# Pitfall of the Strongest Cells in Static Random Access Memory Physical Unclonable Functions
## 4 Proposed New Fuzzy Extractor
### ERFE Architecture
These chips have three independent SRAM arrays as shown in Figure 8. The size of the SRAM1 and SRAM3 were 2048 \(\times\) 32, whereas the size of the SRAM2 was 512 \(\times\) 32. These SRAM blocks are standard components provided by the foundry, compiled by the memory compiler. These SRAMs are powered by the low dropout regulator (LDO) of the ASIC. The power supply range of the chip is 1.65 to 5.5 V. The LDO output is 1.62 to 1.98 V. The max supply voltage drop of these SRAMs is 30 mV. These three SRAMs were used to generate CRPs, and we used the last 32 \(\times\) 32 blocks for experiments. The experimental platform, as shown in Figure 9, included the following equipment:

(1) A desktop computer responsible for data receipt and analysis, and (2) a test-board with a USB-to-RS232 cable responsible for transmitting the power-on value of the test chip. When the power is on, the test-board sends three SRAMs' power-on values to the desktop. After the transmission is over, turn the power off, and wait for more than five minutes to turn power on. Next, perform the transmitting again until all 100 samples are generated. The five-minute waiting time between two transmissions ensures that there is no residual charge affecting the power-on value. The test temperature was 25 \({}^{\circ}\)C. After all samples are transmitted, they are processed and analyzed on a desktop. \(C_{rep}(5,1,2)\) was chosen for the cloning experiment. Figure 8: The layout and photograph of test chip (**a**) layout and (**b**) photograph. Figure 9: Experimental platform for verification of the proposed methods. ### Characteristics of the Power-on Value of SRAMs

Intra distance is the difference between two responses of one SRAM, and the maximum intra distance can be considered as an observed value of \(p_{b}\). Inter distance is the difference between two samples of two different SRAM. Table 2 shows two distances of the tested SRAMs. The weighted sum \(P\) is calculated by 100 response samples according to Equation (5), and Table 3 shows the distribution. The corresponding metastable bits with \(0<P<1\) are 34.18, 28.13 and 14.26% respectively. The stable-0 bits with \(P=0\) are 34.18%, 40.72% and 44.14%, respectively. The stable-0 bits in the three SRAMs are slightly higher than stable-1 bits. ### Weak Responses

Figure 10 shows the maximum, average and minimum value of \(q_{y0}\) in 100 responses. The maximum value for SRAMs are 65.8%, 73.1% and 59.0% respectively. Using the response with maximum \(q_{y0}\) will lead to zero leftover entropy in the reconstruction phase according to Equation (2). Table 4 shows the distribution of \(q_{y0}\) in 100 samples. A response with \(q_{y0}>57.4\%\) is considered weak response, and the distribution of weak responses in SRAMs is 7.8%, 6%, 1.2% respectively. From \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multicolumn{2}{c}{**SRAM1**} & \multicolumn{2}{c}{**SRAM2**} & \multicolumn{2}{c}{**SRAM3**} \\ \cline{2-6}  & **Min** & **Max** & **Min** & **Max** & **Min** & **Max** \\ \hline Intra distance & 0.5\% & 11.7\% & 0.2\% & 13.4\% & 0.4\% & 7\% \\ Inter distance & 44\% & 53\% & 48\% & 50\% & 49\% & 52.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Intra distance and inter distance of test SRAMs. Figure 10: \(q_{y0}\) for the tested SRAMs. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(P\) & **SRAM1** & **SRAM2** & **SRAM3** \\ \hline
0 & 34.18\% & 40.72\% & 44.14\% \\
0 \(<P<0.1\) & 8.98\% & 4.30\% & 3.42\% \\
0.1 \(<P<0.3\) & 1.56\% & 1.56\% & 1.27\% \\
0.3 \(<P<0.7\) & 3.91\% & 4.79\% & 4.10\% \\
0.7 \(<P<0.9\) & 2.34\% & 0.98\% & 1.27\% \\
0.9 \(<P<1\) & 17.38\% & 16.50\% & 4.20\% \\
1 & 31.64\% & 31.15\% & 41.60\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Distribution of the weighted sum of responses. the statistical results, the weak responses appear randomly, and the probability of its occurrence is large.