# 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
#### 4.2.3 Size and Execution Time Performance  
Table 2 shows the size performance of our proposals based on Classic McEliece mceliece348864 and mceliece6688128 parameter sets compared to other post-quantum biometric protection schemes from the literature. These proposals are based on a combination of homomorphic encryption and lattice-based cryptography. Our proposal was the best one in terms of the ratio between protected and unprotected feature sizes. The last row illustrates the total size of protected features for 1000 users. This proves that the communication and storage overheads of protected features with our proposal are lower.  
Table 3 shows the execution times required by the operations of mceliece348864 and mceliece6688128 parameter sets in the platforms described in Section 4.1. These results prove that the authentication of a user can be carried out in real time.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Database** & **Representation** & **Protection** & **Accuracy (\%)** & **FAR (\%)** & **FRR (\%)** \\ \hline \multirow{4}{*}{FERET} & Floating-point & No & 99.2 & 1.15 & 1.15 \\ \cline{2-6}  & Binary & No & 98.9 & 1.69 & 1.69 \\ \cline{2-6}  & Binary & mceliece348864 & 99.8 & 0 & 1.69 \\ \cline{2-6}  & Binary & mceliece6688128 & 99.8 & 0 & 1.69 \\ \hline \multirow{4}{*}{LFW} & Floating-point & No & 99.3 & 0.83 & 0.83 \\ \cline{2-6}  & Binary & No & 99.2 & 1.18 & 1.18 \\ \cline{2-6}  & Binary & mceliece348864 & \(\sim\)100 & 0 & 1.18 \\ \cline{2-6}  & Binary & mceliece6688128 & \(\sim\)100 & 0 & 1.18 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Recognition performance of FaceNet embeddings.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Proposal** & Ideal Lattices [8] & R-LWE [8] & R-LWE [9] & M-LWE [10] & M-LWR [10] & mceliece348864 & mceliece6688128 \\  & & 80 & 80 & 128 & 128 & 256 & 128 & 256 \\ \cline{2-6}
**Unprotected Feature** & \multirow{2}{*}{256} & \multirow{2}{*}{256} & \multirow{2}{*}{48} & \multirow{2}{*}{48} & \multirow{2}{*}{48} & \multirow{2}{*}{48} & \multirow{2}{*}{48} & \multirow{2}{*}{48} \\
**Size (bytes)** & & & & & & & \\ \cline{2-6}
**Protected Feature** & \multirow{2}{*}{19,456} & \multirow{2}{*}{31,744} & \multirow{2}{*}{5632} & \multirow{2}{*}{2181} & \multirow{2}{*}{3133} & \multirow{2}{*}{192} & \multirow{2}{*}{208} \\
**Size (bytes)** & & & & & & \\ \hline
**Protected Feature** & \multirow{2}{*}{76.0} & \multirow{2}{*}{124.0} & \multirow{2}{*}{117.3} & \multirow{2}{*}{45.4} & \multirow{2}{*}{62.3} & \multirow{2}{*}{4.0} & \multirow{2}{*}{4.3} \\
**Size/Unprotected Feature** & \multirow{2}{*}{19,000} & \multirow{2}{*}{31,000} & \multirow{2}{*}{5500} & \multirow{2}{*}{2130} & \multirow{2}{*}{3060} & \multirow{2}{*}{187.5} & \multirow{2}{*}{203.1} \\
**Feature Size** & & & & & & \\ \hline
**Total Feature Size of** & \multirow{2}{*}{19,000 Users (Kbytes)} & \multirow{2}{*}{31,000} & \multirow{2}{*}{5500} & \multirow{2}{*}{2130} & \multirow{2}{*}{3060} & \multirow{2}{*}{187.5} & \multirow{2}{*}{203.1} \\
**1000 Users (Kbytes)** & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Size performance comparison of post-quantum biometric protection proposals based on homomorphic encryption.