This study introduces the Quantum-Resistant Federated Anomaly Detection (QRFAD) framework, a novel approach for addressing the challenges of anomaly detection in Identity and Access Management (IAM) systems in the face of evolving cyber threats and emerging quantum computing risks. By combining federated learning, quantum-resistant cryptography, and Agentic AI, QRFAD overcomes the limitations of traditional anomaly detection models, such as LSTM and SVM. The framework ensures a scalable, secure, and privacy-preserving solution that enables multiple organizations to collaboratively train models without sharing sensitive data. Key performance metrics, including precision, recall, F1-score, latency, and scalability, were evaluated on the ICS-Flow dataset, demonstrating that QRFAD significantly outperformed the LSTM and SVM models. Specifically, QRFAD achieved a precision of 0.94, recall of 0.91, and F1-score of 0.92, all higher than the LSTM (0.85, 0.83, 0.84) and SVM models (0.78, 0.75, 0.76). Moreover, QRFAD reduced the latency by 35.71\% (75 ms vs. 120 ms) and improved the model update overhead by 50\% (1.2s vs. 2.5s). This work addresses key gaps in the literature related to scalability, quantum threats, and autonomous decision-making, providing an adaptive and secure IAM solution capable of evolving with emerging cyber threats.
This paper presents a novel approach to cybersecurity risk management through the development of a cascading risk model that simulates the propagation of risks across interconnected systems and evaluates mitigation strategies. Unlike traditional linear risk models, the proposed model integrates nonlinear wave decomposition and adaptive control mechanisms to capture the dynamic and evolving nature of cybersecurity threats. The model was validated using data from both the Kaggle Cyberattack Dataset and the National Vulnerability Database (NVD), demonstrating its ability to accurately model cascading risks and assess the effectiveness of mitigation measures. The simulation results show significant reductions in risk propagation, with mitigation strategies reducing the overall risk by up to 42% for certain attack types. The findings underscore the model’s ability to address gaps in existing cybersecurity frameworks by providing real-time adaptive risk management in complex, interdependent environments. This work offers a scalable solution for improving cybersecurity resilience in modern infrastructure and IoT ecosystems.
This study presents a mathematical model using non-homogeneous heat equations with dynamic boundary conditions to simulate the spread and mitigation of cybersecurity threats. Our results demonstrate that incorporating adaptive boundary conditions, which represent real-time adjustments to defense mechanisms, improves the robustness of cybersecurity systems against evolving threats. Stability analysis using the Lyapunov criterion shows that the system remains stable over time, with the vulnerability (represented by the Lyapunov function) decreasing as time progresses. Numerical simulations indicate that varying the intensity of cyber-attacks and adjusting boundary conditions dynamically leads to more efficient and effective defense strategies, optimizing both computational load and system security. The mathematical model, validated through several test cases, reveals that dynamic adaptation of defense mechanisms significantly outperforms traditional static models, offering scalable solutions for real-time cyber defense. Furthermore, our results demonstrate the model's ability to simulate the impact of network topology changes and varying attack intensities, providing insights into how network configurations influence the propagation of vulnerabilities.
This paper presents a novel framework for addressing code-level vulnerabilities in critical applications by combining formal verification with risk scoring systems. It ensures the correctness and reliability of code while prioritizing vulnerabilities based on exportability and impact. The approach is applied to high-stakes industries such as healthcare, aerospace, and industrial control, where system failures can have catastrophic consequences. A numerical example demonstrates a 22% reduction in risk (from 1.905 to 1.485) within budgetary constraints. Results show that this combined method offers a robust, cost-efficient solution for improving security, making it practical for real-world deployment. The framework emphasizes risk reduction and cost optimization in resource-constrained environments.
This study addresses an inverse problem for a time-fractional heat equation involving the Caputo derivative, where the objective is to determine an unknown time-dependent thermal coefficient. The governing equation incorporates a fractional order time derivative, a spatially dependent diffusion term, and a known source term. To solve the inverse problem, we employ the Laplace Homotopy Analysis Method (LHAM)—a semi-analytical approach that combines the Laplace transform with the Homotopy Analysis Method. This technique allows for the construction of a convergent series solution for both the temperature distribution and the unknown coefficient . By appropriately selecting the initial guess , the convergence-control parameter h becomes embedded in the solution process, reducing com-computational effort. The proposed method is validated through an illustrative example, demonstrating the effectiveness and accuracy of LHAM in solving time-fractional inverse problems with a source term.
