# Generating a Cancellable Fingerprint using Matrices Operations and Its Fingerprint Processing Requirements - Universitas Negeri Padang Repository

Asian Social Science; Vol. 14, No. 6; 2018

ISSN 1911-2017 E-ISSN 1911-2025 Published by Canadian Center of Science and Education

Generating a Cancellable Fingerprint using Matrices Operations and Its

Fingerprint Processing Requirements

1 Riki Mukhaiyar

1 ISPAI Research Group, Universitas Negeri Padang, Padang, Indonesia

Correspondence: Riki Mukhaiyar. E-mail: riki.mukhaiyar@yahoo.co.uk Received: February 13, 2018 Accepted: April 19, 2018 Online Published: May 28, 2018 doi:10.5539/ass.v14n6p1 URL: https://doi.org/10.5539/ass.v14n6p1

**Abstract **

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.** **

**Keywords:** cancellable biometric, fingerprint processing steps, elementary row operation, Kronecker product

operation, inverse matrix operation

**1. 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

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operations s have their ow wn objectives i .e. INV for inv verting matrix elements, ERO O for changing g rows or colu umns, and KP fo or enlarging s size of the ma atrix. The com mbination of t these operation ns can produc ce a non-inver rtible matrix.

Figure 1. R Re-Issuing Proc cedure This resea arch aims to d develop a canc cellable templ late for finger rprint feature, such as minu utiae, based on n the similarity between a non n-inverted nee eded of the fin ngerprint temp plate in cancel llable system a and a non-inv ersed matrix in m matrices opera ations. A temp plate can be ca ategorized as a a cancellable te emplate when it is non-inver rtible to the orig ginal image. By y similar token n, matrices can nnot be inverte ed when the fo llowing three conditions are met.

Firstly, the ere is at least o one zero row. Next, there is s a row that is s a multiple of f another row. Finally, the m matrix form is no t a square. The imple ementation of these matrice s operations in nto a fingerpr rint image req quires several conditions suc ch as clarity and d square form o of the input im mage. Working g in matrix dom main means tha at every eleme ent of matrix/im mage should be e determined to avoid mis scalculation in n process. Va alue of each e element has t to be “true” as a representa ative of the orig ginal condition n of the image e/matrix. True means that th he amount of e ach element is s free from unqu ualified thing a as known as n noise. Therefo ore, in this res earch, several l fingerprint pr rocessing step s are demanded d to support th he system to obtain a fing gerprint input with better qu uality to ensu ure that no fe ature informatio on of the finger rprint is missed d.

### 2. Related d Works

The secur rity requiremen nt in authenti ication system m based on bio ometric techn nology has to be the bench mark mainstay o of the system as its characte eristic will be permanently a associated with h the eligible u user and cann ot be cancelled or withdrawn whenever it is s used inappro opriately. Since e someone’s b biometric chara acteristic cann ot be easily repl laced, the imp post data will be lost. As th he result, there e is a possibili ity that the us er will lose al ll the access to t the application n using those biometric data

a. In order to overcome this s possibility, th he susceptibili ity of biometric system needs s to be system matically ident tified and reco ognized (Boll e, Connell, & & Ratha, 2002 . pp. 2727-2738 8; Schneier, 19 999, p. 1). Thu us, protecting biometric info formation beco ome the main concern as we ell as main chall lenge to all res searchers in thi is field.

Cancellabl le biometric is s a concept wh here its biomet tric template is s protected by y combining bo oth security sy ystem and replac cement feature e into the biom metric system. The main ide ea of this syst tem is that can ncellable biom metric transformi ing and chang ging all image es and feature es of biometric c before conti inuing to mat tching process s, yet maintainin ng the natural characteristic of its cancella able scheme. T The proper can ncellable biom metric system h has to have these e criterion; dis stinctive, reusa able, unidirecti ional transform mation, and pe erformance (M Maltoni, Maio, Jain, & Prabhak kar, 2003).

The transf formation proc cess implemen nted in various s biometric tec chnologies ha s several func ctions such as, face identificati ion ((Boult, 20 006, pp. 560-5 566; Ross & G Govindrajan, 20 005, pp. 196-2 204; Li & Jain n, 2004; Cardin naux, Sanderson n, & Bengio, 2006, pp. 3 361-373), sign nature identifi fication (Camp pisi, Maioran

a, & Neri, 2 2008; Bhattachar rrya, Bandopa adhaya, Das, G Ganguly, & M Mukherjee, 20 08, pp. 181-1 85), iris ident tification (Kan nade, Petrovska- -Delacretaz, & & Dorizzi, 200 09, pp. 120-1 127; Ganorkar r & Ghatol, 2 2007, pp. 91-9 96; Wayman, Jain,

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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.

### 3. Cancellable Supporting Elements

As aforementioned previously, several fingerprint processing steps are required in this research to obtain an appropriate fingerprint image as input of the cancellable system i.e. fingerprint pre-processing (Maltoni, Maio, Jain, & Prabhakar, 2003), core-point identification (Cappelli, Lumini, Maio, & Maltoni, 1999, pp. 402-421; Mukhaiyar, 2017, pp. 146-150; Jain, Prabhakar, Hong, & Pankanti, 2000, pp. 846-859), Region of Interest (RoI) (Mukhaiyar, 2017, pp. 146-150), fingerprint classification (Bolle, Connell, & Ratha, 2002, pp. 2727-2738; Nillson & Bigun, 2003, pp. 2135-2144; Mukhaiyar, 2017, pp. 118-123), minutiae extraction (Amengual, Juan, Prez, Prat, Sez, & Vilar, 1997, pp. 871-875; Kasaei, Deriche, & Boashash, 1997, pp. 303-306), and fingerprint

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authentica ation (Cardina aux, Sanderso on, & Bengio o, 2006, pp. 361-373), sig gnature identi ification (Cam mpisi, Maiorana, & Neri, 2008 8). Pre-process sing step is req quired to prov vide a better q quality fingerpr rint as an inpu ut for cancellable e fingerprint a algorithm. This s stage can mi inimize the po ossibility of ob btaining false-f feature inform ation caused by noises, scars, unclear ridge s/valleys, etc. Core-point is needed as a r reference point t to select a ce ertain region for fingerprint in nput. Moreove er, core-point i is also utilized d as an import tant requireme ent in classific ation step. Lastl y, minutiae ex xtraction is use d as one of the e input of the c cancellable sys stem.

Producing a cancellable fingerprint us sing matrices operations dem mands a squar re form image as an input. S Since mostly fin ngerprint reco ognition image es are not sq quare form, R Region of Int terest step is appropriate t o be implement ted. Still, this stage is able t to omit a usele ess part of fing gerprint so tha at only a true f feature extract ed in feature ext traction proces ss.

Fingerprin nt classificatio on aims to sp plit fingerprint ts in database e into a diffe erent type ba sed on its pa attern combinatio on. This step is required in this research because by cl lassifying the fingerprint eit ther a registere ed or verified o one, time con nsuming probl lem in authen ntication proc cess could be e solved. Mo reover, finger rprint classificati ion can confid dentially gain a accuracy to rec cognize an auth henticity of fin ngerprint.

In this res search, the pos ssibility to est tablish a canc ellable fingerp print except b by using an en nhanced finger rprint image like e minutiae extr raction is deter rmined as well l. The reason i s because natu urally minutiae e by naked eye es not showing a as a fingerpri int anymore. It just looks like scattered d figured poin nts. However, , implementin ng an improved m minutiae extra action approach h is needed to omit false-rec corded informa ation for finger rprint recogniti ion.

### 4. Matrice es Operations s The main n aim in gene erating cancel llable biometr ric is produci ing a reliable e revocable b biometric temp plate.

Cancellabl le biometric is s needed to pr eserve informa ation of an au uthorized perso on from an imp mpostor. One w way is by random mizing the orig ginal biometric feature to gen nerate a vague image. In this s research, the disguising pro ocess is obtaine ed using three e matrices op perations: Elem mentary Row Operation (E ERO), Kronec cker Product (KP) operation, and inverse m matrix operation n.

This idea is to deliver as one of the e cancellable b biometric appr roaches becau use using ERO O, KP, and inv verse operations s can verily giv ve us a lot of alternatives to o randomize th he original ima age as long as it is able to sa atisfy three requi irements of no on-inverted ma atrices. First of f all, at least on ne row or colu umn of the orig ginal matrix sh hould be zero (0) ) value. Secon ndly, the origin nal matrix mus st be modified into non-squar re matrix form m. And the last t is to make sure that none of e each row is a m multiple of ano other row. Furthermo ore, the use of f Kronecker/Te ensor Product t is based on d due that are n needed a large

e, non-inverted d and totally diff ferent cancella able biometric image than the e original biom metric image.

*4.1 Elemen ntary Row Ope eration (ERO)* Generally, Elementary R Row Operation n, ERO, can be e defined as m multiplication an nd addition fo orce to matrix r rows.

The three operations cor rresponding to o the operation ns on rows of ERO are mult tiply a row thr rough by a non nzero constant, i nterchange tw wo rows, and ad dd a multiple o of one row to a another row (A Anton & Rorre s, 2005).

Figu ure 2. Illustatio on of the Opera ation of ERO

*4.2 Kronec cker Product O Operation (KP) P) * In (Laub. 2 2005. pp. 139- -142), the defi inition of Kron necker Product t or Tensor Pro oduct can be o obtained as foll lows.

Let , . Then the Kronecker r Product of A and B is defin ned as the matr rix

∈ ∈

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⋯ (1)

⋮ ⋱ ⋮ ⊗ ∈

⋯ Obviously y, the same defi finition holds if f *A *and *B* are c complex-value ed matrices. There are two advantag ges that are ab le to be obtain ned using this s operation. Fi irst of all, it is s obviously ab ble to change the e value of each h element of th he original ma atrix. And seco ondly, as if *B* i is any kind of matrix’s form , it is mean that a new larger m matrix can be g generated in an ny form of mat trix.

### 4.3 Inverse e Matrix Oper ration (INV)

In matrice es domain, wh hether a given n (squar re) matrix A h has a multipli ication inverse e matrix (that is, a

- 1 -1 -

matrix A such that AA = I ) is going g to be conside ered. Interestin ngly, not all sq quare matrices have multiplic cative

n

inverses, b but most do. T These inverses can be found by examining some properti ies of multipli cative inverses s and illustrating g methods for f finding when t these exist.

Figu ure 3. Illustatio on of the Inver rse Operation

### 5. Cancell lable Fingerpr rint Method

### 5.1 Basic C Concept

A feature can be catego rized as a can ncellable featur re when it is n non-invertible to the origina al image. The same thing appl ies to matrices s. The matrice es cannot be in nverted when satisfying thre ee situations. F Firstly, there is s one zero row a at least. Next, , there is a row w that is a mu ultiple of anot ther row. And d lastly, the m atrix form is n not a square.

Related to the first requi irement, it can n be achieved b by using Elem mentary Row O Operation (ERO O) where a sele ected row is mu ultiplied by zer ro. For the sec cond requireme ent, since in im mage system i it is rare to fin nd a row which h is a multiple o f another row, , hence by usin ng ERO this c ondition can b be created. Fur rthermore, to e ensure the obta ained cancellable e matrix is co ompletely mas ked and able to meet the la ast requiremen nt of non-inve ertible matrix, each element o f the transform med matrix is s multiplied by y an arbitrary y matrix/eleme ent using the K Kronecker Pro oduct operation. By using this s process, the outcome is a matrix that ha as more nume erous elements s and an adjus stable matrix form m (whether rec ctangle or squa are matrix). Since the p proposed meth hod deals with h matrices, ther re should be n no noise in the e system becau use the existen ce of noise may y add specific information to o the biometric c feature. Rela ated to cancel lable biometri ic, since the en nd of this system m is authentic cation process s, even a very y little noise will affect th he quality of c cancellable fe ature significant tly and will ce rtainly resultin ng low precisio on in verificati ion later on. T Thus, the early process to be done toward the e result of est tablished finge erprint is the e enhancement step. The enh hanced fingerp print will prov ide a feature wi ith the precise value of fing erprint inform mation so that w when it is ext tracted to dom main matrices, there will be no unnecessary v values that go into it. After th he fingerprint enhancement step, the cance ellable input im mage will subjec ct to several m matrices transfo ormations. To s simplify the ne ext appellation n, we name it a as matrix A.

Meanwhile

e, the acquired d fingerprint i image is in ma atrices domain n, we next dis scuss how to b build the syste em of cancellable e biometrics u using matrix A A as an input. F Firstly, matrix A will be inv ersed as the fi irst step to disg guise the real fe eature. This ide ea is tentativel ly, because it w will be consid dered whether directly invers sing matrix A is an effective w way or, on the e other hand, inversing mat trix A after an nother matrix o operation. The e next step wi ill be applying t the Elementary y Row Operat tion (ERO) to o matrix A to obtain zero-v value row or to o apply Krone ecker

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Product (K KP) operation . In this resea arch, it will b e analysed of f how much z zero rows need ded to achiev e the requiremen nt of maximu um non-inverti ible. Besides the use of ER RO to obtain zero rows, an nother thing t to be considered d in this resear ch is the use o of ERO to creat te rows that ar re the multiple of the other ro ows.

Figure 4. Steps Flow C Chart In case of f the ERO as th he step taken, matrix A that t has been imp posed ERO op eration; we na ame it as matri ix K; that will g go through KP P operation to produce KP m matrix which e every initial el lement is unre ecognizable. L Let us name it as s matrix M. In this KP opera ation, matrix K K will be multi iplied by tenso or factor that c can be in a for rm of matrix or integer with c constant value. . Let name it a as B. The form m and the valu ue of factor B will be one o of the analysis m materials in thi is research. Fo or example, if factor B is m matrix B, then the value can be taken from m the numbers g given by a pers son who have r registered his b biometrics wh hen he registere ed himself as a an authentic pe erson of a biome etric whose the e cancellable f feature is bein ng built. In this s research, the steps of using g ERO and KP P will be analyse ed as well, wh hether the use of ERO in th he beginning a and KP afterwa ards is better, or vice versa. . The result of th he process abo ove will be a cancellable m matrix of matrix x A, and be n amely as matr rix C which is s as a cancellable e template. To secure the original input, this al gorithm shoul ld be execute ed using one way transform m concept. H ence,

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identificati ion attempt by y imposter can n be eluded b ecause the sys stem does not t provide a loo oping process. . The following figure illustrat tes the concept t used in this r esearch.

Fig gure 5. Cancel llable System F Flow Chart These afor rementioned p processes can be illustrated as following mathematical l steps. Let sa ay that the ori ginal input matr rix is A which a three-by-thr ee matrix is. A As said before that the first a alternative step p that is going to do is to invers se the original matrix to cam mouflage it. Let t say it as

| |

(2) .

2 5 7 S Supposing , 3 2 0

8 9 6 where | | | 11, and

12

33

11 ,

18

44

21

11

22

11 that,

3

4

1

2

### 1 To obtain a Kronecker P Product, anoth her matrix shou uld be determi ined. In order to give more o overview, ther re are

11

11 two alterna atives of that m matrix. Firstly, , a non-square form matrix. L Let say it as m matrix . The rea asons

11

11 to establish h this matrix a are firstly to sh how why a non n-square matri x cannot be in nverted and sec condly why if there is at least o one zero rows cannot be inve erted as well. F Furthermore,

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3 11 11 ⨂ ⨂

4 11 11

1

2

1 12 12 33 33

14

14 12 12 33 33

14

14

18

18

44 44 21 21

18

18

44 44 21 21 11 11 22 22

11

11 11 11 22 22

11

11 KP matrix is a 9 x 6 form (non-square matrix).

- 1

Remenber that a matrix can be said having an inverse as if A.A = 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.

11 11 11 The next alternative is a square form matrix. Let say that the matrix . 11 11 11

That,

12 12 12 33 33 33

14

14

14

12

14 12 12 12 33 33 33

14

14

14

3 11 11 11

18

18

18

44

44 44 21 21 21

11

11 ⨂ ⨂

18

21

4 11 11 11

18

18

18

44

44 44 21 21 21

11

11 11 11 11 22 22 22

11

11

11

1

2

1 11 11 11 22 22 22

11

11

11

- 1

Now, the form of matrix KP is square (9 by 9). This 9 by 9 matrix can be inverted when KP.KP = I. In this case,

- 1

let we symbolize the matrix identity as matrix C and the KP 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.

**-1**

The computation can be simplified by firstly checking the diagonal elements of **KPxKP** or **KP x P** (*C , C , *

*11*

*22* *C , C , C , C , C , C , C* ). Where,

*33*

*44*

*55*

*66*

*77*

*88*

### 99 C = (12xP ) + (12xP ) + (12xP ) + (33xP ) + (33xP ) + (33xP ) + (-14xP ) + (-14xP ) + (-14xP )

*11*

*11*

*21*

*31*

*41*

*51*

*61*

*71*

*81*

*91* *C *= (0x*P* ) + (0x*P* ) + (0x*P* ) + (0x*P* ) + (0x*P* ) + (0x*P* ) + (0x*P* ) + (0x*P* ) + (0x*P* )

*22*

*12*

*22*

*32*

*42*

*52*

*62*

*72*

*82*

*92*

= 0 ========> it means that C ≠ I ( matrix C is not equal to matrix identity) In conclusion, it can be said that matrix KP is a non-inverted matrix.

### 5.2 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

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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

## KP ERO

operation. It is possible for intruder to extract the result of the KP (A ) and ERO (A ) operations because of

## KP ERO

the similarity appearance of A, A , and A . 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.

### 6. 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. ass.ccsenet. .org **Transsformed Temp**

Asian **Orig** **BRC** **KP and **

Five Row Five Co

Five Ro

**plates ** n Social Science **ginal Input ** **C Database ** **ERO Formul**

ws Interchangi olumns Zeroin ows Multiplyin

**las: **

ing ng ng

**Histogram m Presentatio** Vol. 14, No. 6 **on **

2018 ass.ccsenet. .org Asian n Social Science Vol. 14, No. 6 2018

ass.ccsenet. .org Asian n Social Science Vol. 14, No. 6 2018

Figure 6. Th he Variant of F ingerprint Tra ansformed Proc cedures In this res search, we util lized one finge erprint as a re egistered data of each databa ase we used. A And another s six of fingerprint t for BRC and eight for FVC C2002&2004 a are as an enqui red fingerprint t. It means tha t there are 80 k kinds of fingerpr rints existing i in this databas se where one of those is sel lected as the o owner represen ntative in data base. From the 7 79 fingerprints s left, only sev ven fingerprint ts that are cate egorized into a accepted, reject ted, false acce pted, and false r rejected, while e the remainin ng 72 are tota ally rejected an nd are not inc cluded in thos e categories a as the results of c classification s step implemen ntation. This st tep is not only y saving time d during the proc cess, but also h helps the system m to shrink num mber of fingerp prints to analy yze. During thi is stage, an enq quired input w will be grouped d into its particul lar class so th hat an inapprop priate fingerpr rint would be rejected autom matically befor re it continues s to a matching step since eac ch fingerprint in the same database is a lready categor rized into its own class. In n this experimen nt, we used min nutiae extracti ion feature [7, 8, 9] as an inp put of the canc cellable system m. The main re eason is because e minutiae alre eady have a d different appea arance contras sted with the original finger rprint. Hence, it is become an n idea to optim mize the minuti iae extraction a as an input of t the system. In term of f the performan nce evaluation of the system, , we used the a authentication step to evalua ate the ability o of the proposed m method to aut thenticate whe ether the inpu uts of fingerpri int are a genu uine owner or an impostor. This categorizin ng process jus tifies the genu uineness of the e fingerprint by y implementin ng some criteri ion as a scorin ng for both an e stablished fing gerprint and t the input fing gerprint as an enquiry finge erprint. The fi first criterion i is by directing t the input into its fingerprin nt classificatio on group to sh hortage the id dentification pr rocess. Next i is by calculating g the distance between core e and tent arch h (TA) of the fingerprint. Th he third criteri ion is by scor ing a minimum and maximum m distances of f matrices valu ues of minutiae e between an original finge erprint register ed in database a and several fin ngerprints from m the same ow wner as inform mation to calc culate the dista ance value of each pixel of th he fingerprint, so that varian nt possibility o of a genuine f fingerprint can n be decided la ater even when n the acquisition n process of e each fingerprin nt is taken dif fferently. The next criterion n is by evaluat ting the scorin ng of minimum and maximum m distances of f matrices valu ues of minutiae e between the genuine data and a false da ata to score the value to rejec ct an input. Th he last criterio on is by settin ng a threshold d value of acc cepted and reje ected decision a s the result of f the third and the fourth crit teria. The eval luation is starte ed by determin ning an equal error rate (EER) ) of each datab base. ass.ccsenet.

Table 1. EE

0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.083 0.083

**ld ** Vol. 14, No. 6 2018

0.475 0.475 0.375 0.425 0.525 0.175 0.175 0.325 0.675 0.625

n Social Science **Thresho**

1/0.125 1/0.125 1/0.125 1/0.125 1/0.125 1/0.125 1/0.125 1/0.125 1/0.167 1/0.167

Databases

Asian

**EER **

**Da**

I Test Training ion amon All D

4 DB1 DB2 DB3 DB4

2 DB1 DB2 DB3 DB4

**atabases **

ER Comparasi

.org

## GAR/FAR

FVC2002 FVC2004 BRCDBI

ass.ccsenet. .org Asian n Social Science Vol. 14, No. 6 2018

BRCDBI I - 0.083 1/0.167 0.675 It has beco ome commonp place in the au uthentication s step that not al ll the accepted d or rejected fi fingerprints are e true genuine an nd true impost tor. These con nditions are kn nown as false g genuine and fa false impostor. False genuine e and impostor w would create a problem if its rates (EER R) are huge. H Hence, fingerp print with the lowest EER h has a chance to b become a bette er fingerprint i in the database e. However, EE ER is not the o only requireme ent to acknowl ledge which fing gerprint has a better error ra ate. In this res search, thresho old value is al lso determined d as a paramet ter to know whi ch fingerprint in the same d database has t the lowest erro or rate. The re eason is becau use threshold v value would sho ow an excuse le evel for the au uthentication sy ystem to decid de the authentic city of the fing gerprint. Findin ng an error rate for each fing gerprint in the database is r required to dis scover the cha aracteristic of the database after imposed b by the propose ed algorithm. B Based on the experiment, th he lowest leve el of the error r rate for datab bases FVC2002 and FVC2004 4 is in 0.063. . Meanwhile, the highest E EER and the th hreshold of ea ach EER coul ld be dissimilar. In term of the e threshold sco ore, the highes st score would d represent a be etter condition n of the fingerp print. If a fingerp print has a hig gh threshold sc core, it means that the enquir red fingerprint t would be rec cognized by sy ystem as an auth orized fingerp print even with h a high qualifi fication matchi ing score. How wever, the thre shold rate doe es not become a p prior regulatio on to decide wh hich fingerprin nt has a better error rate but E EER with the l lowest score d oes. The next thing to be ev valuated is du uration needed d to execute th he proposed a algorithm. Tim me consuming g is a concerning g issue to be d determined sin nce there are tw wo different in nput of the fing gerprints adap pted in generat ing a cancellable e feature and i its authenticat ion process. T This first comb bination of inp put is cancellab ble step; core- point step; class ification step; authentication n step (using an an original fing gerprint image) ). The second is cancellable step; core-point t step; classific cation step; Ro oI step; authen ntication step ( (using a croppi ing input). Fur rthermore, the total times of e each combinati ion are compa ared to see wh hich combinati ion is better. T The approach has been teste ed by using Intel l Core i5-2430

0M CPU@2.4 40GHz; 4.00 G GB installed R RAM; and MA ATLAB version n 7.10.0 (R20 10a). The follow wing tables illu ustrate time ta aken by system m to execute a all steps of th he research. Fr rom each table

e, the compariso on among diffe erent sub-data abases in the s same database e is shown to provide the d different percen ntage between or riginal input an nd RoI input in n order to show w which input t has a better ti ime to run all s steps. Table 2. Ti ime Needed fo or Database FV

VC 2002 (in Se econd)

Steps

Region T ime No. Ti ime Needed Cancellable Core-Time Classification C of Aut thentication Total De eficitsInterest ( (%) Original 0.8589 0.5542 0.7269 0.00 00187 2 .140187

1. DB1

23.85 RoI 0.4834 0.4099 0.5048 0.2316 0.00 00130 1 .62983 Original 1.1610 0.9232 0.7592 0.00 00204 2 .843604

2. DB2

39.33 RoI 0.5269 0.4190 0.5255 0.2538 0.00 00142 1 .725342 Original 0.8333 0.6627 0.6941 0.00 00187 2 .190287

3. DB3

27.89 RoI 0.4825 0.3837 0.4811 0.2320 0.00 00130 1 .57943 Original 0.9826 0.7814 0.6855 0.00 00184 2 .449684

4. DB4

36.33 RoI 0.4765 0.3789 0.4751 0.2291 0.00 00128 1 .559728

Table 3. Ti ime Needed fo or Database FV

VC 2004 (in Se econd)

Steps

Region T ime No. Ti ime Needed Cancellable Core-Time C Classification of Aut thentication Total De eficitsInterest ( (%) Original 1.0951 0.8709 0.6966 0.00 00187 2 .662787

1. DB1

40.47 RoI 0.4842 0.3850 0.4829 0.2328 0.00 00130 1 .58503 ass.ccsenet.org Asian Social Science Vol. 14, No. 6 2018 Original 0.7731 0.6148 0.6820 0.000183 2.070083

2. DB2

25.06 RoI 0.4738 0.3768 0.4725 0.2280 0.000127 1.551227 Original 1.0568 0.8218 0.6878 0.000190 2.566590

3. DB3

38.29 RoI 0.4903 0.3805 0.4772 0.2357 0.000132 1.583832 Original 0.8942 0.7111 0.7009 0.000188 2.306388

4. DB4

30.84 RoI 0.4873 0.3875 0.4860 0.2343 0.000131 1.595231

Table 4. Time Needed for Database BRC (in Second)

Steps Region Time No. Time Needed Cancellable Core-Time Classification of Aunthentication Total Deficits

Interest (%) Original 0.5049 0.4015 0.7120 0.000191 1.618591 DB1 1.

0.0057 Test RoI 0.4943 0.3931 0.4929 0.2380 0.000133 1.618433 Original 0.4762 0.3787 0.6842 0.000184 1.539284

DB1 2.

- 1.04 Training RoI 0.4750 0.3777 0.4737 0.2287 0.000128 1.555228 Original 0.6159 0.4898 0.7584 0.000203 1.864303

3. DB2

7.59 RoI 0.5262 0.4184 0.5247 0.2535 0.000142 1.722942

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

No. Time Needed FVC 2002 FVC 2004 BRC

Size 43.13

54.86

1.81

1. DB1 DB1 Test

Time 23.85 40.47 0.0057 Size 53.95

38.08

0.25

2. DB2 DB1 Training

Time 39.33 25.06 -1.04 Size 41.11

53.38

14.04

3. DB3 DB2

Time 27.89

38.29

7.59 Size 51.21

45.30

4. DB4 Time 36.32