## 2 Related Work
### Cross-domain authentication Based on IBA and Blockchain
The first protocol ensures extended Canetti-Krawczyk (eCK) security, while the second protocol further achieves continuous after-the-fact leakage resilience (CAFL-eCK) security, resistant to side-channel attacks. Both protocols are lightweight and suitable for edge and end devices with limited computational resources. [PERSON] et al. [21] presented a blockchain-assisted distributed identity-based signature scheme for resource-constrained IoT applications. They propose a tree-based broadcasting strategy that reduces communication complexity from O (\(n^{2}\)) to O (nlogn), optimizing bandwidth efficiency for IoT devices. They further employ oblivious transfer protocols instead of homomorphic encryption for signature construction, achieving lightweight computational overhead without compromising security. To reduce storage overhead, [PERSON] et al. [27] proposed a blockchain-based IoT architecture for securing healthcare data using identity-based encryption (IBE). The system combines blockchain with Swarm off-chain storage to efficiently manage large-scale healthcare datasets. IBE secures data at rest, while Swarm enables decentralized data distribution, effectively addressing storage challenges. Second, privacy risks emerge from the immutable nature of blockchain, as identity or key-related metadata, once written to the ledger, may be susceptible to linkage attacks over time. [PERSON] et al. [20] proposed a privacy-preserving identity-based data rights governance scheme (IDRG) for blockchain-empowered human-centric metaverse communications. They protect user privacy by enabling encrypted identity-based data access policies that hide both policy content and size, ensuring data, identity, and policy privacy while supporting accountability and revocation via cryptographic techniques and blockchain. Although prior studies have made notable progress in addressing the challenges introduced by integrating blockchain into IBA systems, several critical issues remain. One key concern is the inherent privacy risk of using a user's identity as their public key [22; 23; 24; 25; 26; 27]. While this design eliminates the need for digital certificates, it also exposes identity-related information. Once written to the immutable blockchain ledger, such data becomes vulnerable to linkage attacks and long-term privacy compromises. To address these risks, researchers have proposed various privacy-preserving techniques. These include cryptographic obfuscation [19] and zero-knowledge proofs [20; 21]. However, implementing these mechanisms often introduces significant computational overhead and increased protocol complexity. This is particularly problematic in resource-constrained environments such as the Internet of Things (IoT) and Industrial Internet of Things (IIoT). As a result, while blockchain helps alleviate the trust and key escrow issues in traditional IBA by removing the need for a centralized KGC, it simultaneously necessitates more sophisticated and computationally intensive mechanisms to preserve user privacy. Our scheme assigns IoT devices pseudonyms that are periodically generated using Chebyshev chaotic maps, effectively mitigating traceability risks during cross-domain operations and preserving device privacy. Furthermore, Chebyshev chaotic maps have demonstrated superior computational efficiency compared to traditional privacy-preserving techniques in most blockchain-based IBA frameworks.