## 4 Test Result
### Results and Discussion  
The results of the statistical fault injection testing using the ACMFI tool are summarized in Table 3. The table includes resource information, the fault injection range, the test results, and the final SER estimation results for the four target security circuits (AES, SHA, RSA, and DES). To calculate the \(SER_{est}\), as determined in this study, we utilized the \(SER_{bit}\) values from reports and papers conducted on the same 28-nm Zynq-7000 series board. Using linear regression analysis of AVF, according to DUT coverage, we have confirmed that the ACMFI tool developed in this study can mitigate the side effect problem. The side effect problem occurs when the AVF falls below the ideal result due to defect injection into an area other than the specific target intended for analysis. With the ACMFI tool developed in this study, we were able to address this issue by intentionally injecting defects into specific target locations within the device under test (DUT). Figure 12 displays AVF values according to DUT coverage for the AES circuit. DUT coverage refers to the range of the target DUT versus the range of the defect injection. Figure 11: Open-source-based ATPG system architecture. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & **Information** & **AES128** & **DES** & **SHA** & **RSA** \\ \hline \multirow{4}{*}{Resource} & FF & 4802 & 0 & 6244 & 2926 \\  & LUT & 2926 & 1102 & 6488 & 7143 \\  & BRAM & 99.5 & 0 & 1.5 & 1.5 \\ \hline \multirow{4}{*}{Test Setting} & Test Vector & 3092 & 87 & 1000 & 52 \\  & X\_L & 26 & 36 & 24 & 52 \\  & Y\_L & 100 & 108 & 44 & 50 \\  & X\_H & 66 & 49 & 46 & 92 \\  & Y\_H & 124 & 128 & 72 & 75 \\  & Number of CM bits & 65,600 & 18,816 & 69,536 & 42,688 \\  & CI & 95\% & 95\% & 95\% & 95\% \\ \hline \multirow{4}{*}{Test Results} & Total Test & 8378 & 6359 & 8439 & 7840 \\  & Normal & 7784 & 6300 & 7420 & 6962 \\ \cline{1-1}  & Failure & 543 & 59 & 1010 & 878 \\ \cline{1-1}  & AVF & 6.52\% & 0.93\% & 11.98\% & 11.20\% \\ \hline \multirow{4}{*}{SER Estimation} & Atmospheric Neutron \({}^{1}\) & 2.23 & 0.32 & 4.10 & 3.84 \\ \cline{1-1}  & Thermal Neutron \({}^{1}\) & 4.67 & 0.67 & 8.59 & 8.03 \\ \cline{1-1}  & Alpha Particle \({}^{1}\) & 15.98 & 2.27 & 29.35 & 27.44 \\ \hline \hline \end{tabular} \({}^{1}\) Ref [39].  
\end{table} 
Table 3: Soft error rate estimation. The higher the DUT coverage, the smaller the side effect. The graph reveals two key findings. Through the linear regression of the AVF values, with respect to DUT coverage, the equation \(y=0.0656x-0.0002\) was derived, and the coefficient of determination (\(R^{2}\)) was found to be 0.9757. This high \(R^{2}\) value signifies a strong linear relationship between DUT coverage and AVF values, indicating that higher DUT coverage leads to more accurate AVF estimations. This observed trend is also consistent with the results of other studies conducted under similar experimental conditions. This is a study that performed a neutron beam test by synthesizing a AES circuit [36; 42; 43; 44]. Beam testing was performed on the entire memory, but the bitstreams synthesized in the memory were different depending on the option. Using this, the DUT coverage was obtained, and the corresponding AVF results are summarized in Figure 12. Looking at the graph in Figure 12, we can see that the AVF increases according to DUT coverage. In this study, to perform reliability analysis on the target board, we applied reliability modeling following an exponential distribution using the obtained \(SER_{est}\)[31]. Since the  
Figure 12: DUT coverage and AVF comparison graph [36; 42; 43; 44]. target board was a single board without redundancy, we used exponential distribution reliability modeling with a constant failure rate (\(\lambda\)). The failure rate was directly derived from the formula \(\lambda=1/MTTF\), where \(MTTF\) stands for mean time to failure, and this could be replaced by SER (\(\lambda=SER\)).