Security protocols are the basis of modern network communication, proving that the security problem of protocols is one of the hot research topics today. The data in industrial IoT are usually transmitted through insecure channels, which brings certain security risks. The Logic of Events is a formal method for proving the security properties of protocols based on event systems. The new theoretical extension is based on the Logic of Events theory, which proposes new event classes Compurte, TimeGap, Construct, and Reconstruct and an axiom AxiomRe and related inference rules for malicious attacks and security privacy issues in emerging protocols, as well as extending the matching descriptions of protocol behaviours in complex cryptographic algorithms and information sharing techniques for applications for the formal analysis of authentication protocols for the Industrial Internet of Things. Finally, formal analysis is carried out using the example of a secure multi-factor authentication protocol for the industrial IoT, which proves the security of the protocol.