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In this section the proposed scheme for biometric templates protection is presented. As already mentioned, it is basically based on Juels proposal of fuzzy commitment using error correcting codes [33]. The proposed approach is twofold, allowing the system both to manage cancelable biometrics [87] and to handle the intra-class variability exhibited by biometric signatures. As can be expected from behavioral biometrics, different signature realizations, taken from a user, can exhibit a lot of variability,
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20.2 Signature-Based User-Adaptive Fuzzy Commitment
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Figure 20.1. Signature-based fuzzy commitment: Enrollment scheme. The acquired data are
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analyzed, quantized and summed to error correcting codes. The stored data are , RFs , FCs , ECCs , and h(ms ).
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mainly due to lack of user s habit and to the different conditions of execution (seated or standing position, wide or narrow area for resting the arms, etc.). The signature variability is here handled by considering the obtained templates as noisy versions of the ideal template, where the noise power is related to the actual signature deviation from the noise free template. The schemes of the proposed enrollment and authentication procedure are illustrated in Figures 20.1 and 20.3, respectively.
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Enrollment Stage
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The proposed enrollment scheme is presented in Figure 20.1. In brief, during the enrollment phase, a number I of signatures are recorded for each subject s. Some features, properly chosen, are extracted from the signatures acquired from the user s and collected in the vectors fs , i = 1, . . . , I, which are then binarized using the i intra-class s and the inter-class vector mean, which are stored in the template regarding the user s. Then, for each subject s, only the most reliable features are selected, their indices are saved, and the representative binary vector xs is obtained. Protection is performed by summing to xs a codeword cs , generated as the output of a BCH encoder fed by a randomly generated binary word ms . The so obtained vector FCs is then stored together with the hashed version h(m)s of ms and the information regarding the BCH code employed. The stored information can be used to perform user authentication without revealing any information about the original data, as indicated in Section 20.2.2. The proposed scheme is described in detail in the following text. Feature Extraction, Statistics Evaluation, and Binarization During enrollment, I signatures are acquired from each user s and from each of them P parametric features are extracted and collected in the features vectors fs , i = 1, . . . , I. i In Table 20.1 the features employed hereafter are detailed.
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Table 20.1. Features Extracted from On-Line Signatures ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 24 25 26 27 28 29 40 41 42 43 44 45 46 47 48 49 50 Description Number of pen-down events Writing duration Sample count Local maximum count Aspect ratio Pen-up/Pen-down ratio X and Y integral X and Y average absolute writing velocity X and Y average absolute writing acceleration X and Y distribution velocity X and Y segmented areas ( ve equal-length segments) Path length Delta X and Y Effective average speed Sectors pixel count (signature images divided in 4 3 sectors) Cumulated integral error X and Y Integral error sign X and Y Cumulated radiant Average radiant Cumulated distance Average distance Average X and Y position
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The intra-class
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and the interclass
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vector mean are then estimated as = 1 S
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where S is the number of enrolled subjects. From the I signatures acquired from the user s, a binary vector bs representative of the considered P features is then obtained comparing the intraclass s with the interclass vectors: bs [p] = 0 1 if if
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