## 4 DRAM Experiments and Observations  
In this section, we present DRAM PUF implementation results and check the behavior of responses that are generated using latency-based technologies (i.e., \(\text{t}_{\text{RCD}}\) and \(\text{t}_{\text{RP}}\) PUFs). The experimental evaluations are conducted using a DDR3 DRAM module. Figure 5 shows our experimental setup. We examine the characteristics of both latency PUFs to make a better decision considering the CNN requirements. We read DRAM values in different conditions to evaluate the robustness and uniqueness of DRAM blocks.  
Table 1 shows the parameter values of our experiments that are the same for both evaluated structures. To measure the robustness of each PUF, we extract multiple responses over several iterations at varying temperatures (25-55 \({}^{\circ}\)C). Figure 5(a) shows the intra-Jaccard  
Figure 4: The authentication phase includes communication process and verification steps in the server.  
Figure 5: Experimental setup.  
of PUF responses using both \(\mathrm{t_{RCD}}\) and \(\mathrm{t_{RP}}\) reduction-based methods. The intra-Jaccard index determines the similarity of two PUF responses for the same challenge. This is calculated as \(\frac{\mathrm{R_{1}}\cap\ \mathrm{R_{2}}}{\mathrm{R_{1}}\cup\ \mathrm{R_{2}}}\) for two sets of responses, where \(\mathrm{R_{1}}\cap\ \mathrm{R_{2}}\) indicates the size of the shared failures and the \(\mathrm{R_{1}}\cup\ \mathrm{R_{2}}\) is the total number of failures in \(\mathrm{R_{1}}\) and \(\mathrm{R_{2}}\). A Jacard index close to 1 shows the more similarity between \(\mathrm{R_{1}}\) and \(\mathrm{R_{2}}\). In this work, this metric is used to check the repeatability and robustness of DRAM PUF responses. These results are based on the average values that we have gathered by checking multiple samples at each temperature. We also have tested the sensitivity of PUF responses to temperature variations by intra-HD calculations; the results are shown in Figure 6b, indicating the reliability of DRAM PUF responses and also the similarity of samples creating a class. Another principal factor affecting the performance of deep PUF is uniqueness, which measures the difference between failure distributions into two different memory blocks. We have analyzed this factor by comparing multiple samples belonging to various blocks of the DRAM module using inter-HD. Table 2 presents the average uniqueness for \(\mathrm{t_{RCD}}\) and \(\mathrm{t_{RP}}\)-based methods considering the average number of bit failures in each block.  
\begin{table}
\begin{tabular}{c c} \hline \hline Reduced time & 5 ns \\ Block size & 200 Kb \\ Input pattern & All “1” s \\ Block address & Various \\ Number of tested blocks & 200 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental parameters used for \(\mathrm{t_{RCD}}\) and \(\mathrm{t_{RP}}\) reduction-based DRAM PUFs.  
Figure 6: (**a**) Distributions of intra-Jaccard indices calculated between responses for \(\mathrm{t_{RCD}}\) and \(\mathrm{t_{RP}}\) PUFs. (**b**) The average intra-Hamming distance (HD) for \(\mathrm{t_{RCD}}\) and \(\mathrm{t_{RP}}\) PUFs with different temperatures (reference temperature is 25 \({}^{\circ}\)C).  
After analyzing the robustness and uniqueness for both t\({}_{\text{RCD}}\) and t\({}_{\text{RP}}\) PUFs, we realize that they have desirable characteristics to develop a classifier and organize deep PUF. These characteristics include the similarity among the samples into each class and variety among samples from different classes. Table 3 summarizes the generic HD values for stable and unstable conditions, which can be two possible scenarios during a deep PUF configuration. We focus on the t\({}_{\text{RCD}}\)-based PUF that comparatively has more intra-class consistency.