## 3 Integrated Adaptive Security Framework for IoT (IASF-IoT)
### Quantum-Resistant Cryptography Integration  
To future-proof the framework against quantum computing threats, a hybrid approach integrating quantum-resistant cryptography is implemented. This strategy combines classical and post-quantum algorithms, providing a robust defense against current and future cryptographic vulnerabilities. The hybrid model is represented as  
\[E(m)=w1\cdot Ec(m)+w2\cdot Epq(m), \tag{3}\]  
where \(E(m)\) is the encrypted message, \(Ec(m)\) is classical encryption, \(Epq(m)\) is post-quantum encryption, and \(w1\) and \(w2\) are dynamically adjusted weights. This approach maintains compatibility with existing systems while gradually introducing quantum resistance. The weights are calibrated based on the current threat landscape, allowing for adaptive security. Performance analysis shows that post-quantum algorithms generally need larger key sizes and might add in some extra computational overhead compared to their classical counterparts. For instance, lattice-based schemes like NTRU or CRYSTALS-Kyber [64] typically show a 10-20% increase in encryption time and a 20-30% increase in ciphertext size. However, the hybrid approach allows for the fine-tuning of the performance-security trade-off by adjusting the weights. Scalability remains a bit of a concern, particularly for resource-constrained IoT devices, as the increased computational and storage requirements might limit widespread adoption. To potentially address the added computational burden of post-quantum encryption, the proposed framework considers the integration of hybrid cryptographic models that combine classical and quantum-safe algorithms. While the practical implementation of such models remains constrained by the current maturity of quantum-resilient libraries, recent developments--such as the NIST-selected CRYSTALS-Kyber and CRYSTALS-Dilithium schemes--indicate feasible pathways for secure integration. Existing toolkits like the Open Quantum Safe (QQS) project offer partial support for these algorithms, but their adaptation for highly resource-constrained IoT devices is still an active area of research. Accordingly, this study does not claim a working implementation of quantum cryptographic operations. Instead, it focuses on architectural placement, performance modeling, and compatibility analysis as a preparatory step for future PoC development. This simulation-based integration strategy aligns with similar early-stage validation efforts in recent literature, where the full implementation of post-quantum cryptography remains impractical in IoT testbeds. Also, edge security is enhanced by implementing a federated learning approach, allowing edge devices to collaboratively learn a shared prediction model while keeping all training data local. This method is chosen for its ability to maintain data privacy, reduce network bandwidth usage, and enable real-time adaptation to local threats. Federated learning addresses the challenge of data silos in distributed IoT networks and allows for the creation of robust, generalized security models without centralizing sensitive data. The approach is particularly suitable for IoT environments where data privacy regulations or bandwidth limitations prevent traditional centralized learning. The federated learning process is modeled as \[w(t+1)=w(t)-\eta\cdot\frac{1}{n}\sum\
abla Fi(w(t)), \tag{4}\]  
where \(w(t)\) is the model at time \(t\), \(\eta\) is the learning rate, \(n\) is the number of edge devices, and \(Fi(w(t))\) is the local objective function for device \(i\). This iterative process allows the model to improve over time, incorporating insights from diverse edge devices while maintaining their autonomy and data confidentiality. Insights obtained from the federated learning models are periodically fed into the Digital Twin component to improve threat prediction accuracy. This integration allows the Digital Twin simulations to evolve over time, reflecting the learning outcomes from distributed edge observations.