Lsb steganography with improved

David C. Wyld et al. (Eds) : ITCS, CST, JSE, SIP, ARIA, DMS - 2015
pp. 89–105, 2015. © CS & IT-CSCP 2015 DOI : 10.5121/csit.2015.50110
LSB STEGANOGRAPHY WITH IMPROVED
EMBEDDING EFFICIENCY AND
UNDETECTABILITY
Omed Khalind and Benjamin Aziz
School of Computing, University of Portsmouth, Portsmouth, United Kingdom
Omed.khalind@port.ac.uk, Benjamin.Aziz@port.ac.uk
ABSTRACT
In this paper, we propose a new method of non-adaptive LSB steganography in still images to
improve the embedding efficiency from 2 to 8/3 random bits per one embedding change even for
the embedding rate of 1 bit per pixel. The method takes 2-bits of the secret message at a time
and compares them to the LSBs of the two chosen pixel values for embedding, it always assumes
a single mismatch between the two and uses the second LSB of the first pixel value to hold the
index of the mismatch. It is shown that the proposed method outperforms the security of LSB
replacement, LSB matching, and LSB matching revisited by reducing the probability of
detection with their current targeted steganalysis methods. Other advantages of the proposed
method are reducing the overall bit-level changes to the cover image for the same amount of
embedded data and avoiding complex calculations. Finally, the new method results in little
additional distortion in the stego image, which could be tolerated.
KEYWORDS
Steganography, Embedding efficiency, Probability of detection, Single Mismatch, LSB
matching, LSB replacement
1. INTRODUCTION
Steganography is the art and the science of keeping the existence of messages secret rather than
only their contents, as it is the case with cryptography. Both steganography and digital
watermarking belong to information hiding, but they differ in their purpose. Digital watermarking
is intended to protect the cover, whereas steganography is used to protect the message. So,
steganography is considered broken when the existence of the secret message is detected. Hence,
the most important property for every steganographic method is undetectability by the existing
steganalysis techniques.
LSB steganography is the most widely used embedding method in pixel domain, since it is easy
to implement, has reasonable capacity, and is visually imperceptible. Unfortunately, both methods
of LSB steganography (LSB replacement and LSB matching) are detectable by the current
steganalysis approaches discussed in later sections.
There are some methods proposed to improve the capacity of LSB replacement like[1,2], or to
avoid changing the histogram of the cover image like [3] which reduce the embedding capacity
by 50%. As mentioned earlier, the undetectability, or the probability of detection is the most
important property for any steganographic method. In this paper a new method of non-adaptive

90 Computer Science & Information Technology (CS & IT)
LSB steganography is proposed to reduce the probability of detection for the same amount of data
embedded with LSB replacement, LSB matching, and LSB matching revisited [4]by the current
detection methods. The proposed method also results in fewer ENMPP (Expected Number of
Modifications Per Pixel) in both pixel and bit-level to the cover image, and changes the histogram
of the cover image in a different way without any complex calculation.
The paper is organized like the following; it starts with clarifying adaptive and non-adaptive
steganography and the related embedding methods in the literature. Then, it starts analysing both
LSB replacement and LSB matching in grey-scale images from different perspectives such as the
embedding efficiency, histogram changes, and bit-level ENMPP. Then, the proposed method is
explained and followed by the same analysis process. After that, the experimental results are
shown for the proposed method against both steganalysis methods; LSB replacement and LSB
matching. Finally, the conclusion and future work are discussed in the last section.
2. ADAPTIVE AND NON-ADAPTIVE LSB STEGANOGRAPHY IN IMAGE
The embedding process of LSB steganography relies on some methods for selecting the location
of the change. In general, there are three selection rules to follow in order to control the location
of change, which are either sequential, random, or adaptive [5].
A sequential selection rule modifies the cover object elements individually by embedding the
secret message bits in a sequential way. For example, it is possible to embed the secret message
by starting from the top-left corner of an image to the bottom-right corner in a row-wise manner.
This selection rule, sequential, is very easy to implement, but has a very low security against
detection methods.
A pseudo-random selection rule modifies the cover object by embedding the secret message bits
into a pseudo randomly chosen subset of the cover object, possibly by using a secret key as a
pseudo-random number generator (PRNG). This type of selection rule gives a higher level of
security than sequential methods.
An adaptive selection rule modifies the cover object by embedding the secret message bits in
selected locations based on the characteristics of the cover object. For example, choosing noisy
and high textured areas of the image, which are less detectable than smooth areas for hiding data.
This selection rule, adaptive, gives a higher security than sequential and pseudo-random selection
rules in terms of detection.
So, the non-adaptive image steganography techniques are modifying the cover image for message
embedding without considering its features (content). For example LSB replacement and LSB
matching with sequential or random selection of pixels are modifying the cover image according
to the secret message and the key of random selection of pixels without taking the cover image
properties into account. Whereas, adaptive image steganography techniques are modify the cover
image in correlation with its features [6]. In other words, the selection of pixel positions for
embedding is adaptive depending on the content of the cover image. The bit-plane complexity
segmentation (BPCS) proposed by Kawguchi[7] is an early typical method of adaptive
steganography.
As adaptive steganographic schemes embed data in specific regions (such as edges), the
steganographic capacity of such method is highly depend on the cover image used for embedding.
Therefore, in general it is expected to have less embedding rate than non-adaptive schemes.
However, steganographers have to pay this price in order to have a better security or less
detectable stego image.

Computer Science & Information Technology (CS & IT) 91
3. RELATED WORKS
The undetectability is the most important requirement of any steganographic scheme, which is
affected by the choice of the cover object, the type of embedding method, the selection rule of
modifying places, and the number of embedding changes which is directly related to the length of
secret message[8].
If two different embedding methods share the same source of cover objects, the same selection
method of embedding place, and the same embedding operation, the one with less number of
embedding changes will be more secure (less detectable). This is because the statistical property
of the cover object is less likely to be disrupted by smaller number of embedding changes[8].
The concept of embedding efficiency is introduced by westfeld[9], and then considered as an
important feature of steganographic schemes[10,11], which is the expected number of embedded
random message bits per single embedding change[12].
Reducing the expected number of modifications per pixel (ENMPP) is well studied in the
literature considering the embedding rate of less than 1 , like westfeld’s F5-algorithm[13], which
could increase the embedding efficiency only for short messages. However, short messages are
already challenging to detect. Also, the source coding-based steganography (matrix embedding)
proposed by Fridrich et al.[8,12], which are extensions of F5-algorithm improved the embedding
efficiency for large payloads but still with embedding rate of less than 1. The stochastic
modulation proposed by Fridrich and Goljan[14], is another method of improving the security for
the embedding rate of up to 0.8 bits/ pixel.
For the embedding rate of 1, there have been some methods for improving the embedding
efficiency of LSB matching like Mielikainen[4], which reduced the ENMPP with the same
message length from 0.5 to 0.375. The choice of whether to add or subtract one to/from a pixel
value of their method relies on both the original pixel values and a pair of two consecutive secret
bits. However, this method of embedding cannot be applied on saturated pixels (i.e. pixels with
values 0 and 255), which is one of the drawbacks of this method. Then, the generalization method
of LSB matching is proposed by Li et al.[15] with the same ENMPP for the same embedding rate
using sum and difference covering set (SDCS). Another method of improving the embedding
efficiency of LSB matching is proposed by Zhang et al.[16], using a combination of binary codes
and wet paper codes, The embedding efficiency of this method can achieve the upper bound of
the generalized ±1 embedding schemes.
However, no method could be found in the literature to improve the embedding efficiency of non-
adaptive LSB replacement, which is 2 bits per embedding change, for the embedding rate of 1.
So, developing such a method could be more useful than other adaptive methods in reusability
perspective. Moreover, the non-adaptive LSB embedding methods with higher embedding
efficiency can be used by existing adapted embedding methods to improve the steganographic
capacity and reduce the probability of detection. A good example is the LSB matching
revisited[4], which has been extended by[17,19].
Also, moving from non-adaptive to adaptive LSB embedding method does not mean that
improving the non-adaptive methods are impossible or useless, as we mentioned earlier, the LSB
matching revisited[4] is a very good example to support this fact.
4. ANALYSIS OF LSB REPLACEMENT
In this section, LSB replacement is analysed in three perspectives; the embedding process itself
(with its embedding efficiency), its effect on the intensity histogram after embedding process, and

the bit-level ENMPP for each bit of the secret message. Also, the main weaknesses of this
embedding method are highlighted with the steganalysis methods that can detect it.
LSB replacement steganography simply replaces the LSB of the cover image pixel value with the
value of a single bit of the secret message. It leaves the pixel values unchanged when their LSB
value matches the bit value of the secret message and changes the mismatched LSB by either
incrementing or decrementing the even or odd pixel values by one respectively[4], as shown in
Figure 1.
Figure1. Possible pixel value transitions with LSB replacement
The embedding algorithm of the LSB replacement can be formally described as follows:
ܲ௦ = ቐ
ܲ௖ + 1 , ݂݅ ܾ ≠ ‫ܤܵܮ‬ሺܲ௖ሻ ܽ݊݀ ܲ௖ ݅‫ݏ‬ ݁‫݊݁ݒ‬
ܲ௖ − 1 , ݂݅ ܾ ≠ ‫ܤܵܮ‬ሺܲ௖ሻ ܽ݊݀ ܲ௖ ݅‫ݏ‬ ‫݀݀݋‬
ܲ௖ , ݂݅ ܾ = ‫ܤܵܮ‬ሺܲ௖ሻ
To analyse the influence of the LSB replacement on the cover image intensity histogram, we
should consider that there is a probability of 50% for the LSB of the cover image pixel value to
already have the desired bit value. Therefore, the probability of modified pixel values will be
(P/2) for an embedding rate of P and the unmodified pixel values will be (1-P/2) after embedding
process, which means that embedding each message bit needs 0.5 pixel values to be changed. In
other words, it has an embedding efficiency of 2 bits of the secret message per one embedding
change. Hence, the intensity histogram of the stego image could be estimated as follows:
hୱሺnሻ = ൬1 −
P
2
൰ hୡሺnሻ +
P
2
൜
hୡሺn + 1ሻ , n is even
hୡሺn − 1ሻ , n is odd
Where n is a greyscale level which ranges from 0 to 255, and hሺnሻ indicates the number of pixels
in the image with greyscale value of n.
This type of embedding, LSB replacement, leads to an imbalance distortion and produces ‘Pairs
of Values’ on the intensity histogram of the stego image. Since LSB replacement is inherently
asymmetric, current steganalysis methods can detect it easily[20], like: RS[21], SP[22], and
WS[23,24].
Another way of analysing LSB embedding is the bit-level ENMPP, which is the expected number
of bit modifications per pixel. This would be important too, as there are some steganalysis
methods that can detect the existence of the secret message based on calculating several binary
similarity measures between the 7th
and 8th
bit planes like[25]. Hence, an embedding process with
less bit-level ENMPP would be better and less detectable by such detection methods.

The overall bit-level ENMPP for LSB replacement could be estimated by multiplying the
probability of having mismatched LSBs, P୰ሺMሻ, which is 0.5 by the number of bits that needs to
be changed in each case, as shown below.
bit − level ENMPP = P୰൫M൯ × no. of modiϐied bits
bit − level ENMPP = 0.5 × 1 = 0.5 bits per message bits
Hence, the overall bit-level ENMPP for LSB replacement is 0.5 bits for each bit of the secret
message.
5. ANALYSIS OF LSB MATCHING
To analyse LSB matching steganography, we again consider the embedding process (with its
embedding efficiency), its effect on the intensity histogram of the cover image, and bit-level
ENMPP.
LSB matching or ±1 embedding is a modified version of LSB replacement. Instead of simply
replacing the LSB of the cover image, it randomly either adds or subtracts 1 from the cover image
pixel value that has mismatched LSB with the secret message bit[26]. The possible pixel value
transitions of ±1 embedding are shown in Figure 2.
Figure 2. Possible pixel value transitions with LSB matching
The random increment or decrement in pixel values should maintain the boundary limitation and
pixel values should always be between 0 and 255 [27]. In other words, the embedding process
should neither subtract 1 from pixel values of 0 nor add 1 to the pixel values of 255.
This random ±1 change to the mismatched LSB pixel values avoids the asymmetry changes to the
cover image, which is the case with LSB replacement. Hence, LSB matching is considered harder
to detect than LSB replacement[4]. The embedding procedure of LSB matching can be formally
represented as follows[28]:
Pୱ = ቐ
Pୡ + 1 , if b ≠ LSB(Pୡ) and (K > 0 ‫ݎ݋‬ Pୡ = 0)
Pୡ − 1 , if b ≠ LSB(Pୡ) and (K < 0 ‫ݎ݋‬ Pୡ = 255)
Pୡ , if b = LSB(Pୡ)
Where K is an independent and identically distributed random variable with uniform distribution
on ሼ−1, +1ሽ.

For the intensity histogram we consider an embedding rate of P. There is a chance of 50% that the
clean image pixel value contains the desired LSB, which means that (P/2) of the cover pixel
values will change after the embedding process. Hence, the estimated unmodified pixel values
will be (1 − P/2) , which means that embedding each message bit needs 0.5 pixel values to be
changed. In other words, its embedding efficiency is 2 bits of the secret message per one
embedding change. The intensity histogram of the stego image could be obtained as follows[28].
hୱ(n) = ൬1 −
P
2
൰ hୡ(n) +
P
4
ሾhୡ(n + 1) + hୡ(n − 1)ሿ
As mentioned earlier, the LSB matching will avoid the asymmetric property in modifying the
cover image. However, as claimed by[29], ±1 embedding is reduced to a low pass filtering of the
intensity histogram. This implies that the cover histogram contains more high-frequency power
than the histogram of the stego image [28], which offers an opportunity to steganalyzers to detect
the existence of the secret message embedded with LSB matching.
Apart from the supervised machine learning detectors of ±1 embedding like[30-33], which
usually have problems in choosing an appropriate feature set and measuring classification error
probabilities[34], the methods of detecting LSB matching steganography could be divided into
two categories; the centre of mass of the histogram characteristic function (HCF) and the
amplitude of local extrema (ALE)[35].
A number of detection methods have been proposed based on the centre of mass of the histogram
characteristic function (HCF-COM) like Harmsen and Pearlman[36], which has better
performance on RGB images than grey-scale. This method is modified and improved by Ker[27],
who applied the HCF in two novel ways: using the down sampled image and computing the
adjacency histogram.
Based on the amplitude of local extrema (ALE), Zhang et al.[29] considered the sum of the
amplitudes of all local extrema in the histogram to distinguish between stego and clean images.
This method is improved by Cancelli et al. [32] after reducing the border effects noise in the
histogram and extending it to the amplitude of local extrema in the 2D adjacency histogram.
The bit-level ENMPP of LSB matching is also important and should be considered for the same
reason, binary similarity measures. Since the probability of having mismatched LSB is also 50%,
the bit-level ENMPP would be as follows:
bit − level ENMPP = P୰൫M൯ × no. of modiϐied bits
bit − level ENMPP = 0.5 × (≥ 1)
bit − level ENMPP ≥ 0.5 (bits per message bits)
Where P୰ is the probability of having mismatched LSBs, which is 0.5. However, the number of
modified bits would be more than 1, because of the random ±1 changes to the pixel values, as
could be noted from the following examples:
127 (0111111)2 + 1 = 128 (10000000)2 , 8-bits changed
192 (11000000)2 - 1 = 191 (10111111)2 , 7-bits changed
7 (00000111)2 + 1 = 8 (00001000)2 , 4-bits changed
240 (11110000)2 - 1 = 239 (11101111)2 , 5-bits changed
Hence, the overall bit-level ENMPP for LSB matching is expected to be more than or equal to 0.5
bits for each bit of the secret message.

6. THE PROPOSED METHOD
Based on highlighting the weakest part of both LSB replacement and ±1 embedding, in this
section we propose a new method of LSB embedding to improve the embedding efficiency and
reduce the probability of detection by current steganalysis methods. Moreover, the new proposed
method should also minimize the bit-level ENMPP to the cover image after embedding.
The new method, single mismatch LSB embedding (SMLSB), takes two bits of the secret
message at a time and embeds them in a pair of selected pixel values of the cover image. The
embedding method always assumes a single mismatch between the 2-bits of the secret message
and the LSBs of the selected pair of pixel values. For each 2-bits of the secret message we
consider two consecutive pixel values for simplicity. However, the selection could be based on
other functions as well.
Since the proposed method embeds 2-bits at a time, there are four cases of having match (M) or
mismatch (M) between the LSBs of the selected two pixel values and the 2-bits of the secret
message, as shown in Figure 3.
Figure 3. The possible cases of Match/ Mismatch
As the embedding method always assumes a single mismatch (MM or MM) between pixel values
and secret message bits, the 2nd
LSB of the first pixel value should always refer to the index of the
mismatch; 1 for MM and 0 for MM. If the case is MM, then it changes one of the LSBs according
to 2nd
LSB of the first pixel value. If the 2nd
LSB value was 0, then it flips the LSB of the first
pixel value to create MM. Otherwise, if it was 1, it flips the LSB of the second pixel value to
create MM. For the MM case, the embedding will also change one of the LSBs according to 2nd
LSB of the first pixel value. But this time, if the 2nd
LSB was 0, then it flips the LSB of the
second pixel value to create MM. Otherwise, if it was 1, it flips the LSB of the first pixel value to
create MM.
For the other two cases, MM and MM, the embedding will be done by changing the 2nd
LSB of the
first pixel value based on the index of the mismatch. If it was MM, then the 2nd
LSB of the first
pixel value will be set to 1. Otherwise, if it was MM, then the 2nd
LSB value of the first pixel
value will be set to 0. Hence, after each embedding there is only MM or MM with the right index
in the 2nd
LSB of the first pixel value. The embedding algorithm is shown in Figure .

Figure 4. The embedding algorithm of SMLSB embedding
Table 1, shows some examples of the embedding process by the proposed method.
Table 1. Examples of SMLSB embedding process.
Clean pair of pixels Two message bits Stego pair of pixels
xxxxxx01
xxxxxxx1
11
xxxxxx00
xxxxxxx1
xxxxxx11
xxxxxxx0
10
xxxxxx11
xxxxxxx1
xxxxxx01
xxxxxxx1
00
xxxxxx01
xxxxxxx0
xxxxxx11
xxxxxxx0
01
xxxxxx10
xxxxxxx0
xxxxxx11
xxxxxxx0
11
xxxxxx11
xxxxxxx0
xxxxxx01
xxxxxxx1
10
xxxxxx11
xxxxxxx1
xxxxxx11
xxxxxxx0
01
xxxxxx01
xxxxxxx0
xxxxxx00
xxxxxxx0
10
xxxxxx00
xxxxxxx0

7. ANALYSIS OF SMLSB EMBEDDING
To analyse the proposed LSB embedding, just like other embedding methods mentioned earlier,
we consider the embedding process itself (with its embedding efficiency), its effect on the
intensity histogram of the image, and the bit-level ENMPP as well.
SMLSB embedding modifies the pixel values based on the match/mismatch cases between LSBs
of the selected two pixel values and the 2-bits of the secret message. As it uses the 2nd
LSB of the
first selected pixel value to refer to the index of the mismatch, it modifies the first pixel value
differently from the second one in the selected pair of pixels. The embedding algorithm could be
formulated in two separate forms as follows.
‫݌‬௦
ሺଶ௜ሻ
=
‫ە‬
ۖ
ۖ
ۖ
‫۔‬
ۖ
ۖ
ۖ
‫ۓ‬‫݌‬௖
ሺଶ௜ሻ
+ 2 , ݂݅ ܾଶ௜ = ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ ‫ܦܰܣ‬ ܾଶ௜ାଵ ≠ ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ାଵሻ
൯ ‫ܦܰܣ‬ 2௡ௗ
‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 0
‫݌‬௖
ሺଶ௜ሻ
− 2 , ݂݅ ܾଶ௜ ≠ ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ ‫ܦܰܣ‬ ܾଶ௜ାଵ = ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ାଵሻ
൯ ‫ܦܰܣ‬ 2௡ௗ
‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 1
‫݌‬௖
ሺଶ௜ሻ
+ 1 , ݂݅ ܾଶ௜ = ൣ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 0൧‫ܦܰܣ‬ ܾଶ௜ାଵ = ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ାଵሻ
൯ ‫ܦܰܣ‬ 2௡ௗ
‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 0
ܱܴ ܾଶ௜ ≠ ൣ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 0൧ ‫ܦܰܣ‬ ܾଶ௜ାଵ ≠ ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ାଵሻ
൯ ‫ܦܰܣ‬ 2௡ௗ
‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 1
‫݌‬௖
ሺଶ௜ሻ
− 1 , ݂݅ ܾଶ௜ = ൣ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 1൧ ‫ܦܰܣ‬ ܾଶ௜ାଵ = ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ାଵሻ
൯ ‫ܦܰܣ‬ 2௡ௗ
‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 0
ܱܴ ܾଶ௜ ≠ ൣ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 1൧ ‫ܦܰܣ‬ ܾଶ௜ାଵ ≠ ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ାଵሻ
൯ ‫ܦܰܣ‬ 2௡ௗ
‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 1
‫݌‬௖
ሺଶ௜ሻ
, ܱ‫ݐ‬ℎ݁‫݁ݏ݅ݓݎ‬
‫݌‬௦
ሺଶ௜ାଵሻ
=
‫ە‬
ۖۖ
‫۔‬
ۖۖ
‫ۓ‬‫݌‬௖
ሺଶ௜ାଵሻ
+ 1 , ݂݅ ܾଶ௜ = ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ ‫ܦܰܣ‬ ܾଶ௜ାଵ = ൣ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ାଵሻ
൯ = 0൧ ‫ܦܰܣ‬ 2௡ௗ
‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 1
ܱܴ ܾଶ௜ ≠ ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ ‫ܦܰܣ‬ ܾଶ௜ାଵ ≠ ൣ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ାଵሻ
൯ = 0൧ ‫ܦܰܣ‬ 2௡ௗ
‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 0
‫݌‬௖
ሺଶ௜ାଵሻ
− 1 , ݂݅ ܾଶ௜ = ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ ‫ܦܰܣ‬ ܾଶ௜ାଵ = ൣ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ାଵሻ
൯ = 1൧ ‫ܦܰܣ‬ 2௡ௗ
‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 1
ܱܴ ܾଶ௜ ≠ ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ ‫ܦܰܣ‬ ܾଶ௜ାଵ ≠ ൣ‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ାଵሻ
൯ = 1൧ ‫ܦܰܣ‬ 2௡ௗ
‫ܤܵܮ‬൫‫݌‬௖
ሺଶ௜ሻ
൯ = 0
‫݌‬௖
ሺଶ௜ାଵሻ
, ܱ‫ݐ‬ℎ݁‫݁ݏ݅ݓݎ‬
Where i is the index of the secret message bit. The pୱ
ሺଶ୧ሻ
and pୡ
ሺଶ୧ሻ
refer to the stego and clean
pixel values respectively for the 2ith
secret message bit embedding. The pୱ
ሺଶ୧ାଵሻ
and pୡ
ሺଶ୧ାଵሻ
are
again refer to the stego and clean pixel values used for embedding 2i+1th
secret message bit.
The possible pixel value changes with SMLSB embedding could be simplified by separating the
first pୱ
ሺଶ୧ሻ
and second pୱ
ሺଶ୧ାଵሻ
pixel values from the selected pair, as shown in Figure 5 and Figure
6.
Figure 5. Possible pixel value transitions for pୱ
ሺଶ୧ሻ
with SMLSB embedding

Figure 6. Possible pixel value transitions for pୱ
ሺଶ୧ାଵሻ
with SMLSB embedding
As could be noted from Figure and Figure , the pixel value transitions of pୱ
ሺଶ୧ାଵሻ
are like LSB
replacement. While pୱ
ሺଶ୧ሻ
is more complicated and has more transitions between clean and stego
pixel values.
To analyse the impact of the SMLSB embedding on the intensity histogram, again we consider an
embedding rate of P. Since the secret message is considered as a random sequence of 0 and 1,
based on the fact that it will be close to its encrypted version [37], equal probabilities should be
considered for match/mismatch cases. Hence, for each case of (MM, MM, MM, MM) the
probability of occurrence would be 0.25.
For MM and MM, the embedding process will change one of the two selected pixel values
according to the 2nd
LSB of the pୡ
ሺଶ୧ሻ
to get either MM or MM. The change will be -1 or +1 for the
odd and the even pixel values respectively. So, (P/4) of the pixel values will be modified by
adding or subtracting 1 according to their values, even or odd values respectively.
However, for MM and MM there is a probability of having 50% of the 2nd
LSB of the pୡ
ሺଶ୧ሻ
to have
the desired value, which needs no change. The other 50% will be modified by flipping the 2nd
LSB of the pୡ
ሺଶ୧ሻ
only. In other word (P/8) of the pixel values will either incremented or
decremented by 2 according to their 2nd
LSB value. Hence, the remaining ሺ1 − 3P/8ሻ pixel
values will stay unchanged after embedding the secret message with the embedding rate of P,
which means that embedding each message bit needs 0.375 pixel values to be changed. This
ENMPP, 0.375, is better than LSB replacement and LSB matching, which are 0.5 pixels per
message bit. Hence, it improves the embedding efficiency from 2 to 8/3 bits per embedding
change. The intensity histogram of the stego image could be estimated by the following:
hୱሺnሻ = ൬1 −
3P
8
൰ hୡሺnሻ +
P
8
ቊ
hୡሺn + 2ሻ , if 2୬ୢ
LSBሺnሻ = 0
hୡሺn − 2ሻ , if 2୬ୢ
LSBሺnሻ = 1
+
P
4
൜
hୡሺn + 1ሻ , n is even
hୡሺn − 1ሻ , n is odd
Where, n is again the greys-cale level valued between 0 and 255. Both hୱሺnሻ and hୡሺnሻ refer to
the number of pixels in the stego and clean image respectively with the greyscale value of n.
As only (P/4) of the pixel values are modified like LSB replacement, it is expected to effectively
reduce the probability of detection with LSB replacement steganalysis methods. Also, it is
expected to reduce the probability of detection by LSB matching steganalysis methods as well,
based on the dissimilarity in pixel value transitions and its influence on the intensity histogram
after embedding.

The bit-level ENMPP for the proposed method could be calculated based on the match/mismatch
cases, in which equal probabilities are considered.
bit − level ENMPP =
∑ሺP୰[each case] × no. of modiϐied bitsሻ
2
P୰ሺMMሻ × 1 + P୰൫MM൯ × 0.5 + P୰൫MM൯ × 0.5 + P୰൫MM൯ × 1
2
0.25 × 1 + 0.25 × 0.5 + 0.25 × 0.5 + 0.25 × 1
2
0.75
2
= 0.375 bits per message bit
The bit-level ENMPP is divided by two, as it embeds two bits of the secret message at a time. In
this case the overall bit-level ENMPP for the proposed method will be 0.375 bits per message bit.
Hence, the proposed method will result in fewer bit-level changes to the cover image after
embedding the same amount of secret message.
8. EXPERIMENTAL RESULTS
To make the experimental results more reliable, two sets of images are considered. The first set is
3000 images from ASIRRA (Animal Species Image Recognition for Restricting Access) public
corpus pet images from Microsoft research website[38], which are random with different sizes,
compression rates, texture ...etc. The other group is a set of 3000 never compressed images from
Sam Houston state university – Multimedia Forensics Group image database [39]. Both sets are
used after converting them into grey-scale images.
To check the efficiency of the proposed LSB embedding, both detection methods are considered;
the LSB replacement and LSB matching steganalysis methods. In all experiments, streams of
pseudo random bits are considered as a secret message. This is due to the fact that it will have all
statistical properties of encrypted version of the secret message according to[40]. Also, to
eliminate the effect of choosing the embedding place (random or sequential embedding), the
embedding rate of 1 bit per pixel (i.e. the images’ total capacity) is considered. Then it is tested
against both LSB replacement and matching steganalysis methods as shown in the following
sections.
8.1 SMLSB against LSB replacement steganalysis methods
There are many methods for detecting LSB replacement steganography in the literature, this
paper considers two structural steganalysis methods, the Sample Pair (SP) analysis[41] and
Weighted Stego (WS)[24]. As mentioned earlier, for each case, the image is loaded with the
maximum capacity of the random secret message twice; one with LSB replacement and the other
with SMLSB embedding.
The experimental results showed that the proposed method effectively reduce the probability of
detection for both detection methods over both sets of images compared to LSB replacement, as
shown in Table 2.

100 Computer Science & Information Techno
Table 2. The o
Image set
ASIRRA
Uncompressed
ASIRRA
Uncompressed
Also, there is a noticeable reduction in
the LSB replacement by SMLSB embedding as shown in
Figure 7. The probability of detection vs. detection threshold for ASIRRA images with WS.
Figure 8. The probability of detection vs. detection threshold for uncompressed images with WS.
Figure 9. The probability of detection vs. detection threshold for ASIRRA images with SP.
Computer Science & Information Technology (CS & IT)
overall reduction rates in probability of detection.
Detection method
The overall reduction in
probability of detection
WS 46.5%
WS 48.4%
SP 30.9%
SP 39.8%
Also, there is a noticeable reduction in probability of detection for the threshold values that suits
the LSB replacement by SMLSB embedding as shown in Figures 7-10.
The probability of detection vs. detection threshold for ASIRRA images with WS.
The probability of detection vs. detection threshold for uncompressed images with WS.
The probability of detection vs. detection threshold for ASIRRA images with SP.
for the threshold values that suits
The probability of detection vs. detection threshold for ASIRRA images with WS.
The probability of detection vs. detection threshold for uncompressed images with WS.
The probability of detection vs. detection threshold for ASIRRA images with SP.

Figure 10. The probability of detection vs. detection threshold for uncompressed images with SP.
8.2 SMLSB against LSB matching steganalysis m
As mentioned earlier, there are two main categories of LSB matching steganalysis methods. In
this paper we use one detection method in each category. For the centre of mass of the histogram
characteristic function (HCF-COM) we used Ker’s method in
extrema we used the method proposed by Zhang et al.
The proposed method, SMLSB, o
embedding methods in terms of detection. Figures 11
images with two different detection methods.
ALE based steganalysis method is no more than a random classifier for the stego images
embedded with SMLSB. Also, the performance of the HCF
considerably reduced by applying the SMLSB embedding method, as shown in Figures 13 and
14.
Figure 11. ROC graph of ALE steganalysis for LSB matching, LSB matching revisited
The probability of detection vs. detection threshold for uncompressed images with SP.
matching steganalysis methods
detection method in each category. For the centre of mass of the histogram
COM) we used Ker’s method in[27], and for the amplitude of local
extrema we used the method proposed by Zhang et al.[29].
The proposed method, SMLSB, outperforms both LSB matching and LSB matching revisited
embedding methods in terms of detection. Figures 11-14, show the ROC graph for each group of
images with two different detection methods. As could be noticed from Figures 11 and 12, the
steganalysis method is no more than a random classifier for the stego images
embedded with SMLSB. Also, the performance of the HCF-COM based steganalysis method is
ROC graph of ALE steganalysis for LSB matching, LSB matching revisited, and
ASIRRA images.
101
The probability of detection vs. detection threshold for uncompressed images with SP.
detection method in each category. For the centre of mass of the histogram
, and for the amplitude of local
utperforms both LSB matching and LSB matching revisited [4]
14, show the ROC graph for each group of
As could be noticed from Figures 11 and 12, the
steganalysis method is no more than a random classifier for the stego images
COM based steganalysis method is
, and SMLSB for

102 Computer Science & Information Techno
Figure 12. ROC graph of ALE steganalysis for LSB matching, LSB matching revisited
Figure 13. ROC graph of HCF-COM steganalysis for LSB matching, LSB matching revisited
Figure 14. ROC graph of HCF-COM steganalysis for LSB matching, LSB matching revisited
Like any other steganography methods, the SMLSB cannot avoid all limitations and cannot
totally defeat the detection methods. As could be noticed from
possible to entirely avoid the detection. Also, there is another weak
quality measurement PSNR (Peak Signal to Noise Ratio)
The proposed method results in a slightl
LSB matching and LSB matching revisited
lower limit value of PSNR (38 dB)
ROC graph of ALE steganalysis for LSB matching, LSB matching revisited, and
Uncompressed images.
COM steganalysis for LSB matching, LSB matching revisited
for ASIRRA images.
COM steganalysis for LSB matching, LSB matching revisited
for Uncompressed images.
totally defeat the detection methods. As could be noticed from Table 2 and Figures 7
possible to entirely avoid the detection. Also, there is another weakness regarding
quality measurement PSNR (Peak Signal to Noise Ratio) between the cover and a stego image.
The proposed method results in a slightly lower PSNR than other methods; LSB replacement,
and LSB matching revisited, which is imperceptible and still very far from the
dB) according to [42, 43].
, and SMLSB for
COM steganalysis for LSB matching, LSB matching revisited, and SMLSB
COM steganalysis for LSB matching, LSB matching revisited, and SMLSB
Figures 7-14, it is not
ness regarding the image
between the cover and a stego image.
LSB replacement,
very far from the

Table 3 shows the PSNR values for some standard images after embedding random binary
streams with a maximum capacity using different embedding methods.
Table 13. PSNR values vs. embedding methods.
Images LSB Replacement LSB Matching
LSB Matching
Revisited
SMLS
B
Lena 50.88 50.88 52.13 49.12
Pepper 50.17 50.17 51.41 48.42
Baboon 50.28 50.28 51.53 48.52
9. EXTRACTION PROCESS
The extraction process is very simple, let sଵsଶ denote the least significant bits of the first and
second selected pixel values respectively. It looks at the 2nd
LSB of the first pixel value in the pair
of pixels. If it is 0, then the LSBs of the pair of pixels would be extracted in the form of sଵഥ sଶ as
two secret message bits, since, in this case, the mismatched LSB is in the first pixel value. If, on
the other hand, it is 1, then it takes sଵsଶഥ as an extracted message bits. Table 4, shows all different
cases of extraction process.
Table 4. The extraction process.
The stego images pixel pair Extracted message bits
‫ݏ0ݔݔݔݔݔݔ‬ଵ
‫ݏݔݔݔݔݔݔݔ‬ଶ
‫ݏ‬ଵഥ ‫ݏ‬ଶ
‫ݏ1ݔݔݔݔݔݔ‬ଵ
‫ݏݔݔݔݔݔݔݔ‬ଶ
‫ݏ‬ଵ‫ݏ‬ଶഥ
Table 5, shows some examples of message bits extracted from stego pixel values.
Table 5. Examples of SMLSB extraction process.
The stego images pixel pair Extracted message bits
xxxxxx01
xxxxxxx1
01
xxxxxx00
xxxxxxx1
11
xxxxxx11
xxxxxxx1
10
xxxxxx10
xxxxxxx1
00
10. CONCLUSION
In this study, we have shown that the proposed SMLSB method can improve the embedding
efficiency in compare to LSB replacement and LSB matching from 2 to 8/3 and reduce the
probability of detection by the two LSB steganalysis methods; LSB replacement and LSB
matching. It also leaves a higher rate of pixel values unchanged for embedding the same amount
of secret messages compared with other two LSB steganography methods. Moreover, the
proposed method outperforms the LSB matching revisited, which has the same embedding
efficiency, in terms of detection. Also, it can be applied to any pixel without restricting the
saturated values (0 and 255). All embedding methods are analysed in detail including SMLSB
and highlighted the cause of reducing the probability of detection. As could be noticed, the

proposed method is very simple to implement with no complex calculation, less bit-level ENMPP
on the cover image, and no reduction in the embedding capacity compared to other two LSB
steganography methods, LSB replacement and LSB matching.
Finally, reducing the probability of detection by LSB replacement steganalysis methods is limited
and the new method cannot totally avoid it. Also, it results in slightly more distortion in
comparison to LSB replacement and LSB matching methods. As future work, it might be possible
to modify the proposed method to give lower probability of detection and lower ENMPP for the
same message length.
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