Cancelable Templates for Sequence-Based Biometrics with ... - ATVS

MAIORANA et al.: CANCELABLE TEMPLATES FOR SEQUENCE-BASED BIOMETRICS 535properly employed to transform the original signature representations,while keeping fixed the decomposition vector d,will be estimated. As defined in Section III-B1, a scramblingmatrix C consists of F rows and W columns. The total numberof matrices which can be defined is then equal to (F !) (W −1) ,which corresponds to 14! = 87 178 291 200 when consideringF =14and W =2. However, among all the possible scramblingmatrices, only those which allow fulfilling the diversityproperty can be employed.Given two generic matrices C (1) and C (2) , let us define thedistanceΩ(C (1) , C (2))= number of different rows between C (1) and C (2) . (16)Following the approach illustrated in Section III-B1, two transformationsobtained by using the same decomposition vectord, while employing two distinct scrambling matrices C (1)and C (2) , produce more distinct templates as the distanceΩ(C (1) , C (2) ) increases. Considering the entire MCYT database,each user is then enrolled by using his first E =10signatures,to which the transformation process in Section III-B1is applied. Specifically, the transformations employed duringenrollment are ruled by a decomposition vector d and ascrambling key matrix C (e) . The remaining signatures of eachuser, after being transformed using the same keys d and C (e)applied during enrollment, are employed to estimate the FRR.Moreover, the FAR related to skilled and random forgeries iscomputed by transforming the available signature according tothe decomposition vector d and to the same scrambling matrixC (a) = C (e) employed during enrollment (Ω(C (e) , C (a) )=0). The RTMR related to the use of the mixing approach iscomputed by transforming the genuine signatures of each useraccording to the same decomposition key d employed duringenrollment, but with different scrambling keys C (a) , characterizedby distances Ω(C (e) , C (a) ) ∈{8, 9, 10, 11} from C (e) .The matching statistics obtained for a system with E =10and W =2are reported in Fig. 6(b). Specifically, the renewabilityproperty of the mixing approach is verified by comparingthe ROC curve where the FAR for random forgeries is takeninto account with the pseudo-ROC curves where the RTMR fordifferent distances Ω(C (e) , C (a) ) is considered. The obtainedperformances show that the use of different scrambling matricesbetween enrollment and authentication, when keeping fixed thedecomposition keys, allows obtaining matching rates which aresimilar to those associated with the use of random forgeries, butonly when Ω(C (e) , C (a) ) ≥ Ξ=11(over F =14consideredfunctions).Therefore, the total number of scrambling matrices whichcan be considered still satisfying the diversity property, guaranteedby a distance Ω(C (e) , C (a) ) ≥ Ξ=11, has an upperbound that is equal to (F !/(Ξ − 1)!) = 24 024. Moreover,keeping in mind that, as explained in Section IX-A, Γ=4distinctdecomposition vectors can be defined for each scramblingmatrix C, the total number of renewable templates which canbe properly generated, following the approach in Section III-B1with W =2,is4 · 24 024 = 96 096.C. Shifting ApproachIn this section, we verify how the renewability property of thebaseline approach in Section III-A is improved when using themethod described in Section III-B2, which employs a decompositionvector d and a shifting parameter φ as transformationkeys. Following an approach that is similar to the one employedin Sections IX-A and B, each user available in the entire MCYTdatabase is enrolled by using his first E =10signatures, whichare then transformed according to the transformation keys dand φ (e) . Then, the remaining genuine signatures of each userare transformed using the same decomposition key d employedduring enrollment, but with a different initial shift, indicatedas φ (a) , to determine the RTMR that is used to analyze therenewability capacity of this approach. The values of the shiftsare taken in the range between 0 and 95, considering onlymultiples of five: In this way, 20 different possible values aretaken into account. Having defined a distance between theshifting parameters taken during enrollment and verification as(Φ φ (e) ,φ (a)) ∣∣= ∣φ (e) − φ (a) ∣∣ , (17)Fig. 6(c) shows the RTMR statistics obtained by considering thesame decomposition keys during enrollment and verification,at an increasing distance Φ(φ (e) ,φ (a) ) between the employedshifting parameters. A comparison with the FAR performancesobtained considering skilled and random forgeries, transformedwith the same transformation keys d and φ (e) employed inenrollment, is also given. The obtained experimental resultsshow that the RTMR pseudo-ROC curves, related to the useof different shifting parameters for the enrollment and theauthentication stage, are similar to the ROC curve obtainedwhen random forgeries are taken into account when the distanceΦ(φ (e) ,φ (a) ) is equal or greater than the 20% of the signaturelength N. This implies that the number of values φ whichcan be properly considered is limited to Υ=5. Applying themodification described in Section III-B2 to the baseline approachin Section III-A, we obtain an increase of the number oftemplates that can be generated by a factor of five, thus obtaininga number of Γ · Υ=4· 5=20templates. Obviously, thisnumber is still too small for a practical application. However, ifthe considered modification is applied in conjunction with themethod described in Section III-B1, it is possible to properlyproduce renewable templates with an upper limit of Γ(F !/(Ξ −1))Υ = 96 096 · 5 = 480 480 discriminable templates.In conclusion, although with the proposed approaches, it isnot possible to obtain an infinite number of discriminable templates,almost 500 000 templates can be generated from a singleoriginal signature, properly fulfilling the diversity requirement.It is also worth pointing out that, having the possibility ofmanaging almost 500 000 different templates, a user could issuea new biometric template each hour, for 60 years.X. DISCUSSION AND CONCLUSIONThe security and privacy issues probably represent the mostimportant problems that have to be tackled during the design ofa biometric-based automatic recognition system. In this paper,Authorized licensed use limited to: Univ Autonoma de Madrid. Downloaded on May 06,2010 at 15:31:46 UTC from IEEE Xplore. Restrictions apply.