Reducci´ on de dimensi´ on

The performance of the system is illustrated in Tables 3.1 to 3.6. Tables 3.3 and 3.6 show sample results for the authentication system for genuine and impostor users (five tests for each user, each requiring five samples to be provided). In Table 3.3, the observed failure of one modality does not necessarily cause the system as a whole to fail; samples 1 to 3 (face failure) and sample 4 (fingerprint failure) demonstrate the exception-handling potential of the system. As shown in sample 5, multiple failures still lead to overall failure. A summary of the overall performance of the system for all quoted samples, in terms of the false acceptance and false rejection rates of the Shamir component of the system for the three polynomial orders, are shown in Table 3.5.

Table 3.5 FRR and FAR results for authentication.

Linear equation Quadratic equation Cubic equation

FRR 1.8% 4.8% 8,2%

FAR 5.2% 2.59% 0%

Table 3.6 Sample performance for passive forgery. Impostor

user

Claimed Identity for user

Test Face Fingerprint Iris Secret Share Techniques

Thumb Index

finger

Right Left Linear equation Quadratic equation Cubic equation 1 2 1 x √ √ x X √ X X 2 x √ √ x X √ X X 3 x √ √ x X √ X X 4 x X X x X X X X 5 √ X √ √ √ X X X

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Table 3.5 shows the results for three different polynomials of Shamir‘s secret scheme. The linear equation requires at least two points to generate the secret key S. The false rejection rate of 1.8% in the linear equation method is good by comparison with the quadratic and cubic techniques, but it must also be noted that the false acceptance rate is greater (5.2%) by comparison with the other techniques. At 0%, the false acceptance rate for the cubic equation technique is very good, as this technique requires at least four points to generate the secret key S. However, the false rejection rate is relatively high (8.2%). For the quadratic equation technique, the false rejection and acceptance rates are both intermediate. Because this technique requires at least three out of five points to generate the secret key S, it reflects a balanced probability in terms of both FRR and FAR. These results are very interesting, as they demonstrate the relative merits of the polynomial orders when considering the desired performance of the system. However, the outcomes of these tests are in part dependent on the quality of the biometric samples employed and on the algorithms employed for the individual modalities.

3.6 Summary

This chapter has explored the technique of secret sharing to allow an encryption key to be created from multimodal biometric samples. The results show the potential of the system for efficiently deriving encryption keys while also allowing for exception handling, which is currently a significant impediment to the practical deployment of biometric systems. This improved robustness property represents a significant enhancement. A further significant advantage of the proposed technique is that the biometric key itself need not actually be stored, which along with the unlimited length of the biometric encryption key further enhances the security of the system.

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Chapter 4.

Investigations of Iris Direct Key Generation

4.1 Introduction

Biometrically constructed security is theoretically strengthened if an encryption key is extracted directly from biometric samples as provided by a given user. Such a system means that the retained encryption key would not be copied and also a template or reference sample would not be required, significantly enhancing potential system security. However, two probable weaknesses intrinsic to this scheme are that the generated encryption key would not easily be revoked and, where a user is unable to provide a biometric sample, the scheme would not be robust in this condition [41, 44].

This chapter introduces several schemes for integrating direct biometric key generation

schemes with Shamir‘s secret sharing algorithm [11] to directly address these two disadvantages of revocability and exception handling. Within the proposed scheme, individual points on a polynomial curve are directly derived from iris samples taken from an individual by applying a user function, which is created for each user to minimise the amount of data stored and enabling Shamir‘s secret scheme to be applied to derive the required key. The proposal is robust, in that the new technique generates an encryption key from biometric modality samples, using a minimal amount of stored data. The system‘s potential has been investigated in relation to passive forgeries. The current chapter reports preliminary work on how an encryption key may be generated directly from the biometric modality by extracting points on a parabolic curve derived from actual biometric samples. These schemes returned negative results, indicating that the Equal Error Rate (EER) is high or that the level of performance or security is

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low. Each scheme will be presented in detail, including an explanation of how it works, why this scheme might be used, and any feedback from it.

Figure4.1 Three Different Scenarios for Direct Key Generation from Individual ‏Biometric Samples

Figure 4.1 shows how the direct key could be generated from individual biometric

samples applying Shamir‘s secret scheme. Each point in the curve represents a different biometric modality enabling the biometric secret key generated by Shamir‘s

secret scheme. In the field of biometric encryption, this proposal must satisfy security considerations as well as level of performance flexibility. From the security point of view, this scheme uses a multimodal, template-free biometric system, and the length of the biometric encryption key is unlimited because, as shown in Figure 4.1, the y-axis extends to infinity. From a performance perspective, three different techniques using

Shamir‘s secret scheme are presented: Linear, Quadratic, and Cubic equations. For the

multimodal biometric system in this proposal, at least two biometric modality points would be sufficient to release the biometric secret key in the linear equation technique, with three points needed in the quadratic and four points in the cubic.

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