
Research Article


Comparative Analysis of (5/3) and Haar IWT Based Steganography 

V. Thanikaiselvan,
P. Arulmozhivarman,
Siddhanta Chakrabarty,
Ashutosh Agarwa1,
S. Subashanthini
and
Rengarajan Amirtharajan



ABSTRACT

Steganography is the technique of hiding information inside
other information. It provides data security. Image steganography can be implemented
in both, the spatial and transform domain. In this study, transform domain steganography
has been adopted. A cover image is transformed to the frequency domain using
Integer Wavelet Transform (IWT) and a secret image is embedded in it using Least
Significant Bit (LSB) substitution. The secret data is embedded only in high
frequency subbands of the frequency domain transform of the cover image. Both
adaptive and nonadaptive embedding techniques are employed and the results
are compared. Also, random traversing for embedding the secret data is implemented
for higher security. Haar and (5/3) IWT based algorithms are used. The Peak
Signal to Noise Ratio (PSNR) values and payload capacity are obtained and compared
for above algorithms.





Received: April 19, 2014;
Accepted: August 10, 2014;
Published: September 29, 2014


INTRODUCTION
With the susceptibility of electronic information to attack and malicious distortion,
a need for security of electronic data has become imperative. Steganography
conceals secret information within some ‘cover’ media. This aids in
hiding the very existence of sensitive information from malicious users. Steganography
can be applied to various fields such as text, image, audio and video. Text
steganography is the oldest form of information hiding. Essentially, a secret
message was hidden in an otherwise harmless message. For example, every nth
letter of a sentence or paragraph spelled out a message. However, text steganography
greatly limits the type and amount of information that can be concealed. Image
steganography hides information within an image called the ‘cover image’.
The hidden information can be another image, text or any other type of data
(Amirtharajan and Rayappan, 2013; Amirtharajan
et al., 2013aj; Cheddad
et al., 2010).
Image steganography can be carried out either in the spatial domain (image
domain) (Amirtharajan and Rayappan, 2013; Amirtharajan
et al., 2013aj; Chan
and Cheng, 2004; Cheddad et al., 2010; Dey
et al., 2011; Janakiraman et al., 2013,
2014a, b; Nithyanandam
et al., 2011) or in the transform (frequency) domain (Le
Gall and Tabatabai, 1988; ElSafy et al., 2009;
Peng et al., 2012; Nag
et al., 2010, 2011; Thanikaiselvan
et al., 2011, 2012a, b,
c, 2013a, b;
Wong et al., 2007). Numerous systems exist for
both methods for communication information security (Praveenkumar
et al., 2014al, 2012a,
b, 2013a, b;
Rajagopalan et al., 2014ad;
Ramalingam et al., 2014a, b).
Transform domain steganography provides higher security and better hiding capabilities
with less degradation to the cover image. Spatial domain steganography can usually
be detected by statistical means if a large number of pixels of the image have
been modified to contain secret information. Dey et
al. (2011) and Nag et al. (2010) and
(2011) have used a transform based scheme. The former
has observed PSNR values below 30 dB which makes the encoding vulnerable to
steganalysis attacks. Nag et al. (2010, 2011)
and Nithyanandam et al. (2011) have employed
Huffman coding procedure for added security.
A common and effective method for information hiding proposed by Chan
and Cheng (2004) is simple and easy to use yet highly efficient. The LSB
substitution has been adopted in this study too, following Chan
and Cheng (2004). Thanikaiselvan et al. (2012b)
proposed a random traversing method which echoed the movements of a knight on
a chess board without effecting image quality and enhancing security. Adaptive
steganography has been explored by (ElSafy et al.,
2009; Peng et al., 2012). El Safy et
al’s method is effective while being low in complexity. This study
uses modified basic adaptive scheme to implement adaptive steganography. Transform
domain steganography (Ramalingam et al., 2014a,
b; Thanikaiselvan et al., 2011,
2012b,c, 2013a,
b) provides high security. The DCT (Discrete Cosine Transform)
based steganography is quite common (Fazli et al.,
2010; Kumar et al., 2010; Sarita
and Choudhary, 2012).
In this study, transform domain steganography techniques are proposed and their
efficiency and suitability is compared for use in steganography. The transformations
that are compared are Haar integer wavelet transform and (5/3) integer wavelet
transform. Both adaptive and nonadaptive techniques to embed the secret information
are also compared. Additionally, random traversing and blockcoding have also
been adopted. The embedding is done by LSB substitution. Blockcoding helps
to increase security.
MATERIALS AND METHODS
(5/3) Integer wavelet transform: Wavelets are basis functions used to
represent signals. Integer Wavelet Transforms (IWT) are the wavelet transforms
that map integers to integers. Every subband or wavelet transformation is connected
with filters of finite length which can be obtained as integer wavelet succeeded
by lifting steps. The integer wavelet divides the signal into even and odd samples.
A wavelet transform that maps integers to integers can be obtained by combining
the lifting steps and rounding off. Didier Le Gall and Tabatabai
(1988) developed a new and efficient subband coding of digital images.
Out of the two solutions provided for the design of symmetric short tap filters,
the second one produces visually pleasant and smooth outputs. This filter has
unequal lengths for the high pass and low pass coefficients 5 and 3, respectively.
Thus, the name (5/3) filter is obtained.
Let d(n) contain the odd samples and s(n) contain the even samples. The odd
samples are replaced by Eq. 1 (prediction step) and then the
even samples are replaced by Eq. 2 (updating step):
The even samples s(n) give the high frequency wavelet coefficients and odd
samples d(n) give the low frequency wavelet coefficients.

Fig. 1: 
Transform domain subbands 
The wavelet transform creates 4 subbands as shown in the Fig.
1. Secret information is embedded in the HH (High High), HL (High Low) and
LH (Low High) bands. The low frequency LL (Low Low) bands contain the approximations.
The inverse of this transformation is reversible. It is easily implemented
by inverting the Eq. 1 and 2 by making the
d(n) and s(n) on the right hand side of the equations and following the above
steps in reverse, for example, instead of splitting there will be merging.
This process was adapted for 2 dimensional samples by following the usual procedure,
that is, the above equations were first applied to the image matrix row wise,
treating them as 1D samples and then the result was subjected to the equations
column wise. This gave us the final transformed matrix with 4 subbands.
Haar transform: The Haar wavelet is a sequence of rescaled "squareshaped"
functions which together form a wavelet family or basis.
The image matrix is separated into even and odd columns basis and Fhigh (High
frequency components) and Flow (low frequency components) are found using the
following equation:
Leven, Lodd, Heven, Hodd matrix is developed:
First level decomposition of the image can be obtained through the following
equations:
where, HH1 is the diagonal coefficients, HL1 is the horizontal coefficients,
LH1 is the vertical coefficients and LL1 is the approximation coefficients.
Adaptive embedding: In this study, the information is embedded using
both methods adaptive and nonadaptive and their results are compared. Non adaptive
embedding refers to the process where a fixed number of message bits (either
1, 2, 3 or 4) are embedded in each coefficient. In adaptive embedding, on the
other hand, each coefficient is analyzed and depending on its value the number
of bits that can be substituted is determined. The equation which determines
the number of bits as suggested by ElSafy et al.
(2009), is given below:
where, L is the number of bits to be embedded, k is the minimum number of bits
to be embedded and C_{o} is the transform domain coefficient.
In this study, the above equation is slightly modified for comparison. In Eq.
13, assuming k = 1 and L = 4 if C_{o} is greater than equal 2^{4}
and so on. The modification proposed is that instead of 2^{4} following
equation uses 2^{6}:
This modification increases the PSNR value and improves the image quality.
However, the payload capacity is significantly affected. Proposed work entitled
the adaptive scheme implementing Eq. 13 as ‘adap1’
and the one implementing Eq. 14 as ‘adap3’.
This is because, taking the example of the last case, in Eq.
13 one LSB bit is replaced if the coefficient is of two bits or less. This
leaves, at most, one MSB (Most Significant Bit) untouched, thus the name ‘adap1’.
In Eq. 14, one LSB is replaced if the coefficient value is
of four bits or less, thus leaving a maximum of three MSB untouched and hence
‘adap3’.
Random traversing: A random traversing algorithm has been adopted to
enhance security of the hidden information. Randomness has been employed in
2 stages. In the first stage, the blocks in which the image was divided are
chosen randomly. For example, consider an image with dimensions 512x512. Assume
that, it is divided into blocks of size 128x128. This implies that the image
is divided into 16 blocks each of size 128x128. The first stage of random traversing
randomizes the sequence of the blocks before embedding, so that the hidden information
is spread all over the final image in a random fashion.
The second stage involves randomization of the coefficients within a particular
block. A block consists of the 4 transform domain subbands; HH, HL, LH and
LL. Embedding is done in 3 of those subbands excluding LL. Hence, the second
stage random traversing randomizes the sequence of coefficients that are selected
for embedding within a particular block. This random pattern, however, remains
constant for every block. Both random patterns are stored separately and these
serve as the “keys”
with which the information can be extracted. Without these “keys”
extraction of information will result in meaningless or incorrect data. Consequently
the receiver needs to possess the keys beforehand in order to ‘unlock’
or decrypt the information.
PROPOSED ALGORITHM
Embedding process: The embedding process refers to the hiding of the secret
information in the cover image and the steps that precede it for the preparation
of the cover image.
Embedding has been done by LSB substitution using the equation given below.
This formula was suggested by Chan and Cheng (2004).
It is simple yet efficient:
where, C is the transform domain coefficient, m is the segment of the secret
information (in base 10) to be embedded in this coefficient and k denotes the
number of bits to be replaced.
The steps are enumerated below:
• 
Step 1: Read the cover image 
• 
Step 2: Split it into blocks. The block sizes can be any of 8x8,
16x16, 32x32, 64x64, 128x128, 256x256 or 512x512 
• 
Step 3: Transform each block using IWT. (Haar or (5/3)) 
• 
Step 4: Prepare the keys for random traversing. The keys are the
random patterns according to which the blocks are traversed and also the
random order in which the blocks are selected 
• 
Step 5: For adaptive embedding, run the analysis to determine number
of bits for each coefficient 
• 
Step 6: Read secret message or information in binary 
• 
Step 7: Traverse the blocks according to the keys and insert the
information using Eq. 15; adaptively or nonadaptively
as the case may be using Eq. 1314,
respectively 
• 
Step 8: Once all the information has been inserted by LSB substitution,
perform inverse IWT on each block to transform the image back to spatial
domain 
• 
Step 9: The image now carries the secret information hidden safely
inside and can now be used for transmission or other purposes. This image
is called the stego image 
Extraction process: The process to extract the data is almost same as
that for embedding. Extraction is implemented by the following Eq.
16:
where, the variables denote the same values as in Eq. 15.
The steps followed in the extraction process are:
• 
Step 1: Read the stego image 
• 
Step 2: Split it into blocks. The block sizes can be any of 8x8,
16x16, 32x32, 64x64, 128x128, 256x256 or 512x512 
• 
Step 3: Transform each block using IWT (Haar or (5/3)) 
• 
Step 4: It is assumed that the keys used to determine the traversing
pattern are available with the receiver. Traverse the blocks using the keys 
• 
Step 5: Apply Eq. 16 on each coefficient. ‘k’
is fixed if it is nonadaptive and for adaptive it is obtained through Eq.
1314. This gives us the hidden message 
RESULTS AND DISCUSSION
The main feature of steganography is that the stego image should hold up to
visual scrutiny. However, mathematical methods also exist to compare the performance
or quality of the embedding algorithm. The PSNR and MSE (Mean Square Error)
are widely used in steganographic algorithms for this purpose. The PSNR stands
for peak signal to noise ratio. It is the ratio of the square of the maximum
value that the signal is allowed to have to the noise MSE. The MSE is a cumulative
squared error between the original image and stego image:
where, I denotes the original image, K denotes the stego image and n and m
are the image dimensions.
The performance and capacity of (5/3) IWT and Haar transform are compared in
adaptive and nonadaptive schemes with varying block sizes. The PSNR values
and embedding capacities have been recorded. They have been organized into 2
main categories, those obtained by (5/3) IWT and those obtained by Haar transform.
Under these two headings, they have been further divided into nonadaptive and
adaptive embedding. Within each of these types, classifications exist based
on the number of bits embedded; 1 bit, 2 bit etc., for nonadaptive and adap1
and adap3 for adaptive. The results obtained are given below with Lena image
used as a sample and shown in Fig. 2. The image is compared
before and after embedding the secret information.
The PSNR values of all different types of steganography explored in this project
are recorded below. All images have dimensions 512x512. ‘Globe’
is the only RGB color image, all others are grayscale. It is clear from the
tables that block sizes have negligible effect on PSNR values. Also, the variation
of PSNR value between different images under any one particular type of steganography
is very little. Table 1 and 2 record the
PSNR values of nonadaptive embedding and Table 36
record the PSNR values as well embedding capacity of adaptive embedding.
For easier comparison of the PSNR values and number of bits embedded, figure
were plotted with the values from the tables above for the ‘Lena’
image. From the approximately straight lines of all configurations, it is clear
that block sizes have very little influence on PSNR values. Analyzing Fig.
3, for 1 bit LSB embedding for nonadaptive (5/3) IWT system gives the best
PSNR and ‘adap1’ (5/3) IWT gives the lowest. The 1 bit nonadaptive
embedding and ‘adap3’ with Haar transform take the second and third
places respectively. They are followed by 2 bit with (5/3) IWT and 2 bit with
Haar IWT. Below the 40dB threshold, in this order, are 3 bit with (5/3) IWT,
‘ adap1’ with Haar, 3 bit with Haar, ‘adap3 (5/3) with IWT and
‘adap1’ with (5/3) IWT. The 4 bit LSB substitution has been excluded
from the figure as the PSNR values are below 35 and hence, the method loses
significance as a strong security measure.

Fig. 2(ag): 
(a) Original Lena image, (b) Haar transform
with nonadaptive embedding (1 bit), (c) (5/3) IWT with nonadaptive embedding
(1 bit), (d) Haar transform adaptive with ‘adap1’, (e) (5/3)
adaptive with ‘adap1’, (f) Haar transform adaptive with ‘adap3’
and (g) (5/3) adaptive with‘adap3’ 
Table 1: 
PSNR (dB) values of nonadaptive embedding with (5/3) IWT 

Table 2: 
PSNR (dB) values of nonadaptive embedding with Haar transform 

Table 3: 
PSNR (dB) values of adaptive embedding (adap1) with (5/3)
IWT 

Table 4: 
PSNR (dB) values of adaptive embedding (adap1) with Haar transform 

Table 5: 
PSNR (dB) values of adaptive embedding (adap3) with (5/3)
IWT 

On analysis of Fig. 4, it is quite obvious that in nonadaptive
embedding, the embedding capacity does not vary based on block size or transform
technique.
Table 6: 
PSNR (dB) values of adaptive embedding (adap3) with haar transform 


Fig. 3: 
Comparison of PSNR values (with sample image lena) 

Fig. 4: 
Comparison of payload capacity 
Payload capacity also remains constant in the case of adaptive embedding with
Haar transform. However, for adaptive embedding with (5/3) IWT it varies with
block size. This difference between the 2 transform techniques is due to the
reason that Haar transform calculations involve the current value whereas (5/3)
IWT calculations require previous and next values too. Therefore, with varying
block sizes these previous and next values change, thus giving different coefficients
associated with each block size. However, for block sizes greater than 64, the
capacity becomes almost constant. Of course, ‘adap1’
has higher capacity than ‘adap3’
by virtue of their natures. Also, it is quite clear that (5/3) IWT provides
higher embedding capacity than Haar transform for adaptive embedding.
Table 7: 
Comparative analysis 

Steganalysis: Steganalysis is the blind extraction of secret data in
stego images. This proposed method is highly secured and robust against blind
steganalysis or attacks. This method has been done in transform domain method.
Therefore, secret data cannot be extracted from the spatial domain. There are
three keys used for embedding (Key 1, 2 and 3) these keys impart high randomness
for embedding. Following number of iterations are required to extract the hidden
information from the stego image generated by the proposed method with block
size of nxn. Complexity of the extraction based on the block size only.
Generalized Total number of Iterations (GTI):
For example 16x16 (n = 16) block is considered and substituted for the above
equation, then the total number of Iterations (TI):
TI = (1024!*3!*64!*4*64*3)*1024
Where:
1024! 
= 
Possible order of traversal among 1024 number of 16x16 sized
blocks 
3! 
= 
Gives the possible order of the subbands into which the data is embedded 
64! 
= 
Represents different random traversing on a subband 
4 
= 
Represents the maximum bit length. 
64 
= 
Represents the total number of coefficients in each subband 
3 
= 
Represents the total number of subbands 
1024 
= 
Represents the total number of 16×16 blocks 
The proposed methodology is compared with the existing techniques and the TI
values are tabulated in Table 7. Thus the large difference
observed in the total number of iterations required for the proposed technique
and the existing technique clearly elucidate the enhanced data security against
blind attacks.
CONCLUSION
In this study, secret information embedded inside an image using 2 different
transform techniques, namely Haar transform and (5/3) IWT with adaptive and
nonadaptive technique. The results of the combinations of all 4 configurations
were observed, recorded and compared. If PSNR value is important to the user
then (5/3) IWT is the better choice for nonadaptive embedding and for adaptive,
it is haar transform. If payload capacity is more important than PSNR values,
then the reverse is true for adaptive embedding. The advantage of (5/3) transform
over Haar transform is its relatively simple equations which reduce computation
time and complexity. The only disadvantage that (5/3) IWT faces is its dependence
on next and previous values which varies the transform domain output when the
block sizes are varied. Haar transform on the other hand, gives uniform output
for all block sizes. For future study, other transform methods, like (9/7) IWT
can be compared with Haar transform and (5/3) IWT.

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