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A PAPER PRESENTATION ON HIDING DATA IN IMAGES BY SIMPLE LSB SUBSTITUTION

Hiding data in images by simple LSB substitution

Abstract

In this paper, a data-hiding scheme by simple LSB substitution is

proposed. By applying an optimal pixel adjustment process to the stego

-image obtained by the simple LSB substitution method, the image

quality of the stego-image can be greatly improved with low extra

computational complexity. The worst case mean-square-error between the

stego-image and the cover-image is derived. Experimental results show

that the stego-image is visually indistinguishable from the original

cover-image. The obtained results also show a significant improvement

with respect to a previous work.

Keywords: Data hiding; LSB substitution

1. Introduction

Data hiding is a method of hiding secret messages into a cover-media

such that an unintended observer will not be aware of the existence of

the hidden messages. In this paper, 8-bit grayscale images are selected

as the cover media. These images are called cover-images. Cover-images

with the secret messages embedded in them are called Stego-images. For

data hiding methods, the image quality refers to the quality of the

stego-images.

In the literature, many techniques about data hiding have been proposed

[1-5]. One of the common techniques is based on manipulating the least

significant bit (LSB) planes by directly replacing the LSBs of the

cover-image with the message bits. LSB methods typically achieve high

capacity.

Wang et al. [6] proposed to embed secret messages in the moderately

significant bit of the cover-image. A genetic algorithm is developed to

find an optimal substitution matrix for the embedding of the secret

messages. They also proposed to use a local pixel adjustment process

(LPAP) to improve the image quality of the stego-image. Unfortunately,

since the local pixel adjustment process only considers the last three

least significant bits and the fourth bit but not on all bits, the

local pixel adjustment process is obviously not optimal. The weakness

of the local pixel adjustment process is pointed out in Ref. [7]. As

the local pixel adjustment process modifies the LSBs, the technique

cannot be applied to data hiding schemes based on simple LSB

substitution.

Recently, Wang et al. [8] further proposed a data-hiding scheme by

optimal LSB substitution and genetic algorithm. Using the proposed

algorithm, the worst mean-square-error (WMSE) between the cover-image

and the stego-image is shown to be 1/ 2 of that obtained by the simple

LSB substitution method.

In this paper, a data-hiding scheme by simple LSB

substitution with an optimal pixel adjustment process (OPAP) is

proposed. The basic concept of the OPAP is based on the technique

proposed in Ref [7]. The operations of the OPAP is generalized. The

WMSE between the cover-image and the stego-image is derived. It is

shown that the WMSE obtained by the OPAP could be less than 1/2 of that

obtained by the simple LSB substitution method. Experimental results

demonstrate that enhanced image quality can be obtained with low extra

computational complexity. The results obtained show better performance

than the optimal substitution method described in Ref. [8].

The rest of the paper is organized as follows. Section 2

briefly describes the simple LSB substitution. In Section 3, the

optimal pixel adjustment process is described and the performance is

analyzed. Experimental results are given in Section 4. Finally, Section

5 concludes this paper.

2. Data hiding by simple LSB substitution

In this section, the general operations of data hiding by simple LSB

substitution method is described.

Let C be the original 8-bit grayscale cover-image of pixels

represented as

(1)

M be the n-bit secret message represented as

(2)

Suppose that the n-bit secret message M is to be embedded into the k-

rightmost LSBs of the cover-image C. Firstly, the secret message M is

rearranged to form a conceptually k-bit virtual image represented as

(3)

Where the mapping between the n-bit secrets message M = { } and the

embedded message = { } can be defined as follows:

Secondly, a subset of pixels is chosen from the cover-image C in a

predefined sequence. The embedding process is completed by replacing

the k LSBs of by Mathematically, the pixel value of the chosen pixel

for storing the k-bit message is modi7ed to form the stego-pixel as

follows:

(4)

In the extraction process, given the stego-image S, the embedded

messages can be readily extracted without referring to the original

cover-image. Using the same sequence as in the embedding process, the

set of pixels storing the secret message bits are selected from the

stego-image. The k LSBs of the selected pixels are extracted and lined

up to reconstruct the secret message bits. Mathematically, the embedded

message bits can be recovered by

= (5)

Suppose that all the pixels in the cover-image are used for the

embedding of secret message by the simple LSB substitution method.

Theoretically, in the worst case, the PSNR of the obtained stego-image

can be computed by

(6)

Table 1

Worst PSNR for k = 1-5 by simple LSB substitution

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----

k 1 2 3 4

5

PSNR 48.13 38.59 31.23 24.61 18.30

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Table 1 tabulates the worst PSNR for some k = 1-5. It could be seen

that the image quality of the stego-image is degraded drastically when

k 4.

3. Optimal pixel adjustment process:

In this section, an optimal pixel adjustment process (OPAP) is proposed

to enhance the image quality of the stego-image obtained by the simple

LSB substitution method. The basic concept of the OPAP is based on the

technique proposed in Ref. [7].

Let be the corresponding pixel values of the ith pixel in the

cover-image C, the stego-image obtained by the simple LSB substitution

method and the refined stego-image obtained after the OPAP. Let be

the embedding error between and . According to the embedding

process of the simple LSB substitution method described in Section 2,

is obtained by the direct replacement of the k least significant

bits of with k message bits, therefore,

(7)

The value of can be further segmented into three intervals, such that

Interval 1:

Interval 2:

Interval 3: (8)

Based on the three intervals, the OPAP, which modifies to form the

stego-pixel , can be described as follows:

Case 1 ( If, then

otherwise ;

Case 2 ;

Case 3 If , then

Otherwise .

Let be the embedding error between and . can be calculated as

follows:

Case 1 and

Case 2 and

Case 3

Case 4 and

Case 5 and

From the above five cases, it can be seen that the absolute value of

may fall into the range only when (Case 2) and (Case 5); while for

other possible values of falls into the range . Because is obtained

by the direct replacement of the k LSBs of with the message bits,

and are equivalent to and , respectively. In general, for grayscale

natural images, when , the number of pixels with pixel values smaller

than or greater than 256 - is insignificant. As a result, it could

be estimated that the absolute embedding error between pixels in the

cover-image and in the stego-image obtained after the proposed OPAP is

limited to

(9)

Let WMSE and WMSE* be the worst-case mean-square error between the

stego-image and the cover-image obtained by the simple LSB substitution

method and the proposed method with OPAP, respectively. According to

Eq. (9) WMSE* can be derived by

WMSE* (10)

Combining Eqs. (6) and (10), we have

WMSE*

WMSE when k

=1;

= (4/9)WMSE when k=2;

(16/49)WMSE when k=3;

(64/225)WMSE when k=4;

(11)

Equation (11) reveals that WMSE*<1/ 2 WMSE, for k 2; and WMSE*

(1/4) WMSE when k = 4. This result also shows that the WMSE* obtained

by the OPAP is better than that obtained by the optimal substitution

method proposed in Ref. [8] in which

WMSE* = (1/2) WMSE.

Moreover, the optimal pixel adjustment process only requires a checking

of the embedding error between the original cover-image and the stego-

image obtained by the simple LSB substitution method to form the final

stego-image. The extra computational cost is very small compared with

Wangâ„¢s method [8], which requires huge computation for the genetic

algorithm to find an optimal substitution matrix.

4. Experimental results

This section presents experimental results obtained for two cover-image

sets. The first set of cover-images consists of four standard grayscale

images, 'Lena', 'Baboon', 'Jet' and 'Scene', each of 512 Ãƒâ€”512 pixels,

as depicted in fig. 1.

Fig 1. The first set cover images of size 512 512 pixels.

The second set consists of 1000 randomly generated grayscale

images. There are two set of secret messages. The first set of secret

message consists of 1000 randomly generated message of 512 Ãƒâ€” 512 Ãƒâ€” k

bits, where k refers to the number of LSBs in the cover image pixels

that are used to hold the secret data bits. For example, suppose that

the last two LSBs of the cover image pixels are used to hold the secret

data, then the secret data is of size 512 Ãƒâ€” 512 Ãƒâ€” 2 = 524 288 bits. The

second set consists of the reduced-sized images of the grayscale image

'Tiff' as shown in fig. 2.

Fig 2. Test image used as second set of secret message.

The reduced-sized images are of size 512 Ãƒâ€” 256 pixels (for 4-bit

insertion), 384 Ãƒâ€” 256 pixels (for 3-bit insertion), 256 Ãƒâ€” 256 pixels

(for 2-bit insertion) and 256 Ãƒâ€” 128 pixels (for 1-bit insertion),

respectively. The results of embedding the first set of secret messages

into the first set of cover-images are listed in Table 2. Referring to

Table 2, the column labeled OPAP is our proposed Table 2, method with

the optimal pixel adjustment process; the column labeled LSB is the

simple LSB substitution method; and the column labeled OLSB in the

optimal LSB substitution method proposed in Ref. [8]. For the OPAP and

LSB methods, the obtained PSNR values are the average values of

embedding the 1000 sets random messages into the cover-images. For the

OLSB method, for k =1; 2, the obtained PSNR values are the average

values of embedding the 1000 sets random messages into the cover-

images, for k = 3, the obtained PSNR values are the average values of

embedding the 10 out of 1000 sets random messages into the cover-images

while for k = 4, no experiments are conducted due to the large number

of searching space for the optimal substitution matrix. The results

reveal that our proposed method has much better performance than the

LSB and OLSB methods for k =2-4.

The results of embedding the reduced-sized image of fig. 2 into the

first set of cover-images are listed in Table 3. The results also

reveal that our proposed method has much better performance than the

LSB and OLSB methods for k =2-4.

Table 4 also shows the percentage of

cover image pixels associated with the five cases:

Case 1 ( and

Case 2 and

Case 3

Case 4 and

Case 5 and (12)

Table 2.

The results of embedding the random messages into the first set of

cover-images

Cover image k OPAP LSB OLSB

Lena 1 51.1410 51.1410 51.1483

2 46.3699 44.1519 44.1651

3 40.7271 37.9234 37.9467

4 34.8062 31.7808 -

Baboon 1 51.1414 51.1414 51.1477

2 46.3691 44.1579 44.1619

3 40.7253 37.9226 37.9480

4 34.8021 31.8588 -

Jet1 1 51.1405 51.1405 51.1478

2 46.37000 44.1149 44.1276

3 40.7273 37.9557 37.9978

4 34.8065 31.8487 -

Scene1 1 51.1410 51.1410 51.1480

2 46.3702 44.1497 44.1628

3 40.7270 37.8914 37.9849

4 34.806 31.8467 -

Table 3

The results of embedding the reduced-sized image of fig. 2 into the

first set of cover-images

Cover image k Case 1(%) Case 2(%) Case 3(%)

Case 4(%) Case 5

Lena 2 9.52 0 86.55 3.93 0

3 14.15 0 80.86 4.99 0

4 21.30 0 73.27 5.43 0

Baboon 2 9.53 0.01 86.51 3.95 0

3 14.03 0.02 80.90 5.05 0

4 20.78 0.05 73.85 5.32 0

Jet 2 9.67 0 86.32 4.01 0

3 13.91 0 81.20 4.89 0

4 20.31 0 74.22 5.47 0

Scene 2 9.58 0 86.53 3.89 0

3 14.17 0.01 80.78 5.04 0

4 21.01 0.01 73.74 5.24 0

Table 4

The percentage of cover image pixels associated with the five cases

(Eq.12) when the reduced-sized images of Fig.2 are embedded into the

cover images.

Cover image k Case 1(%) Case 2(%) Case 3(%)

Case 4(%) Case 5

Lena 2 9.52 0 86.55 3.93 0

3 14.15 0 80.86 4.99 0

4 21.30 0 73.27 5.43 0

Baboon 2 9.53 0.01 86.51 3.95 0

3 14.03 0.02 80.90 5.05 0

4 20.78 0.05 73.85 5.32 0

Jet 2 9.67 0 86.32 4.01 0

3 13.91 0 81.20 4.89 0

4 20.31 0 74.22 5.47 0

Scene 2 9.58 0 86.53 3.89 0

3 14.17 0.01 80.78 5.04 0

4 21.01 0.01 73.74 5.24 0

For illustrative purpose, fig. 3 shows a pair of stego-images obtained

by embedding the reduced-sized image 'Tiff' of size 512 Ãƒâ€” 256 pixels

into the cover-image 'Lena' of size 512 Ãƒâ€” 512 pixels using the simple

LSB method and the proposed OPAP method. From fig. 3(a) (stego-image

obtained by the simple LSB-substitution method), one can see some false

contours appearing on the shoulder of 'Lena'. The unwanted artifacts

may arise suspicion and defeat the purpose of steganography. However,

there is no such artifacts appearing on the stego-image (fig. 3(b))

obtained by the proposed method. The visual quality of stego-images

obtained by the proposed method is much better than that of obtained by

the simple LSB-substitution method.

To further evaluate the performance of the proposed method, the

reduced-sized image of fig. 2 is embedded into 1000 sets randomly

generated cover-images and the obtained average PSNR values are listed

in Table 5.

(a)

(b)

Fig. 3. Stego-images obtained by

(a) Simple LSB-substitution method;

(b) Proposed method, where the secret-image is of size 512 Ãƒâ€” 256 pixels

(4-bit insertion).

Table 5

The results of embedding the reduced-sized image of fig. 2 into the

second set of cover-images.

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----

Cover image k OPAP LSB

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----

Random 1 51.1410 51.1410

2 46.3215 44.0217

3 40.6023 37.8621

4 34.4868 31.337

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----

The results show that similar PSNR values can be obtained for different

type of cover-images.

5. Conclusion:

In this paper, a data hiding method by simple LSB substitution with an

optimal pixel adjustment process is proposed. The image quality of the

stego-image can be greatly improved with low extra computational

complexity. Extensive experiments show the effectiveness of the

proposed method. The results obtained also show significant

improvement than the method proposed in Ref. [8] with respect to image

quality and computational efficiency.