Abstract. In this paper, we propose a low computational cost cancelable fingerprint template, namely the multi-line codes. The generation of a line code involves ...
A Low Complexity Multi-line Code for Cancelable Fingerprint Template Wei Jing Wong, Mou Ling Dennis Wong and Yau Hee Kho School of Engineering, Computing and Science, Swinburne University of Technology (Sarawak Campus) {wjwong, dwong, ykho}@swinburne.edu.my
Abstract. In this paper, we propose a low computational cost cancelable fingerprint template, namely the multi-line codes. The generation of a line code involves the inspection of minutiae distribution along a straight line constructed based on the reference minutia. Multi-line code is also introduced to elevate the performance of the original single-line code representation. Comprehensive experiments on FVC databases further ascertain that the proposed method yields relatively low computational complexity as compared to existing minutiae distribution-based methods, while preserving the performance. The average equal error rate obtained for stolen-key scenario is 6.69%, and the total arithmetic operations utilized are 14,520 additions and zero multiplication. Keywords: Cancelable Fingerprint Template, Line Code, Minutiae Distribution-Based Methods
1 Introduction
2 Related Work
Biometric authentication systems offer a great range of advantages over the conventional informationbased and token-based authentication systems, such as passwords, user IDs, identification cards and PINs. However, biometric systems, once compromised, suffer from permanent privacy exposure. Therefore, biometric template protection schemes are required to shield the original biometric information. Cancelable biometrics is one of the promising candidates of biometric template protection techniques. It utilizes a systematic transformation of the derived biometric features to protect the original biometric information. If a cancelable biometric template is compromised, the transformation characteristics can be changed and the user biometrics is mapped onto a new template, which replaces the compromised template. The three principle objectives of cancelable biometrics are [1]: 1) Non-reversibility: it should be computationally infeasible to recover the original biometric data from the biometric template. 2) Accuracy: the accuracy of fingerprint recognition should not deteriorate after transformation. 3) Diversity: no same biometric template can be used in various applications. This leads to revocability, of which new template can be reissued in the event of compromise. This paper presents a low computational cost and alignment-free technique of generating cancelable fingerprint template. The fingerprint template is represented in a number string, which is a composition of several specially generated minutia codes, namely the multi-line codes.
Recently, various cancelable biometrics generation schemes have been proposed. Ang et al. [2] presented a geometric transformation based on the reflection of minutiae. In this approach, a line passing through the core point is drawn, and the minutiae below the line are reflected while the minutiae above remain. The gradient of the line is determined by a user-specific key. Confusion occurs when dealing with fingerprints with no core point (arch) and with more than one core point (whorl). On the other hand, Tulyakov et al. [3], [4] used symmetric hash functions to convert the minutiae into hash values. In this algorithm, a minutia is represented by a complex number . For each minutia in the fingerprint, a triplet ( , , ) is formed with its two nearest neighboring minutiae and is hashed using predefined hash functions. A secret key is introduced to seed the choices and order of hash functions for different fingerprints. This work was extended [5] by combining more than one hash functions during implementation to increase the security of the template. Also, k-plets of minutiae were used instead of triplets, where k can be more than three. For aforementioned approaches, matching of fingerprint templates requires pre-alignment of the minutiae. This increases the computational time during fingerprint matching and thus reduces its applicability in real-time authentication systems. One of the solutions of eliminating minutiae alignment is to use invariant features of minutiae in the generation of fingerprint template as proposed by Lee et al. [6]. These features are extracted following the same fashion as in [7]. Together with a user-specific PIN, the invariant features are used to parameterize two changing functions which contribute to the
transformation of the minutiae, namely the distancechanging function and the orientation-changing function. Another cancelable template utilizing invariant features based on triplets was proposed by Farooq et al. [8]. The features measured are the length of the three sides, the orientations of the three vertex minutiae and the height of the longest side of a triplet. The template is a binary string of quantized feature values, so it requires less database storage as compared to [6]. A bit-string representation of fingerprint template was introduced by Lee et al. [9], where each minutia is described by a three dimensional array. The width and height of the three dimensional array is the x-y plane of the fingerprint image, while the depth represents the orientation of minutiae. The array is divided into cells of equal size, and the numbers of minutiae in the cells form the final bit-string. Other string-based cancelable fingerprint templates include [10], [11] and [12]. One of the state-of-the-art fingerprint template representations is called the minutiae cylinder-code (MCC) [13]. It forms a cylinder around a minutia and the cylinder is tessellated in the similar manner as in [9]. Instead of counting the number of minutiae in the cells, MCC considers all minutiae around the cell within certain range. The contribution of each minutia towards the cell value is regulated by its positional and orientation distance from the center of the cell. Such approach uses the basis of fixed radius-based minutia descriptor without neglecting the area outside but nearby the perimeter. BioHashing [14], [15] is the pioneer of correlationbased template protection schemes. BioHashing employs the wavelet Fourier-Mellin transform (WFMT) features of fingerprints in the transformation. The transformation involves inner product of the WFMT features with a user-specific tokenized key. User-dependent multi-state discretization was used [16] in the generation of binary bit-string to improve the performance of BioHashing specifically for stolen-token scenario.
3 Proposed Scheme In this section, we present the procedures of our proposed cancelable fingerprint template generation scheme. The proposed method represents each minutia with a minutia code, namely the line code, by observing the distribution of minutiae around a line drawn based on the reference minutia. 3.1
Line Code Generation
In the proposed scheme, we first construct a straight line of length, l centered at the reference minutia, , . The orientation of the line is equivalent to the orientation of , and is denoted by . On the
line, we take s sample points uniformly distributed with distance, d in between one another so that 1 . The position of the sample points is calculated by: ;
(1)
.
(2)
For ∈ | and given cos and sin . For each sample point, we apply a circular bit-wise AND mask (with radius r) to obtain the number of minutiae within the area in different angular partitions, ∆ . The angular partition that a minutia falls in is determined by the relative angle between and the orientation of the neighboring minutia. Fig 1 provides a visual illustration of the proposed method. In Fig 1(b), the number of minutiae in each overlapping cylinder (left region and right region are separated) are arranged sequentially to form a line code that describes the reference minutia, . … … , Therefore, it can be written as where 2 is the length of the line code, is the number of angular divisions, and is ∆
the total number of sample points on the line. is assigned an invalid value, -1 if the sample point is located outside the boundaries of the fingerprint image. In a nutshell, a fingerprint template can be … , where is the total concluded as number of minutiae in the fingerprint. 3.2
Permutation of Line Code
In order to achieve revocability and diversity of the template, we have to introduce an external factor that offers huge variety of transformations unto the generated line code. In this paper, we simply permute the code based on a user specific secret key. The secret key, obtained from a pseudo-random number generator (PRNG), will seed the permutation order of the minutia code. It is important to ensure that no two individuals or two applications of one individual can be assigned the same key. Therefore, the PRNG should generate random numbers with no duplicate. In addition, permutation of the line code improves the performance of cancelable fingerprint template. By introducing a unique “personality” to every fingerprint, it greatly reduces the false acceptance rate (FAR) of the system. 3.3
Fingerprint Matching
Local Similarity Score. Given a line code … ) from the template fingerprint ( from the query fingerprint and a line code ( … ), where and is the total number of minutiae in and respectively. The
For , ∈ |0 , 1 . Similarity of 0 and , while indicates a total mismatch between 1 indicates a perfect match between them. During fingerprint matching, each line code in is cross-matched with every line code in , so we will have a similarity matrix containing similarity scores among all line codes between two fingerprints. Each element in the similarity matrix is then reevaluated with the following criterion to eliminate double-matching: ,
,
Condition 1; otherwise.
0
Condition 1 implies that , maximum among all values of , and , (for ∈ 1, ).
∑ #
∑
, ,
4 Experiments Evaluation 4.1 (b) 3D view. Fig 1. Illustration of the proposed scheme, showing relevant parameters: length of the straight line (l), radius threshold of neighboring minutia contribution (r), gap between two sample points (d) and angular division (∆ ). The region of interest around the sample points is divided into left (shaded) and right (without shade).
local similarity score between and signifies the likelihood of in being a correspondence to in . We use Dice’s coefficient [17] to measure the similarity between two line codes in our proposed scheme. The similarity score between can be formulated as: and
,
must be the (for ∈ 1, )
Global Matching Score. To perform overall matching between and , a global matching score is used to measure the likelihood of and being two instances of the same fingerprint. From the similarity matrix obtained by eq. ( 3 ) and ( 4 ), we calculate the matching score with the following formula [9]:
(a) Plane view with minutiae.
more than 50% of either 0 or are invalid; 2∑ otherwise. ∑ ∑
(4)
(3)
0
and
.
(5)
Performance
Parameters Tuning
Prior the testing, a series of experiments are carried out on a smaller dataset (set B of FVC2002 DB1, DB2 and FVC2004 DB1) to fine-tune the parameters so that the results obtained in section 4.2 is optimal. The parameters under consideration are listed in Table 1, accompanied by the values which produce the best performance. Table 1. Variable parameters of the proposed method. Parameter symbol
Description
∆
Length of line Distance between two sample points Range of angular division Radius threshold of minutiae around a sample point
Value 320 8 ⁄3 25
Through experiments, we discovered that using more than one line to describe a minutia improves the performance of single-line code representation. This is because with multiple lines of different directions, we can capture not only the minutiae distribution along
ROC Curves
the dominant orientation, but also information in other directions. However, adding in a line greatly increases the computational complexity and the template size. In order to balance the trade-off between accuracy and computational complexity, we use three lines per minutia in this paper. Hence, the multi-line code relating to a minutia can be written as ⁄ ⁄ .
100
90
GAR(%)
80
70
FVC2002 DB1 genuine-key FVC2002 DB1 stolen-key FVC2002 DB2 genuine-key FVC2002 DB2 stolen-key FVC2004 DB1 genuine-key FVC2004 DB1 stolen-key EER line
60
4.2
Testing and Analysis 50
The proposed algorithm is evaluated on fingerprint images taken from FVC2002 DB1, DB2 and FVC2004 DB1. Each dataset contains 100 fingerprints, and each fingerprint has 8 samples with different way and level of perturbations. We enroll the first impression of every fingerprint as the template and use the remaining seven impressions to match against the templates, and thus resulting in 70,000 tests in total, which include 700 genuine tests and 69,300 imposter tests for each dataset. Accuracy. Table 2 provides a comparison of EER between the proposed algorithm and other minutiae distribution-based algorithms [9], [13]. It is notable that the performance of the proposed cancelable template is ideal (zero EER) provided that the secret key is secure. However, if the key is compromised, the EER increases due to intra-class variation and inter-class similarity among the fingerprints. Note that the proposed algorithm performs as well as Lee’s algorithm while using FVC2004 DB1, that is, both algorithms yield an EER of approximately 10.3%. Fig 2 shows the ROC curves of the proposed algorithm. Table 2. EER of the proposed algorithm and other existing algorithms. Algorithm
Multi-line code (proposed) Lee’s algorithm [9]
Minutia cylinder-code [13] (without relaxation)
EER (%) Genuine Stolen-key key scenario scenario 0 4.69 0 5.03 0 10.36 0 10.3 0 9.5 0 6.8 0.33
Fingerprint database used
FVC2002 DB1 FVC2002 DB2 FVC2004 DB1 FVC2004 DB1 FVC2004 DB2 FVC2004 DB3 FVC2006 DB2
Computational Complexity. One of the metrics of measuring computational complexity is by evaluating the number of arithmetic operations used in the algorithm. In particular, the operations we consider in this paper are additions (hereafter denoted by ) and multiplications (hereafter denoted by ). The values of trigonometric functions are usually pre-calculated and thus can be implemented with lookup tables. Even though the proposed method is alignment-
40 -2 10
-1
0
10
10 FAR(%)
1
2
10
10
Fig 2. ROC curves of the proposed method tested on various datasets.
free, it requires calculation of the positions of sample points for each reference minutia. In eq. ( 1 ) and ( 2 ), since we assume that the trigonometric functions are and can also be pre-calculated, treated as constants. Therefore, it requires only 2 and no . From experiments, the average number of minutiae contributing to a sample point is 2, so we need an average of 1 to sum up the number of neighboring minutiae around a sample point. Let be the number of sample points on a single line and be the total number of minutiae, the total arithmetic operations involved in the generation of a fingerprint template (multi-line codes) is 3 1 2 1 . According to the parameter values given in Table 1, we get 41. Table 3 summarizes the computational complexity of the proposed algorithm and the referencing algorithms when 40. The inputs of most of the arithmetic operations are x and y coordinates of the minutiae. Assuming that the dimension of a fingerprint image does not exceed 1024) binary ’s and 1024 1024, 10-bit (2 ’s are sufficient enough for the calculations. Knowing that a 10-bit is 9 times more complex than a 10-bit , we can conclude that the proposed algorithm yields the lowest computational complexity among the three. Table 3. Number of mathematical operations required in the computation of fingerprint template. Algorithm 1 Multi-line code (proposed) 1
Lee’s algorithm [9] Minutia cylinder-code [13] 2 (without relaxation) 1
Number of operations 14,520 4,680 230,240
6,240 201,600
complexity of permutation is excluded so that the figures are comparable with [13]. 2 complexity of the algorithm is not reported in the original paper, so the estimation is based on our own assumptions. High complexity shown is mostly caused by the calculation of Gaussian-based contribution value for each cell in the cylinders.
Revocability. The revocability (or cancelability) of a cancelable template can be assessed by the number of possible templates that the algorithm is able to produce out of one fingerprint. Since the revocability of the proposed scheme is engendered by the permutation of multi-line code, the variety of templates generated from one fingerprint depends on the length of the code. With the given parameters in Table 1, we can conclude that the length of the multiline code is 1,476. Therefore, there are 1,476! possible permutations for each database, and can accommodate more than a hundred worldwide applications.
5 Conclusions In this paper, we proposed a cancelable fingerprint template generation method based on the distribution of minutiae around a reference minutia in different orientations. The following statements show the realization of the three requirements of a template protection scheme (corresponds to Section 1) via the proposed method: 1) Non-invertibility of the transformation is taken care by the many-to-one mapping while grouping minutiae. 2) As a result of alignment-free implementation and inspection of minutiae in a reduced dimension, we showed that the proposed method established a relatively low computational cost whilst preserving the recognition accuracy. 3) Permutation of the multi-line codes provides diversity and revocability to the proposed scheme. However, the proposed method requires large storage capacity as the template is stored as a real number string. We can resolve this by converting the resulting number string into a bit string. A reliable quantization method is required to prevent or minimize the decay in performance after conversion. Furthermore, some other distinctive features have to be introduced to ameliorate the EER value. Acknowledgement. W. J. Wong would like to thank Swinburne University of Technology (Sarawak Campus) for his PhD studentship.
References 1. Maltoni, D., Maio, D., Jain, A.K., Prabhakar, S., Handbook of Fingerprint Recognition. Springer-Verlag, London, 2009. 2. Ang, R., Safavi-Naini, R., McAven, L., Cancelable KeyBased Fingerprint Templates, in Proceedings of 10th Australasian Conference on Information Security and Privacy, pp. 109-128, 2005.
3. Tulyakov, S., Farooq, F., Gavindaraju, V., Symmetric Hash Functions for Fingerprint Minutiae, in Proceedings of 3rd International Conference on Advances in Pattern Recognition, pp. 30-38, 2005. 4. Tulyakov, S., Farooq, F., Mansukhani, P., Gavindaraju, V., Symmetric Hash Functions for Secure Fingerprint Biometric Systems. Pattern Recognition Letters. Vol. 28, pp. 2427-2436, 2007. 5. Kumar, G., Tulyakov, S., Gavindaraju, V., Combination of Symmetric Hash Functions for Secure Fingerprint Matching. 20th International Conference on Pattern Recognition,pp. 890-893, Istanbul, 2010. 6. Lee, C., Choi, J.Y., Toh, K.A., Lee, S., Kim, J., Alignment-Free Cancelable Fingerprint Templates Based on Local Minutiae Information. IEEE Transactions on Systems, Man and Cybernetics – Part B: Cybernetics. Vol. 37,pp. 980-992, 2007. 7. Tico, M., Kuosmanen, P., Fingerprint Matching Using an Orientation-Based Minutia Descriptor. IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. 25,pp. 1009-1014, 2003. 8. Farooq, F., Bolle, R.M., Jea, T.Y., Ratha, N., Anonymous and revocable Fingerprint Recognition. IEEE Conference on Computer Vision and Pattern Recognition, pp. 1-7, Minneapolis,2007. 9. Lee, C., Kim, J., Cancelable Fingerprint Templates Using Minutiae-Based Bit-Strings. Journal of Network and Computer Applications. Vol. 33, pp. 236-246, 2010. 10. Jin, Z., Teoh, A.B.J., Ong, T.S., Tee, C., Generating Revocable Fingerprint Template Using Minutiae Pair Representation. 2nd International Conference on Education Technology and Computer, pp. 251-255, Shanghai, 2010. 11. Jin, Z., Ong, T.S., Tee, C., Teoh, A.B.J., Generating Revocable Fingerprint Template Using Polar Grid Based 3-Tuple Quantization Technique. IEEE 54th International Midwest Symposium on Circuits and Systems, pp. 1-4, Seoul, 2011. 12. Ahmad, T., Hu, J., Wang, S., String-Based Cancelable Fingerprint Templates. 6th IEEE Conference on Industrial Electronics and Applications, pp. 1028-1033, Beijing, 2011. 13. Cappelli, R., Ferrara, M., Maltoni, D., Minutia CylinderCode: A New Representation and Matching Technique for Fingerprint Recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. 32, pp. 2128-2141, 2010. 14. Teoh, A.B.J., Ngo, D.C.L., Goh, A., Biohashing: Two Factor Authentication Featuring Fingerprint Data and Tokenised Random Number. Pattern Recognition. Vol. 37, pp. 2245-2255, 2004. 15. Teoh, A.B.J., Kuan, Y.W., Lee, S., Cancellable Biometrics and Annotations on BioHash, Pattern Recognition. Vol. 41, pp. 2034-2044, 2008. 16. Teoh, A.B.J., Yip, W.K., Toh, K.A., Cancellable Biometrics and User-Dependent Multi-state Discretization in BioHash. Pattern Analysis & Applications. Vol. 13, pp. 301-307, 2010. 17. Dice, L.R., Measures of the Amount of Ecologic Association Between Species. Ecology. Vol. 26, pp. 297302, 1945.
