# Multimodal Biometric Template Protection Based on a
## 7 Conclusions  
In this paper, we propose a deep-learning-based multimodal cancelable biometrics scheme which we call CSMoFN. Our scheme fuses two biometric traits, namely the face and the periocular region, and is composed of three modules: a feature extraction and fusion module, a PSMoT module, and an MDC module. CSMoFN is trained by minimizing the ArcFace loss and the pairwise angular loss. Experiments were conducted on six datasets, with the verification performance approximately preserved with respect to its original counterpart. In addition, we have analyzed four conditions for our cancelable biometrics scheme and have shown that the proposed method satisfies them. In future research, we will consider more than two biometric modalities. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Datasets** & \(q\) & \(m\) & \(UB_{imp}\) & \(\tau\) & \(q^{m}\) & \((\tau-UB_{imp})\) & **Total Attack Complexity** & **GAR** \\ \hline AR & & & 0.783 & 0.821 & & 0.038 & \(\approx\)\(2^{117}\) & \\ Ethnic & & & 0.771 & 0.805 & & 0.034 & \(\approx\)\(2^{104}\) & \\ Facescrub & \multirow{2}{*}{26} & \multirow{2}{*}{512} & 0.789 & 0.824 & \multirow{2}{*}{\(2^{6\times 512}=2^{3072}\)} & 0.035 & \(\approx\)\(2^{108}\) & \\ IMDB Wiki & & & 0.792 & 0.817 & & 0.025 & \(\approx\)\(2^{77}\) & \\
**Pubfig** & & & 0.784 & 0.811 & & 0.027 & \(\approx\)\(2^{83}\) & \\ YTF & & & 0.785 & 0.818 & & 0.033 & \(\approx\)\(2^{101}\) & \\ \hline AR & & & 0.783 & 0.807 & & 0.024 & \(\approx\)\(2^{74}\) & \\ Ethnic & & & 0.771 & 0.790 & & 0.019 & \(\approx\)\(2^{58}\) & \\ Facescrub & \multirow{2}{*}{26} & \multirow{2}{*}{512} & 0.789 & 0.811 & \multirow{2}{*}{\(2^{6\times 512}=2^{3072}\)} & 0.022 & \(\approx\)\(2^{68}\) & \\ IMDB Wiki & & & 0.792 & 0.805 & & 0.013 & \(\approx\)\(2^{40}\) & \\
**Pubfig** & & & 0.784 & 0.798 & & 0.014 & \(\approx\)\(2^{43}\) & \\ YTF & & & 0.785 & 0.802 & & 0.017 & \(\approx\)\(2^{52}\) & \\ \hline AR & & & 0.783 & 0.794 & & 0.011 & \(\approx\)\(2^{34}\) & \\ Ethnic & & & 0.771 & 0.785 & & 0.014 & \(\approx\)\(2^{43}\) & \\ Facescrub & \multirow{2}{*}{26} & \multirow{2}{*}{512} & 0.789 & 0.803 & \multirow{2}{*}{\(2^{6\times 512}=2^{3072}\)} & 0.014 & \(\approx\)\(2^{48}\) & \\ IMDB Wiki & & & 0.792 & 0.787 & & \(-\)0.005 & \(N/A\) & \\ Pubfig & & & 0.784 & 0.786 & & 0.002 & \(\approx\)\(2^{6}\) & \\ YTF & & & 0.785 & 0.791 & & 0.006 & \(\approx\)\(2^{18}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Complexity of the false acceptance attack on the proposed system. **Author Contributions:** Conceptualization, J.K. and A.B.J.T. ; methodology, J.K.; software, J.K. and Y.G.J. ; validation, J.K. and A.B.J.T. ; formal analysis, J.K.; investigation, J.K.; resources, J.K. and Y.G.J. ; data curation, J.K.; writing--original draft preparation, J.K.; writing--review and editing, J.K. and A.B.J.T. ; visualization, J.K.; supervision, A.B.J.T. ; project administration, A.B.J.T. ; funding acquisition, A.B.J.T. All authors have read and agreed to the published version of the manuscript. This work was supported by a grant from the National Research Foundation of Korea (NRF), funded by the Korean government (MSIP) (no. NRF-2019R1A2C1003306). **Infrared Consent Statement:** Not applicable. **Data Availability Statement:** Publicly available datasets (AR dataset) were analyzed in this study. This data can be found here: [[https://www2.ece.ohio-state.edu/~aleix/ARdatabase.html](https://www2.ece.ohio-state.edu/~aleix/ARdatabase.html)]([https://www2.ece.ohio-state.edu/~aleix/ARdatabase.html](https://www2.ece.ohio-state.edu/~aleix/ARdatabase.html)) (accessed on 10 February 2022).