERSON] et al. [26] proposed two novel identity-based key agreement protocols tailored for the blockchain-powered intelligent edge.