This paper proposes an improved device authentication algorithm for industrial Internet of Things (IIoT) systems. The proposed algorithm is implemented based on blockchain technology using BLAKE3 hash function, certificateless signature scheme and signature aggregation. Experimental modeling is performed in GNU/Linux environment using simulation of attacks of 3 types: public key spoofing, master key attacks, consensus attacks. The proposed algorithm allows to minimize the computational cost by optimizing hashing and signing operations, and to reduce the volume of transmitted data. Experiments confirmed the resistance of IIoT devices to the selected 3 types of attacks, which makes the algorithm effective for use in real IIoT systems.