AUTHOR=Wan Tao , Shi Buhai , Xiao Jiongen TITLE=An efficient and privacy protection group authentication scheme in the industrial internet of things JOURNAL=Frontiers in Physics VOLUME=Volume 13 - 2025 YEAR=2025 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2025.1582969 DOI=10.3389/fphy.2025.1582969 ISSN=2296-424X ABSTRACT=Industrial Internet of Things (IIoT) integrates the latest information and communication technology with the industrial economy, driving the intelligent transformation of the industry. However, with the rapid development of IIoT, its security challenges are increasingly severe. Therefore, this paper focuses on the security protection of industrial Internet, especially the application and challenges of group schemes. By analyzing the security requirements of IIoT, this paper proposes a secure and effective group authentication scheme for IIoT. Based on the Chinese remainder theorem, this scheme supports authorizing users to remotely access a set of industrial sensor devices and uses a three factor authentication method to verify the legitimacy of user identity. At the same time, through Chebyshev chaotic mapping, symmetric encryption, secret sharing technique and the Chinese remainder theorem, this scheme constructs a secure group session key to ensure encrypted transmission and integrity verification of data. The experimental results show that this scheme performs well in both security and computational efficiency, especially in large-scale group communication scenarios, which can significantly reduce communication latency and overhead.