Analyses of Pixel-Value-Differencing Schemes with LSB Replacement in

Stegonagraphy

Cheng-Hsing Yang1, Shiuh-Jeng Wang2, , and Chi-Yao Weng3

1Department of Computer Science, National Pingtung University of Education,Pingtung, Taiwan, 900

2Department of Information Management, Central Police University,Taoyuan, Taiwan 333

3Department of Computer Science, National Tsing-Hua University,Hsinchu, Taiwan, 300

{chyang1, bm0941083}@mail.npue.edu.tw{sjwang2}@mail.cpu.edu.tw

Correspondence addressee: Shiuh-Jeng Wang, Dept. of Information Management,

Central Police University, Taoyuan, Taiwan 333

E-mail: sjwang@mail.cpu.edu.tw, Fax: +886-3-3272038

Abstract

This paper shows that a steganographic scheme-value differencing (PVD)

and least-significant-bit (LSB) replacement method istoo conformable to the LSB approach. TheirPVD+LSB method can embed secret data larger thanthe PVD method, however, it is detectable by Fridrichet al. s method but PVD method is not. Some of theshortcomings of the PVD+LSB method are shown inthis paper. At the same time, some techniques areproposed for improving the image quality of thePVD+LSB method without sacrificing the capacity. Allproposed techniques are demonstrated by experimentalresults.Keywords: Pixel-Value Differencing; LSB;Steganography

1. Introduction

secret data into digital media such as images, texts, and

audio. The purpose of steganography is to prevent

unauthorized or malicious use of as well as attacks on

the secret data by hiding it in a stego-image [1-7]. The

embedding capacity and the quality of the stego-image

are the two main factors in the techniques of

steganography.

One of the well-known steganographic techniques is

least-significant-bits (LSB) substitution, in which the

least significant bits of the cover image are replaced

with secret bits [8-12]. Without loss of generality, LSB

approaches usually obtain a considerably high capacity

in addition to retaining good quality.

Although LSB approaches are efficient with regards

to capacity and image quality, the existence of

embedded data is easily detected by bit planes or

programs [3, 17]. Therefore, some hiding approaches

are based on the concept of the human visual system

and are different to the LSB approach [13-16]. Wu and

pixel-v

steganographic method that uses the difference value

between two pixels in a block to determine how many

secret bits should be embedded [13]. Chang and Tseng

proposed a side-match approach to embed secret data

[14]. In their approach the number of bits to be

embedded in a pixel is decided by the difference

between the pixel and its upper and left side pixels. We

also proposed a multi-pixel differencing approach that

uses three difference values in a four-pixel block to

determine how many secret bits should be embedded

[15]. Those steganographic methods obeyed the

principle that blocks in edged areas can tolerate larger

changes than the blocks in the smooth areas. Wu et al.

proposed a PVD+LSB approach [16], which combined

the PVD method with the LSB method, in order to

improve the capacity and PSNR of the PVD method.

In this paper, we will

PVD+LSB approach is too conformable to the LSB

approach. Their approach combines PVD with LSB.

The PVD approach is applied if the 2-pixel blocks have

a large differencing values and the LSB approach is

applied if the 2-pixel blocks have a small differencing

values. In our analysis, the blocks with smaller

differencing values occupy the majority of a cover

image. Therefore, most of their embedding operations

belong to the LSB approach. We will show that their

results can be detected by the program of Fridrich et al

[17

detected [13]. In spite of the above negative findings of

techniques to improve the image quality of their

approach.

The remainder of this paper is organized as follows.

provide the experimental results to demonstrate our

Some techniques to improve the quality of their

approach are shown in Section 4. Finally, our

conclusions are drawn in Section 5.

2. Review of relevant literatures

PVD

method and

2.1. Wu and Tsa -value differencing

PVD method uses the pixel-value

differencing of two pixels to embed secret data. The

gray-valued host image is partitioned into non-

overlapping blocks of two consecutive pixels by

running through all the rows of the host image in a

zigzag manner. The block difference value di iscalculated by | pi pi+1 |, where pi and pi+1 are twopixels in the block. All possible values of di (0 through255) are considered and they are classified into a range

table with n contiguous ranges, say Rk where k = 1, 2,n. The width wk of Rk is uk lk + 1, where uk is

the upper bound of Rk and lk is the lower bound of Rk.The number of embedding bits is determined by the

width of Ri, where di falls into, and is equal toiw2log . Let b be the decimal value of embedded bits.

Then, the embedding operation is to replace di with anew difference value d i, where d i = li + b. Finally, an

inverse calculation of d i is performed to yield the newgray values of the two pixels in the block. For instance,

assume (pi, pi+1) = (110, 124), R2 = [8, 15] and thesecret bits are 010(2). So di = 14, Ri = R2, wi = 8. b =010(2) = 2(10), d i = 10. The inverse calculation of d igets new gray values (p i, p i+1) = (112, 122), so as tohide 3-bit secret data into the cover image. Note that

one must avoid the condition where the new gray

values of the two pixels fall outside the boundaries of

the range [0, 255]. Therefore, if one of the gray values,

which are calculated by the inverse calculation of ui,falls outside the boundaries of the range [0, 255], then,

the block must be abandoned for embedding data.

PVD+LSB approach, the data is

embedded into smooth areas by the LSB method and

the edged areas by PVD method. The range table is

divided by a value Div into a lower-level (i.e. smoothareas) and a higher-level (i.e. edged areas). The gray-

valued host image is partitioned into non-overlapping

blocks of two consecutive pixels by running through all

rows of the host image in a zigzag manner. The block

difference value di is calculated from the two pixels,

say pi and pi+1, by | pi pi+1 |. Then, find the range Ri,that di falls into. If Ri belongs to the lower-level, eachpixel of pi and pi+1 is embedded using simple 3-bit LSBsubstitution. Let p i and p i+1 be the embedded results ofpi and pi+1, respectively. After embedding secret data, ifthe new difference d i > Div (i.e. id ' higher-level),

then re-adjust the pi and pi+1rule:

11

11

1''),8',8'(

''),8',8'()','(

iiii

iiiiii ppifpp

ppifpppp (1)

Otherwise, Ri belongs to the higher-level, and two

For instance, assume pi = 64, pi+1 = 52, b = 111000(2),and Div =15. Note that the difference value d is | 6452 | = 12, which belongs to the lower-level. After

embedding data, p i = 71, p i+1 = 48, so d i = 23 > Div =15. After re-adjusting, p i = 63, p i+1 = 56, and the pixeldifference value d i = 7 (63 56) belongs to the lower-

level.

3. The PVD-based countermeasure against

Wu et al. schemes

ingeniously combines the PVD method with the LSB

method, some further analyses will expose the

shortcomings of their approach, as will be shown in this

section.

method, their PVD+LSB approach is too conformable

to the LSB approach. We know that two pixels of a

block are embedded by simple 3-bit LSB substitution

method if their difference value belongs to the lower-

level. Table 1 shows the distributions of difference

value di of some images. According to Table 1, as Div= 15, almost 90% of the difference values belong to the

lower-

using mainly LSB substitution.

Second, both LSB and PVD+LSB approaches are

In Figure 1(a),

we can see that the approach of PVD+3-bit LSB

method is easily detected. When more than 50% of

pixels are embedded with random data, the percentages

of the singular pixel groups and regular pixel groups

become unequal and the track of Rm crosses the track ofSm. However, the results of the pixel-value differencingmethods, as shown by the RS-diagrams of Figure 1(b),

indicate that the stego-images seemingly do not contain

any embedded data in their LSBs, because the expected

value of Rm is seen to be close to R-m and Sm close to S-m , where Rm, Sm, R-m, and S-m are relative numbers ofpixel groups (regular and singular) with masks m = [0 11 0] and m = [0 1 1 0]. This proves that the PVD

method can pass the detection of the dual statistics

detecting method, but the others methods can not.

Table 1. The distributions of difference values for 10 images, including Lena, etc.

Differencing ranges 0 ~ 7 8 ~ 15 16 ~ 31 32 ~ 63 64 ~127 128 ~ 255

Distributions 73.73 % 15.33 % 7.48 % 2.76 % 0.65 % 0.05 %

(a) (b)

Figure 1. RS-diagrams yielded by the dual statistics method of Fridrich et al. [17] for stego-images created by (a)

and (b): (a) PVD+3-bit LSB method; (b) PVD method.

4. Improvements of Wu et al.

method

In this section, we propose some methods to

improve the PSNR value of approach. In

Wu et al dibelongs to the lower-level, pi and pi+1 are embedded bysimple LSB substitution method. After embedding, if

the new difference value id ' does not belong to thelower-level, Eq. (1) is applied to re-adjust the pixel

values. We change the above embedding strategy as

follows: For the case that difference value di belongs tolower-level, the following strategy is performed

Selective lower-level strategy:

IF1'' ii pp , choose the best pair of values from

)','( 1ii pp , )2','( 1

lii pp , )',2'( 1i

li pp , and

)2',2'( 1

li

li pp .

Otherwise, choose the best pair of values from

)','( 1ii pp , )2','( 1

lii pp , )',2'( 1i

li pp , and

)2',2'( 1

li

li pp .

The best pair of values, say ),( 1ii xx , means that it

satisfies the conditions Divxx ii 1

and 255,0, 1ii xx , moreover, the value of

2

11

2)()( iiii pxpx is smallest.

In Table 2, PSNR values using Eq. (1)

to re-

using a selective strategy to select the best pair of

pixels. Also, l = 3 and Div = 15 are used in Table 2. Asshown in Table 2, all PSNR values

are better than that of

In order to improve the PSNR values further, we

apply the well-known LSB substitution method, called

the modified LSB substitution method [3, 10, 12]. The

modified LSB substitution method, which improves the

image quality of the simple LSB substitution method,

can be applied directly to the PVD+LSB method. The

concept of the modified LSB substitution is simply to

increase or decrease the MSBs part by 1 in order to

improve the image quality. Similarly, the selective

lower-level strategy can be applied to PVD+Modified

LSB method. Table 2 shows that the results of

PVD+Modified LSB method have higher PSNR than

PVD+LSB method. In a summary, without losing

capacity, our skills improve the PSNR value of Wu et

to 38.87 in average.

Table 2. The average PSNRs of embedding random bit

stream into various cover images by PVD+LSB and

PVD+ Modified LSB methods.

PVD+LSB PVD+ Modified LSB

Original Selective Original Selective

36.84 37.07 38.74 38.87

5. Conclusions

In this paper, we pointed out some drawbacks of Wu

et al. s PVD+LSB method. First, the PVD+LSB

method is too conformable to the LSB method. Second,

both the LSB substitution method and the PVD+LSB

method are easily detected

At the same time, we propose two strategies to improve

the image quality of the PVD+LSB method. One is the

PVD+modified LSB method, and the other is the

selective lower-level strategy.

Acknowledgements: This work was supported in part bythe National Science Council of the Republic of China under the

Grant NSC 95-2221-E-015-002-MY2, and by the iCAST project

sponsored, National Science Council under the Grants NSC 95-

3114-P-001-001-Y02, NSC 95-3114-P-001-002-Y02 and NSC 96-

3114-P-001-002-Y.

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