Algebraic topology methods in network security

Attack surfaces are becoming dynamic, communications are increasingly encrypted and coordinated attacks are growing in complexity, creating more challenges for modern network security; traditional graph-based security solutions struggle to see the big picture and understand relationships among entities in the network.To secure the network an effective intrusion detection system, the authors propose a new model for Network Security-Persistent Homology-Based Network Security Model (PHNSM) which combines simplicial complex construction with homology computation, persistent homology, topological feature extraction, and graph neural networks-based threat classification.The proposed model is a multidimensional communication pattern, which is represented algebraically to be used for the effective identification of stealthy and distributed cyber-attacks in the global network, while maintaining the entire network function.Experimental evaluation is able to attain detection accuracy of 94.67%, precision of 94.18%, recall of 93.86%, F1-score of 94.02% and ROC-AUC of 96.08% and a 18.3% reduction in false-positive rate when compared to conventional graphbased security methods.The novelty is that the integration of persistent homology and deep topological learning for a cyber threat analysis with interpretation.The proposed framework provides mathematically sound, scalable and robust approach to anomaly detection, localization of attacks and large scale communication networks.