Optimizing Cybersecurity and Risk Management for Intrusion Mitigation in IoT Applications

Abstract

This study presents a C*-algebraic framework for optimizing intrusion mitigation in Internet of Things (IoT)networks by integrating mathematical models for cyberattack propagation with optimization-based security strategies.Theoretical results demonstrate that the spectral radius of the attack operator ρ(A) governs the recovery of IoTnetworks under attack, where ρ(A) < 1 ensures system recovery, and ρ(A) ≥ 1 leads to persistent or growing attackimpact. The framework combines blockchain-based trust, AI-driven intrusion detection systems (IDS), and Zero-TrustArchitecture (ZTA) to provide a multi-layered, adaptive defence system. Unlike probabilistic models that simplifyattack dynamics, this approach rigorously models threats using bounded linear operators, thereby offering scalabilityand robustness. Optimization ensures computational efficiency, making the model suitable for resource-constrained IoTenvironments, with the operator norm and the spectral radius acting as key constraints. Validation on real-worlddatasets such as CIC-IoT2023, UNSW-NB15, and BoT-IoT revealed that the AI-IDS models achieved near-perfectperformance, while the unified model integrating blockchain, IDS, and ZTA showed an accuracy of 51.0