It is crucial to improve the robustness of the IoT against malicious attacks. For scenarios where the network topology is split due to malicious attacks, but can still reconnect fragmented networks by adjusting links between nodes, existing algorithms offer limited robustness improvements, exhibit high computational complexity, incur significant energy consumption, and produce optimized network topologies lacking scalability. To address these issues, we propose a network robustness optimization algorithm called the ’Recovery Algorithm’. Based on this algorithm, the IoT can automatically adjust its topology to effectively resist malicious attacks. Compared with other algorithms, the optimized network of this algorithm possesses higher robustness and higher communication efficiency without affecting the scalability of the original network. Furthermore, the computational complexity and energy consumption of this algorithm are several orders of magnitude lower than existing algorithms.

Federated learning (FL) has emerged as a promising technique in the Industrial Internet of Things (IIoT) by enabling distributed devices to collaboratively train models without sharing raw data. In FL, ensuring data privacy and secure authentication becomes essential due to the sensitivity of industrial data and the potential for adversarial attacks. This paper highlights a security flaw in a recently proposed FL authentication protocol designed for IIoT environments. Specifically, the scheme is analyzed to be susceptible to public-key replacement attacks. We propose a secure, lightweight authentication scheme for privacy-enhanced federated learning (SLAPE) to address vulnerabilities in participant registration, group key distribution, local data training, and aggregation processes. SLAPE leverages the Elliptic Curve Cryptography with the Chinese Remainder Theorem to support malicious group member traceability, revocation of compromised identities, and efficient batch verification of multiple messages. It effectively resists Type-I attacks that previous schemes could not, while also incorporating forward and backward security essential for IIoT applications. We rigorously demonstrate SLAPE’s resilience against prevalent threats through both formal and informal analyses. Our evaluation results indicate that SLAPE demonstrably enhances the security and privacy of existing schemes, with improvements in computational efficiency for both proof generation and verification, while keeping communication overhead relatively low.

Cheeger’s inequality is used to estimate a lower bound on the number of edges that need to be cut off to split a regular graph into two subgraphs with the same number of nodes. Therefore, we design a network topology that is robust under malicious attacks based on Cheeger’s inequality. Considering that Cheeger’s inequality cannot be directly used to optimize complex networks in reality, we generalize the conclusion of Cheeger’s inequality and use this conclusion to propose the Good Regular Graph algorithm (GRG) for generating strongly robust network topologies under malicious attacks. In addition, we explain the design principle of the algorithm from a graph-theoretic perspective and give the corresponding network topology expansion algorithm. GRG, after appropriate processing, can be applied to optimize the substructures of a wide range of real-world network topologies to enhance their robustness. Experiments show that the algorithms proposed in this research perform better compared to other algorithms. We prove from both theoretical and experimental perspectives that Cheeger’s inequality can serve as a basis for designing robust network topologies under malicious attacks.