With the rapid development of Internet of Things (IoT) technology, there has been exponential growth in the number of IoT systems, making domain-based management increasingly critical. As the number of domains continues to proliferate, the demand for inter-domain communication has become more frequent. Consequently, the development of an efficient and secure cross-domain authentication protocol to ensure the security and efficiency of inter-domain communication has emerged as a pressing issue within the IoT domain that requires immediate attention. Concurrently, the rise of quantum computers has rendered traditional cryptographic systems based on complex mathematical problems insecure, as these problems become solvable in the context of quantum computing. Therefore, the resistance of cryptographic systems to quantum attacks has become particularly important, and cryptographic systems built on lattice theory have shown significant advantages in dealing with quantum attacks. To address these issues, this paper proposes a new cross-domain Direct Anonymous Authentication (DAA) scheme with shared private key for Internet of Things System (SPCD-LDAA). The scheme relies on post-quantum key exchange protocols and anonymous authentication protocols, aiming to provide a new cross-domain communication solution for IoT systems in the era of quantum computing. The paper compares the proposed scheme with existing schemes, demonstrating improvements in both efficiency and security.