# Post-Quantum Biometric Authentication Based on Homomorphic Encryption and Classic McEliece
## 4 Practical Realization of the Proposed Biometric Protection Scheme for Facial Recognition
### Experimental Results
#### 4.2.4 Security Performance  
The framework proposed in [42] was applied to evaluate unlinkability and revocability. Unlinkability is evaluated by considering the distributions of mated and non-mated instances. Revocability is evaluated by considering the distributions of the same sample and non-mated instances. Distributions of mated instances are generated by genuine comparisons of protected features from the same instance created by using different feature transformations (different embeddings from the same individual, different secret paddings and different random positions). Distributions of non-mated instances are generated by impostor comparisons of protected features from different instances created by using different feature transformations (different embeddings from different individuals, different secret paddings and different random positions). Distributions of same samples are generated by genuine comparisons of protected features from the same sample created by using different feature transformations (same sample, different secret paddings and different random positions). These distributions must coincide to prove unlinkability and revocability scenarios. Figure 6 shows that unlinkability and revocability were satisfied for the distributions in the LFW database by considering protection based on the Classic McEliece mceliece6688128 parameter set (similar results were obtained with mceliece348864 parameter set). The LFW database was selected for this evaluation because the numbers of samples and comparisons are higher.  
The resistance to similarity-based attacks in case protected features could be accessed was evaluated using the method described in [12]. This method considers that protected biometric features are secure if there is no correlation between the distances of the impostor comparisons in the protected and in the unprotected domains. The results obtained for the LFW database by considering protection based on the mceliece6688128 parameter set (similar results were obtained with mceliece348864 parameter set) are shown in Figure 7.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Operations** & **mceliece348864** & **mceliece6688128** \\ \hline Feature extraction, transformation and ENCODE & 25.3 & 55.7 \\ \hline XOR, DECODE and threshold comparison & 36.5 & 85.0 \\ \hline Total & 61.8 & 140.7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Execution times (ms) for the authentication operations.  
Figure 6: Revocability and unlinkability evaluation for the LFW database with Classic McEliece mceliece6688128 parameter set.  
This figure depicts the distances of the impostor comparisons in the protected domain on the vertical axis and the distances of the impostor comparisons in the unprotected domain on the horizontal axis. The figure illustrates that the impostor-protected distances do not change with respect to their impostor-unprotected distances. Therefore, their correlation is quite small, which proves the resistance to similarity-based attacks of our proposal.  
Another issue to consider is the stolen-device scenario. The attacker employs his/her biometrics and the client device of a genuine user extracts the associated embeddings. These embeddings are transformed with the same secret padding and random positions employed to enroll the genuine user. In this scenario, as illustrated in Figure 8 with the comparison of FAR and FRR (DET curve) for the LFW database by considering protection based on the mceliece6688128 parameter set (similar results were obtained with mceliece348864 parameter set), the recognition performance was almost the same as in the unprotected approach.  
Figure 8: DET Curves for the unprotected and the stolen device scenario obtained from LFW database with Classic McEliece mceliece6688128 parameter set.  
Figure 7: Evaluation of the resistance to similarity-based attacks for the LFW database with Classic McEliece mceliece6688128 parameter set.