A Novel Approach to Secure Distance Matrix Domination in Fundamental Graphs

Abstract

Distance matrix domination in fundamental graphs plays a critical role in various applications, such as network design, communication systems, and social network analysis. Ensuring the security of these distance matrices is essential to protecting the integrity and privacy of the underlying graph structure. This paper presents a novel approach to secure distance matrix domination by integrating advanced cryptographic techniques and privacy-preserving mechanisms.We propose the use of homomorphic encryption to allow computations on encrypted distance matrices, safeguarding data while maintaining functionality. Additionally, secure multi-party computation (MPC) enables collaborative domination in distributed networks without revealing individual node or edge data. To further protect graph structure, we employ graph perturbation techniques and differential privacy, ensuring that sensitive details about the graph are not exposed.Randomized shortest path computations are introduced to obscure direct inferences about the graph's topology, while zero-knowledge proofs (ZKP) allow verification of domination results without revealing the distance matrix. A decentralized framework leveraging blockchain ensures that the domination process remains transparent and secure. Finally, machine learning algorithms are integrated for real-time anomaly detection, enhancing the robustness of the domination process against adversarial attacks.This novel approach enhances the security and privacy of distance matrix domination in fundamental graphs, making it applicable to sensitive and large-scale network environments. The proposed methods ensure both accuracy and confidentiality, offering a significant advancement in secure graph analysis and optimization.