The Internet of Things (IoT) has experienced rapid growth in recent years, drawing significant attention from both academics and industry. As IoT gradually gains popularity in the industrial market, industrial internet of things(IIoT) has emerged as a necessary solution to meet the demands of the times. The limitations posed by the small storage space of certain devices, restricted network throughput coupled with timing and reliability requirements, and the need for safety assurance in the IIoT, all present significant challenges. In particular, security threats are constantly increasing, posing a significant risk to the rapid development of IIoT. Therefore, CLAST scheme was proposed to address these issues, which based on elliptic curve cryptography and bilinear mapping to ensure the security of information. The security analysis of the scheme in the random oracle model was proved, affirming that it satisfies the security requirements for signature verification. Furthermore, the scheme reduces the complexity of the cryptographic operation process and reduces the computational overhead of the signature verification algorithm. These benefits have been substantiated through security analysis performance analysis.