
Research Article


Brownian Motion of Binary and GrayBinary and Gray Bits in Image for Stego 

Rengarajan Amirtharajan
and
John Bosco Balagurn Rayappan



ABSTRACT

Computers have invaded all premises of the human world, starting from a grocery store to a missile launching center. Because of the omnipresence of computers, it becomes more and more difficult everyday to secure the confidential information from misuse. The fairly common technique of cryptography has been proved inadequate in recent years. Steganography, a contemporary yet an ageold technique to hide secret data into an unsuspected cover media like an image, thereby preventing the recognition of the very presence of secret data, is an alternative. In this study, an improved image steganographic approach is proposed. This method reduces the mean square error (MSE) by localizing the errorreduction process to every row. The error reduction is performed by selective embedding of the actual secret, its binary complement, graycoded version or inverted graycoded version. Of the four versions, the version giving the least MSE is embedded on a rowbyrow basis. This method reduces the MSE by a factor of 1.8 and boosts the peak signal to noise ratio (PSNR) by a 0.25 db and considerably increases the security.





Received: December 12, 2011;
Accepted: January 27, 2012;
Published: April 03, 2012


INTRODUCTION
Power has taken several incarnations ever since its genesis. Right from Stone
Age to the present day, power has kept its possessor at the summit of hegemony
and thus it is the most sought after commodity. In the electronic epoch power
has manifested itself in the form of classified and critical information. Since
the human race has succumbed to enticing power to such an extent that iniquity
today is skyrocketing, there is a need to protect information from falling into
the wrong hands and to prevent clandestine and unscrupulous activities. Providentially,
the advancements in technology have begot many techniques to maintain the veracity
and variability of the crucial information giving rise to an entire discipline
called information hiding. Information hiding is stratified into several subsets
namely cryptography (Schneier, 2007), steganography and
watermarking (Stefan and Fabin, 2000; Zaidan
et al., 2010).
Cryptography (Schneier, 2007) is the art of writing esoteric
information in an occult fashion thereby rendering it scrutable only to the
authorized receiver. In contrast to cryptography which focuses on keeping the
contents of a message secret, steganography (Stefan and Fabin,
2000; Zaidan et al., 2010) focuses on keeping
the very existence of a message secret. Steganography is implemented in digital
audio (Zhu et al., 2011), video (AlFrajat
et al., 2010) and images (Amirtharajan and Balaguru,
2009, 2010, 2011; Amirtharajan
et al., 2012; Bender et al., 1996)
of which image steganography has gained much appreciation and commendation in
the recent past. In image steganography the vital information is dissembled
in a cover image with assiduous efforts resulting in a stego image. The embedded
secret information is imperceptible to the human eye thereby rendering the image
impregnable (Yang, 2008).
In the available literature many researchers proposed an assortment of approaches
to information hiding. These methodologies have different characteristics like
capacity, imperceptibility and robustness (Amirtharajan
and Balaguru, 2009, 2010, 2011;
Kumar et al., 2011). These characteristic are
inevitable for different applications, such as secret communication (Stefan
and Fabin, 2000), copyright protection (Wang and Lin,
2004; Yen and Tsai, 2008) and tampering detection
or integrity check (Lin et al., 2005).
Information hiding techniques could be categorized into two types: methods
in the spatial domain and methods in the frequency domain. In the spatial domain
approach, the secret messages are embedded by directly injecting secret data
in the image pixels (Chan and Cheng, 2001, 2004;
Wang et al., 2001; Chang
et al., 2003; Yang, 2008; Thien
and Lin, 2003). Whereas in the later case, the frequency domain approach
the image is first transformed into its frequency domain (Amirtharajan
and Rayappan, 2012a,b; Chang
et al., 2002) then the secret messages are embedded in the transformed
coefficients.
The major concern is about the objective of transmitting secret data, the stego
method should possess high capacity, high quality and imperceptibility. More
number of research papers have been intended for this theme and performs the
embedding operations in the spatial domain either using raster scan or random
scan (Amirtharajan and Balaguru, 2009, 2010;
Amirtharajan et al., 2011, 2012;
Yen and Lin, 2010). A detailed survey on Information
hiding till 1999 is available by Petitcolas et al.
(1999). A complete survey on image steganography could be found by Cheddad
et al. (2010) and on random image steganography and steganalysis
in Amirtharajan et al. (2012) three more survey
on Field Programmable Gate Array (FPGA) for steganography, middle ware for cryptography/
steganography and Orthogonal Frequency Division Multiplexing (OFDM)+Code Division
Multiple Access (CDMA)+stego for secure communication is available by Rajagopalan
et al. (2012), Janakiraman et al. (2012a)
and Thenmozhi et al. (2012), respectively. There
are three kinds of approaches called LSBbased (Chan and
Cheng, 2001, 2004; Wang et
al., 2001; Chang et al., 2003; Yang,
2008; Thien and Lin, 2003; Amirtharajan
and Balaguru, 2009, 2010), PVDbased (Wang
et al., 2008; Amirtharajan et al., 2010)
and modbased (Chan and Cheng, 2004; Thien
and Lin, 2003; Wang et al., 2008) are commonly
available in literature and sometimes it could be combined to offer both capacity,
imperceptibility and to improve the security (Chang et
al., 2003; Hmood et al., 2010a, b;
Xiang et al., 2011; Lin et
al., 2005; Janakiraman et al., 2012b;
Zaidan et al., 2010, 2011
and Zanganeh and Ibrahim, 2011). The counter attack
on steganography called steganalysis are detailed (Xia et
al., 2009; Qin et al., 2009). A detailed
review on steganalysis is reported by Qin et al.
(2010).
In LSBbased approaches, secret data are embedded by directly substituting the leastsignificantbits (LSBs) with equal bits of the secret for each pixel. Furthermore, techniques based on pixelvalue differencing (PVD) modify the difference value between a pair of pixels to fit the value of the embedded secret. Finally, mod based approaches which use the modular operation, are similar to kbit LSBbased approaches if the modulus is 2^{k}. Motivated by this study, a simple and effective stego method has been proposed to improve the stego image quality and to introduce cryptic effect while embedding.
PRELIMINARY RELATED WORKS
Chan and Cheng (2004) proposed an LSBbased hiding
scheme using an optimal pixel adjustment process (OPAP). Their method adjusts
each pixel after the message is embedded to improve the quality of the stego
object and their experimental results showed that their method yielded quicker
results. Yang (2008) proposed new LSBbased approach,
named as the Inverted pattern (IP) LSB substitution approach. Later this method
combined with OPAP called IPLSB to improve the quality of the stego image. In
this study, we have adapted a new LSBbased approach based on Yang
(2008), named as the inverted pattern binary and gray (IPBG) LSB substitution
approach, to further highlight the quality of the stegoimage Before secret
messages are embedded, some secret messages are transformed by inverting operation
and some secret messages are not. A simple strategy is used to judge whether
a section of messages is inverted and a bit string named as the IPKey is used
to record these inverting actions. Also, we combine the concept of the OPAP
with our approach to improve image quality further. The experimental results
show that the proposed approach results in a better image quality than that
of the optimal LSB substitution approach (Wang et al.,
2001; Chan and Cheng, 2001; Thien
and Lin, 2003), the OPAP LSB substitution approach (Chan
and Cheng, 2004) and inverted pattern approach (Yang,
2008).
In a normal LSB substitution the RGB (red blue green) image is converted in to gray image and then last few least significant bits of gray image are selected according to key length k and the message which is to be embedded is converted to series of ASCII values of the characters in the message and then to binary. Message is then stored in the cover according to the method of embedding. The series of operations done in LSB substitution are as follows: Let C be the original 8bit grayscale coverimage of M_{c}xN_{c }pixels represented as:
C = {x_{ij} 0 ≤ I ≤ M_{c},
0 ≤ j ≤ NC
x_{ij} ∈ :0, 1, 2,,,,, 225} 
D be the nbit secret data represented as:
D = {d_{i} 0 ≤ I ≤ n, d_{i}
∈ {0, 1}} 
Suppose that the nbit secret data D_{d} (decimal representation) is
to be embedded into the krightmost LSBs of the coverimage C:
S = CC mod 2^{k} + D_{d} 
Here, S is the Stego object, C cover object and D_{d} is the decimal equivalent of the secret data.
In the extraction process, given the stegoimage S, the embedded messages can
be readily extracted without referring to the original coverimage. The k LSBs
of the selected pixels are extracted and lined up to reconstruct the secret
message bits. Mathematically, the embedded message bits D can be recovered by:
The OPAP simply improves the stego object after embedding the secret data, either by adding or subtracting 2^{k} without affecting the rightmost k secret data bits in the stego cover. THE PROPOSED METHOD
Embedding: A schematic diagram of the proposed method is given in Fig.
1 and 2. Initially the secret data or message is encrypted
using Data Encryption Standard DES (Schneier, 2007), is
a symmetric key cryptography algorithm. The cover image is split into separate
rows. The order of rows considered for embedding data is chosen using a Pseudo
random number generator with a chosen seed. For each row, a try is made to embed
data, inverse data, gray code of data and the inverted gray code of data. The
encoded form of the confidential information on the selected row which offers
minimum Mean Square Error (MSE) is chosen and fixed for the same. This binary/
inverted binary/gray and inverted gray data pattern is stored as IPKEY. Thus,
on an average MSE is reduced to a greater extent. The Stego image, IPKEY and
the seed are communicated.
Mathematical model for row wise, inverted pattern LSB embedding
• 
General formulae: 1’s complement of a No.: 
Where: 
k 
= 
No. of bits 
x 
= 
Number to be inverted in bits 

= 
1’s complement of the number 
For example, take a 4 bit binary representation of a number ‘2’ [0010]
as x here:
k 
= 
4 so, 2
= (161)2 

= 
13[1101] complement of [0010] ‘2’ 
Where: 
k 
= 
No. of bits to be embedded 
C_{i } 
= 
Cover pixel 
S_{i } 
= 
Stego pixel 
m_{i } 
= 
k – bit message block in decimal 
For example, let k = 4. C_{i} = 16[0001000] and m_{i }is ‘2’
[0010] as m_{i}:
S_{i } 
= 
16 16 mod 2^{4} + 2 = 1616mod16+2 = 18 
S_{i } 
= 
8[00010010] 

Fig. 1: 
Proposed schematic diagram for embedding 

Fig. 2: 
Block diagram for extraction 
where, symbols are same as Eq. 2:
Let S_{i} = 18[00010010]
To Extract the last 4[since k = 4] bits, we have:
m_{i } 
= 
18 mod 
2^{4 } 
= 
18 mod 
16 
= 
2 [0010] 
• 
General IDEAS 

Four flavours of secret data: 
• 
Plain datam (i,j) 
• 
Inverted data 
(i, j) 
• 
Grey Coded datag (i,j) 
• 
Inverted Grey Coded datag' (i,j) 
• 
R rows: In each cover image, there are ‘R’
No. of rows, each of same length D, where: 
where, the M_{c}xN_{c }are dimensions of the cover image. Each row is denoted as ri, where, i∈N and I≤R i.e., Set of rows = {ri, ∀ i∈N and i≤R} • 
Each row r_{i} is in turn a matrix, denoted as: 
In other words, each row has D pixels.
• 
Message data (secret) to be embedded [k bit length]:
m (i, j), where: 
i 
= 
Row identifier 
j 
= 
Pixel inside a row 
The complement of m (i, j) is denoted as
(i, j)
• 
Embedding procedure: Let the cover image be C with
M_{c}xN_{c }pixels. 
Let it be divided into R blocks named r_{i}, r_{i},_{…….}, r_{iR}, each having equal number of pixels D: Also, r_{i} = [r_{i1}, r_{i2},_{…….}, r_{iD}], where i ∈ N and i ≤ R Let ‘k’ be the number of LSBs to be replaced in cover pixels.
Let the secret message be a matrix M, where each elements of M is made up of
k bits. Then we can denote the message to be embedded in the i^{th}
row, j^{th} pixel as m (i, j). Let s (i, j) denote the stego value of
j^{th} pixel in the i^{th} row, when message m (i, j) is embedded
in cover pixel r_{ij}. Alternatively
(i, j) is embedded instead of m (i, j) then the stego pixel is denoted as
(i, j):
If we consider R blocks of stego image as s_{1},s_{2},…………..s_{R}.
Then, s_{i} = s (i) or
(i) or s_{g} (i) or s_{g}' (i) where MSE is minimum and s (i)
= {s (i, j), j∈N and j≤D}
key matrix is denoted as:
K = [K_{1},K_{2},……..K_{R}] 
where, K_{i }is chosen based on the following conditions 00if m (i,j)
is embedded:
01 
= 
if
(i, j) is embedded 
10 
= 
if g (i,j) is embedded 
11 
= 
if g' (i,j) is embedded 
• 
Retrieval procedure: Key matrix is denoted as: 
K = [K_{1},K_{2},……..K_{R}] 
The preliminary, unprocessed message m_{u} (i,j) can be extracted from
pixels in stego image as: m_{u} (i,j) = s (i,j) mod 2^{k} from
Eq. (3) the actual message m (i,j) can be extracted by processing
m_{u} (i,j) as follows:
• 
m (i,j) is chosen from the following conditions based on K_{i}
value 
• 
m_{u} (i,j)  if corresponding K_{i} = 00 
• 
(2^{k}1)m_{u} (i,j), if K_{i} = 01 
• 
g^{1} (i,j), if K_{i} = 10 (if g^{1} denotes
inverse of grey code function) 
• 
g'^{1} (i,j) = (2^{k}1)g^{1} (i,j) (if K_{i}
= 11 ) 
• 
(if g'^{1} denotes inverse of inverted grey code function) 
WORST CASE MSE
The worst case MSE for a block with D pixels is defined as: MSE for i^{th} row, when m (i) (actual data) is embedded, is given as:
When inverted data
(i) is embedded, then, MSE for the same parameters is denoted as:
When grey coded data g (i) is embedded, then MSE for the same parameters is
denoted as:
When inverse grey coded data g’ (i) is embedded, then MSE for the same
parameters is denoted as:
According to the embedding procedure, minimum MSE is chosen. The minimum MSE
for a row is defined as:
= D^{1}
(2^{k} – 1)^{2} ( since sum of all s,,
s_{g} and
components:
We know that, if any n numbers x_{1}, x_{2,} x_{3,} x_{4,…,} x_{n} add up to produce a total T, then:
Thus, applying (10) in (9), we get:
MSE_{min} (i)≤(1/2) MSE_{w} (i) for all I≤R
Thus, we get MSE for any block to be less than or equal to ½ of the worst case MSE. Random kbit Adaptive Embedding Inputs:
• 
Sampled Cover Image C 
• 
Secret data bit stream M 
• 
Key E for Encryption 
Outputs:
• 
Stego Image (S), containing embedded secret data 
• 
KEY (Used for recovery) 
Algorithm for embedding:
• 
Step 1: Encrypt the secret data (M) using DES (Data
Encryption Standard) with key E 
• 
Step 2: Let P = length of secret data stream M (in number of bits)
got from Step1 
• 
Step 3: Split the cover image C into separate rows . Let N = Total
number of rows 
• 
Step 4: Generate a array PRN of N pseudorandom numbers in the
range [0,N1] where each No. occurs only once. Let the seed be stored in
a text file 
• 
Step 5: Invert the bit array M to give .
Encode the bit array M using Grey Code to give G and invert G to give 
• 
Step 6: Let i = 1 (Here, i is the row counter) 
• 
Step 7: Select PRNG[i]^{th} block and perform the following
operations 
Selective embedding 
• 
{a. Let r = pixel index array (for traversal) 
• 
b. For ( j = 1 to length (r) ) do (Here j is the pixel counter) 

{ 
Replace k LSBs of jth pixel of the selected
block with k bits from M to give O[i,1] 

} 
• 
c. Compute MSE 
• 
d. For ( j = 1 to length (r) ) do (Here j is the pixel counter) 

{ 
Replace k LSBs of jth pixel of the selected
block with k bits from
to give O[i,2] 

} 
• 
e. Compute 
• 
f. For ( j = 1 to length (r) ) do (Here j is the pixel counter) 

{ 
Replace k LSBs of jth pixel of the selected
block with k bits from G to give O[i,3] 

} 
• 
g. Compute MSEGray 
• 
h. For ( j = 1 to length (r) ) do (Here j is the pixel counter) 

{ 
Replace k LSBs of jth pixel of the selected
block with k bits from
to give O[i,4] 

} 
• 
g. Compute MSE gray 
• 
h. If MSE is greatest 
KEY[i] = ”00”
Else if
is greatest
KEY[i] = ”01”
Else if MSEGray is greatest
KEY[i] = ”10”
Else
KEY[i] = ”11”
Assign MSE[i] = Minimum MSE
}
• 
Choose STEG[i] as the value of O for which MSE is minimum 
• 
P = Pk. (Reduce length as k bits have been embedded) 
• 
If P>0 then assign i = i+1. Else, goto step8 (that is check whether
message is finished) 
• 
If i>N then goto step8 (check whether EOF is reached for cover image) 
• 
Step 7: F. Goto 
• 
Step 8: Save the array STEG as the stego image array S 
• 
Step 9: Save S into a image file and KEY in a text file 
• 
Step 10: Communicate S,KEY and seed used to generate PRN 
Recovery process: The same Pseudo random number sequence is generated
using the received seed. Using the KEY, the pattern is identified for different
rows. Recovery modules are run to recover the secret. The result is then decrypted
using DES to get the message back.
Random kbit adaptive recovery
• 
Stego Image (S), containing embedded secret data 
• 
Key E for decryption. KEY in text file from embedding process 
• 
Seed (to generate Pseudo Random Number Generator PRNG) 
• 
Secret data bit stream M 
Algorithm for extraction
• 
Step 1: Split the stego image S into separate rows.
Let N = Total number of rows 
• 
Step 2: Generate a array PRNG of N pseudorandom numbers in the
range [0,N1] where each No. occurs only once 
• 
Step 3: Let i = 1 (Here, i is the row counter) 
• 
Step 4: Select PRNG[i]th row and perform the following operations: 
• 
Get Message M using retrieval 
• 
B. If KEY[i,1] = ”01” 
M[i] =
[I] 
Else if KEY[i,1] = ”10” 
M[i] = MGray[i] 
Else if KEY[i,1] = ”11” 
M[i] = 
Else 
M[i] = M[i] 
• 
Assign i = i+1 (increment row count) 
• 
If i>N goto step5 else goto Step4 


• 
Step 5: Decrypt M using DES and write it to text file as output 
RESULTS AND DISCUSSION
In this present implementation Lena, Baboon, Gandhi and Temple 256x256 pixel Images have been considered by varying k = 1, 2, 3 and 4 bit LSB embedding, then stego image quality has been improved with OPAP. The effectiveness of the proposed system has been estimated by computing the MSE and PSNR of the Stego object with cover object. The MSE is calculated by using the equation: where, M and N denote the total number of pixels in the horizontal and the vertical dimensions of the image Xi,j represents the pixels in the original image and Yi, j, represents the pixels of the stegoimage. The Peak Signal to Noise Ratio (PSNR) is calculated using the equation:
where, I_{max} is the intensity value of each pixel which is equal
to 255 for 8 bit gray scale images. Higher the values of PSNR better the image
quality. The cover image is given in Fig. 3a and the corresponding
stego images for k = 1 in Fig. 3b, k = 2 in Fig.
3c, k = 3 in Fig. 3d, k = 4 in Fig. 3f
and the proposed stego results in Fig. 3g for k = 4, MSE,
PSNR is given in Fig. 4 and 5, respectively.
In the case of simple LSB embedding for full embedding capacities 256x256 bits
for k = 1, 256x256x2 bits for k = 2 and so on. While using secret data in binary
format alone for k = 4 the MSE is 36.60, inverted binary is 36.90, gray is 41.17,
inverted gray is 40.88 and the proposed is 34.84. The proposed method MSE by
adapting quantum of 64 pixels further reduces it to 32.81. These values are
shown in Table 1 3.
The corresponding PSNR value of the proposed method improved to 35.03826 dB
which is for better than Chan and Cheng (2004) method
PSNR of 34.8 dB. The corresponding MSE value of the proposed method reduced
to 20.38 which is for better than Chan and Cheng (2004)
method MSE of 21.6 and Yang (2008).
Image steganography is successfully implemented using a novel encoding method
in which various bit representations namely binary, inverted binary, gray and
inverted gray are employed.
Table 1: 
Comparative MSE values for Full Embedding capacity on Lena
and Baboon by splitting into 256 pixels as one block 


Fig. 3(ag): 
(a) Cover Images Lena, Baboon, Gandhi and Temple, (b) k =
1, (c) k = 2, (d) k = 3, (e) k = 4, (f) k = 4 Proposed 256 Stego Images
Lena, Baboon, Gandhi and Temple and (g) k = 4 Proposed 64 Stego Images Lena,
Baboon, Gandhi and Temple 
Table 2: 
Comparative MSE values for full embedding capacity on Lena
and Baboon by splitting into 64 pixels as one block 

Table 3: 
Comparison of MSE values with other methods for full embedding
capacity in Lena, Baboon, Gandhi and Temple 


Fig. 4: 
Comparative MSE values for full embedding capacity on Lena 
Here the secret data, encoded in all the four representations is embedded
in a row of the cover image and the MSE is calculated exclusively for each of
the four encoding bit representations. Of the representations the one that yields
the least MSE is adopted for the respective row. In this way all the four forms
of representation are used in each row and the form resulting in the least MSE
and PSNR is espoused and the results are given in Fig. 4 and
5.
Finally a key is formulated using a code to depict the bit representation format
employed in each row which again is arcane thereby protecting the stego image
from malicious aggressors.

Fig. 5: 
Comparative PSNR values for full embedding capacity on Lena 
Considering an image of dimensions 256x256, key bits per row is 2. Therefore, in order to account for 256 rows, we get 256x2 = 512 bits. These 512 bits of data form a secret key array. Thus, we can define keytodata ratio as 512/(256x256x8) = 512/ (65536x8) = 0.00098 = 0.098%. Furthermore one more experiment has been carried out to improve the quality of the stego image by splitting each row into 4 quantum units of 64 pixels. The results are encouraging with slight increase in the key length. Since the embedding depends upon the Least Mean Square Error which is dynamically determined by the combination of cover image pixels and secret data bits, any attack to recover the data without using the secure key becomes impossible. COMPLEXITY ANALYSIS
• 
The DES cryptography system introduces a complexity of 2^{64} 
• 
For 256*256 pixel image, total number of rows will be 256 
• 
These 256 rows can be selected in a random manner in 256! Ways 
• 
In each row one embedding technique out of four is chosen 
• 
If we are embedding k bits in each pixel then 
• 
The total complexity = 2^{64} *256!* 4*8/k 
• 
So total complexity in this case will be 2^{64} *256!* 4 *8/k 
For proposed 64 method:
• 
The DES cryptography system introduces a complexity of 2^{64} 
• 
For 256*256 pixel image, total number of rows will be 256 
• 
These 256 rows can be selected in a random manner in 256! Ways 
• 
Each row is grouped into 4 blocks of 64 pixels. 
• 
For each block a particular technique is selected out of 4 
• 
If we are embedding k bits in each pixel then 
• 
Total complexity is 2^{64} *256!* 4 *8/k 
• 
If we select the blocks in each row in a random manner, there will be
4 blocks and we can select it in 4! Ways and if we select the pixels in
a block in a random manner then 
• 
Total complexity is 2^{64} *256!* 4 *4!*8/k 
• 
This security level estimation reveals the of the proposed stego against
hackers 
CONCLUSION
By simultaneously serving two ultimate requirements of security, i.e., greater imperceptibility (least MSE) and high complexity (cryptic effect created by the choice of rowwise embedding), the proposed technique promises untampered transmission and authorized use of secret data. Usage of nominal key length reduces the cost associated with the transport of key over a secure channel. To summarize the key points in this paper:
• 
An improved image steganographic method has been proposed,
implemented and tested called Brownian motion of Binary and GrayBinary
and Gray Bits in Image for stego 
• 
It is a variation of Yang (2008) method with additional
choices of Gray code and inverted Gray code along with binary and inverted
binary. This provides four choices for the data to be embedded. Thus, it
further reduces the effective Mean Square Error to make the stego image
more imperceptible and also gives cryptic effect 
• 
A mathematical model has been developed to justify the work 
• 
The worst case Mean square error is derived MSE_{Proposed}≤
(1/2) MSE_{wLSB} and the results are discussed in detail 
• 
This method reduces the MSE by a factor of 1.8, without compromising the
data embedding capacity and marginal improvement in imperceptibility. (In
Information hiding with respect to magic triangle capacity, imperceptibility
and Robustness). The proposed method will not consider robustness, because
robustness will come for watermarking definitely not for spatial domain
steganography 
• 
Security analysis has been made to highlight its firmness against hackers 
• 
Total complexity is 2^{64} *256!* 4 *4!*8/k 
• 
The work tested for 10 cover images, due to large data values, only four
frequently used cover images are given in the result & discussion. Table
3 highlights the superiority of the proposed method with available literature 
• 
Usage of nominal key length reduces the cost associated with the transport
of key over a secure channel about 0.098% of the embedded text 

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