Comparative Performance of Image Scrambling in Transform Domain using Sinusoidal Transforms

H. B. Kekre, Tanuja Sarode, Pallavi N. Halarnkar & Debkanya Mazumder
International Journal of Image Processing (IJIP), Volume (8) : Issue (2) : 2014 49
Comparative Performance of Image Scrambling in
Transform Domain using Sinusoidal Transforms
H.B.Kekre hbkekre@yahoo.com
Sr. Professor, Computer Engg.
MPSTME, NMIMS University
Mumbai, 400056, India
Tanuja Sarode tanuja_0123@yahoo.com
Associate. Professor, Computer Engg.
TSEC, Mumbai University
Pallavi N. Halarnkar pallavi.halarnkar@gmail.com
PhD. Research Scholar
Debkanya Mazumder rimjhim.mazumder17@gmail.com
Student, Computer Engg.
Abstract
With the rapid development of technology, and the popularization of internet, communication is
been greatly promoted. The communication is not limited only to information but also includes
multimedia information like digital Images. Therefore, the security of digital images has become a
very important and practical issue, and appropriate security technology is used for those digital
images containing confidential or private information especially. In this paper a novel approach of
Image scrambling has been proposed which includes both spatial as well as Transform domain.
Experimental results prove that correlation obtained in scrambled images is much lesser then the
one obtained in transformed images.
Keywords: Scrambling, Key Based Scrambling, Sinusoidal Transforms, DCT, DST, DFT, Real
Fourier, Discrete Hartley.
1. INTRODUCTION
Traditional permutation encryption algorithm is not robustness for noise disturbing and shear
transformation attacks. An Image encryption algorithm is introduced based on location
transformation in [1]. The method is robust against noise and shear transformation attacks which
is the advantage over traditional encryption algorithms. The algorithm encrypts the image based
on chaotic system and stores the pixel values in multiple places. A variation of extended magic
square matrix generating algorithm is also presented. The variation has a good efficiency over the
traditional magic square matrix generation algorithm. Experimental results show a good
improvement when encrypted image is modified with noise and shear transformation attack.
The unique property of chaotic functions gives its way to Image Encryption. A new combined
technique is given in [2] which has better chaotic behavior than the traditional ones. The
technique involves the concept of confusion and diffusion in encryption of Digital images. The
experimental results show that the method has a higher security level and excellent performance.

Chaotic sequences ranking is used as a base for encryption algorithm and the technique is
presented in [3]. The method is aimed at the deficiency of the existing color image encryption
method. As the first step the scrambling algorithm scrambles the positions of color image and
sets one to one relationship between the image matrix and chaotic sequence. In the next step the
row and column of the image matrix ranking were guided by the chaotic sequence ranking. In
order to improve the security , the pixel vales of the scrambled color image is shuffled. The
shuffling is based on the chaotic sequence ranking. Overall the method has a good encryption
effect.
An image encryption is proposed in [4] which is based on logistic map and hyper-chaos. The
logistic map is used to generate the chaotic key 1 which has a good randomness. The
Hyperchaos system is used to produce the chaotic key2. Encryption algorithm has two rounds
each with the two different keys generated with two different chaotic maps. The experimental
results show that the method has good results, high efficiency, good statistical characteristics and
differential characteristics
Using the Baker map , an image encryption algorithm is presented in [5]. The proposed method
makes use of discrete cosine transform (DCT), the discrete sine transform (DST), the discrete
wavelet transform (DWT) and the additive wavelet transform (AWT) for Image encryption
approach. Chaotic encryption is performed in these transform domains to make use of the
characteristics of each domain. Different attacks are studied for all the transforms used for
encryption. DST transform gives good results compared to others if degree of randomness is of
major concern.
An image encryption algorithm is implemented in transform domain using DWT and stream
ciphers. A stream cipher helps to make information (plain text) into an unreadable format. A
comparative study on DCT and DWT is also discussed in [6].
A novel approach of Image encryption is proposed in [7], it transforms an encrypted original
image into another image which is the final encrypted image and same as the cover image
overcoming the drawback of transmitting the noise like image over the network and making it
suspicious for intruders. The proposed algorithm is based on Wavelet decomposition.
Experimental results show simulation and security analysis results
An extended version of TJ-ACA: advanced cryptographic algorithm is been proposed named as
TJ SCA: supplementary cryptographic algorithm for color images in [8]. A white blank image
whose preview is not available in transform domain is generated, which makes the brute force
attacks ineffective. The proposed method makes use of 2-D fast Fourier transform, ikeda
mapping are used to get a highly secured image. The method also gives a Lossless decryption.
Therefore the method is applicable to stego images.
A new encryption algorithm based on bit plane decomposition to improve the security level is
introduced in [9]. The technique combines parametric bit plane decomposition, bit plane
shuffling, resizing, pixel scrambling and data mapping techniques for encryption. For bit plane
decomposition, Fibonacci P-code is used and 2D P-Fibonacci is used for image encryption.
Experimental result shows the ability of the method against several common attacks. The method
can be used to encrypt images, biometrics and videos.
An extension to ScaScra is proposed in [10]. It is used to scramble a digital image in the diagonal
direction. The diagonal blocks are first decided, the pixels in these blocks are scrambled using
unified constructive permutation function. The scrambling technique is scalable by varying the
block size. Subjective and objective experiments were carried out to test the performance of the
proposed technique and the results were compared to ScaScra. Experimental parameters like
correlation and entropy were used.

An optical information hiding technique for digital images is proposed in[11]. The technique
combines the scrambling technique in fractional Fourier domain. Firstly image is randomly shifted
using the jigsaw transform algorithm and then a scrambling technique based on Arnold transform
is applied. Then the image is iteratively scrambled in fractional Fourier domains using randomly
chosen fractional orders. The parameters of the jigsaw transform, Arnold and fractional Fourier
forms a huge key space and thus resulting in high security of the proposed encryption method.
Experimental results demonstrate the flexibility and robustness of the proposed method.
In [12] the periodicity of scrambling process is analyzed using Arnold transformation to get some
universal rules, then improved intersecting cortical Model Neural Network (ICMNN) is used to
extract 1D signatures of the original image and scrambled images which reflects the image
structure changing process. L1 norm is been adopted to evaluate the scrambling degree and the
universal rules obtained above are used to verify the results. The experimental results showed
that the proposed method could analyze and evaluate the scrambling degree efficiently.
A symmetric encryption algorithm based on bit permutation, using an iterative process combined
with chaotic function is proposed in [13]. The advantage of this technique is secured encryption
and getting confusion and diffusion and distinguishability properties in the cipher. The output of
the cryptosystem is measured based on the statistical analysis of randomness, sensitivity and
correlation on the cipher-images.
Information security and confidentiality is important at different levels of communication. The
applications find their way into different fields like personal data, patient’s medical data, military
etc. With the advancement in Research in the field of Image processing, Image encryption and
steganographic techniques have gained a popularity over the other forms of hidden
communication. A new Image Encryption technique using Fibonacci and Lucas is proposed in
[14]. The approach makes use of Arnold Transform matrix, and uses the generalized Fibonacci
and lucas series values in the Arnold transform to scramble the image.
An encryption technique based on pixels is proposed in[15]. Firstly the image is scrambled using
the method of watermarking making it difficult for decoding purpose. Lastly a camouflaged image
to vision or the pixels of the true image to get the final encrypted image. The key parameters are
encrypted using Elliptic curve cryptography (ECC). The algorithm security, reliability and
efficiency is analyzed via experimental analysis.
A new invertible two dimensional map is proposed in [16] called as Line Map, for image
encryption and decryption. The method maps the digital image to an array of pixels and then
maps it back from array to image. A Line Map consists of two maps, a left map and a right map.
The drawback of the traditional 2D maps which can be used only for permutation is overcome by
Line Map which can perform two processes of image encryption , permutation and substitution
simultaneously using the same maps. The proposed method does not have a loss of information,
it is also fast and there is no restriction on the length of the security key.
Non Sinusoidal Transforms , such as Walsh, Slant, Kekre and Haar have been tried for this
approach in [19]. Experimental results have have shown Kekre transform performs better then all
other Non Sinusoidal Transfoms. In this paper , we are exploring Sinusoidal Transforms such as
DCT, DST, Real Fourier, Hartley and DFT.
2. SINUSOIDAL TRANSFORMS
A Transform is a technique for converting a signal into elementary frequency components.
Transform coding relies on the premise that pixels in an image exhibit a certain level of
correlation with their neighboring pixels. Consequently, these correlations can be exploited to
predict the value of a pixel from its respective neighbors. A sinusoidal unitary transform is an
invertible linear transform whose kernel describes a set of complete, orthogonal discrete cosine
and/or sine basis functions

2.1 Discrete Cosine Transform
A Discrete Cosine Transform (DCT) expresses a sequence of finitely many data points in terms of
a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous
applications in science and engineering, from lossy compression of audio and images (where
small high-frequency components can be discarded), to spectral methods for the numerical
solution of partial differential equations. The use of cosine rather than sine functions is critical in
these applications: for compression, it turns out that cosine functions are much more efficient,
whereas for differential equations the cosines express a particular choice of boundary conditions.
The DCT can be written as the product of a vector (the input list) and the n x n orthogonal matrix
whose rows are the basis Vectors. We can find that the matrix is orthogonal and each basis
vector corresponds to a sinusoid of a certain frequency. The general equation for a 2D (N data
items) is given below
‫ܨ‬ሺ݉, ݊ሻ =
ଶ
√୑୒
‫ܥ‬ሺ݉ሻ‫ܥ‬ሺ݊ሻ ∑ ∑ ݂ሺ‫,ݔ‬ ‫ݕ‬ሻܿ‫ݏ݋‬
ሺଶ௫ାଵሻ௠గ
ଶெ
ܿ‫ݏ݋‬
ሺଶ௬ାଵሻ௡గ
ଶே
ேିଵ
௬ୀ଴
ெିଵ
௫ୀ଴ (1)
Where C(m),C(n)=1/√2 for m, n=0 and C(m) , C(n)=1 otherwise
2.2 Discrete Sine Transform
The Discrete Sine Transform (DST) is a member of sinusoidal unitary transforms family.DST is
real, symmetric, and orthogonal. It is used as an alternative transform in Transform Coding
system. The general equation for a 2D (N data items) is given below.
߮ሺ݇, ݊ሻ = ට
ଶ
ேାଵ
sin
గሺ௞ାଵሻሺ௡ାଵሻ
ேାଵ
(2)
Where 0≤ k, n ≤N-1
2.3 Real Fourier
The Real Fourier of a finite real data sequence {f(m)} of length N(even) is defined as[17]
‫ܨ‬ሺ݇ሻ =
ଵ
ே
∑ sin
గሺ௞ାଵሻሺଶ௠ାଵሻ
ଶே
ேିଵ
௠ୀ଴
‫ܨ‬ሺ݇ + 1ሻ =
ଵ
ே
∑ cos
ଶே
, ݇ = 0,2, … , ሺܰ − 2ሻேିଵ
௠ୀ଴
ቑ (3)
Where
݂ሺ݉ሻ = 2 ෍ ‫ܨ‬ሺ݇ሻ sin
ߨሺ݇ + 1ሻሺ2݉ + 1ሻ
2ܰ
+
ேିଶ
௞ୀ଴
௞ୀ௘௩௘௡
2 ∑ ‫ܨ‬ሺ݇ + 1ሻܺ cos
ଶே
, ݉ = 0,1, … . , ሺܰ − 1ሻேିଶ
௞ୀ଴
௞ୀ௘௩௘௡
(4)
2.4 Discrete Hartley Transform
The Discrete Hartley Transform (DHT) pair is defined for a real- valued length-N sequence x(n), 0
≤ n ≤ N-1, by the following equation
‫ܪ‬ሺ݇ሻ = ∑ ‫ݔ‬ሺ݊ሻܿܽ‫ݏ‬ ቀ
ଶగ
ே
݇݊ቁ 0 ≤ ݇ ≤ ܰ − 1ேିଵ
௡ୀ଴ ሻ (5)

H. B. Kekre, Tanuja Sarode, Pallavi N
International Journal of Image Processing (IJIP
‫ݔ‬ሺ݊ሻ
Where cas(x) = cos(x)+sin(x)
The symmetry of the transform pair is a valuable feature of the DHT.
2.5 Discrete Fourier Transform
A discrete formulation of the Fourier transform, which takes place at regularly spaced data
values, and returns the value of the Fourier transform for a set of values in frequency space
which are equally spaced. The 2D DFT is given as
‫ܨ‬ሺ‫ݑ‬
3. KEY BASED IMAGE SCRAMBLING IN TRANSFORM DOMAIN
In this paper we are presenting a novel approach for Image scrambling involving both the spatial
as well as transform domain. As we know whenever a transform is applied to an image, image is
converted from spatial domain to transform domain, and transform coefficients are obtained. To
obtain the original image the inverse transform is applied to the transform coefficients. Bu
transform coefficients are affected due to any transformation we will not obtain the original image.
Using this concept in this paper we have used Key based scrambling
Random numbers generation based on the size of the image is used for scrambling purpose. The
proposed approach is not limited to a particular scrambling method or a transform, the said
approach can make use of any scrambling techniqu
3.1 Image Scrambling
Following are the steps used for Image Scrambling
1) Read the image, convert it to grayscale
2) Apply a Transform on the image
3) Transform coefficients which are obtained in step 2
scrambling method.
4) Apply inverse transform on the scrambled transform coefficients obtained in step 3.
5) The image obtained in spatial domain will now be scrambled
The scrambling process is also shown in the figure 1.
FIGURE
Original Image
• BMP
• JPEG
Sinusoidal
Transform
• DCT
• DST
• Fourier
• Hartley
• DFT
Kekre, Tanuja Sarode, Pallavi N. Halarnkar & Debkanya Mazumder
Image Processing (IJIP), Volume (8) : Issue (2) : 2014
ሺ ሻ =
ଵ
ே
∑ ‫ܪ‬ሺ݇ሻܿܽ‫ݏ‬ ቀ
ଶగ
ே
݇݊ቁ 0 ≤ ݊ ≤ ܰ − 1ேିଵ
௞ୀ଴
The symmetry of the transform pair is a valuable feature of the DHT.
Discrete Fourier Transform
formulation of the Fourier transform, which takes place at regularly spaced data
which are equally spaced. The 2D DFT is given as
ሺ‫,ݑ‬ ‫ݒ‬ሻ =
ଵ
ேெ
∑ ∑ ݂ሺ‫,ݔ‬ ‫ݕ‬ሻ݁ିଶగ௜ሺ
ೣೠ
ಿ
ା
೤ೡ
ಾ
ሻெିଵ
௬ୀ଴
ேିଵ
௫ୀ଴
KEY BASED IMAGE SCRAMBLING IN TRANSFORM DOMAIN
in. As we know whenever a transform is applied to an image, image is
obtain the original image the inverse transform is applied to the transform coefficients. Bu
Using this concept in this paper we have used Key based scrambling[18] which is based on the
approach can make use of any scrambling technique or transform on the image.
Following are the steps used for Image Scrambling
Read the image, convert it to grayscale
Apply a Transform on the image
Transform coefficients which are obtained in step 2 are now scrambled using key based
Apply inverse transform on the scrambled transform coefficients obtained in step 3.
The image obtained in spatial domain will now be scrambled
The scrambling process is also shown in the figure 1.
IGURE 1: This Different Steps of Scrambling Process.
Scrambling
Technique
• Key Based
Scrambling
• R-prime
• Perfect
Shuffle
Inverse
Transform
• idct
• idst
• ifourier
• ihartley
• idft
53
(6)
formulation of the Fourier transform, which takes place at regularly spaced data
(7)
in. As we know whenever a transform is applied to an image, image is
obtain the original image the inverse transform is applied to the transform coefficients. But if the
which is based on the
are now scrambled using key based
Apply inverse transform on the scrambled transform coefficients obtained in step 3.
Scrambled
Image
• BMP
• JPEG

3.2 Image Descrambling
The descrambling process is as follows
1) Read the scrambled image
2) Apply the Transform on the image
3) Transform coefficients which are obtained in step 2
based descrambling method.
4) Apply inverse transform on the descrambled transform coefficients obtained in step 3.
5) The image obtained in spatial domain will now be original Image
The descrambling process is also shown in the
FIGURE 2
4. EXPERIMENTAL RESULTS
For Experimental purpose, five images of size 256X256 were used with all the five sinusoidal
transforms. Figure 3(a) shows the Original Image which
converted to grayscale as shown in Figure 3(b), Although the novel approach proposed can also
be extended on 24-bit color images.
(a) Original Image (b) Gray Image
Figure 4(a-c) shows the scrambled images obtained in spatial domain by applying DCT row, DCT
Column and DCT Full transform along with Key
descrambled images obtained after applying the descrambling steps are shown in F
Scrambled Image
• BMP
• JPEG
Sinusoidal
Transform
• DCT
• DST
• Fourier
• Hartley
• DFT
The descrambling process is as follows
Read the scrambled image
Apply the Transform on the image
Transform coefficients which are obtained in step 2 are now descrambled using key
based descrambling method.
Apply inverse transform on the descrambled transform coefficients obtained in step 3.
The image obtained in spatial domain will now be original Image
The descrambling process is also shown in the figure 2.
2: This Different Steps of De-Scrambling Process.
EXPERIMENTAL RESULTS
transforms. Figure 3(a) shows the Original Image which is a 24-bit color image which is first
bit color images.
(a) Original Image (b) Gray Image
FIGURE 3
c) shows the scrambled images obtained in spatial domain by applying DCT row, DCT
Column and DCT Full transform along with Key-based scrambling on the grayscale images. The
De-scrambling
Technique
• Key Based
Scrambling
• R-prime
• Perfect Shuffle
Inverse
Transform
• idct
• idst
• ifourier
• ihartley
• idft
54
are now descrambled using key
Apply inverse transform on the descrambled transform coefficients obtained in step 3.
bit color image which is first
c) shows the scrambled images obtained in spatial domain by applying DCT row, DCT
based scrambling on the grayscale images. The
descrambled images obtained after applying the descrambling steps are shown in Figure 4(d-f).
Original Image
• BMP
• JPEG

(a)DCT Row Transform
Scrambled
(d)DCT Row Transform
Descrambled
Figure 5(a-c) shows the scrambled images obtained in spatial domain by applying DST row, DST
Column and DST Full transform along with Key
(a)DST Row Transform
Scrambled
(d) DST Row Transform
Descrambled
(b)DCT Column Transform
Scrambled
(c)DCT Full Transform
Scrambled
(e)DCT Col Transform
Descrambled
(f)DCT Full Transform
Descrambled
FIGURE 4
c) shows the scrambled images obtained in spatial domain by applying DST row, DST
Column and DST Full transform along with Key-based scrambling on the grayscale images. The
(b)DST Column Transform
Scrambled
(c)DST Full Transform
Scrambled
(e) DST Col Transform
Descrambled
(f) DST Full Transform
Descrambled
FIGURE 5
55
(c)DCT Full Transform
Scrambled
(f)DCT Full Transform
Descrambled
c) shows the scrambled images obtained in spatial domain by applying DST row, DST
descrambled images obtained after applying the descrambling steps are shown in Figure 5(d-f).
(c)DST Full Transform
Scrambled
DST Full Transform
Descrambled

Figure 6(a-c) shows the scrambled images obtained in spatial domain by applying Real Fourier
row, Real Fourier Column and Real Fourier Full transform along with Key
the grayscale images. The descrambled images obtained after applying the descra
are shown in Figure 6(d-f).
(a)Real Fourier Row Transform
Scrambled
(d)Real Fourier Row Transform
descrambled
c) shows the scrambled images obtained in spatial domain by applying Real Fourier
row, Real Fourier Column and Real Fourier Full transform along with Key-based scrambling on
the grayscale images. The descrambled images obtained after applying the descra
(b)Real Fourier Column Transform
Scrambled
(c)Real Fourier Full
Transform Scrambled
(e)Real Fourier Column Transform
descrambled
(f)Real Fourier Full
Transform descrambled
FIGURE 6
56
c) shows the scrambled images obtained in spatial domain by applying Real Fourier
based scrambling on
the grayscale images. The descrambled images obtained after applying the descrambling steps
(c)Real Fourier Full
Transform Scrambled
(f)Real Fourier Full

Figure 7(a-c) shows the scrambled images obtained in spatial domain by applying Hartley row,
Hartley Column and Hartley Full transform along with Key
images. The descrambled images obtained after applying the descrambling steps ar
Figure 7(d-f).
(a)Hartley Row Transform
Scrambled
(d)Hartley Row Transform
descrambled
c) shows the scrambled images obtained in spatial domain by applying Hartley row,
Hartley Column and Hartley Full transform along with Key-based scrambling on the grayscale
images. The descrambled images obtained after applying the descrambling steps ar
(b)Hartley Column Transform
Scrambled
(c)Hartley Full Transform
Scrambled
(e)Hartley Column Transform
descrambled
(f)Hartley Full Transform
descrambled
FIGURE 7
57
c) shows the scrambled images obtained in spatial domain by applying Hartley row,
based scrambling on the grayscale
images. The descrambled images obtained after applying the descrambling steps are shown in
(c)Hartley Full Transform
Scrambled
(f)Hartley Full Transform
descrambled

Figure 8(a-c) shows the scrambled images obtained in spatial domain by applying DFT row, DFT
Column and DFT Full transform along with Key
descrambled images obtained after applying th
(a)DFT Row
Transform Scrambled
(d)DFT Row
Original Image :Lena [ Row:
Transform Row
Transform
Row
Transform
Scrambled
DCT Row: 0.9938
Col: 0.1958
Row: 0.5546
Col: 0.3890
DST Row: 0.9940
Col: 0.2079
Row: 0.5383
Col: 0.3316
Real
Fourier
Row: 0.9956
Col:0.2131
Row: 0.5771
Col: 0.2237
Hartley Row: 0.9947
Col:0.2136
Row: 0.2385
Col: 0.2224
DFT Row: 0.9961
Col: 0.1736
Row: 0.2697
Col: 0.1677
c) shows the scrambled images obtained in spatial domain by applying DFT row, DFT
Column and DFT Full transform along with Key-based scrambling on the grayscale images. The
descrambled images obtained after applying the descrambling steps are shown in Figure 8(d
(b) DFT Column
Transform Scrambled
(c)DFT Full
Transform Scrambled
(e) DFT Column
(f)DFT Full
Transform
FIGURE 8
Original Image :Lena [ Row: 0.8439 and col: 0.6937]
Row
Transform
Scrambled
Column
Transform
Column
Transform
Scrambled
Full
Transform
Row: 0.5546
Col: 0.3890
Row: 0.1907
Col: 0.9932
Row: 0.4802
Col: 0.6521
Row: 0.2062
Col: 0.2202
Row: 0.5383
Col: 0.3316
Row: 0.1910
Col:0.9909
Row: 0.4543
Col: 0.5676
Row: 0.3048
Col: 0.3395
Row: 0.5771
Col: 0.2237
Row: 0.1901
Col:0.9930
Row: 0.4507
Col: 0.2054
Row: 0.2093
Col:0.2345
Row: 0.2385
Col: 0.2224
Row: 0.2160
Col:0.9931
Row: 0.1969
Col:0.2175
Row: 0.3966
Col: 0.4995
Row: 0.2697
Col: 0.1677
Row: 0.1860
Col: 0.9961
Row: 0.1308
Col:0.2117
Row: 0.4178
Col: 0.4599
58
c) shows the scrambled images obtained in spatial domain by applying DFT row, DFT
e descrambling steps are shown in Figure 8(d-f).
(c)DFT Full
Transform Scrambled
(f)DFT Full
Full
Transform
Full
Transform
Scrambled
Row: 0.2062
Col: 0.2202
Row: 0.5576
Col: 0.5835
Row: 0.3048
Col: 0.3395
Row: 0.5271
Col:0.5232
Row: 0.2093
Col:0.2345
Row: 0.3222
Col:0.2601
Row: 0.3966
Col: 0.4995
Row: 0.2096
Col:0.2048
Row: 0.4178
Col: 0.4599
Row: 0.1877
Col: 0.1780

Original Image :Pepper [ Row: 0.8891 and col: 0.8468]
Transform Row
Transform
Row
Transform
Scrambled
Column
Transform
Column
Transform
Scrambled
Full
Transform
Full
Transform
Scrambled
DCT Row: 0.9926
Col: 0.1890
Row: 0.5381
Col: 0.3483
Row: 0.1888
Col: 0.9932
Row: 0.4156
Col: 0.6019
Row: 0.2278
Col: 0.3145
Row: 0.5571
Col: 0.5680
DST Row: 0.9919
Col: 0.1892
Row: 0.5707
Col: 0.3907
Row: 0.2013
Col: 0.9899
Row: 0.3830
Col: 0.5207
Row: 0.3547
Col: 0.2044
Row: 0.4879
Col: 0.5080
Real
Fourier
Row: 0.9955
Col: 0.2018
Row: 0.5126
Col: 0.2291
Row: 0.1892
Col: 0.9929
Row: 0.3722
Col: 0.2334
Row: 0.2384
Col: 0.2374
Row: 0.4108
Col: 0.3003
Hartley Row: 0.9941
Col: 0.2004
Row: 0.3166
Col: 0.1965
Row: 0.2032
Col: 0.9933
Row: 0.1857
Col: 0.2439
Row: 0.5053
Col: 0.5722
Row: 0.2656
Col: 0.2227
DFT Row: 0.9961
Col: 0.1559
Row: 0.3901
Col: 0.1383
Row: 0.1605
Col: 0.9961
Row: 0.1265
Col: 0.2696
Row: 0.4932
Col: 0.5445
Row: 0.2429
Col: 0.2116
Original Image :Lotus [ Row: 0.8163 and col: 0.8461]
Transform Row
Transform
Row
Transform
Scrambled
Column
Transform
Column
Transform
Scrambled
Full
Transform
Full
Transform
Scrambled
DCT Row:0.9839
Col: 0.1847
Row: 0.3744
Col: 0.4335
Row: 0.1950
Col: 0.9915
Row: 0.3806
Col: 0.4547
Row: 0.2391
Col: 0.2292
Row: 0.4567
Col: 0.5137
DST Row: 0.9795
Col: 0.1901
Row: 0.4459
Col: 0.4601
Row: 0.1996
Col: 0.9879
Row: 0.3821
Col: 0.2824
Row:0.3615
Col: 0.3170
Row: 0.4182
Col: 0.4148
Real
Fourier
Row: 0.9918
Col: 0.1914
Row: 0.3810
Col: 0.2458
Row: 0.2012
Col: 0.9892
Row: 0.3649
Col: 0.2126
Row: 0.2531
Col: 0.2311
Row: 0.2906
Col: 0.3091
Hartley Row: 0.9884
Col: 0.2290
Row: 0.2134
Col: 0.2146
Row: 0.1860
Col: 0.9915
Row: 0.2061
Col: 0.2148
Row: 0.3902
Col: 0.4168
Row: 0.2153
Col: 0.1902
DFT Row: 0.9939
Col: 0.1908
Row: 0.2007
Col: 0.1426
Row: 0.1369
Col: 0.9954
Row: 0.1415
Col: 0.2143
Row: 0.3442
Col: 0.3701
Row: 0.1844
Col: 0.1405
Original Image :Baboon [ Row: 0.7179 and col: 0.6935]
Transform Row
Transform
Row
Transform
Scrambled
Column
Transform
Column
Transform
Scrambled
Full
Transform
Full
Transform
Scrambled
DCT Row: 0.9912
Col: 0.2006
Row: 0.6365
Col: 0.3851
Row: 0.2721
Col: 0.9935
Row: 0.3866
Col: 0.6583
Row: 0.2778
Col: 0.2159
Row:0.5723
Col: 0.5739
DST Row: 0.9923
Col: 0.2029
Row: 0.7196
Col: 0.3702
Row: 0.2912
Col: 0.9927
Row: 0.3789
Col: 0.5446
Row: 0.3865
Col: 0.3444
Row:0.4690
Col: 0.5042
Real
Fourier
Row: 0.9953
Col: 0.2096
Row: 0.6600
Col: 0.2457
Row: 0.1987
Col: 0.9937
Row: 0.3794
Col: 0.1922
Row: 0.2179
Col: 0.2179
Row:0.2420
Col: 0.2749
Hartley Row: 0.9928
Col: 0.2144
Row: 0.2002
Col: 0.2370
Row: 0.2633
Col: 0.9937
Row: 0.1911
Col: 0.1918
Row: 0.4242
Col: 0.3475
Row:0.1825
Col: 0.1937
DFT Row: 0.9961
Col: 0.1684
Row: 0.1945
Col: 0.1575
Row: 0.2569
Col: 0.9961
Row: 0.1350
Col: 0.1754
Row: 0.3952
Col: 0.2750
Row:0.1422
Col: 0.1430

TABLE 1: Average Row and Average Column correlation obtained in Row Transform , Row Transform
scrambled , Column Transform , Column Transform Scrambled , Full Transform and Full Transform
scrambled images for DCT, DST, Real Fourier , Hartley and DFT Tran
The Figure 9 – Figure 13 shows the blockwise cummulative energy in the transform coefficients
after applying row transform, column transform and full transform. Energy in the coefficients is
calculated by dividing the image in to blocks. The first block is of size 2x2 ,the second block
considered is 4X4 which includes the first block and an increase in the block size by 2 and so on.
FIGURE 9: Block wise Energy obtained in original, DCT row, DCT column, DCT full, DCT row scrambled,
DCT Column Scrambled, DCT Full scrambled, DCT row Inverse scrambled, DCT col Inverse scrambled,
0
20
40
60
80
100
120
1
11
21
31
Energyin%
Transform Row
Transform Transform
Scrambled
DCT
Row: 0.9945
Col: 0.1887
Row: 0.7014
Col: 0.5178
DST
Row: 0.9944
Col:0.2056
Row:
Col:
Real
Fourier
Row: 0.9959
Col: 0.2185
Row: 0.7298
Col: 0.2971
Hartley
Row: 0.9949
Col: 0.2605
Row: 0.2700
Col:
DFT
Row: 0.9961
Col: 0.2406
Row: 0.3027
Col: 0.1623
Average Row and Average Column correlation obtained in Row Transform , Row Transform
scrambled images for DCT, DST, Real Fourier , Hartley and DFT Transforms
Figure 13 shows the blockwise cummulative energy in the transform coefficients
by dividing the image in to blocks. The first block is of size 2x2 ,the second block
dered is 4X4 which includes the first block and an increase in the block size by 2 and so on.
Block wise Energy obtained in original, DCT row, DCT column, DCT full, DCT row scrambled,
and DCT full Inverse scrambled.
31
41
51
61
71
81
91
101
111
121
Blocks
DCT Energy Plot
original Image
DCT row
DCT Col
DCT Full
DCT Scr Row
DCT Scr Col
DCT Scr Full
DCT Row Inv
DCT Col Inv
DCT Full Inv
Original Image :Cartoon [ Row: 0.8027 and col: 0.8070]
Row
Transform
Scrambled
Column
Transform
Column
Transform
Scrambled
Transform
Row: 0.7014
Col: 0.5178
Row: 0.2556
Col: 0.9955
Row: 0.5230
Col: 0.7489
Row: 0.2897
Col: 0.2238
Row: 0.8154
Col: 0.4576
Row: 0.2646
Col: 0.9953
Row: 0.4515
Col: 0.6254
Row:
Col: 0.5047
Row: 0.7298
Col: 0.2971
Row: 0.2217
Col: 0.9954
Row: 0.4903
Col: 0.2254
Row: 0.2613
Col: 0.2383
Row: 0.2700
Col: 0.2675
Row: 0.1983
Col:0.9954
Row: 0.2046
Col: 0.2337
Row: 0.3954
Col: 0.5162
Row: 0.3027
Col: 0.1623
Row: 0.1492
Col: 0.9961
Row: 0.1299
Col: 0.2483
Row: 0.3068
Col: 0.4806
60
Average Row and Average Column correlation obtained in Row Transform , Row Transform
sforms
Figure 13 shows the blockwise cummulative energy in the transform coefficients
by dividing the image in to blocks. The first block is of size 2x2 ,the second block
dered is 4X4 which includes the first block and an increase in the block size by 2 and so on.
Block wise Energy obtained in original, DCT row, DCT column, DCT full, DCT row scrambled,
original Image
and col: 0.8070]
Full
Transform
Full
Transform
Scrambled
Row: 0.2897
Col: 0.2238
Row:0.6601
Col: 0.6596
Row: 0.3048
Col: 0.5047
Row: 0.5924
Col: 0.5571
Row: 0.2613
Col: 0.2383
Row: 0.3178
Col: 0.3187
Row: 0.3954
Col: 0.5162
Row:0.2412
Col: 0.2146
Row: 0.3068
Col: 0.4806
Row: 0.2410
Col: 0.1872

FIGURE 10: Block wise Energy obtain
DST Column Scrambled, and DST Full scrambled
FIGURE 11: Block wise Energy obtained in original, Real Fourier row, Real Fourier column, Real Fourier
full, Real Fourier row scrambled, Rea
0
20
40
60
80
100
120
1
10
19
28
Energyin%
0
20
40
60
80
100
120
1
10
19
28
Energyin%
Real Fourier Energy Plot
Block wise Energy obtained in original, DST row, DST column, DST full, DST row scrambled,
DST Column Scrambled, and DST Full scrambled.
Block wise Energy obtained in original, Real Fourier row, Real Fourier column, Real Fourier
full, Real Fourier row scrambled, Real Fourier Column Scrambled, and Real Fourier Full scrambled
28
37
46
55
64
73
82
91
100
109
118
127
Blocks
DST Energy Plot
original Image
DST row
DST Col
DST Full
DST Scr Row
DST Scr Col
DST Scr Full
28
37
46
55
64
73
82
91
100
109
118
127
Blocks
Real Fourier Energy Plot
original Image
Fourier row
Fourier Col
Fourier Full
Fourier Scr Row
Fourier Scr Col
Fourier Scr Full
61
ed in original, DST row, DST column, DST full, DST row scrambled,
Block wise Energy obtained in original, Real Fourier row, Real Fourier column, Real Fourier
l Fourier Column Scrambled, and Real Fourier Full scrambled.
original Image
DST Scr Row
original Image
Fourier Scr Row
Fourier Scr Col
Fourier Scr Full

FIGURE 12: Block wise Energy obtained in original, Hartley row, Hartley column, Hartley full,
Hartley row scrambled, Hartley Column Scrambled, and Hartley Full scrambled
FIGURE 13: Block wise Energy obtained in original, DFT row, DFT column, DFT full, DFT
row scrambled, DFT Column Scrambled, and DFT Full scrambled
0
20
40
60
80
100
120
1
10
19
28
Energyin%
0
20
40
60
80
100
120
1
9
17
25
33
Energyin%
Block wise Energy obtained in original, Hartley row, Hartley column, Hartley full,
Hartley row scrambled, Hartley Column Scrambled, and Hartley Full scrambled
Block wise Energy obtained in original, DFT row, DFT column, DFT full, DFT
row scrambled, DFT Column Scrambled, and DFT Full scrambled.
37
46
55
64
73
82
91
100
109
118
127
Blocks
Hartley Energy Plot
original Image
Hartley row
Hartley Col
Hartley Full
Hartley Scr Row
Hartley Scr Col
Hartley Scr Full
33
41
49
57
65
73
81
89
97
105
113
121
Blocks
DFT Energy Plot
original Image
DFT row
DFT Col
DFT Full
DFT Scr Row
DFT Scr Col
DFT Scr Full
62
Block wise Energy obtained in original, Hartley row, Hartley column, Hartley full,
Hartley row scrambled, Hartley Column Scrambled, and Hartley Full scrambled.
Block wise Energy obtained in original, DFT row, DFT column, DFT full, DFT
original Image
Hartley Scr Row
Hartley Scr Col
Hartley Scr Full
original Image
DFT Scr Row
DFT Scr Col
DFT Scr Full

5. EXPERIMENTAL RESULTS DISCUSSION
A Transform is a technique for converting a signal into elementary frequency components.
Transform coding relies on the premise that pixels in an image exhibit a certain level of
correlation with their neighboring pixels. consequently, these correlations can be exploited using
Image Scrambling techniques. The main goal of an Image Scrambling is to decorrelate the image
pixels as much as possible so that image data is scrambled and appears in an unreadable
format. Reducing the correlation between the rows and columns of the image will be helpful for
any scrambling technique. Using this as an experimental parameter, Average correlation between
rows and columns is calculated. As we know that applying a transform on the image decorrelates
the image pixels, to find out whether a further reduction of this correlation can be obtained by our
novel approach, five sinusoidal transforms were tested on a number of images. The experimental
results obtained are shown in Table No 1 for five images. The highlighted cells in the Table No 1
show that DHT and DFT proves to be the best in all the three cases of transform applied on a
digital image , that is row transform , column transform and full transform. Although the other
three that is DCT , DST and Real Fourier gave good results of decorrelation in row transform.
However other cases of these three transform does not increase the correlation by a very large
value, it is in a marginal range.
To Test these transforms further, we have taken into consideration the energy distribution in
original, Transformed and Transform scrambled images. The observations made from the Energy
Plot for DCT, DST, Real Fourier, Discrete Hartley and DFT are as follows
Origina
l Image
Row
Transforme
d Image
Column
Transforme
d Image
Full
Transforme
d Image
Row
Transform
Scramble
d Image
Column
Transform
Scramble
d Image
Full
Transform
Scramble
d Image
Linear
Increas
e in
energy
Small step
linear
increase in
energy
Small step
linear
increase in
energy
High in the
initial blocks
and den
small
increases to
reach 100%
Small step
linear
increase in
energy
Small step
linear
increase in
energy
Very less
value in
the initial
blocks and
a sudden
jump after
blocks size
>20
6. CONCLUSION
In this paper we have presented a Novel Approach for Image scrambling in Transform Domain
using Sinusoidal Transforms like DCT, DST, Real Fourier, Hartley and DFT. From the
experimental results it is clear that our proposed approach can be used for secured image
scrambling. The Correlation obtained for Discrete Hartley and DFT proves to be very less which
was our main goal of Image scrambling. The energy plot observations can also be used as a
measure for detecting Image scrambling in transform domain for full sinusoidal transforms. The
Proposed Approach is a combination of both transform as well as spatial domain, hence it is very
useful for Image scrambling and provides more security.
In the previous case[19] , we have found that Kekre transform gave the best performance as
compared to all other Non Sinusoidal transforms. The transforms used in this paper gave the
performance close to Kekre transform with DFT and Discrete Hartley proving better than that.

7. REFERENCES
[1] J.-L. Fan and X.-F. Zhang, “Image encryption algorithm based on chaotic system,” in
International Conference on Computer-Aided Industrial Design and Conceptual Design.
CAIDCD, 2006, pp. 1–6.
[2] Chen, C.L.P, Tong Zhang , Yicong Zhou, “Image encryption algorithm based on a new
combined chaotic system”, IEEE International Conference on Systems, Man, and
Cybernetics (SMC), 2012, pp. 2500 – 2504
[3] M. Jian-liang, P. Hui-jing, and G. Wan-qing, “New color image encryption algorithm based on
chaotic sequences ranking,” in Proceedings of the International Conference on Intelligent
Information Hiding and Multimedia Signal Processing, 2008. IIHMSP ’08, August 2008, pp.
1348–1351.
[4] Lei Li-hong; Bai Feng-ming; Han Xue-hui, "New Image Encryption Algorithm Based on
Logistic Map and Hyper-Chaos," Fifth International Conference on Computational and
Information Sciences (ICCIS), 2013, vol., no., pp.713,716, 21-23 June 2013
[5] Naeem, E.A.; Elnaby, M.M.A.; Hadhoud, M.M., "Chaotic image encryption in transform
domains," International Conference on Computer Engineering & Systems, 2009. ICCES
2009., vol., no., pp.71-76, 14-16 Dec. 2009.
[6] Sapna Anoop, Anoop Alakkaran, “A Full Image Encryption Scheme Based on Transform
Domains and Stream Ciphers”, International Journal of Advanced Information Science and
Technology (IJAIST), Vol. 17, pp. 5-10, September 2013
[7] Long Bao , Yicong Zhou , C. L. Philip Chen, “Image encryption in the wavelet domain”, in
Proc. SPIE 8755, Mobile Multimedia/Image Processing, Security, and Applications 2013
[8] Taranjit Kaur, Reecha Sharma, “Image Cryptography by TJ-SCA: Supplementary
Cryptographic Algorithm for Color Images”, International Journal of Scientific & Engineering
Research, Volume 4, Issue 7, pp 1355-1360, July-2013.
[9] Y. Zhou, K. Panetta, S. Agaian, and C. L. P. Chen, "Image encryption using P- Fibonacci
transform and decomposition," Optics Communications, vol. 285, pp. 594-608, 2012.
[10]K. Wong and K Tanaka, “Scalable Image Scrambling Method Using Unified Constructive
Permutation Function on Diagonal Blocks,” IEEE Proc. 28
th
Picture Coding Symposium PCS,
pp. 138-141, 2010.
[11]Liu, S., Sheridan, J.T.: Optical Information Hiding by Combining Image Scrambling
Techniques in Fractional Fourier Domains. In: Irish Signal and Systems Conference, pp.
249–254, 2001.
[12]C. Li, G. Xu, C.Song and J. Jing, “Evaluation of Image Scrambling Degree with Intersecting
Cortical Model Neural Network”, International Journal of Hybrid Information Technology, Vol.
5, No. 2, pp. 31-40, 2012.
[13]M François, T Grosges, D Barchiesi, R Erra,“ Image Encryption Algorithm Based on a
Chaotic Iterative Process”, Applied Mathematics, Vol. 3, No. 12, 2012, pp. 1910-1920.
[14]Mishra, Minati, Priyadarsini Mishra, M. C. Adhikary, and Sunit Kumar. "Image Encryption
Using Fibonacci-Lucas Transformation." International Journal on Cryptography and
Information Security (IJCIS),Vol.2, No.3, September 2012 pp 131-141

[15]Zhu, Guiliang, Weiping Wang, Xiaoqiang Zhang, and Mengmeng Wang. "Digital image
encryption algorithm based on pixels." In Intelligent Computing and Intelligent Systems
(ICIS), 2010 IEEE International Conference on, vol. 1, pp. 769-772. IEEE, 2010.
[16]Feng, Yong, and Xinghuo Yu. "A novel symmetric image encryption approach based on an
invertible two-dimensional map." In Industrial Electronics, 2009. IECON'09. 35th Annual
Conference of IEEE, pp. 1973-1978. IEEE, 2009.
[17]H.B.Kekre and J.K.Solanki, “Comparative performance of various trigonometric unitary
transforms for transform image coding” , International Journal of Electronics, Vol. 44, No. 3.
pp. 305-315, 1978.
[18]P. Premaratne & M. Premaratne, "Key-based scrambling for secure image communication,"
in Emerging Intelligent Computing Technology and Applications, P. Gupta, D. Huang, P.
Premaratne & X. Zhang, Ed. Berlin: Springer, 2012, pp.259-263.
[19] H.B.Kekre, Tanuja Sarode, Pallavi Halarnkar, Debankya Mazumder, “Image Scrambling
using Non Sinusoidal transforms and Key based Scrambling Technique”, International
Journal of Computer Technology (IJCT), Volume 12 issue no 8, pp. 3809- 3822. February
2014.

Comparative Performance of Image Scrambling in Transform Domain using Sinusoidal Transforms

More Related Content

What's hot (20)

Similar to Comparative Performance of Image Scrambling in Transform Domain using Sinusoidal Transforms (20)

Recently uploaded (20)

Comparative Performance of Image Scrambling in Transform Domain using Sinusoidal Transforms