Generating a Cancellable Fingerprint using Matrices Operations and Its Fingerprint Processing Requirements

Cancellable fingerprint uses transformed or intentionally distorted biometric data instead of the original biometric data for identifying person. When a set of biometric data is found to be compromised, they can be discarded, and a new set of biometric data can be regenerated. This initial principal is identical with a non-invertible concept in matrices operations. In matrix domain, a matrix cannot be transformed into its original form if it meets several requirements such as non-square form matrix, consist of one zero row/column, and no row as multiple of another row. These conditions can be acquired by implementing three matrix operations using Kronecker Product (KP) operation, Elementary Row Operation (ERO), and Inverse Matrix (INV) operation. KP is useful to produce a non-square form matrix, to enlarge the size of matrix, to distinguish and disguise the element of matrix by multiplying each of elements of the matrix with a particular matrix. ERO can be defined as multiplication and addition force to matrix rows. INV is utilized to transform one matrix to another one with a different element or form as a reciprocal matrix of the original. These three matrix operations should be implemented together in generating the cancellable feature to robust image. So, if once three conditions are met by imposter, it is impossible to find the original image of the fingerprint. The initial aim of these operations is to camouflage the original look of the fingerprint feature into an abstract-look to deceive an un-authorized personal using the fingerprint irresponsibly. In this research, several fingerprint processing steps such as fingerprint pre-processing, core-point identification, region of interest, minutiae extration, etc; are determined to improve the quality of the cancellable feature. Three different databases i.e. FVC2002, FVC2004, and BRC are utilized in this work.


Introduction
Cancellable biometrics has been a challenging but essential approach to protect the privacy of biometric.The biometric trait of a person cannot be easily replaced.Once a biometrics is compromised, it would mean the loss of a user's identity forever (Schneir, 1999. p. 1).The proper cancellable biometric system has to have these criterion; distinctive, reusable, unidirectional transformation, and performance.
Cancellable biometrics offers a solution for preserving user privacy since the user's true biometric is never reveal in the authentication process.It ensures that template protection is achieved at the feature level with the assistance of the auxiliary data/non-invertible transforms.On the other hand, cancellable biometrics has certain limitations that need to be taken into account.For non-invertible transforms, non-invertible enhances the security of the template space by employing a transformation process to reset the order or position of the feature set.However, this weakens the discriminatory power (performance) of the transformed features due to the enlargement of intra-class variation in the biometrics.In this content, if performance is the main concern in the design of a biometric system, then the system is expected to be lacking in randomness are required for the design of a secure and unpredictable template space.Hence, it becomes a challenge to design a non-invertible function that satisfies both performance and non-invertible requirements.
These above basic concepts are similar with the idea of inverse matrix and elementary row operation in matrices domain.Biometric image as a digital image definitely can be processed in matrices domain.This means the acquired biometric image can undergo a series of matrices operations such as inverse matrix (INV) operation, elementary row operation (ERO), and Kronecker product (KP) operation.In matrices domain, these three these matrice of the input im to avoid mis ginal condition as known as n he system to rprint is missed nt in authenti as its characte whenever it is post data will n using those s to be system 999, p. 1).Maltoni, & Maio, 2005;Daugman, 2003, pp. 279-291), voice identification (Xu & Cheng, 2008, pp. 263-266;Furui, 1997, pp. 856-872), etc.Many recent literatures state that fingerprint is one of the technologies that are mostly discussed about protection method toward its biometric template (Ratha, Chikkerur, Connell, & Bolle, 2007, pp. 561-572;Mukhaiyar, 2014, pp. 163-166;Lee & Kim, 2010;Lee, Choi, Toh, Lee, & Kim, 2007, pp. 980-992;Farooq, Bolle, Jea, & Ratha, 2007).One of the literatures is as reported in (Ratha, Chikkerur, Connell, & Bolle, 2007, pp. 561-572).In his research, the writer proposed three types of transformation to be implemented in fingerprint images; Cartesian transformation, polar transformation, and image folding.
The first two transformations have a disadvantage in boundary issue.If the original minutiae point is out from its boundary and then divide the area of the feature as the result of minor distortion of image alignment, or if the original fingerprint image is damaged, then the transformation version of minutiae points will be placed on far from where it is supposed to be.Meanwhile, the third method relates to the functional use of smoothing local value to flipping through the space of fingerprint feature.In (Lee, Choi, Toh, Lee, & Kim, 2007, pp. 980-992), Local smoothing function is used to create cancellable fingerprint template by maintaining the original geometric connection (rotation and movement) between the registered template and the questionable template after transformation process is conducted.Therefore, the template transformation result can be used to identify a person without requesting the alignment of image fingerprint used as an input.
However, this analysis security method is yet sufficient enough as a protection over a biometric data.As an example, an impostor might narrow down the candidate owners of the original minutiae design based on the limitation in orientation continuity of minutiae feature and local smoothing process of transformation function.The result of this action can be seen in research report (Ratha, Chikkerur, Connell, & Bolle, 2007, pp. 561-572).Several investigations had been conducted regarding to this issue.For instance, in (Farooq, Bolle, Jea, & Ratha, 2007), the writer presented the conversion of a fingerprint into a binary-string area based on its minutiae series.The representations of binary numbers are transformed into an anonymous representation using a unique personal key.According to the writer, not only that the offering transformation cannot possibly be inverted, but also when it is being misused by someone else, then the template will disappear and can be renewed by entering different key of information.One of the advantages of this representation is that the existed methods like bio-hashing could be implemented.
In (Chikkerur, Ratha, Connell, & Bolle, 2008, pp. 1-6), a secure method to produce a template of cancellable fingerprint is introduced.This method is extracting local image of fingerprint filled with minutia into small pieces and then transforming them into projection matrices without changing the space between each minutia in those small pieces.However, the disadvantage of this method is the poor accuracy in the container of transformation results.In the same year, an author (Bringer, Chabanne, & Kindarji, 2008, pp. 43-51) had presenting an idea in constructing cancellable biometric system and secure sketches in order to protect the privacy of biometric template while supervising the matching process between the protected data and referenced data.The standard process in cancellable biometric is to perform a transformation to create an unchangeable image and to produce a matching process for those transformed images.This research showed that the use of correction system on the sketches that secured from cancellable biometric system resulting a system that supervising the proper matching process.
In (Yang, Busch, Derawi, Bours, & Gafurov, 2009, pp. 490-499), geometric transformation system of minutiae position is proposed to create template of cancellable fingerprints which is useful in alignment process.In order to create template of cancellable fingerprint, a supervising parameter over the encryption of minutiae features is conducted in the surrounding area of minutiae.Then, all the encrypted minutiae will be superimposed to form a protected template.The parameters to control the minutiae encryption are created from the arranged minutiae geometric.Compared with the parameters where the algorithms of cancellable templates use the information of minutiae that have to be encrypted, this minutiae encryption can guaranty the solidity of non-inevitability concept.

Obviously
There are change the mean that

Inverse
In matrice matrix A -1 inverses, b illustrating

Basic C
A feature thing appl zero row a square.Remenber that a matrix can be said having an inverse as if A.A -1 = I; where I is a matrix identity.Meanwhile, a matrix is able to be told as a matrix identity as if the diagonal elements of matrix are 1 (one).Whereas, the others element are 0 (zero).Based on this requirement, it can be ensured that a matrix identity should be a square form matrix. Since 9 by 6 is not a square form matrix, it proves that KP matrix does not have an inverse.Now, the form of matrix KP is square (9 by 9).This 9 by 9 matrix can be inverted when KP.KP -1 = I.In this case, let we symbolize the matrix identity as matrix C and the KP -1 as matrix P. Where, 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 From the matrix above, it is obvious that the diagonal elements of C should be 1 and the others are 0. In conclusion, it can be said that matrix KP is a non-inverted matrix.

Processing Requirements
Referring to the explanation aforementioned, it is clearly that matrix operations like Elementary Row Operation (ERO) and Kronecker Product (KP) Operation can be implemented into generate a cancellable biometric especially for fingerprint proposed.This concept is based on the similarity approach between cancellable biometric and non-inversed matrix.In the former, a cancellable method is said successful when the yielded image cannot be reverted to the original image.The same goes for the latter.In matrix domain, if the goal is to obtain a revocable matrix, then the non-inverse matrix requirement should be done to make the matrix non-invertible.
The required conditions of the transformation process are used as parameters to quantize the non-invertibility standard of the cancellable template.Suppose the input A is not imposed by one of the condition, such as INV operation.It is possible for intruder to extract the result of the KP (A KP ) and ERO (A ERO ) operations because of the similarity appearance of A, A KP , and A ERO .The same case happens as well if ERO operation is eliminated from the generating cancellable system.The only implementation of KP and INV is not enough to shield the cancellable template from an inversion attempt of the intruder.The intruder can experiment to inverse the cancellable template and disannul the arbitrary matrix of the KP operation.Thus, the three conditions of the non-invertibility requirement have to be implemented concurrently.
Furthermore, this situation requires a qualified input A for the system.No noise is allowed in each element of the input to avoid mismatch result in the matching step of the system.The noise can alienate an authorized person from his own cancellable template.So, he will be judged as an imposter hereupon.Therefore, fingerprint pre-processing step is required to enhance the quality of the input image to reduce the false matching.
As we know, this research works in matrices domain.Hence, the requirement of a square form image is determined as well.Region of Interest (RoI) process is used to select a particular area of fingerprint as an input.Moreover, this research offers a new approach of RoI step by optimizing the using of another step in fingerprint process i.e. ridge orientation, ridge frequency, and core-point identification].Ridge orientation and -frequency is needed to specific an area dense with ridge and valley of fingerprint pattern.Meanwhile, core-point is needed as a reference point of RoI.
Another fingerprint step that is required in this research is fingerprint classification.This step is need for enrolment and verification process.Fingerprint classification step will classify a registered and acquired into its classification to simplify the acknowledging process of the fingerprint.The classification process will join a registered fingerprint into its particular pattern class.Then by using this standard, an acquired fingerprint will be pointed into its pattern class as well to ease the searching process.

Experimental Results
The proposed cancellable approach is implemented into several fingerprint's databases i.e.FVC 2002: DB1_B to DB4_B, FVC 2004: DB1_B to DB4_B, and BRC: DBI-Training/Test/DBII.This implementation aims to observe the performance result of the proposed approach based on the specific character of each databases.However, to short the time, we only use several variant of the fingerprint in database BRC DBI to check the diversity and reusability character of the algorithm.
The term of diversity and reusability is used to check the ability of the cancellable system to distinguish and modify the cancellable template from the same input in case of compromising trial by imposter.Variable to be determined is the dissimilarity between the transformed template and transformed template for diversity; and the original input and the cancellable template for reusability.The experiment is conducted into the same fingerprint in the database.For BRC database, every fingerprint has ten different variants divided into two parts.It means that each part has five different variants of the same fingerprint.
Two fingerprints of each part are used for this experiment.One is as registered data and the other as acquired one.Meanwhile, the three others are utilized in authentication step.One of the two fingerprints used for the experiment will be transformed into ten transformed template (cancellable template).Each transformed template is generated by a different arbitrary KP matrix and different ERO order.Later, the other one is used as an acquired transformed template.The following figure illustrates the transformation process of the original fingerprint input into a transformed form by combining the arbitrary matrix in KP and the order in ERO.
Figure 6 shows a complete transformation of the original input of the fingerprint.The transformed template camouflages the appearance of the fingerprint into a distinctive presentation.The histogram presents the different sight of each template to show the variant of the template regarding to the kind of KP and ERO formulas implemented into the input fingerprint.As aforementioned in the previous sub-chapter, the one way transformation guarantees system from revertible trial of the imposter.The variant of the transformed templates show a huge possibility to reproduce a dissimilar template in case that the registered template is compromised by an authorized person.The diversity of the transformed template enables the system confidently to generate the cancellable template automatically as a response of the invalid usage.Overall, it is obvious that the system using a RoI input consumes less time than an original input except for database BRCDB1Training even though the former system has one more step included in process (RoI step).The size of the input fingerprint significantly contributes to reduce time taken for the process.The following table shows the contribution of the size differences to time taken by the process.Table 5 clearly shows the affiliation between the size of the input of fingerprint and the duration taken to complete all the processes.A big input would require more time in the process.However in this research case, it cannot be denied that the size difference should not be narrow such as database BRCDB1Training.Because the system that is used a fingerprint with RoI size needs RoI selection step in its process.It means that it would demand more time to execute the process.Nevertheless, table 6.15 proves that this case is not a big obstacle in this research.
Another parameter considered in the performance of the system is the size of the arbitrary matrix that is used to produce a cancellable feature of the fingerprint.The reason is because the size of that matrix could affect the time consumed in running the process.Therefore, the variant of matrix size was simulated to check its influence into the time taken along the running of the process for databases FVC2002, FVC2004, and BRC.
Figure 7 shows the simulation trend by increasing the size of matrix started from 1 x 1 until 25 x 25 while recording the time consuming along the simulation.During the simulation, it is found that the time taken would be tended to increase as well as the increasing of the size of the matrix.However, at matrix 3 x 3, the trend is tended to lower before going up again at matrix 4 x 4. Therefore, the size of the arbitrary matrix used in this research is matrix 3 x 3.In ERO operation, the most important issue to be discussed is the best number of zero rows and columns needed to make sure that the cancellable template is safe from the impostor.The analysis is done by doing several simulations i.e. increasing number of the zero rows, increasing number of the zero columns, and using the zero rows and columns simultaneously while increasing the number zero rows and columns as well.These increasing simulations is done by starting from one until n/3 rows/columns, where n is size of the input of the fingerprint.The reason to choose n/3 as the limit to increase the number of rows and columns is because it would erase the detail information of the fingerprint feature.The following figure is illustrated all simulation done in the research.
- continuous approach to fulfil these three issues.Matrix application such as KP operation, ERO operation, and Inverse operation can be used as a solution to solve the issues number 1 and 2. Meanwhile, fingerprint regular steps such as fingerprint enhancement, core-point identification, region of interest, fingerprint classification, and minutiae extraction processes can be utilized to complete the last case.
Three kinds of evaluation i.e. error rates evaluation, time take evaluation, and matrices operations requirement evaluation; are performed in here to check the level/score of eleven different databases of the fingerprint.One of the evaluation shows that each database has its own characteristic depend on the type of the fingerprint acquired from the scanner of databases.If the scanner of the fingerprint produces a fingerprint with a good qualification, the error rate and the threshold of the database can be reliable as well as vice versa.
Furthermore, the time consuming along the execution depends on the size of the input of the fingerprint.The time taken would be lessened if the size is small, vice versa.So then, for the small input of the fingerprint, even though one step would be augmented into the algorithm, the total time used of the process would not be changed significantly with the proviso that the size deficit of the input is not too thin.

Figure 7 .
Figure 7.The Correlation between the size of the arbitrary matrix and the time taken of the process The next alternative is a square form matrix.Let say that the matrix

Table 5 .
Correlation between the size differences of the input fingerprint and the time taken by the process (%)