# Cancelable Multimodal Biometrics Based on Chaotic Maps
## 4 Experimentation Results
### Diversity and Revocability Analysis  
To satisfy the requirements of revocability and diversity, the protected template should not match the original template, and it should be sufficiently difficult to recover the raw biometric data when the stored template is disclosed. Additionally, matching should not exist between multiple protected templates using the same features in order to avoid cross-matching between different databases. The diversity criterion is evaluated by generating various templates from a single biometric datum using diverse keys and measuring the feasibility to recover the original biometric features when using different keys to decrypt the protected templates. To implement this scenario, a new database of protected templates was generated. The proposed system efficiently denied user attempts to gain access when the key is different, categorizing the attempt as an illegal intrusion.  
We also evaluated the ability to produce revocable templates for each subsystem. In the fingerprint system, we created new protected sets. The key is represented by the values of the transformation matrix (\(a\), \(b\), and \(N\)), the rotation angle, and the scaling factor. The proposed cancelable technique is shown to satisfy this requirement, as illustrated in the following Figures 7-10.  
Figure 7 clarifies that the matching score between the original fingerprint features and the protected fingerprint features is equal to 0.1668. Figures 8 and 9 depict that the matching between templates in the same database is effective, and the transformation process does not deteriorate the recognition rate. Furthermore, it preserves the inter-class and intra-class variations. Figure 10 depicts the matching between two protected templates using different transformation parameters, which is equal to 0.1282. These results are an indication that the effectiveness of the proposed method allows the disassembling of the relation between the original and the protected templates and, additionally, between two protected templates created using different keys.  
Figure 6: The ROC curve of the unimodal face system in the case of stolen-kernel.  
Figure 8: Matching score between two transformed fingerprint templates of the same user in the same database.  
Figure 7: Matching score between original and transformed fingerprint templates.  
Figure 10: Matching score between two transformed fingerprint templates of two different users in the same database.  
Figure 9: Matching score between two transformed fingerprint templates of the same user in two different databases.  
Now, to validate the revocability criterion in the proposed multimodal system, we demonstrate the pseudo-impostor distribution (illustrated in Figure 11) by creating new biometric templates of the same original biometric datum using different keys [27]. Then, the new protected templates are matched with the stored (i.e., enrolled) templates in the database. Obtaining identical EER compared to genuine/impostor authentication is an indicator of attaining good diversity and revocability. The EER is 1.77% for the pseudo-impostor distribution, which reveals a good diversity.