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(20.7)
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is then used to characterize the intra-class variability of the user s. Speci cally, the BCH code whose ECC is equal to the nearest integer of [Avgs + ECC ], where ECC is a system parameter common to all the enrolled users, is chosen. The selected error correction capability ECCs for the user s is stored in the database. As described in Section 20.2.1.3, the binary vector rs is zero padded in order to reach the same length n of the selected BCH codewords, resulting in the vector xs .
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Figure 20.3. Signature-based fuzzy commitment: Authentication scheme. When a subject claims
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his identity, a response is given using the stored data , RFs , FCs , ECCs , and h(ms ).
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20.2 Signature-Based User-Adaptive Fuzzy Commitment
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The fuzzy commitment FCs is then generated using a codeword cs obtained from the encoding of a random message ms : FCs = FC(xs , cs ) = xs cs . (20.8)
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A hashed version h(ms ) of ms , created using the SHA-1 algorithm, is eventually stored. The proposed framework provides security, being impossible to retrieve fs from the stored templates , RFs , FCs , h(ms ), and ECCs . In fact, in order to infer about the extracted features, or to reconstruct their binary counterparts, it is necessary to possess, among the other data (see Figure 20.1), the BCH codeword cs employed for data protection. However, neither the binary word ms at the input of the BCH encoder nor its output cs are stored. In fact, only the hashed value of ms , generated by means of the hash function h( ), is stored, thus guaranteeing the impossibility to recover useful information from the saved data. Then, as shown in [33], it can be concluded that the disclosure of the secret xs is as dif cult as nding a collision for the SHA-1 hash h(ms ), which leads to the observation that the security of the system is the same of the employed hash function. However, it is worth pointing out that several attacks, being able to generate collisions when using the SHA-1 algorithm and having less computational complexity than the brute force attack, have already been proposed in the literature [91 93] . Therefore, in order to solve this problem and thus to improve the system security for practical application, two novel hash functions could be used in our scheme without affecting its architecture: either the SHA-256 with 32-bit words or the SHA-512 with 64-bit words. The cryptographic security of these hash functions has not been investigated as deeply as the SHA-1 s one; however, no weakness has been found so far.
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Authentication Stage
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The authentication phase follows the same steps as the enrollment stage (see Figure 20.3). When a subject claims his identity, he provides his signature, which is s converted in the features vector . Then the quantization is done using the interf s class mean , thus obtaining b . The reliable features rs are selected using RFs , and later extended using zero padding, generating xs . A binary vector cs , representing a possibly corrupted BCH codeword, results from the XOR operation cs = xs FCs . (20.9)
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The BCH decoder is selected depending on the encoder used in enrollment, obtaining ms from cs . Finally, the SHA-1 hashed version h(ms ) is compared to h(ms ): If both values are identical, the subject is authenticated.
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20.2.3 Signature-Based Fuzzy Commitment: Experimental Results
In this section, an extensive set of experimental results, concerning the performances of the proposed system together with comparisons with other approaches proposed in the literature, are presented. In our experimentations, on-line signatures are acquired using an Interlink Electronics ePad-ink, based on a resistive touchpad with 300 dpi resolution. The proposed approach consists in extracting a number P of parametric features from the acquired signals, further processed as detailed in Section 20.2 to obtain security and renewability of the stored templates. Speci cally, we have rst performed experimentations in order to compare the adaptive approach detailed in Section 20.2.1.4 with the nonadaptive one described in Section 20.2.1.3. Moreover, the proposed approach has been compared with the algorithm proposed in [54], which relies on the processing of parametric features extracted from signatures. The selected feature set, composed by 50 parameters enumerated in Table 20.1, is the same as in [53]. Thirty subjects have been enrolled. Each of them has given 50 signatures that have been recorded at different times in a week time span. As in [53], I = 6 signatures are considered in the enrollment stage. In our experiments we have tested the system performance either with an a priori choice of the BCH correction code or with a user-adaptive BCH code selection. The performances have been assessed using the FRR, FAR, and the receiver operating characteristic (ROC) as gures of merit. More in detail, the FRR has been estimated using for each subject the 44 signatures not used in the enrollment stage. The FAR is referred to conditions of random forgeries [76], indicated as FARRF , and to conditions of skilled forgeries, indicated as FARSF . For each subject, the 50 signatures of all the remaining 29 users are used as random forgeries. When skilled forgeries are considered, a test set of 10 skilled forgeries is created for each subject, using a training time of 10 min for each signature whose original was made available. In our experimental setup, the forgers had the ability to observe the genuine users when signing, in order to gain a better understanding of the signature dynamics. The whole set of the employed BCH codes, with different ECC, is detailed in Table 20.3. In Figure 20.4(a) the system performances using the whole set of features for authentication (P = 50), are given. In order to show the better performances obtainable using the feature selection procedure detailed in Section 20.2.1.2, in Figure 20.4(b) the system performances achieved when a lower number of features are considered (P = 40) are displayed. The results are shown with respect to the ECC employed in the system. The ROC curves in Figure 20.5(a) report the FARSF /FRR system behavior for both P = 50 and P = 40. As can be seen, the achieved equal error rate (EER) is approximately 23% for P = 50 and 22% for P = 40 when considering skilled forgeries. As for random forgeries, the obtained EER is about 10% for P = 50 and 9% for P = 40.
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