# Cancelable Multimodal Biometrics Based on Chaotic Maps
## 5 Conclusions and Future Research  
This paper presented a novel cancelable protection approach that ensures the security, revocability, diversity, and performance of a multimodal biometric system based on face and fingerprint templates. In this approach, we used a Logistic map and Torus Automorphism to protect the biometric features. To protect the face features, we used a Logistic map to generate a user-specific kernel. The generated kernel was convolved with the face features via a convolution process. In the proposed procedure, the original face template does not match with the protected templates. To protect the fingerprint features, we used transformation methods which include Torus Automorphism-based shifting, rotation, and scaling. The strong chaotic behavior of the Torus Automorphism resulted in the disassembling of the relationship between the original and the transformed templates. Experiments were conducted using the ORL and FVC2002 DB1 databases. However, extensive experiments are required to validate the effectiveness of the proposed approach.  
With respect to the next step in this research, future work will assess the application of the proposed approach for large-scale biometric databases and for different biometric modalities. In addition, a technique to detect the image noise will be implemented to maintain a high performance rate.  
Conceptualization, S.G., A.W., O.N.; methodology, O.N., S.G.; validation, O.N., A.W.; writing--original draft preparation, O.N.,S.G.; writing--review and editing, S.G., O.N.,A.W.,M.H.; supervision, S.G., A.W., M.H.; funding acquisition, A.W. All authors have read and agreed to the published version of the manuscript.  
This Project was funded by the National Plan for Science, Technology and Innovation (MAARIFAH), King Abdulaziz City for Science and Technology, Kingdom of Saudi Arabia, Award Number (13-INF2114-02).  
Not applicable.  
**Data Availability Statement:** ORL and FVC2002 DB1 databases are publicly available.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Schema**} & \multirow{2}{*}{
\begin{tabular}{c} **Biometric** \\ **Modalitiy** \\ \end{tabular} } & \multirow{2}{*}{**Database**} & \multirow{2}{*}{**Technique**} & \multirow{2}{*}{**Performance**} & \multicolumn{2}{c}{**Requirements**} \\  & & & & & **(S: Security;** \\  & & & & & **D: Diversity;** \\  & & & & & **R: Revocability)** \\ \hline
[9] & Face & ORL & \
\begin{tabular}{c} Biohashing and chaos-based \\ cancelable biometrics \\ \end{tabular} &
\begin{tabular}{c} \(GAR_{PCA}=58.5\%\) \\ \(GAR_{LDA}=67.4\%\) \\ \end{tabular} & S \\ \hline
[11] & Fingerprint & — & \
\begin{tabular}{c} Fingerprint template \\ protection based on chaotic \\ encryption \\ \end{tabular} &
\begin{tabular}{c} \(FAR=10^{-6}\%\) \\ \(FRR=10^{-2}\%\) \\ \end{tabular} & S \\ \hline
[13] & Face & \begin{tabular}{c} Extended Yale B, \\ CMU PIE, FEI \\ \end{tabular} & \
\begin{tabular}{c} Binarization, chaos-based \\ feature permutation, \\ and fuzzy commitment \\ \end{tabular} &
\begin{tabular}{c} \(GAR=96.52\%\) \\ \(GAR=90.7\%\) \\ \(GAR=93.7\%\) \\ \end{tabular} & S, R, D \\ \hline
[15] & Iris & CASIA-IrisV3 & \
\begin{tabular}{c} chaotic encryption-based \\ cancelable IrisCodes \\ \end{tabular} &
\begin{tabular}{c} \(EER=1.17\%\) \\ \end{tabular} & S, R \\ \hline
[16] & Fingerprint, face & \begin{tabular}{c} FVC 2002 DB1, \\ ORL \\ \end{tabular} & \begin{tabular}{c} Multimodal approach based \\ on watermarking and \\ hyper-chaotic map \\ \end{tabular} & \begin{tabular}{c} \(EER=3.87\%\) \\ \end{tabular} & S, D \\ \hline Proposed & Fingerprint, face & \begin{tabular}{c} FVC2002 DB1, \\ ORL \\ \end{tabular} & \
\begin{tabular}{c} Chaos-based cancelable \\ biometrics \\ \end{tabular} &
\begin{tabular}{c} \(EER=0\%\) \\ \end{tabular} & S, D, R \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of the proposed approach with related works.