Security-Scalable Signature-Based Authentication System in .NET

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20.3 Security-Scalable Signature-Based Authentication System
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related to the signature pressure, typically considered as an on-line characteristic. In order to select, among the I signatures acquired for the user u, a representative signature, the mean u and the variance 2 feature vectors are calculated from vectors u s(i) . A distance measure Du is introduced and estimated for each of the I enrolled u signatures of user u as follows:
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68 (i) Du = f =1
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(su [f ] u [f ])2 , 2 [f ] u
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(i) and the signature image giving the lowest value Du , where i = 1, . . . , I, is then selected for each user. The selected signature represents the one whose static features are the closest to the estimated mean, and it becomes the host image where the selected user s dynamic features can be embedded.
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In the authentication stage, the user is asked to provide his signature by means of an electronic pad. His prototype signature with the embedded signature dynamic information can be stored either in a centralized database or in a card. When a lowsecurity level is required, the authentication is performed on the base of the selected static features only. With reference to Figure 20.8, for a given user u the static features given in Table 20.6 are extracted from the provided signature, collected in the vector su , and compared with the static signature feature vector su . If a higher security level is required, dynamic features are obtained from the acquired signature, collected in the vector du , and compared with the dynamic signature features du extracted from the stored watermarked signature image.
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Figure 20.8. Security-scalable signature-based authentication system using data hiding. Proposed
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A Mahalanobis distance is used to compare the extracted features vectors as follows: D( u , vu ) = v
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( u [f ] vu [f ])2 v , 2 [f ] vu
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where vu represents either the stored static or dynamic feature vector, vu represents the one obtained from the provided signature, and 2 u represents the variance of v vu , estimated during enrollment. If the distance is less than a threshold TA , the user is authenticated. As far as the variance 2 u is concerned, in order to reduce the v information that has to be stored and in order to protect the data extracted from each user, it is possible to use in Eq. (20.29) the same value 2 for all the enrolled v users, taking the mean value of each individual variance 2 u estimated during the v enrollment. This can be made for both the static and the dynamic features. In fact, the use of a common variance for all the users can increase the security of the system, thanks to the fact that less information regarding the users has to be stored. Fusion Approach
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When required by the application, a higher level of security can be obtained by combining both dynamic and static features using score fusion techniques [94]. In Section 20.3.5, the performances achievable using only either the static features or the dynamic features, and a combination of both, are presented. Speci cally, in order to combine the scores derived from static and dynamic features, a score normalization stage has to be implemented, followed by a score fusion stage. The rst step is necessary because the matching scores at the output of the individual matchers may not be homogeneous and on the same numerical scale, or may follow different statistical distributions. Score normalization is therefore essential to transform the scores of the individual matchers into a common domain prior to combining them. Among the possible score normalization techniques, in our experiments we used the double sigmoid normalization technique [94], which is robust to outliers in the score distribution. The normalized score is then obtained as 1 if sk < t, 1 + exp( 2((sk t)/r1 ) sk = (20.30) 1 otherwise 1 + exp( 2((sk t)/r2 ) where t is the reference operating point, and r1 and r2 denote respectively the left and right edges of the region in which the function is linear. In our implementation, we performed a xed score normalization [94], which consists in using the same parameters for the normalization of the scores derived from each considered user. In order to estimate these parameters, the scores obtained considering the enrollment genuine signature, together with two skilled forgeries for each user, have been considered as evaluation test. This scheme is robust with respect to the outliers, but it requires a careful tuning of the employed parameters to obtain good ef ciency. Speci cally,
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