# Challenge-Response Pair Mechanisms and Multi-Factor Authentication Schemes to Protect Private Keys
## 4 Experimental Section and Analysis
### Combination of Multiple Factors
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Gender** & **Age Range** & & **Skin Tone** & **True (\%)** & **False (\%)** \\ \hline \multirow{8}{*}{Female} & \(\bullet\) & Yellow Level \(-\)10 & 94.28 & 5.72 \\  & \(\bullet\) & Dark Brown Level \(+\)15 & 98.33 & 1.67 \\  & 20–34 & \(\bullet\) & Black Level \(+\)25 Yellow Level \(-\)15 & 93.33 & 6.67 \\  & \(\bullet\) & Yellow Level \(+\)20 & 94 & 6 \\  & \(\bullet\) & Light Brown Level \(+\)10 & 95.38 & 4.62 \\ \hline \multirow{8}{*}{Female} & \(\bullet\) & Yellow Level \(-\)10 & 100 & 0 \\  & \(\bullet\) & Dark Brown Level \(+\)15 & 91.67 & 8.33 \\  & \(\bullet\) & Black Level \(+\)25 Yellow Level \(-\)15 & 95 & 5 \\  & \(\bullet\) & Yellow Level \(+\)20 & 95.71 & 4.29 \\  & \(\bullet\) & Light Brown Level \(+\)10 & 94.55 & 5.45 \\ \hline \multirow{8}{*}{20–34} & \(\bullet\) & Yellow Level \(-\)10 & 95 & 5 \\  & \(\bullet\) & Dark Brown Level \(+\)15 & 92.22 & 7.78 \\  & \(\bullet\) & Black Level \(+\)25 Yellow Level \(-\)15 & 91.78 & 8.22 \\  & \(\bullet\) & Yellow Level \(+\)20 & 90 & 10 \\  & \(\bullet\) & Light Brown Level \(+\)10 & 98.57 & 1.43 \\ \hline \multirow{8}{*}{Male} & \(\bullet\) & Yellow Level \(-\)10 & 93.33 & 6.67 \\  & \(\bullet\) & Dark Brown Level \(+\)15 & 95.38 & 4.62 \\  & \(\bullet\) & Black Level \(+\)25 Yellow Level \(-\)15 & 98.61 & 1.39 \\  & \(\bullet\) & Yellow Level \(+\)20 & 96.67 & 3.33 \\  & \(\bullet\) & Light Brown Level \(+\)10 & 96 & 4 \\ \hline \multirow{8}{*}{Male} & \(\bullet\) & Yellow Level \(-\)10 & 95 & 5 \\  & \(\bullet\) & Dark Brown Level \(+\)15 & 89.23 & 10.77 \\ \cline{1-1}  & \(\bullet\) & Black Level \(+\)25 Yellow Level \(-\)15 & 96.37 & 3.64 \\ \cline{1-1}  & \(\bullet\) & Yellow Level \(+\)20 & 96.67 & 3.33 \\ \cline{1-1}  & \(\bullet\) & Light Brown Level \(+\)10 & 92 & 8 \\ \hline \multirow{8}{*}{51–65} & \(\bullet\) & Yellow Level \(-\)10 & 97 & 3 \\ \cline{1-1}  & \(\bullet\) & Dark Brown Level \(+\)15 & 98.18 & 1.82 \\ \cline{1-1}  & \(\bullet\) & Black Level \(+\)25 Yellow Level \(-\)15 & 100 & 0 \\ \cline{1-1}  & \(\bullet\) & Yellow Level \(+\)20 & 89.33 & 10.67 \\ \cline{1-1}  & \(\bullet\) & Light Brown Level \(+\)10 & 94.55 & 5.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Verification percentage based on gender, age, and skin tone. The observed variations are not statistically significant and are well within the expected range. same fragmentation level, we observe that the wrong person is positively detected only 1.01% of the time, while correctly rejected 98.98% of the time. This is extremely promising, as, in this test case scenario, we are assuming that the attacker will have the tokenized PUF, VT token, and password in their possession and that the authentication will solely rely on biometric information. Figure 12 illustrates the distribution of stable \"1\" and \"0\" and unstable \"X\" values obtained after compiling the results of 1970 verification cycles performed on 6000 images, generating 1970 reference tables across five different fragmentation levels. The number of flaky or unstable cells is around 50%. This indicates that, during the seed generation for digital signing, we need to select more cells to obtain at least 256 stable cells. This does not compromise the security at all, as we are selecting both stable and unstable cells in this process and also utilizing the unstable state as information. Later, we only take 256 bits from the stable cells, and we utilize the password as the seed for the selection process of these 256 bits, as, for verification, the server and the client need to have same password. Figure 13 shows the latency of the RBC error correction process. When there is no error, fragmentation level 1--treating the entire seed as a single block--is the optimal choice. However, as the error rate increases, the latency rises exponentially. Additionally, for higher error rates, the fragmentation level hits a 5 s cap. This occurs because our test considers a verification attempt failed if it reaches the 5 s limit.