With the rapid development of the Industrial Internet of Things, the security and privacy of identity authentication for smart devices have become critical issues. Traditional authentication mechanisms face challenges such as physical attacks and data privacy breaches in distributed environments. To address these issues, this paper proposes a consortium blockchain-based secure and efficient authentication scheme for smart devices. The scheme leverages Physical Unclonable Functions, zero-knowledge proofs, and consortium blockchain technology to achieve an efficient, decentralized, and scalable identity authentication method. First, we combine SRAM PUF, hash algorithms, and elliptic curve cryptography to generate unique device identifiers, which are then mapped to elliptic curve group elements, thereby enhancing the resistance of device identity authentication against attacks. Second, zk-SNARKs are used to construct non-interactive zero-knowledge proofs, enabling devices to be authenticated efficiently without revealing sensitive information, thus improving the privacy and efficiency of the authentication process. Finally, the consortium blockchain enables distributed storage and multi-party verification of authentication information, ensuring the transparency and credibility of the authentication process. Security analysis demonstrates that the proposed scheme can resist replay attacks, man-in-the-middle attacks, and forgery attacks, effectively ensuring the anonymity of device identities and the integrity of data. The results show that this scheme provides robust technical support for IIoT and offers an innovative approach to identity authentication in large-scale device management.