## 5 Experimental Results and Analysis
### Machine Learning-Based Modeling Attacks  
The behavior of the PUFs can be modeled by analyzing their CRPs, thus making them vulnerable to ML attacks. Numerous ML algorithms, such as k-nearest neighbor (KNN), random forest (RF), logistic regression (LR), decision tree (DT), and Support Vector Machine (SVM), have been used to predict PUF responses, with SVMs being widely recommended. The resilience of the PUFs against ML-based attacks is an indicator of their security. The ML model was developed in Python 3.12.3 within a Version Control System (VCS) environment. It began with the collection and preprocessing of APUF CRP data, which is normalized and cleaned to suit ML purposes. Suitable models, such as SVM, LR, or a feedforward artificial neural network (ANN), an MLP model for device classification, supervised random forest clustering for anomaly detection, and an ensemble gradient boosting technique, were \begin{table}
\begin{tabular}{c c c c} \hline \hline
**ML Model** & **Hyperparameters** & **Range** & **Selected Value** \\ \hline SVM & C, \(\gamma\), Kernel & [0.1, 0.2, 0.3, 0.4], & 10, 0.1, RBF \\  & & [0.001, 0.01, 0.1, 1], RBF & 10, 0.1, RBF \\ \hline LR & Regularization C, Max Iterations & [0.001, 0.01, 0.1, 1], & 0.1, 100 \\ \hline MLP & Hidden Layers, Learning Rate, Epoch & [[64, 32], [128, 64], [100]], [0.001, Early Stopping) & [100], 0.01, Early Stopping \\ \hline RF & n\_estimators, max\_depth, criterion & [50, 100, 200], [5, 15, 25], entropy & 100, 15, entropy \\ \hline GB & n\_estimators, learning\_rate, max\_depth, loss & [50, 100, 200], [0.01, 0.05, 0.1], & 100, 0.1, 3, log\_loss \\ \hline \hline \end{tabular}
\end{table} 
Table 5: ML model parameters. Figure 14: Confusion matrix of the proposed models. implemented using Python libraries like scikit-learn, pandas, and pypuf. The workflow proceeds with training and evaluating the model by dividing the data into training and testing sets, refining the model's parameters, and evaluating accuracy metrics to ensure effective generalization to new challenges without overfitting. The extracted CRPs were used to train the intended ML model capable of predicting responses against specific challenges. Table 6 lists the prediction accuracy of APUF-based ML models available in the literature of varying CRP sizes. The results obtained by the researchers establish that accuracy does not significantly increase beyond 80% with additional CRPs, demonstrating the robust defense of the PUFs against such attacks. The linear characteristics of delay-based PUFs, like APUFs, align well with SVM, which is trained on 80% of CRPs to predict specific response bits [140]. It is established that the ML models with an adequate number of CRPs can mimic the target device and gain access to sensitive data [141]. Next, we will discuss the resilience of APUFs against ML attacks, as well as the accuracy of ML models in predicting response outputs for random challenge inputs. The resistance of APUFs to modeling attacks is evaluated to determine how easily an attacker could predict the responses of the PUF based on its challenges. APUF CRPs were collected to test the modeling attack accuracy against various modeling techniques, such as gradient boosting, Multi-Layer Perceptron (MLP), Support Vector Machine (SVM), logistic regression (LR), and random forest, as shown in Figure 15.  
The resilience of a strong PUF against ML attacks is a key indicator of its suitability in a secure IoT network. The resistance against ML attacks on APUF is established using various ML modeling techniques against varying CRP sample sizes, and this is summarized in Table 7. It verifies that the accuracy of SVM, LR, and gradient boosting does not go beyond 63%.