Biometric Encryption and Bio-Fusion Authentication ...

A. Senthil Arumugam et. al. / International Journal of Engineering Science and Technology Vol. 2(10), 2010, 5357-5369

Biometric Encryption and Bio-Fusion Authentication using Combined Arnold Transition and Permutation Matrices A.Senthil Arumugam#1 Research Scholar Centre for Information Technology and Engineering Manonmaniam Sundaranar University Tirunelveli

Dr.N.Krishnan#2 Professor and Head Centre for Information Technology and Engineering Manonmaniam Sundaranar University Tirunelveli Abstract: Biometrics is used for person identification and verification. Combining Private Key cryptography and Biometrics is a new research in industry. In this paper, a biometric encryption has been proposed based on Pseudo Random Numbers and Permutation Matrices. Henon Map is used to generate pseudo random numbers and then encrypt the biometric trait pixels one by one using permutation matrices. Biometrics is used for person identification and verification. Authentication is done by Two Levels 1.Henon Key based verification and followed by Biometric Encryption Based Verification. Keywords: Henon Map, Permutation Matrices, Biometric Encryption 1.INTRODUCTION Security is a major field in Signal Processing and Biometrics. At present, secure communication plays an increasing and ever-growing role in many fields of common-life, such as banking and networking. The chaos is a process of definite pseudo-random sequence produced by non-linear dynamics system. It’s non-periodic and non-astringe. ‘Deterministic chaos’ is a term used to denote the irregular behavior of dynamical systems arising from a strictly deterministic time evolution without any source of noise or external stochasticity. This irregularity manifests itself in an extremely sensitive dependence on the initial conditions, which pre-includes any long-term prediction of the dynamics. Most surprisingly, it turned out that such chaotic behavior can already be found for systems with a very low degree of freedom and it is, moreover, typical for most systems. Biometric System always produces Yes/No response, which is essentially one bit of information. Therefore, an obvious role of biometrics in the conventional cryptosystem is just password management, as mentioned by Bruce Schneier [1]. Upon receiving Yes Response, the system unlocks a password or a key. The key must be stored in a secure location. This scheme is still prone to the security vulnerabilities. Biometric Templates or Images stored in a database can be encrypted by conventional methods [1]. This would improve the level of security. A new Scheme is suggested in this for secure Biometric Image Encryption. Pseudo Random Number is generated by Chaotic Henon Map. The Organization of this paper is as follow. In Section 2, the design of the proposed chaos based 3 D image Shuffling and biometric image encryption scheme is discussed in details. In Section 3, Interactive Data Language (IDL) Implementation outcomes are described. In Section 4, Security analysis is give. In Section 5, conclusion remarks are drawn. II.THE PROPOSED COMBINED ARNOLD MAP AND BIOMETRIC ENCRYPTION ALGORITHM The Biometric Encryption algorithm includes two steps. Firstly Biometric Trait is shuffled by Arnold 3D Transformation. Then, the pixel value of the scrambled biometric trait is encrypted by permutation matrices. 2.1. Arnold Transformations The Classical cat map, a kind of cut-out transformation, is originally introduced into traverse theory by Arnold and so-called Arnold transformation [2]. The 2D Arnold cat map including two control parameters is as follows:

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x '  ( a  b ) mod n

(1)

y '  ( a  2 b ) mod n

(2)

Where a and b are two positive integers and x , y  0,1,2........N  1 2D Matrix Transformation: '

'

m  m(m 2 ) square matrix, let x 2  ( x1 , x 2 ) denote the element coordinate in this square matrix 2 and y  ( y1 , y2 ) be the mapped element coordinate. Arnold transformation is commonly known as cat face transformation. Suppose ( x, y ) is a point in unit square, the transformation that change the point ( x, y ) to ' ' another point ( x , y ) is showed as formula (1) and (2)

for a given

3D Cat Map [3] is extended by introducing another two control parameters c and d.

 x'  x   '    y   A y  mod M z'   z   

(3)

In order to scramble the 3-color values of a pixel, we generalized the 2-dimensional Arnold transformation to the 3-dimensional case as follows. Where A is used to generate Shuffled-Bio-encrypt Image. 2.1.1. 2D Transformation of the Biometric Trait and implementation in IDL (a) Step 1: Load the Biometric trait using IDL Function (b) Step 2: Initialize the Iteration steps to Arnold function (c) Step 3: Use While Loop to start the Shuffling of Biometric Traits (d) Step 4: Arnold formulae is (x+y) mod N and (x+2y) mod N , where N is the Image size (e) Step 5: Remainder values are used to shuffle the Biometric Position. The following Figure (2) and Figure (4) are 2D and 3D Arnold Transformation to Fingerprint Traits.

Figure.1. Input Biometric

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Figure.2. 3D Scrambling

The Following Figure (3) and Figure (5) shows the First and 10th level Iteration of Arnold Scrambling.

Figure.3. 2 D Arnold First Level Scrambling

Figure.4. 2 D Arnold 10th Level Scrambling (10th Iteration)

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Figure.5. Arnold Modulus Plot

Figure (1) and Figure (2) are shows the Biometric trait input and 3D Arnold scrambling output. Figure3, 4 shows the 2D Arnold Scrambling of different Iteration level position scrambling. Figure (5) shows the Arnold modulus values plot in IDL. Image data having strong correlations among adjacent pixels. Statistical analysis on large amounts of images shows that averagely adjacent 8 to 16 pixels are correlative in horizontal, vertical and also diagonal directions for both natural and computer-graphical images. In order to disturb the high correlation among pixels, we adopt Arnold cat map to shuffle the pixel positions of the plain Biometric trait. After Several iterations, the correlation among the adjacent pixels can be disturbed completely. The following figure is the correlation of original and scrambles Biometric Image.

Figure.6. Correlation for Horizontal adjacent Pixels

2.2. BiometricEncryption using Henon and Permutation Matrices Cryptographic systems require a secret key or a random number which must be tied to an individual through an identifier. This Identifier indeed could be a globally unique user id or biometric data. The objective of the biometric encryption algorithm is to provide a mechanism for the linking and retrieval of a digital key using Biometric. The Biometric might be a 2D Image such as fingerprint, face and iris. The resulting digital key is then used as cryptographic key. 2.2.1. Henon Map: The Henon system [4] is described by

xi 1  1  axi2  yi

(4)

yi 1  bxi , i  0,1,2.............

(5)

Where a and b are two real parameters. When a is equal to 0.3 and b is equal to 1.4, the Henon system is chaotic. Now the above Henon map is converted into one Dimensional Henon Chaotic Map.

xi  2  1  axi21  bxi

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Graphical view of Henon map (IDL Widget output)

Figure.7. Graph View of Henon Sequence

Figure.8.Bifurcation of Henon Chaotic System in IDL

Pseudo Random Numbers view in IDL Software:

Figure 9.Henon Chaotic Pseudo Random Numbers (IDL Text Output)

The Above Henon Pseudo Random Keys are Stored in the Database. The following Diagram Shows the Overall Biometric Authentication System Architecture:

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A. Senthil Arumugam et. al. / International Journal of Engineering Science and Technology Vol. 2(10), 2010, 5357-5369 Live Trait

Digital Key

3D Arnold Shuffling

Permutation Matrix

Henon Chaotic Map

Bio PseudoRN +BioEncr Data

Biometric Encryption

Figure.10. Enrollment of Biometric Authentication System

 

Phase 1: Digital Key is a unique, retrieved from Live Biometric Fingerprint. Pseudo Random Number is generated by Henon map. Numbers are stored in a database. Phase 2: This is Biometric Encryption. Biometric Live Trait is shuffled by Arnold Cat Map Equations Equation (1) and Equation (2). First Live Trait is Shuffled by two dimensional Arnold Cat Map after that shuffled by three dimensional Arnold cat Map. This will make a high level of security to biometric enrollment System. This means Combination of 2D and 3D Arnold Cat Map Shuffled Biometric Trait. System Flow is like this.

Live Trait

2D Arnold Map+3D Arnold

Combined Arnold Shuffled Image

Figure.11. Proposed Combined Arnold Shuffling

2.2.2. Algorithm of Combined Arnold Shuffled Image: (a). Step.1: 2D Shuffled Image is the input to 3D Arnold Algorithm (b). Step.2: Declare the Array [1, 1, 1], [1, 2, 2], [1, 2, 3] (Arnold 3D Shuffling Matrix Values) (c). Step.3. Initialize three Loops to read 2D Shuffled Biometric Trait (d). Step.4: Use IDL Language Matrix Multiplication Operator. Array [1, 1, 1], [1, 2, 2], [1, 2, 3]## [Two Dimensional Shuffled Image] (e). Step.5: Display the Image. The IDL Language Output of the Combined Arnold Shuffled Image is

Figure.12 Input Trait

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Figure.13. Combined Shuffled Trait

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A. Senthil Arumugam et. al. / International Journal of Engineering Science and Technology Vol. 2(10), 2010, 5357-5369 2.3. Generation of the Permutation Matrix. Random Permutations of columns and rows of matrix to form a different key for each Biometric Data Encryption. Permutation matrix is defined by

( P A P )  P 1 A 1 P 1  P A P Since P 1  P

(7) (8)

The Following Mathematical example shows the Permutation Matrix

1 3 5  A   6 7 8

(9)

1 6    AT   3 7  5 8  

(10)

1 3 5  ( AT )T    6 7 8   

(11)

Rewritable Rows is

If the Dimension of matrix is m  m , then there will be m ! number permutation matrix and Number of involutory matrix can be generated using the same element.

m!

2.3.1. Algorithm: The Algorithm is defined as follows (a). Step.1: The Combined Arnold Shuffled biometric trait f(i,j) is M × N size. (b). Step.2: Arrange the pixels of Trait from 1 to M × N. (c). Step.3. Choose the Henon Pseudo Random numbers and then apply sorting. (d). Step.4: Store the sorted value to permutation matrix first array (e). Step.5: Check the Permutation Matrix first Array and with Unsorted Pseudo Random Numbers using IF Logic. If found, the value positions is stored in to second Array. (f). Step.6: Store the INIT and End Parameter Values to third Array. This Scheme makes use of “Random” Permutations [5] of columns and rows of a matrix to form a “Different” key for each block of Biometric Encryption. Simply, In the First Cell storing the unsorted or sorted keys, Second Cell is the replacement address set. Position based encryption is done by this replacement address. The Following figure shows the permutation Matrix values (Values from IDL).

Figure.14. Permutation Matrix

In Figure (14) Shows the permutation matrix is used for encrypting and decrypting a Biometric Trait. Declare the cell in three dimensional formats. In the first cell Permut [I, 1] shows the sorted Pseudo Random Numbers. In the Second cell Permut [I, 2] shows the Position values. In the third cell is the initial and end control loop values.

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A. Senthil Arumugam et. al. / International Journal of Engineering Science and Technology Vol. 2(10), 2010, 5357-5369 In this paper proposed Combined Arnold Shuffling and Permutation Matrix based Encryption and Authentication. This will improve the security and privacy level [6] of biometric Authentication System. The main concept of the proposed authentication system is that we store Pseudo Random keys and encrypted Image. The verification is done by Pseudo Random keys and Encrypted Image. The keys are unpredictable, nonrepetition. Encrypted Data also very high level of secure, so hackers will never identify the Biometric Trait and it will improve the statistical Properties of Biometric Trait. The following Figure (15) show the combined output of permutation matrix and combined Arnold transition mapping. These images are used in the purpose of authentication. Figure16 shows the Biometric Authentication Architecture. All the implementations are done by Interactive Data Language version 7.0 (IDL).

Figure.15 Biometric Encryption in IDL

2.4. Proposed Biometric Fusion Authentication Architecture This Proposed Systems shows the Fusion based Architecture. Now day’s authentication systems face various risks. One of the most serious threats is the vulnerability of the templates database. An attacker with access to a reference template could try to impersonate a legitimate user by reconstructing the biometric sample and by creating a physical spoof. In this paper we discussed the Biometric Fusion Authentication in Two Levels. First Level is Key Based Authentication [7]. Second Level is Biometric Encryption based Authentication. Authentication Module is developed by PHP and Mysql. Pseudo Random Keys and Biometric Encrypted Images are stored in the MySql Database. Input Biometric Trait is validated against Keys and Biometric Encrypted Image. This will improve the Higher Level Security in Authentication. 2.4.1. Generating PRN using Henon Map: Majority cryptographic applications use of random numbers. These random numbers are deterministic. However, if the algorithm is good, the resulting sequence will overtake many reasonable tests of randomness. Such numbers are referred to as Pseudo Random Numbers. Here Henon Map will generate the pseudo Random Numbers and the keys from biometric trait. The proposed Architecture is implemented in two different platforms; IDL and PHP-Mysql. Key generation process is completely non-linear and there is no relationship between any two keys produced and as such hill climbing or predication of data is no way possible. In the second step, based on the henon map key, permutation matrix will generate the permutation matrix Figure (14) for biometric encryption. Both the keys and Biometric Encrypted Data are stored in the Database. Authentication is performed in two levels: one is key level authentication and second is biometric encrypted level. The Architecture of Bio-Fusion Authentication is

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Live Trait

Digital Key ********

Non Linear .Henon Map

Key View

Key Store

. Key Based Authentication . Bio-Encrypt

Key DB

Key Retrie

Accept

BE

Pixel Permutation

Cipher

Getting Keys from

Reject

Figure.16. Biometric Enrollment and Authentication Architecture

1. 2. 3. 4. 5.

Input Live Trait Generate keys from Digital Key using Henon Map Storing keys to MySql Database Pixel Permutation to Biometric Live Trait Generate bio-cipher Image using Henon and permutation matrix. Final Stage is Authentication. In period of authentication encrypted Trait is retrieved from the database and decrypted by the same permutation algorithm. There is no difference between encryption and decryption. Apply the inverse operation of permutation swapping or use permutation matrix column 3.

III.SECURITY ANALYSIS AND STATISTICAL TESTING In this section, the performance of the proposed Biometric Image Encryption scheme is analyzed in detail. 3.1. Statistics Histogram.

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A. Senthil Arumugam et. al. / International Journal of Engineering Science and Technology Vol. 2(10), 2010, 5357-5369 The Gray value histogram of explicit image distributed unevenly with the information itself. The cipher text of the biometric trait histogram gray values distributed evenly Figure (17) and Figure (18). HISTOGRAM FOR ORIGINAL IMAGE 250

200

150

100

50

0 0

50

100

150

200

250

Figure.17.Histogram of Original Image

HISTOGRAM FOR ENCRYPTED IMAGE 160 140 120 100 80 60 40 20 0 0

50

100

150

200

250

Figure 18.Biometric Encryption Histogram Image

3.2. Correlation Coefficient of Adjacent Pixels The Correlation analysis is performed by randomly select 2500 pairs of two adjacent pixels in vertical, horizontal, and diagonal direction. This analysis is performed to input Biometric Trait and cipher Biometric Image. The Correlation Coefficient is calculated by the following Formula

cov( x, y )

rxy 

(12)

D( x) D( y ) Where x and y are biometric Image values of the two adjacent pixels in the image. Where

cov( x, y ) 

1 N

E ( x) 

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 ( x  E ( x))( y  E ( y)) i 1

1 N

i

i

(13)

N

x i 1

i

(14)

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D( x) 

1 N

N

 ( x  E ( x )) i 1

i

2

(15)

i

The following Table.1 Shows the Correlation Coefficient Mathematical Implementation. Correlation is a measure of the relation between two or more variables .Correlation coefficients can range from -1.00 to +1.00.The value of -1.00 represents a perfect negative correlation. The value of +1.00 represents a perfect positive correlation. A value of 0.00 represents a lack of correlation. TABLE.1. Original Image Pixel Correlation

of

Correlation Coefficient values 1.00000

of

0.958037

of

0.957843

Original Image Pixel position Correlation coefficient horizontally adjacent pixels Correlation coefficient vertically adjacent pixels Correlation coefficient diagonally adjacent pixels

TABLE. 2. Cipher Image Pixel Correlation

of

Correlation Coefficient values 0.00014483

of

0.00023343

of

0.00453323

BioCipher Image Pixel position Correlation coefficient horizontally adjacent pixels Correlation coefficient vertically adjacent pixels Correlation coefficient diagonally adjacent pixels

The above Table.2 shows the correlation coefficient of Bio-Cipher Image, the Correlation coefficient between the input and Cipher Biometric Images are implemented in IDL. The output images are the following

Figure.19.Trait Correlation

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Figure.20. Bio-Cipher Image Correlation (IDL Output)

3.3. Differential Attack Differential attack is used find out a meaningful relationship between the plain image and the BioCipher Image. If one minor change in the plain image can cause a significant change in the biocipher image with respect to diffusion and confusion. To test survivability of the cryptosystem against differential attacks, two common parameters are defined i.e., Number of pixels change Rate (NPCR) and unified average Changing intensity (UACI) 3.3.1. Number of Pixel change Rate: NPCR Means the change rate of the number of pixel of BioCipher image while one pixel of plain image is changed. Tests have been performed on different size of biometric traits. The results are shown in Table 1, which mean that a swiftly change in the biometric traits in a significant change in the biocipher image. NPCR is defined as D (i, j )

0, C (i, j )  C2 (i, j ) D(i, j )   1 1, C1 (i, j )  C2 (i, j ) Where C1 (i, j ) and C2 (i, j ) be the pixel value at grid

(16)

(i, j ) of the original Biometric Image C1 and

that of the changed Biometric Encrypted Image C2 respectively. W and H denote the width and height of the Image C1 or C2 .

NPCR 

 D(i, j ) 100% W H

(17)

3.3.2. Unified average Changing intensity: UACI Measures the average intensity of the differences between input biometric trait and Encrypted Biometric trait.UACI is defined as

UACI 

C (i, j) C (i, j) / 255100% 1

2

WH

(18)

The NPCR and UACI values in Red, Green and Blue Channels in the Biometric Image are NPCR in Red Channel NPCR in Green Channel NPCR in Blue Channel UACI in Red Channel UACI in Green Channel UACI in Blue Channel

: : : : : :

100 100 100 38.6969 31.5265 64.7209

IDL Command Prompt output is

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Figure.21. Differential Attack Analysis in IDL

IV.CONCLUSION In this paper, an improved Combined Arnold and permutation matrix scheme is proposed, which is based on the Henon chaotic map. It is nothing but, well known two dimensional and three dimensional Arnold map is combined by programmatically to produce combined Arnold transition. This model is used to design a fast and secure Biometric Encryption Scheme. The main concept of the proposed authentication scheme is that we did the authentication is two levels. This newer algorithm significantly increasing biometric resistance to various attacks such as the statistical and differential attacks. Security of our proposed authentication scheme against the attacks of Threat Vectors, false Enrollment using Fake Traits, reuse of residuals and Replay Attacks. REFERENCES [1] [2] [3] [4] [5] [6] [7]

Claus Vielhauer,”Biometric Authentication for IT Security from Fundamentals to handwriting”, 2006Springer Science, Business Media, Inc Zhu Liehuang,”A Novel Algorithm for scrambling Digital Image based on Cat Chaotic Mapping, IIH-MSP’06 X.R.Wang,”An Image encryption algorithm based on chaotic cat map”, Chinese Microelectronics & Computer, 2007, pp, 131134 H.Zang,X.F,Wang,”A Fast Image Encryption Algorithm based on Chaos System and Henon Map”, Chinese Journal of Computer Research and Development,2005,pp,2137-2142. Shujun Li,”Cryptanalysis of a chaotic image encryption method”,2002 IEEE,pp,708-711 U. Uludag, S. Pankanti, S. Prabhakar and A.K. Jain. “Biometric Cryptosystems: Issues and Challenges”. Proceedings of the IEEE. 92(6):948-960. 2004 V. Bjorn. “Cryptographic key generation using biometric data”. U.S. Patent 6035398, Mar. 7, 2000 (Priority date: Nov. 14, 1997).

V.AUTHORS PROFILE A. Senthil Arumugam#1 received M.S.degree in Information Technology and ECommerce from Manonmaniam Sundaranar University, Tirunelveli, India in 2003, M.Tech degree in Computer and Information Technology from Manonmaniam Sundaranar University, Tirunelveli, India in 2007 and M.Phil Degree in Computer Science from Manonmaniam Sundaranar University, Tirunelveli, India. Currently, he is the Ph.D Research Scholar of Centre for Information Technology and Engineering of Manonmaniam Sundaranar University, Tirunelveli, India. His research interests include Biometric Encryption and Image Processing, Cryptography, Open Source Software Development and Web Services. He is a Member of the IEEE. Nallaperumal Krishnan#2 received M.Sc. degree in Mathematics from Madurai Kamaraj University, Madurai, India in 1985, M.Tech degree in Computer and Information Sciences from Cochin University of Science and Technology, Kochi, India in 1988 and Ph.D. degree in Computer Science & Engineering from Manonmaniam Sundaranar University, Tirunelveli. Currently, he is the Professor and Head of Centre for Information Technology and Engineering of Manonmaniam Sundaranar University. His research interests include Signal and Image Processing, Remote Sensing, Visual Perception, and mathematical morphology fuzzy logic and pattern recognition. He has authored three books, edited 18 volumes and published 25 scientific papers in Journals. He is a Senior Member of the IEEE and chair of IEEE Madras Section Signal Processing /Computational Intelligence / Computer Joint Societies Chapter.

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