De-song WANG1 1School of Computer Science and

Engineering, University of Electronic Science and

Technology of China, Chengdu 610054, China

E-mail: sky_wangds@126.com

Jian-ping LI1, 2 2International Centre for Wavelet Analysis and Its Applications, Logistical Engineering University,

Chongqing 400016, China

Xiao-yang WEN1

1School of Computer Science and Engineering, University of

Electronic Science and Technology of China, Chengdu

610054, China

Abstract

According to the fragile watermarking theory and insecure computer network, the integrity authentication scheme of biometric image based on singular value decomposition (SVD) is proposed for remote users via insecure computer network. We make good use of singular values of singular value decomposition (SVD) of biometric image to check the integrity of biometric image. To make authentication data, the singular values are changed to the binary bits using modular arithmetic. The binary bits of authentication data are embedded into the least significant bit (LSB) of the original biometric image. The pixels to be changed are randomly selected in the original biometric image. The advantages of this scheme are that 1) we can detect any modification of watermarked biometric image; 2) the quality of watermarked biometric image is very high because only a few bits of authentication data are embedded. Experimental results show that the proposed fragile watermarking scheme can be applied to the integrity authentication systems based on biometric image.

Keywords: Biometric image, Fragile watermarking, Singular value decomposition (SVD), Authentication

1. Introduction

With the great spread of computer network and the rapid development of multimedia technologies, the biometric image can be easily used, processed, and transmitted via computer networks, which has caused problems relative to the authentication and integrity. Meanwhile, with the present widespread utilization of biometric identification systems, establishing the authentication of biometric images (fingerprint, fingerprint, Retina, face, hand geometry, palm-print etc.) has emerged as an important research topic. So that cryptography and digital watermarking techniques are two possible ways of achieving this. While cryptography focuses on methods of making encrypted information meaningless to unauthorized parties [1], digital watermarking techniques can be used to embed proprietary information in host biometric

images in order to protect the intellectual property rights and authentication of those images [2].

As a result, researchers have been actively investigating methods of information hiding for authenticating and verifying the content integrity of the images. Various types of fragile watermarking schemes [3-10] have been proposed to serve these purposes. Such as Byun et. al. [6] used singular values (SVs) of an image matrix as authentication data, binary bits are generated from the singular value of one image by using modular arithmetic. Hyobin et. al. [8, 9] used an invertible watermark that can also detect malicious manipulations for authentication of biometric images. The watermarks of robust watermarking schemes for copyright protection are expected to survive different types of manipulation to some extent, provided that the manipulated images are still valuable in terms of commercial importance or significant in terms of visual quality. Unlike robust schemes, schemes for the purposes of authentication and content integrity verification are supposed to be fragile, i.e. we expect the watermark to be destroyed when attacks are mounted on its host media so that alarms can be raised when the wrong watermark is extracted. Therefore, the emphasis of fragile watermarking schemes is focused on sensitivity to attacks or even incidental manipulations. To be considered effective, a fragile watermarking scheme must meet common requirements such as localizing tampering, detecting geometric transformations (e.g. cropping and scaling), signaling removal of original objects, addition of foreign objects and alerting other image processing operations (e.g. low-pass filtering). In this paper, the singular values of SVD are used for authentication data. Although we embed only a few bits of authentication data we can detect any modification of the watermarked biometric image.

The remainder of this paper is organized as follows. Statement of the problem is described in Section 2. Singular Value Decomposition is described in Section 3. Proposed watermarking scheme is described in Section 4. Experiments and results of our method with respect to attacks are conducted in Section 5. Finally, conclusions are given in Section 6.

2. Statement of the problem

Biometric Image Integrity Authentication Based on SVD and Fragile Watermarking

2008 Congress on Image and Signal Processing

978-0-7695-3119-9/08 $25.00 © 2008 IEEEDOI 10.1109/CISP.2008.248

679

2008 Congress on Image and Signal Processing

978-0-7695-3119-9/08 $25.00 © 2008 IEEEDOI 10.1109/CISP.2008.248

679

2008 Congress on Image and Signal Processing

978-0-7695-3119-9/08 $25.00 © 2008 IEEEDOI 10.1109/CISP.2008.248

679

As is known to all, digital image systems provide sophisticated processing flexibility, capability and reliability at lower costs and competitive quality. As a result, digital image acquisition, processing and storage have been steadily replacing their analog counterparts. It has been easier to modify or forge information using widely available editing software. Consequently, there must be a security procedure that prevents unauthorized alteration of digital images. So the integrity of the biometric image can be authenticated using a fragile watermark, and fragile watermark system should detect any tampering in a watermarked biometric image.

(a) Original iris image (b) Integrity questionable Figure 1. Integrity and authenticity of digital iris image authentication and

integrity are questionable without security mechanisms. 3. Singular value decomposition

Any m n× real-valued matrix A , with m n≥ can be written as the product of three matrices

TA USV= (1) The columns of the m m× matrix U are mutually

orthogonal unit vectors, as are the columns of the n n× matrixV . The m n× matrix S is a pseudo-diagonal matrix, where its diagonal elements are

1 2 0nσ σ σ≥ ≥ ≥ ≥ (2) and it is called the singular value (SV) of A . While both U and V are not unique, the singular values iσ are fully determined by A . From the viewpoint of image processing application, singular values (SVs) represent intrinsic algebraic image properties [11]. 4. Watermarking algorithm

The basic idea of this scheme is to embed authentication data extracted from the original biometric image to the watermarked biometric image. For authentication we check if the embedded information is changed or not in the receiver side. We consider these points below.

4.1. Watermark embedding

Let’s consider a still biometric image O of size m n× pixels as an original biometric image. The watermark embedding procedure for the original biometric image is shown in Figure 2. n pixels are randomly selected with a key keyK in the original biometric image O . The same key keyK is used in the watermark extraction procedure. The number of n shouldn’t be the same as the dimension of singular values of SVD. And then, in order to make authentication data, we compute singular values of the image O′ which LSBs of the selected pixels are set to zero.

The pseudo-diagonal matrix S is multiplied by multiplying factor α , so that any modification can be detected. In the experiments, we show that the bigger the multiplying factor,

Figure 2. Watermark embedding scheme

Figure 3. Watermark extraction and verification the more sensitive to changes to the image, but which is not in every case. And then, the multiplied values are set to the round integer values:

( )nS round Sα= (3)

In order to generate binary bits from nS , we use modular arithmetic

Insecure Network /Channel

Randomly select n pixels

O

Embed B into the pixels’ LSB

SVD

( )nS round Sα= (mod 2)nB S=

Set to zero of the pixels’ LSB

O ′

S

B

WO

keyK

Yes

Randomly select n pixels

Extract LSBs from the pixels

SVD

( )nS round Sα= (mod 2)nB S=

Set to zero of the pixels’ LSB

S

B

keyK

WO

WO ′

E

?E B=

Authentication

680680680

(mod 2)nB S= (4) Where B is a binary string of size n . Modular arithmetic is

simply division with remainder, where we keep the remainder and throw every thing else away. In general, the expression

(mod )x y means to divide x by y and keep the remainder, where x and y are integer numbers. The result of modular arithmetic consists of binary bits. The binary bits are embedded into the LSBs of randomly selected n pixels. Embedding binary bits B forms a watermarked biometric image WO .

4.2 Watermark extraction and verification

The extraction and Verification procedure for the embedded watermark from received biometric image is shown in Figure 3. We choose n pixels to find the location of the embedded bits. The key keyK used in the embedding processes is used for selection of the pixels. And then, extract the LSBs from the pixels. The computation of feature information is the same as in the embedding procedure. We compare the LSB strings with the computed authentication data.

If the watermarked biometric image is not changed and correct key is used, the extracted watermark from the received watermarked biometric image is equal to the feature information. When the watermarked biometric image was changed by any processing, or improper key is used to extract the watermark, the extracted watermark is not same as authentication data. 5. Experiments and results

Experiments show that our watermark is equal to authentication data if there is no change of the watermarked biometric image. The change of watermarked biometric image results in difference between extracted strings and authentication data extracted from received watermarked biometric image. For the experiments, we use gray “iris” image of size 320×280 as an original biometric image in the CASIA Iris Image Database [12].

Figure 4. (a) Original iris image and (b) watermarked iris image

Figure.4 shows the original biometric and watermarked biometric image. The watermarked biometric image shows the same image quality to the original biometric image as shown in Fig.4 (b). The difference between two iris images is only 280 bits of LSB among the 89600 pixels (i.e.320×280 pixels). If we use a correct user key and follow the watermark extraction procedure given in Fig.3, the extracted strings are equal to extracted authentication data. When the watermark is extracted

from the un-watermarked image, or by using incorrect key, or by changing the watermarked iris image with any processing technique, the extracted watermark is not equal to feature information.

Table 1 shows the number of different bits extracted from watermarked iris image and 1 bit changed watermarked iris image, respectively, according to the multiplying factor α. We can adjust the sensitivity by changing multiplying factor to iσ . In the experiment, we use 10 or 100 as a multiplying factor α. In general, the bigger the multiplying factor, the more sensitive to changes to the iris images. According to the applications, the multiplying factor can be adjusted. For example, if we need high security the multiplying factor should be increased.

Table 1. The number of different bits extracted from watermarked image and 1 bit changed watermarked iris image, respectively,

according to multiplying factor α α 1 10 102 103 104 105

Different bits 57 124 144 123 160 151

The comparison of a few binary bits between watermarked iris image and 1 bit changed watermarked image is given in Table 2. The sequences of bits are completely different except multiplying factor 1α = even if only one bit is changed. Note that although we embed 280 bits of authentication data, only 8 bits of the data are enough to verify the biometric image’s integrity. According to applications we can adjust the number of binary bits of authentication data extracted from biometric images. Because the singular values are very sensitive to any modification, it is enough to embed only a few bits instead of whole n bits of information.

Table 2. Comparison of first eight binary bits extracted from watermarked iris image and 1 bit changed watermarked iris image,

respectively, according to multiplying factor α k ( 1α = ) 1 2 3 4 5 6 7 8

E 1 0 0 1 1 0 0 0

B 1 0 0 1 1 0 0 0

k ( 10α = ) 1 2 3 4 5 6 7 8

E 1 0 1 1 1 0 1 0

B 0 1 1 1 1 0 0 1

k ( 210α = ) 1 2 3 4 5 6 7 8

E 0 1 1 0 0 0 1 1

B 0 0 0 1 0 0 1 1

k ( 310α = ) 1 2 3 4 5 6 7 8

E 0 0 1 1 0 1 1 0

B 0 1 0 1 0 1 0 0

k ( 410α = ) 1 2 3 4 5 6 7 8

E 0 1 0 0 0 1 0 1

B 0 0 0 1 1 0 1 0

681681681

k ( 510α = ) 1 2 3 4 5 6 7 8

E 1 0 1 0 1 1 1 1

B 1 0 0 0 1 0 1 0

Noted: where k denotes the order of binary bits, E denotes the extracted

binary bits, and B denotes the binary bits of authentication data.

Table 4. Authentication results against various attacks Integrity Yes No

Unchanged √

Wrong key used √

Un-watermarked √

Compressed (by wavelet) √

Compressed (by JPEG) √

Filtered √

Scaled (down or up) √

Rotation √

Pixel changed (by positions) √

Pixel changed (by values) √

Cropped √

color reduced √

Sharpened √

Table 4 shows the authentication results against various CheckMark attacks. Only when the fingerprint images are unchanged the fingerprint images are considered as the authentic images. If someone changes some bits of the watermarked biometric image by any image processing techniques, the watermark extraction procedure indicates that the received biometric image is not authentic. 6. Conclusions

In this paper, a fragile watermarking scheme based on the SVD for biometric image is presented. In order to check integrity of the received biometric image, we make good use of the singular values of SVD of biometric image. Biometric image can be represented with unique singular values. The singular values, authentication data, are very sensitive to any modification. The advantages of this scheme are: 1) we can detect any modification such as wavelet compression, JPEG compression, filtering, scaling, rotation, changing of pixel values and positions, cropping, sharpening, color reduction, line removal and using wrong key; 2) the biometric image’s quality is very high because only a few bits of authentication data are embedded. Experimental results show that the proposed fragile watermarking scheme can be applied to the integrity authentication systems based on biometric image. Acknowledgments. This work was supported by the State 863 Program (Grant No. 2003AA148040), the National Natural Science Foundation of China (Grant No. 10471151, 60216263,

6990312), New Century Excellent Talent Support Project of Chinese Ministry of Education, Doctor Station Foundation of Chinese Ministry of Education, Chongqing Tackle Key Problem Program and Chongqing Natural Science Foundation.

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