A Heuristic to Select the Optimal Transformation Matrixes in Bio- convolving with Mixing Transform

Abstract

Bioconvolving with Mixing transform is a cancelable biometric approach to protect biometric data and the user's privacy. This approach uses linear convolutions on biometric features to generate cancelable templates following the random transformation matrixes. This paper shows how the choice of the transformation matrixes impacts the protected system accuracy. Therefore, random matrix selection is not an optimal strategy. A heuristic algorithm is proposed to select the optimal transformation matrix that achieves the optimal protected system performance. The proposed heuristic is based on the minimum distance between the transformed mean template created by the EB-DBA and the transformed reference set. Two online signature verification systems have been protected by Bioconvonlving with Mixing transform to evaluate the proposed algorithm performance in terms of accuracy, False Negative Rate (FNR), and False Positive Rate (FPR). The experiments have been conducted on SVC2004, xLongSignDb, SUSig VisualSubCorpus, and SUSig BlindSubCorpus online signature datasets. The highest calculated Pearson index (r=0.87) shows a high correlation between the pro-posed heuristic and the system's accuracy. Therefore, the selected matrixes by the proposed heuristic allow for optimal system performance. The protected system accuracy improved to 11% using the selected transformation matrixes by the proposed heuristic compared to the random selection matrixes. Moreover, protecting the system using Bioconvolving, revised with the proposed heuristic, reduces accuracy at best by only 0.6 % compared to the unprotected system.

Keywords

• 1 Bioconvolving
• Cancelable biometric
• biometric
• online-signature
• linear convolution
• template protection

1. Introduction

Biometric data must be protected for two main reasons: individuals’ privacy and the usability of the data itself. If the biometric data is compromised, it will not be able to be used anymore since it can be neither revoked nor renewed. Biometric data can be recovered from unprotected biometric templates, leading to severe privacy and security issues [ 1 ]. Therefore, several strategies have been developed to protect biometric templates [ 2 ]. Cancelable biometrics is a proposed methodology that involves intentional and repeatable transformations of biometric signals, providing a comparison of biometric patterns in the trans-formed domain, thus making it extremely complex to retrieve the original data.

This strategy observes the unlikability, revocability, renewability, and non-invertibility requirements of

ISO/IEC 24745 on biometric information protection [3]. However, the performance of the system protected with a cancelable biometrics approach is generally much lower than the performance of an unprotected system [4]. Several strategies based on cancelable biometrics are developed to protect different biometric data. Bioconvolving (BCV) [5] is proposed to protect biometric templates of online

signatures. Recently, BCV has been used to protect different biometric traits such as the face, iris, palm print, fingerprint, and ear [ 6 ].

The signature is considered a “no-invasive” biometric trait, so it is among the most accepted bio

metric data. The purpose of the handwritten signature is individual identification, to secure the individual’s endorsement in a document. The handwritten signature is collected using specific electronic devices (i.e., tablet, PDA, or smartphone) to capture different information about the movement of a specific pen on the device [ 7 ]. The information commonly collected are the horizontal and vertical pen coordinates, the timestamp, and the pen pressure [ 8 ].

BCV consists of dividing the biometric features of each user into a fixed number of parts, and then the feature parts are combined through linear convolution to obtain protected templates. The protected templates reside in the same original template domain. Therefore, the same matcher used for original templates can be used for protected templates. The Bioconvolving with Mixing transform (BCV-MT) is a security strategy to protect the biometric template, but the obtained performance is only sometimes satisfactory. This paper has shown how the choice of the transformation matrixes dramatically impacts system performance. Therefore, the random matrix selection in BCV-MT cannot be considered an optimal strategy, and then a heuristic algorithm to select the optimal transformation matrixes is proposed. The main research contributions are: • • • • •

Show the impact of the transformation matrixes on the protected system accuracy through the matrix distribution analysis.

Develop a heuristic algorithm to select the optimal matrixes through the minimum distance between mean template and reference set.

Verify the correlation between the proposed heuristic and system accuracy.

Submit a comparative analysis of the obtained results by the BCV-MT with the selected matrixes

through the proposed heuristic and the BCV-MT with the random selection matrixes.

Compare the results obtained by the systems protected through the proposed algorithm with the unprotected system results to show the proposed algorithm's effectiveness.

This paper is organized as follows. Section 2 summarizes the main cancelable biometric approaches.

Section 3 details the BCV-MT technique and describes the proposed heuristic. Experiments and results are provided in Section 4, and the conclusions and future development are detailed in Section 5.

2. Related work

The cancelable approaches are based on the intentional and repeatable distortion of the biometric data with the purpose of creating protected biometric templates. Several efforts have used different noninvertible transformation strategies to create protected biometric templates. Harkeerat Kaur et al. [ 9 ] have used polynomial transformation to map biometric information. Other non-invertible transformation strategies used a projection matrix to project the feature vector into another feature vector of fewer dimensions. The projection matrix is generated by the user-specific key [ 10 ], [ 11 ]. To improve system security, random permutations have been used in addition to non-invertible functions.

The permutation key is used to shuffle the feature vector values before applying the non-invertible

function [12 - 14]. Recent efforts have been focused on developing approaches to reduce the tradeoff between performance, security, and privacy. Some efforts have adopted various hybrid approaches to improve recognition performance [15]. The hybrid approaches combine the increased performance of

Biohashing with the increased security provided by non-invertible transformation [16], [17].

Biohashing is used to combine biometric information with user-specific information to protect and increase the discrimination of biometric information. In the same direction, cancelable multimodal biometric systems have been developed. These systems combine different biometric traits with the purpose of improving recognition accuracy [18 - 23]. Recently, WenchengYang et al. have proposed an alternative to BCV to improve the system's performance and security [24]. In contrast to BCV [25], has been applied linear convolution between a feature part ( ) selected by the feature vector = [ 1, … , ], and a support vector (ℎ ) selected from a vector pool ℎ = [ℎ1, … , ℎ ]. Therefore, the transformed feature has been obtained according to the following equation.

Materials and methods

summarized. 3.1.

BCV-MT 100 = ⌈ ∙ ⌉ , = 1, … , For example, given a feature vector of size = 200, = 2 and a key vector = [0, 50,100] is

The following Section detailed the proposed algorithm to select the optimal transformation matrixes

into the matrix selection domain. Before, the BCV-MT [25] approach and the feature-extraction is BCV-MT uses a non-invertible transformation adding the transformation matrixes to improve the template protection and renewability capability. In the first step is defined the key vector of size (W+1) where 0 and

are set to 0 and 100, respectively, and the other elements are different integer values between 1 and 99. Next, each feature of length L is divided into a fixed number of parts (W) of length =

− −1, where computed the as follows. 1 = ⌈ 2 = ⌈ 50 100 100 100 ∙ 200⌉ = 100 (3) (4) =

( , ℎ ) ℎ

= ℎ ℎ( , ,′ ′)

The value of j-index has been generated by a feature-guided index generation algorithm.

Specifically, the hash function ℎ

ℎ(∙) is performed between a user-specific key ( )selected from the key vector

= [ 1, … , ], and a feature part ( ) as following equation.

where ‘SHA’ represents the Secure Hash Algorithm SHA-256. The output of Equation 2 is a hexadecimal, and it is converted into an integer to obtain the j-index value.

Consequently, has been divided into 2 parts: ′ = [ 1, 2, … , 1 ] and ′′ = [ 1+1 , 1+2, … , 2]

In [25] is demonstrated that the recognition performance degradation is due to the increase of the

parameter . In the next step, the transformation matrix ( ) has been created. It is composed of rows and

columns. F is the online signature features number and W is the fixed number of feature parts. An example of a transformation matrix ( ), for F=5 and W=2 is shown below.

C = 3 1 4 5 the transformed features according to the following equation.

= ( ( [ , ]), 1

∗ … ∗ ( [ , ]), ), = 1, … ,

In this way, are generated F transformed features. Therefore, the original number of features is equal

to the number of transformed features. The total number of transformation matrixes which can be generated is then equal to ( !)( −1). It is the matrix selection domain for the proposed algorithm.

To perform deconvolution, an attacker must know at least one feature to obtain the original feature.

So, the only way to achieve the original features is to perform a brute-force attack with an extremely

high computational cost. In the BCV-MT [ 4 ], the transformation matrixes have been randomly generated through a random shuffle. A significant impact of the transformation matrixes on the system accuracy has been verified, as shown in Section 4. Therefore, the proposed algorithm has been developed to select the optimal transformation matrixes. 3.2.

Feature extraction

• • •

Feature–extraction is an important process in implementing the proposed algorithm because it

determines the feature number and thus the matrix selection domain equal to ( !)( −1).

The online signature features generally consist of horizontal and vertical pen coordinates (x, y), timestamp (t), and pen pressure (p). Therefore, the online signature is a sequence of elements: ( ), = 1, … , where each element consists of 4-tuple: ( , , , ). The feature extraction process consists of representing an online signature in fixed feature domains. Five domains are obtained by the 4-tuple in the implemented feature – extraction. They are displacement (s), velocity (v), acceleration (a), path tangent angle (ta), and pressure (p). The five features have been extracted following the equations below.

• •

Displacement: = √( +1 − )2 + ( +1 − )2

Velocity: = ( +1− ) Acceleration: =

( +1− ) Path tangent angle: = tan−1 (( +1− ))

( +1− )

Pressure: the pressure domain is an originally data, therefor no conversion was performed.

Further to the feature extraction, each online signature consists of five features ( , , , , ).

3.3.

Proposed algorithm

The proposed algorithm is applied after the feature–extraction and before the BCV-MT. It is based on a heuristic to select the optimal transformation matrixes in matrix selection domain in BCV-MT. The proposed heuristic is the minimum distance between a mean template ( ) and the users’ genuine signatures [ 1, . . , ]. The mean template is generated using EB-DBA algorithm [26] on the users’ genuine signatures. The first step of EB-DBA is generating a Euclidean Barycenter sequence (EB) by the set of genuine signatures. The EB is the first computed average sequence and the input of the DBA algorithm [27]. DBA is an iterative algorithm used to refine the computed average sequence. Next, the computed mean template is transformed by BCV-MT using a matrix ( ) of the selection domain [ 1, … , ]. The same matrix is used to transform the users’ genuine signatures. For each matrix the following steps are performed.

The mean template and the genuine signatures are transformed according the BCV-MT using the

transformation matrix ( ) according to the following equation. = ( ( [ , ]), 1 ∗ … ∗ ( [ , ]), ), = 1, … , (5)

The average distance ( ) between transformed mean template ( ) and transformed genuine

signatures [ 1, . . , ] is calculated by Dynamic Time Warping (DTW) [28] as details to the following equation. [ 1, … , ]. users’ biometric template.

The computed average distance ( ) is put into the distances vector [ 1, … , ].

The distances vector [ 1, … , ] includes all computed distances between the transformed mean

template and transformed genuine signatures using all the transformation matrixes in the selection domain. The last step is selected the index (min) of the minimum value in the distances vector [ 1, … , ]. Consequently, the optimal transformation matrix is the matrix in the selection domain

The selected matrix is the optimal transformation matrix to be used in BCV-MT to transform the

Details of the proposed algorithm are described in Algorithm 1.

Algorithm 1: Output: Transformation matrix selected.

Input: The set of user’s genuine signatures [ 1, . . , ] and the matrix selection domain [ 1, … , ].

//compute mean template of genuine signatures 2.1| TSEB = Bioconvolving(SEB, Tk) //transform mean template with Tk tgz = Bioconvolving(gz, Tk) //transform genuine signature with Tk = ∑ =1 ( , ) (6) // distance between transformed mean template and transformed genuine signature //put the computed distance in the vector //compute the average distance //put the average distance into the distances vector 1| SEB = EB-DBA([ 1, . . , ]) 2| for k = 1 … N: 2.2| for z = 1 … M: dtz = DTW(TSEB, tgz)

4. Experiments and results

4| min = index_min([ 1, … , ]) //index of the minimum value in the distances vector //matrix with index ‘min’ in selection matrix domain

To prove the validity of the proposed method, three different experiments have been performed. The reported experiments are conducted using 4 online signature datasets outlined below.

• • • •

SVC2004 in the version Task2 [29] xLongSignDb [30].

BlindSubCorpus is a version of the SUSig dataset [31].

VisualSubCorpus is a version of the SUSig dataset [31].

Each dataset is split into a training data set and a test data set. The training data set contains 7 genuine

and 7 false signatures for each user. The test data set contains 3 genuine and 3 false signatures for each user. After the feature – extraction, each signature is defined by 5 features ( ) and each feature has been divided into 2 parts ( ). Consequently, the matrix selection domain is equal to ( !)( −1) = 120. The experiments employ two different online signature verification systems to prove the performance of the protected systems using BCV-MT revised with the proposed algorithm. The first system implements a multiple-template approach comparing a test sample with all the reference samples. The system computes the distances between the signatures using DTW and then classify them into genuine or false class by the SVM with gaussian kernel [32]. The second system implements single-template approach compares a test sample with a mean template generated from the reference samples. It is based on time-series averaging and local stability-weighted dynamic time warping [33]. The system uses a mean template and the references set to construct the local stability sequence (LS). It is used in the

DTW cost function, thus implementing the LS-DTW algorithm. LS-DTW algorithm is used to compute the distances between the mean template and the reference signatures. The distances are classified using a SVM with gaussian kernel into genuine and false class. The conducted experiments and their results are detailed in the following.

4.1.

Distribution of the transformation matrixes

The matrix distribution analysis is conducted to prove the impact of the transformation matrixes in

BCV-MT. The protected multiple-template system accuracy using each matrix of the selection matrix domain and the matrixes frequency into each accuracy class has been calculated. The range [0.5;1] is divided into 13 equal intervals and each one represents an accuracy class. Figure 1 shows the bar charts of the matrix distribution analysis for each dataset.

Table 1 shows the highest variance on dataset BlindSubCorpus, xLongSignDb and SVC2004 Task2.

Therefore, the random transformation matrix selection may not be the correct approach because the system accuracy is highly variable depending on the selected transformation matrix.

4.2.

Correlation between distance and accuracy

The following experiment is conducted to prove the correlation between the computed distance and the

system accuracy. The multiple-template system accuracy is calculated for each transformation matrix in the selection domain. The system accuracy is related to the distance calculated between the mean template and genuine signatures transformed for each matrix in the selection domain. This relationship is reported in the scatter plots in Figure 2 for each dataset.

The Pearson coefficient shows a high linear negative relationship between the distance and accuracy for each dataset. The Pearson coefficient computed on the VisualSubCorpus dataset is lower than the other computed coefficient. Then, in VisualSubCorpus, the system accuracy does not decrease visibly with increasing distance, as shown in Figure 2 and Table 2. However, Figure 2 shows that the highest accuracy values are concentrated where the distance is lowest. Therefore, selecting the transformation matrix based on the minimum distance is a good heuristic for all used datasets. 4.3.

Proposed algorithm performance and comparative analysis

In the last experiment, the multiple-template system and the single-template system are protected by the BCV-MT using the random matrix selection and the matrix selection by the proposed algorithm The random matrix selection is implemented using 4 transformation matrixes randomly generated and shown below.

Matrix 1:

Accuracy, False Negative Rate (FNR), False positive Rate (FPR), and delta average accuracy

(∆ACC) are calculated to evaluate the results. The ∆ACC computes the difference between the unprotected system accuracy and the protected system accuracy average. Table 3 shows the results. BCV-MT with Matrix 1 BCV-MT with Matrix 2 BCV-MT with Matrix 3 BCV-MT with Matrix 4 BCV-MT optimal matrix

Unprotected system

5. Conclusions and future work

In this work, a heuristic approach has been introduced to improve the performance of the online signature verification systems protected using BCV-MT. In BCV-MT, the transformation matrixes significantly impact the system performance. The matrix distribution analysis showed that a random matrix choice could compromise the protected system performance. To solve this issue, the proposed heuristic selects the optimal transformation matrixes through the minimum distance parameter between the transformed mean template and the transformed genuine signatures. This parameter showed a high correlation with the system accuracy. Consequently, using BCV-MT revised with the proposed algorithm is an optimal strategy to protect the biometric template, drastically reducing system performance. A limitation of the proposed heuristic is the increase of the matrix selection domain. The size of the domain grows factorial as features increase and exponential as features part increase. Therefore, a significant number of features or feature parts would expand the matrix selection domain, and then the proposed algorithm would become computationally costly in terms of time. However, the increase of the feature parts involves the reduction of the recognition performance [25]. Moreover, the proposed algorithm is used only in the training phase, and the cost can be acceptable. The proposed heuristic could be implemented in different biometric systems to protect different biometric data in future work. In fact, BCV has also been used to protect biometric traits such as the face, iris, palm print, fingerprint, and ear [ 6 ]. Finally, the proposed heuristic could be improved to automatically generate the optimal transformation matrix based on the input biometric features.

6. Acknowledgements

Francesco Castro is a PhD student enrolled in the National PhD in Artificial Intelligence, XXXVIII cycle, course on Health and life sciences, organized by Università Campus Bio-Medico di Roma.

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