International Journal of Computer Applications (0975 – 8887)
Volume 77– No.2, September 2013
24
Secured Image Steganography using Different
Transform Domain
Akanksha Kaushal
ECE Department
Ujjain Engineering College
Ujjain, India
Vineeta Chaudhary
ECE Department
Ujjain Engineering College
Ujjain, India
ABSTRACT
In today’s communication world, data sharing and transfer is
increasing exponentially. The threat of an attacker accessing
secret information has been an ever existing concern for the
data communication experts. Cryptography and
steganography are the most widely used techniques to
overcome this threat. Steganography is the art of hiding the
existence of the communication message before sending it to
the receiver. In this paper it is proposed to use Discrete
Fractional Fourier transform (DFrFT) as basic tool in image
processing for data hiding technique called steganography. A
comparative study of steganography in spatial domain and
frequency domain based on Discrete Fourier transform (DFT),
Discrete cosine transform (DCT), Discrete Fractional Fourier
transform (DFrFT) is made. Peak signal to noise ratio (PSNR)
and Mean square error (MSE) of cover image and stego image
are used as performance index and it is found that among
three frequency domain methods DFrFT based steganography
gives better results in terms of PSNR and MSE and also
provide more security for communication. MATLAB
platform is used for simulation, results show that the proposed
technique provides more security, better PSNR and lower
MSE of cover image and stego image.
General Terms
Image, Peak signal to noise ratio, Mean square error.
Keywords
Steganography, Cryptography, Discrete Fourier transform,
Discrete cosine transform, Discrete fractional Fourier
transform.
1. INTRODUCTION
In this modern world, internet offers great convenience in
transmitting large amounts of data in different parts of the
world. However, the safety and security of long distance
communication remains an issue. Cryptography was created
as a technique for securing the secrecy of communication and
many different methods have been developed to encrypt and
decrypt data in order to keep the message secret [1].
Unfortunately it is sometimes not enough to keep the contents
of a message secret, it may also be necessary to keep the
existence of the message secret. Steganography is the art and
science of writing hidden messages in such a way that no one,
apart from the sender and intended recipient, suspects the
existence of the message, a form of security through
obscurity. Steganography differs from cryptography in the
sense that where cryptography focuses on keeping the
contents of a message secret, steganography focuses on
keeping the existence of a message secret.
Earlier used spatial domain methods of steganography are
based on Least Significant Bit (LSB) substitution which giver
better PSNR result but fail to prevent attacks and are easily
detected so a need arises for alternative methods for
steganography. Alternatively other methods involve
steganography in frequency domain. Various transforms such
as DFT, DCT have been used for various data hiding
techniques. DFT and DCT found numerous applications in
signal processing and image processing. The area of image
processing applications includes steganography,
watermarking, compression, encryption and image restoration.
In this paper, it is proposed to use discrete fractional Fourier
transform (DFrFT) for steganography, which is a
generalization of Fourier transform (FT) [2].
This paper is organised as follows. Section 2 briefly discusses
the types of steganography i.e. (2.1) the spatial domain
method which involves encoding at the LSBs level and (2.2)
frequency domain methods such as Discrete Fourier
Transform (DFT), Discrete Cosine transform (DCT) and
Discrete Fourier transform (DFrFT). Section 3 shows
simulation work and performance analysis of these methods.
Finally section 4 gives the conclusion.
2. TYPES OF STEGANOGRAPHY
Steganography is a branch of information hiding in which
secret information is camouflaged within other information.
The main objective of steganography is to communicate
securely in such a way that the true message is not visible to
the observer that is unwanted parties should not be able to
distinguish any sense between cover-image (image not
containing any secret message) and stego-image (modified
cover-image that containing secret message).
On the basis of the image formats i.e. Graphics Interchange
Format (GIF), Joint Photographic Experts Group (JPEG), and
to a lesser extent- Portable Network Graphics (PNG), image
steganography are of three types:
Steganography in the image spatial domain
Steganography in the image frequency domain
Adaptive steganography
Steganography in spatial domain and frequency domain are
explained in this section. Adaptive steganography is not
discussed in present work.
2.1 Steganogaphy in Image Spatial Domain
Here spatial features of image are used. This is a simplest
steganographic technique that embeds the bits of secret
message directly into the least significant bit (LSB) plane of
the cover image. In a gray-level image, every pixel consists of
International Journal of Computer Applications (0975 – 8887)
Volume 77– No.2, September 2013
25
8 bits. The basic concept of LSB substitution is to embed the
confidential data at the rightmost bits (bits with the smallest
weighting) so that the embedding procedure does not affect
the original pixel value greatly [3]. The mathematical
representation for LSB is as equation 1:
(1)
In Equation (1), x’
i
represents the i
th
pixel value of the stego-
image and x
i
represents that of the original cover image. m
i
represents the decimal value of the i
th
block in the confidential
data. The number of LSBs to be substituted is k. The
extraction process is to copy the k-rightmost bits directly.
Mathematically the extracted message is represented as in
equation 2:
(2)
Hence, a simple permutation of the extracted mi gives us the
original confidential data [5]. This method is easy and
straightforward but this has low ability to bear some signal
processing or noises and secret data can be easily stolen by
extracting whole LSB plane.A general framework showing
the underlying concept is highlighted in Fig. 1.
PSNR and MSE are used as performance parameters.
Although this method gives good results in terms of PSNR
and MSE but it is more prone to attacks and can be easily
detected thats why frequecy domain methods are
recommended to use for secure steganography
2.2 Steganography in Frequency Domain
Robustness of steganography can be improved if properties
of the cover image could be exploited. Taking these aspects
into consideration working in frequency domain becomes
more attractive. Here, sender transforms the cover image into
frequency domain coefficients before embedding secret
messages in it [4]. Using transform-domain techniques it is
possible to embed a secret message in different frequency
bands of the cover. These methods are more complex and
slower than spatial domain methods; however they are more
secure and tolerant to noises. Frequency domain
transformation like Discrete Fourier transform i.e. DFT,
Discrete Cosine Transform i.e. DCT or Discrete Fractional
Fourier transform i.e. DFrFT can be applied.
The Fourier Transform is an important image processing tool
which is used to decompose an image into its sine and cosine
components. The output of the transformation represents the
image in the Fourier or frequency domain, while the input
image is the spatial domain equivalent. In the Fourier domain
image, each point represents a particular frequency contained
in the spatial domain image [6]. The Fourier Transform is
used in a wide range of applications, such as image analysis,
image filtering, image reconstruction and image compression.
For a square image of size N×N, the two-dimensional DFT is
given by:
)(2
1
0
1
0
),(),(
N
lj
N
ki
i
N
i
N
j
ejiflkF
(3)
where f(i,j) is the image in the spatial domain and the
exponential term is the basis function corresponding to each
point F(k,l) in the Fourier space [7].
Like other transforms, the Discrete Cosine Transform (DCT)
attempts to decorrelate the image data. After decorrelation
each transform coefficient can be encoded independently
without losing compression efficiency. For a square image of
size N×N, the two-dimensional DCT is given by:
N
y
N
x
yxfvuvuC
N
x
N
y
2
12(
cos
2
)12(
cos),()()(),(
1
0
1
0
(4)
The fractional Fourier transform is a generalization of the
ordinary Fourier transform with an order (or power) parameter
‘α’. The FrFT belongs to the class of time–frequency
Fig. 1: Steganography in spatial domain. The effect of altering the LSBs up to the 4th bit plane
Cover
a 20X20 matrix holding gray
value 250
Message
a 20X20 matrix holding gray
value 13
Stego
a 20X20 matrix holding gray
value 253
Recovered
a 20X20 matrix holding gray
value 13
13=00001101
1111 1101=253
1101=13
MSB LSB
250 = 1111 1010
250=1111 1010
International Journal of Computer Applications (0975 – 8887)
Volume 77– No.2, September 2013
26
representations that have been extensively used by the signal
processing community [8].
The FrFT is defined for entire time-frequency plane (time and
frequency are orthogonal quantities). The angle parameter ‘α’
associated with FrFT, governs the rotation of the signal to be
transformed in time-frequency plane from time-axis in the
time-frequency plane [9]. The one-dimensional DFrFT is
useful in processing single-dimensional signals such as speech
waveforms. For analysis of two-dimensional (2D) signals
such as images, we need a 2D version of the FrFT. For an
M×N matrix, the 2D FrFT is computed in a simple way:
Thus, the generalization of the DFrFT to two-
dimension is given by [9].
drdtrtxrtsuKsuX ),(),;,(),(
(5)
Where
),(),(),;,( rsktukrtsuK
(6)
In the case of the two-dimensional DFrFT we have to consider
two angles of rotation α = aπ/2 and β = b π/2. If one of these
angles is zero, the 2D transformation kernel reduces to the 1D
transformation kernel. The parameter ‘ α’ (transform order)
act as security key for DFrFT, by varying the parameter α we
can achieve more security over existing transform techniques.
2.3 Adaptive Steganography
Adaptive steganography is a special case of two former
methods. It is also known as masking. In this paper adaptive
steganography is not discussed.
3. SIMULATTION WORK AND
PERFORMANCE ANALYSIS
The block diagram shown below indicate the flow of
procedure for steganogrpahy in spatial domain (fig 2) and
steganography in frequency domain(fig 3).
Fig.2: Block Diagram for Steganography in Spatial
Domain
.
Fig.3: Block Diagram for Steganography in Transform
Domain
Here for the simulation MATLAB version 7.12.0.635
(R2011a) is used, hidden image is an image to be embedded
in the cover image and transported. Stego-image is the
combination of cover image and hidden image. 2D-DFT, DCT
& DFrFT is used to convert cover-image in spatial domain
into cover-image in frequency domain then LSB substitution
algorithm with no of bits 4 is used. Result images for
steganography of image in spatial domain and transform
domain are shown using fig (4-17). Fig.4 and fig.5 show
cover image and message image which are common for all the
applied methods. Fig.6,fig.7,fig.8 represent steganography in
spatial domain with 4 number of LSB substituted.
Fig.9,fig.10,fig.11show image steganography using 2D-DFT.
Fig.12,fig.13,fig.14 show image steganography using DCT
and fig.15,fig.16,fig.17 show image steganography using
DFrFT for the fractional order value α = aπ/2 and β = b π/2,
here we have shown result for a= 0.256 and b= 1.739.
Fig.4 Cover Image Fig.5 Message Image
Fig.6 Steganographic Image Fig.7 Extracted Message Image
Fig.8 Histogram of Cover Image and Steganographic
Image
Fig.9 Steganographic Image Fig.10 Extracted Message
Using 2D-DFT Image using 2D-DFT
Cover
Image C
Message
Image M
Steganographic
Image S (similar to
cover)
Cover
Image C
Message
Image M
Steganographic
Image S (similar
to cover)
Transform
of Cover
Image C
International Journal of Computer Applications (0975 – 8887)
Volume 77– No.2, September 2013
27
Fig.11 Histogram of Cover Image and Steganographic Image
using 2D-DFT
Fig.12 Steganographic Image Fig.13 Extracted Message
Using DCT Image Using DCT
Fig.14 Histrogram of Cover image & Steganographic Image
using DCT
Fig.15 Steganographic Image Fig.16 Extracted Message
Using DFrFT Image Using DFrFT
Fig.17 Histogram of Cover Image and Steganographic Image
using DFrFT
Comparison of PSNR and MSE values in spatial domain
method and using different transform is given in table no. 1.
Table 1 Comparison of PSNR and MSE values in spatial
domain method and using different transform
Method
Cover
Image
Messa
ge
Image
PSNR
MSE
M to E
C to
S
M to E
C to S
Spatial
domain
rice.png
camer
aman.t
if
29.01
dB
32.46
dB
82.156
37.175
Transfor
m
domain
with
DFT
rice.png
camer
aman.t
if
29.01
dB
6.23
dB
82.156
1.557e
+004
Transfor
m
domain
with
DCT
rice.png
camer
aman.t
if
29.01
dB
7.29
dB
82.156
1.222e
+004
Transfor
m
domain
with
DFrFT
rice.png
camer
aman.t
if
29.01
dB
8.52
dB
82.156
9.201e
+003
*C = Cover image *E = Extracted image
*M = Message image *S =Stego image
It is clear from the above table; DFrFT gives better PSNR and
MSE performance against DFT and DCT. It also add more
security over these two transforms because a wide variation
range for α and β can be used for DFrFT.
4. CONCLUSION
This paper presents a comparative study of image
steganography in spatial domain and frequency domain. LSB
techniques in a spatial domain have a high payload capacity
and give good performance results but they often fail to
prevent statistical attacks and are thus easily detected and if
the presence of hidden information is revealed or even
suspected the purpose of steganography is partly defeated
therefore it is recommended to use the promising frequency
domain techniques for steganography using DFT, DCT and
DFrFT. Results show that DFrFT gives better PSNR and MSE
performance against DFT and DCT. Security of hidden
information is a major issue in communication and the
transform order α of DFrFT acts as a security key.
5. REFERENCES
[1] Wang,H and Wang, S, “cyber warfare steganography vs
steganalysis “ communication of the ACM, 47:10,
october 2004.
[2] Bracewell RN. The fourior transform and its application
McGraw-Hill 1986.
International Journal of Computer Applications (0975 – 8887)
Volume 77– No.2, September 2013
28
[3] Morland,T steganography and steganalysis Leiden
institute of advance Computing science.
[4] Anjali A. Shejul and Umesh L. Kulkarni, “A Secure Skin
Tone based Steganography Using Wavelet Transform”
International journal of Computer Theory and
Engineering, vol. 3, No.1, Feburary,2011, 1793-8201.
[5] John on, N.F. and Jajodia, S, “Exploring Steganography:
Seeing the Unseen. ” IEEE Computer , 31(2):26-34,Feb
1998.
[6] R.Fisher, S.Perkins, Awalker and Walfort “Fourier
Transform”.
[7] Rajiv Saxsena and Kulbir Singh” Fractional Fourier
Transform: A Novel Tool for Signal Processing”Journal
of Indian Inst Scn, Jan.-Feb.2005,85,11-26.
[8] Luis B. Almeida, “ The Fractional Fourier Transform and
Time Frequency Representation” IEEE transactions on
signal processing, vol 42, no. 11, November 1994.
[9] I. S. Yetik, M.A. Kutay, H.M. Ozktas,” Image
representation and compression with fractional fourier
transform”, Opt Communication.197(2001)275-278.
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