The Technique of Information Hiding based on Modification Function and LSB Matching

Tzu-Chuen Lu and Li-Ling Hsu Department of Information Management,Chaoyang University of Technology, Taichung 41349,

Taiwan, R.O.C. tclu@cyut.edu.tw, s9514641@cyut.edu.tw

Abstract

This paper shall propose an effective hiding scheme to embed large number of information and further to control the distortion of the stego image. The proposed scheme compresses the secret information by using run length coding to increase the total number of hiding capacity. Then, the scheme embeds the compressed results into the digital medium in order to create the stego medium. The purpose is to transmit the secret information successfully without detecting by the illegal party. According to the experiment results, the proposed scheme indeed effectively increases the hiding capacity and greatly decreases the image distortion. Keyword: information hiding, run length coding, modification function, LSB matching 1. Introduction

In this era of information explosion, the rapid improvement of Internet has brought the convenience for people. Some potential problems, however, have resulted from the developing Internet, such as the copy and corruption of digital information. Therefore, the information security is considered as one immediate topic. Information hiding technique is one solution to ensure secret information without being detected, destroyed or stolen. The hiding technique embeds the secret information into a digital medium to create the stego medium. Because the stego medium is similar to the original one, the illegal party will be unable to detect that there are some secret information concealed in the medium. Therefore, we can make sure the safety of the secret information [2, 4].

A good information hiding technique shall include the following requirements [1]: (1) Imperceptibility: the difference between the stego

medium and the original one must be very slight

such that the illegal party can not detect the embedded information.

(2) Security: the illegal party can not extract out the hidden information even if he has detected that there are some information concealed in the stego medium.

(3) Capacity: the total number of secret message which can be embedded in the medium.

(4) Robustness: the stego medium shall be able to resist general image processing.

However, capacity and imperceptibility usually present the reverse relationship that means more information hiding it is, more distortion it will be. How to balance the medium quality and capacity becomes one important topic in information hiding field. Therefore, this paper shall propose an effective hiding scheme to embed large number of information and further to control the distortion of the stego image. 2. Related Works

In order to increase the hiding capacity, the proposed scheme adopts data compression technique to encode the secret information. The compression mechanism used in this paper is run length encoding which has been widely used in lossless data compression, especially for the usage of binary image [3, 6]. Because binary image is composed of 1 and 0, it can be expressed as ( )α, , where denotes a count and α denotes a symbol. For example, the expression ( )1,5 means ‘1’ appearing for five times continuously, that is 11111.

In the proposed scheme, the compressed results instead of the original secret information are hid in the host image. The hiding techniques used in this paper are LSB matching and modification function.

Traditional least significant bit (LSB) replacement hiding technique hides the secret information into medium directly that leads LSB of pixels no longer

Eighth International Conference on Intelligent Systems Design and Applications

978-0-7695-3382-7/08 $25.00 © 2008 IEEE

DOI 10.1109/ISDA.2008.65

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being distributed randomly [7]. Therefore, in 2006, Mielikainen proposed LSB matching hiding scheme to improve the disadvantage of LSB replacement hiding technique [5]. The scheme not only protects the secret information from detecting by the illegal party but also improves the pixel correction problem causing by LSB.

In LSB matching scheme, two neighboring pixels 1p and 2p are used to conceal two message bits

1m and 2m . In order to decrease the image distortion, they use a binary function

)2

(),( 21

21 pp

LSBppF LSB +⎥⎦⎥

⎢⎣⎢= (1)

to determine the modified pixel. In the function, )(xLSB is LSB of x . The hiding process is shown in

Fig. 1.

Yes

NoYes

Yes No No

11)( mpLSB =

221 ),( mppFLSB =221 ),1( mppFLSB =−

22

11

pppp

=′=′

11

2

22

11

−+=′

=′

porpp

pp

22

11 1pppp

=′−=′

22

11 1pppp

=′+=′

Figure 1. The tree structure of LSB matching scheme

First they determine whether LSB of 1p is equal to 1m or not. If 11)( mpLSB = then go forward to the left node and use function LSBF to determine whether

221 ),( mppF LSB = or not. If the result of

LSBF function is equal to 2m , then go forward to the left node of next level again. The stego pixels are

11 pp =′ and 22 pp =′ . Otherwise, if the results of LSBF

function is not equal to 2m , then 1p ′ is equal to 1p and 2p ′ is equal to 12 +p or 12 −p .

If LSB of 1p is not equal to 1m , then go forward to right node and use function LSBF to determine whether

221 ),1( mppFLSB =− or not. If the result of LSBF function is equal to 2m , then go forward to the left node of next level again. The stego pixel 1p ′ is equal to 11 −p and

2p ′ is equal to 2p . Otherwise, 1p ′ is equal to 11 +p , and 2p ′ is equal to 2p .

In LSB matching scheme, they only modify one pixel to conceal two bits into two pixels. The modify

ratio of the scheme is low. Hence, the quality of the stego image is good.

In 2006, Zhang and Wang proposed an information hiding technique that uses the modification function to hide the secret data into the medium [8]. In their scheme, n pixels can be used to embed

⎣ ⎦)12(log2 += nk message bits. For example, suppose that there are two pixels, 1p =5 and 2p =10. The total number of embedded message bits is

⎣ ⎦ ⎣ ⎦ 2)122(log)12(log 22 =+×=+= nk . Next, they transfer the message into ( )12 +n system and embed the results into the medium by a modification function. The modification function is

)12(mod)(),...,,(1

21 +⎥⎦

⎤⎢⎣

⎡ ×= ∑=

nippppFn

iinMOD

.

If the transferred message is not equal to the result of MODF function, then they modify one of the pixels to

make the transferred message equals to the result of MODF function. For example, assume the secret

message is ( )210 . The transferred message is ( ) ( )52 210 ==m . The result of the modification function

is ( ) ( ) 0122mod21015)10,5( =+××+×=MODF which is not equal to m .

They use the formula ( )( ) )12(mod...,, ,21 +−= npppFms nMOD

to decide which pixel shall be modified. If s is equal to or less than n , s ≤ n , then they plus one to the s -th pixel and get the stego pixel 1+=′ ss pp . Otherwise, they subtract 1 from ( )( )sn −+ 12 -th pixel and get ( ) ( ) 11212 −=′ −+−+ snsn pp . Following the same example, the number of the modified pixel is

2p , because ( ) 25mod02 =−=s . Thus, the stego pixel is 11110122 =+=+=′ pp . Similar with LSB matching scheme, Zhang and Wang’s scheme only modify one pixel to embed k message bits into n pixels. The embedding efficient is high.

Both of LSB matching scheme and Zhang and Wang’s scheme can effectively control the image distortion. Therefore, we adopt Zhang and Wang’s modification function and LSB matching technique to maintain the image quality and use the compression technique to increase the hiding capacity.

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3. The Technique of Information Hiding based on LSB Matching and Modification Function

The proposed scheme uses run length coding to compress a secret message and adopt modification function and LSB matching technique to hide the compressed results into a host image. The framework of the proposed hiding scheme is shown in Fig. 2.

(a) Host Image

(b) Block

Figure 2. The framework of the proposed hiding scheme

Fig. 2 (a) is a host image. The proposed scheme divides the host image into several 61× non-overlap blocks and let { }221121 ,,,,, pbbpaaB = be the block, such as Fig. 2 (b). The proposed scheme hides the secret message into 1a , 2a , 1b and 2b by using modification function and hides the secret message into 1p and 2p by using LSB matching technique.

Before hiding, the proposed scheme uses run length coding to encode the secret information into ( )α, , where stands for the continuous appearing times, and α is the appearing symbol. During the encoding phase, the proposed scheme gives a limit δ which means the upper bound of . For example, a secret information is ( )2110000001111110001 . The six bits prior to the secret information are 1. It shall be expressed as ( )α, =(6,1). However, suppose the limit is δ = 4. The compressed results of the prior six bits are (4,1) (2,1). In such case, the compressed results of the secret information are (4,1) (2,1) (3,0) (3,1) (4,0) (2,0).

The proposed scheme conceals two pairs ( )11 , α and ( )22 , α of compressed results into the block B .

The values of 1 and 2 are embedded into 1a , 2a ,

1b and 2b . In addition, the values of 1α and 2α are embedded into 1p and 2p . The hiding process is as the following: Input: ( )11 , α , ( )22 , α and

{ }221121 ,,,,, pbbpaaB = Output: { }221121 ,,,,, pbbpaaB ′′′′′′=′ Step 1: Hide 1 into 1a and 2a by the modification function.

(1) Compute ( ) 5mod),(2

121 ∑

=

×=i

iMOD iaaaF .

(2) Determine whether the result of MODF is

equal to 1 or not. If ),( 21 aaFMOD

= 1 , then ii aa =′ , where 21 ≤≤ i . Otherwise, compute the position of the modified pixel by

( )( ) 5mod, 211 aaFs MOD−= . If 2≤s , then 1+=′ ss aa . Otherwise, 155 −=′ −− ss aa .

Step2: Hide 2 into 1b and 2b , the hiding procedure is the same as Step 1 (1)-(2).

Step3: Hide 1α and 2α into 1p and 2p by LSB matching technique. The tree structure of the proposed scheme is shown in Fig. 3. First, the scheme determines whether LSB of 1p is equal to 1α or not. If 11)( α=pLSB , then determine whether ),( 21 ppFLSB

is equal to

2α or not. The LSBF function used in the proposed scheme is the same as that used in LSB matching scheme. If ),( 21 ppFLSB = 2α , then the stego pixels are 11 pp =′ and

22 pp =′ . Otherwise, we have 122 +=′ pp or 122 −=′ pp . If LSB of

1p is not equal to 1α , then determine

whether ),1( 21 ppFLSB − is equal to 2α or

not. If ),1( 21 ppFLSB − = 2α , then 111 −=′ pp and 22 pp =′ . Otherwise, we have

111 +=′ pp and 22 pp =′ .

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Yes

NoYes

Yes No No

11)( α=pLSB

221 ),( α=ppFLSB 221 ),1( α=− ppFLSB

22

11

pppp

=′=′

11

2

22

11

−+=′

=′

porpp

pp

22

11 1pppp

=′−=′

22

11 1pppp

=′+=′

Figure 3. The tree structure of hiding 1α and 2α

into 1p and 2p

Fig. 4 shows an example block. Suppose that the secret information is ( )20001111 . The compressed results of the secret information are (3,0) (4,1). We hide 1 = 3 and 2 into 1a = 30, 2a = 78, 1b = 6

and 2b = 10, respectively, by modification function.

Then, hide 1α = 0 and 2α = 1 into 1p = 33 and 2p = 35 by LSB matching technique. 1a 2a 1p 1b 2b 2p

30 78 33 6 10 35

Figure 4. An example block

First the proposed scheme computes the modification function ( ) =78,30MODF

( ) 15mod278130 =×+× . Because 1 is not equal to the result of F function, the scheme modifies the second pixel 2a to embed 1 . Here

( ) 25mod13 =−=s and 2≤s . Thus, the stego pixel is 791782 =+=′a .

Similarly, the scheme hides 2 = 4 into 1b = 6

and 2b = 10 with modification function,

( ) =10,6MODF ( ) 15mod21016 =×+× . Because 2 = 4 is

not equal to the result of MODF function, the scheme computes the position of the modified pixel by

( ) 35mod14 =−=s . However, 23 >=s . Hence, the position of the modified pixel becomes 2, since ( ) ( ) 2355 =−=− s . The stego pixel is

911011 23535 =−=−=−=′ −− bbb .

Next, the scheme hides 1α = 0 and 2α = 1 into

1p = 33 and 2p = 35 by using LSB matching

technique. Because ( ) 133 =LSB is not equal to 1α , the scheme computes 1)35,133( =−LSBF to determine

whether it is equal to 2α or not. In this case,

)35,133( −LSBF = 2α , then the stego pixels are 32133111 =−=−=′ pp and 352 =′p . The final

stego block is shown in Fig. 5.

Figure 5. The stego block

In the extraction process, the proposed scheme divides the stego image into several 61× non-overlap blocks and let { }221121 ,,,,, pbbpaaB ′′′′′′=′ be the stego

block. Then, the modification function MODF and the

binary function LSBF are used to retrieve the concealed information. The proposed scheme extracts the message pairs ( )11 , α and ( )22 , α from the stego block. The extraction process is as the following: Input: { }221121 ,,,,, pbbpaaB ′′′′′′=′ Output: ( )11 , α , ( )22 ,α

Step 1: Extract 1 from 1a′ and 2a′ by the modification function

1 = ( ) 5mod),(2

121 ∑

=×′=′′

iiMOD iaaaF

.

Step 2: Extract 2 from 1b′ and 2b′ by the modification function

2 = ( ) 5mod),(2

121 ∑

=×′=′′

iiMOD ibbbF .

Step 3: Extract 1α from 1p′ by

1α = )( 1pLSB ′ .

Step 4: Extract 2α from 1p′ and 2p′ by the binary function

2α = ⎟⎟⎠

⎞⎜⎜⎝

⎛ ′+⎥⎦⎥

⎢⎣⎢ ′

=′′ pp

LSBppF LSB 2),( 1

21

.

For example, the extracted message pairs from Fig. 5 are (3,0) and (4,1), because 1 =

( ) 35mod279130),( 21 =×+×=′′ aaFMOD , 2 =

( ) 45mod2916),( 21 =×+×=′′ bbFMOD , 1α =

0)6( =LSB and 2α = 19

26)9,6( =⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎥⎦

⎥⎢⎣⎢= LSBF LSB

.

The proposed scheme uses the modification function to hide two message symbols in four pixels and adopts the LSB matching technique to conceal two message bits in two pixels. The altering probabilities of

30 79 32 6 9 35

629

the modification function and the LSB matching technique are both

21 , it means the scheme only

modifies one pixel to conceal two messages. Hence, the proposed scheme can reduce the distortion of the stego image effectively. In addition, the secret information is compressed by run length coding which can increase the total number of the hiding capacity. 4. Experimental Results

We use four images, Lena, Baboon, Barbara and F16, with different sizes, 256 × 256, 512 × 512 and 1024× 1024, to test the performance of the proposed scheme. A random number generator is used to generate the secret information. The stego images sized 256 × 256, 512 × 512 and 1024 × 1024 are shown in Fig. 6, Fig. 7 and Fig. 8, respectively. The comparing results of capacity and PSNR are shown in Table 1. According to the experimental results, we can see that PSNR values of the stego images are higher than 50 dB. In addition, the LSB of the stego pixels are distributed randomly. Hence, the illegal party will be unable to detect the secret information.

(a) 51.7718 dB (b) 51.7851 dB

(c) 51.7643 dB (d) 51.8350 dB

Figure 6. The stego images sized 256×256

Figure 7. The stego images sized 512×512

Figure 8. The stego images sized 1024×1024

Table 1. The comparing results Image Size 256× 256 512× 512 1024× 1024

Lena Capacity 40677 163565 654773 BPP 0.622 0.624 0.6244 PSNR 51.7718 51.7671 51.7654

Baboon Capacity 41165 164075 654889 BPP 0.6281 0.626 0.6245 PSNR 51.7851 51.7683 51.7593

Barbara Capacity 40986 163830 654889 BPP 0.6281 0.625 0.6245 PSNR 51.7643 51.7675 51.7626

F16 Capacity 40836 163099 654889 BPP 0.6162 0.6222 0.6246 PSNR 51.8350 51.7710 51.7686

5. Conclusions

(a) 51.7671 dB (b) 51.7683 dB

(c) 51.7675 dB (d) 51.7710 dB

(a) 51.7654 dB (b) 51.7593 dB

(c) 51.7626 dB (d) 51.7686 dB

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This paper proposes an information hiding scheme based on modification function and LSB matching technique to decrease the image distortion. In addition, the proposed scheme uses run length encoding to compress the secret information for increasing the total number of hiding capacity. Experimental results show that the proposed indeed controls the image distortion such that the image quality of the stego image is good. Furthermore, the stego medium will be not so easy to be detected by the illegal party. References [1] Li, H. Y., “A study of information hiding based

on image compression technique,” The Master of Thesis, National Pingtung University of Science and Technology Graduate Institute of Information Management, 2003.

[2] Lu, T. C., Chang, C. C. and Liu, Y. L., “A content-based image authentication scheme based on singular value decomposition,” Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications, Vol. 16, No. 3, pp. 506-522, 2006.

[3] Tai, S. C., Wu, Y. G. and Lin, C. W., “Scalable cube technique for medical image compression,” Proceedings of SPIE's Medical Imaging, San Diego, California, USA, 1999.

[4] Fabien, A. P., Anderson, R. J. and Kuhn, M. G., “Information hiding – a survey,” Proceeding of the IEEE Special Issue on Protection of Multimedia Content, Vol. 87, No. 7, pp. 1062-1078, 1999.

[5] Mielikainen, J., “LSB matching revisited,” IEEE Signal Processing Letters, Vol. 13, No. 5, pp. 285-287, 2006.

[6] Sayoood, K. and Fow, E. (EDs.), Introduction to Data Compression, second edition, Morgan Kaufmann, Los Altos, CA, 2000.

[7] Wang, R. Z., Lin, C. F., and Lin, J. C., “Image hiding by optimal LSB substitution and genetic algorithm,” Pattern Recognition, Vol. 34, No. 3, pp.671-683.

[8] Zhang, X. P. and Wang, S. Z., “Efficient steganographic embedding by exploiting modification direction,” IEEE Communications Letters, Vol. 10, No. 11, pp. 781-783, 2006.

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