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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 ×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 × 512 × 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 × 512 × 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 × 256 pixels (for 4-bit
insertion), 384 × 256 pixels (for 3-bit insertion), 256 × 256 pixels
(for 2-bit insertion) and 256 × 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 × 256 pixels
into the cover-image 'Lena' of size 512 × 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 × 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.