CHAPTER 4 EFFECT OF PIXEL SCRAMBLING METHOD ON IMAGE...
Transcript of CHAPTER 4 EFFECT OF PIXEL SCRAMBLING METHOD ON IMAGE...
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CHAPTER 4
EFFECT OF PIXEL SCRAMBLING METHOD
ON IMAGE ENCRYPTION
4.1 TWO CHAOTIC MAPS CSDP BASED IMAGE ENCRYPTION
USING PIXEL SCRAMBLING ALGORITHM
4.1.1 Introduction
In the present chapter a novel image encryption method using
simple logical and scrambling operations are introduced. In the first section of
the chapter, a simple transformation, permutation and two chaotic map CSDP
based scrambling (Ville et al 2003, Xiangdong et al 2008, Jiankun and
Fengling 2009) of image encryption is discussed. In the second section, a
pixel scrambling and simple logical operation based chaotic map image
encryption is shown. In the third section, a combination of above sections as
pixel scrambling, simple logical operation and transformation based two
chaotic map image encryption is exhibited. Finally, the present novel method
has been used to analyze and evaluate its performances through the statistical
measures Viz., histogram, cross correlation co - efficient, entropy, PSNR,
scrambling distance and key sensitivity.
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4.1.2 The Types of Maps used in the CSDP based Image Encryption
using Pixel Scrambling
Chaotic Map
The chaos theory indicates the behaviour of certain nonlinear
dynamic system that under specific conditions exhibit dynamics that are
sensitive to initial conditions. The two basic properties of chaotic systems are:
The sensitivity to initial conditions and Mixing Property (Wu and
Rulkov 1993) proposed 1 D chaotic map to produce the chaotic sequence and
used to control the encryption processes. In the present work the chaotic maps
as Logistic map and Bernoulli map are used and described as below.
Logistic Map
A simple and well-studied example (Parker and Chua 1995, Wu
and Rulkov 1993, Kuo and chen 1991) of a 1D map that exhibits complicated
behavior is the logistic map from the interval [0,1] in to [0,1], parameterised
by and as mentioned in equations (3.11) and (3.12).
Bernoulli Map
The Bernoulli map which is used in the present novel method
(Parker and Chua 1995, Wu and Rulkov 1993) as mentioned in
equation (3.15).
4.1.3 The Present Novel Method for Image Security System to the
CSDP based Image Encryption using Pixel Scrambling
The present encryption algorithm belongs to the category of
combined value transformation and position permutation. Therefore, one
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should initially define two bit-circulation functions with two parameters in
each function. One first bit circulation function is used to control the shift
direction and second bit circulation function is used to control the shifted bit-
number on the data transformation. In the present work, first bit circulation
function and second bit circulation function based scanning is used for their
performances and analyzed for the evaluation. The images in the present case
are treated as a 1D array by performing Raster scanning and zigzag scanning
as studied by Bourbakis and Alexopoulos (1991).
Figure 4.1 Chaos based Image Cryptosystem
Figure 4.1 shows the typical schematic of the present method,
where the scanned arrays are divided into various sub blocks. In each sub
block, position permutation and value transformation are performed and
finally scramble to produce the cipher image.
In continuation, a sub key is generated by applying the suitable
chaotic maps. Based on the initial conditions of chaotic map, the chaotic maps
are generated and allowed to iterate through various orbits. Hence, for each
sub block various chaotic sequence patterns are applied which are further
Plainimage
Secret key
Cipherimage
Seed
Key Generator - chaotic map-Logistic, Bernoulli map
DiffusionDiagonal shifting
Value mod Row
shifting
Position permutation
columnshifting
Scrambling
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used to increase the efficiency of the key to be determined by the brute force
attack.
Further, the chaotic system based binary sequence is generated to
control the bit-circulation functions to perform successive data transformation
on the input data as presented in the section 3.1.4. In order to demonstrate the
correct functionality of the present signal security system, the simulation on
the present scheme has to be made. The following are the steps used for the
implementation of present chaos based mapping method.
4.1.4 The Algorithm used for Pixel Scrambling in the Present Work
Step 1: Covert 2 image into 1 array and then performs the Raster
scanning and the zigzag scanning.
Step 2: Consider a block size of 8 × 8 and convert them in to binary values.
Step 3: Sub key size is 20 bits, hence it is extracted from the chaos maps as
Bernoulli map. The Secret key is SEED, which are the initial conditions of the
each map. From the initial conditions the chaotic maps are allowed to iterate
through various orbits. Then, based on the chaotic system, binary sequence is
generated to control the bit-circulation functions to perform the successive
data transformation on the input data. A pair of and , the combination of
, , , , and resulting in the transformation pair may be non-unique used
as secret key.
Step 4: Convert the chaotic sub key in to binary values of 20 bits.
Step 5: Each 8 × 8 sub block of image pixel values circularly shifted by
chaos sequence generated from maps.
Step 6: The Circular shifting of Diagonal pixels are used as discussed in
section 3.2.5
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Step 7: Perform the encryption by the chaotic sequence key values, which is
obtained from the orbits of chaos maps iteration.
Step 8: Chaos theory Based Image Scrambling (Xiangdong et al 2008)
transformation to a Gray scale image of size × pixels, can have an
arbitrary chaotic iteration = ( ) to generate a
chaotic sequence of real numbers.
The initial value is the secret key. The following scheme has
been applied to scramble and unscramble cipher image .
Step 8.1: Let an initial value be that is associated to the secret key.
Let = 1.
Step 8.2: Iterate from 0 1 times with the chaotic iteration 8.1, and get
the sequence of real numbers , … … , .
Step 8.3: Arrange the chaotic sequence , … … , in descending order, to
get the sorted sequence{ … . . , }.
Step 8.4: Determine the set of scrambling address codes , … … , ,
where {1,2 … . . }. is the new subscript of in the sorted sequence
{ … . . , }.
Step 8.5: Permute the column of the cipher image with permuting
address code , … … , , namely, replace the row pixel with the row
pixel for from1 .
Step 8.6: If = , end of iteration. Otherwise, let = , and = + 1.
Repeat from 8.2 to 8.5, to produce double encrypted cipher image data value
in 1 form.
Step 9: Transform the cipher image from1 Dimension to 2 Dimension.
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Step 10: Transmit the chaotic sub key via secure channel using public key
algorithms.
Step 11: Decrypt the cipher image using the same chaotic sub key and SEED.
Step 12: Finally, performance analysis is carried out by doing correlation,
histogram and PSNR of the original, encrypted and decrypted image.
4.1.5 The Analysis and Evaluation of Present Method for Security
System to CSDP based Image Encryption using Pixel
Scrambling
The analysis of security system for two chaotic image encryption
are performed through the following types: Histogram analysis, correlation
analysis, PSNR and speed analysis and sensitivity analysis.
An image size of 256×265is considered as plain image for example x-ray of chest and should be performed with chaotic map along with orbit key. The most direct method to decide the disorderly degree of the encrypted image is through the sense of sight.
On the other hand, the arising correlation coefficient could provide quantitative measure on the randomness of the encrypted images. The logistic
map (1D) uses four parameters , , and (0) in generating the chaotic bit-stream. The four parameters could be viewed as the keys to the present signal security system. Among them, the parameters and can be fixed in both the transmitter and receiver according to the constraint shown in Step 1.
In order to apply the parameters and must be determined according to Step 1. The selection of and should follow the empirical law.
Based on the experimental experience, general combinations of and canalways result in very disorderly results. In the simulation, = 2 and = 2 are adopted in Step 1.
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The initial conditions of chaotic maps used are, f (x) = 0.5 for Bernoulli map. The offset values for producing various orbits are chosen to be very less than the initial conditions. The visual inspection of Figure 4.2 shows the possibility of applying the algorithm successfully in both encryption and decryption. In addition, it reveals its effectiveness in hiding the information contained in them.
Figure 4.2 (a) Original (b) Cipher Image (c) Cipher Image (d) Decrypted Image with Maps and Scrambling
Histogram Analysis : An image histogram (Shubo et al 2009, Patidar et al 2009, Jiankun and Fengling 2009) illustrates how the pixels in an image are distributed by graphing the number of pixels at each level of intensity. One typical example among them is shown in Figure 4.3(a). The histogram of a plain image contains large spikes.
Figure 4.3 (a) Histogram of Original Image
Figure 4.3 (b) Histogram of Cipher Image
0 50 100 150 200 250
0
0.5
1
1.5
2
2.5
x 104
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100020003000400050006000700080009000
10000
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The histogram of the cipher image as shown in Figure 4.3(b) is uniform, significantly different from that of the original image, and bears no statistical resemblance to the plain image. It is clear that the histogram of the encrypted image is uniform and significantly different from the respective histograms of the original image and hence does not provide any clue to employ any statistical attack on the present image encryption procedure.
Correlation Co-efficient Analysis : In addition to the histogram analysis
(Krishnamoorthi and Sheba Kezia Malarchelvi 2008, Shubo et al 2009,
Patidar et al 2009, Zhang et al 2007), the correlation between two vertically
adjacent pixels, two horizontally adjacent pixels and two diagonally adjacent
pixels in plain image and cipher image are considered in the present
investigation.
The correlation co-efficient analysis is computed as mentioned in
equations (3.4)-(3.6). Figure 4.4 shows the correlation distribution of two
horizontally adjacent pixels in plain image and cipher image for the all image.
The correlation co-efficients are found to be 0.9905 and 0.0308 for both plain
image and cipher image respectively.
Figure 4.4 a) Horizontal, Vertical and Diagonal Correlation of Plain Image
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Figure 4.4 b) Horizontal, vertical and Diagonal Correlation of Cipher Image
The correlation coefficients (Shubo et al 2009, Patidar et al 2009,
Jiankun and Fengling 2009, Fishawy and Zaid 2007 of various maps are also
calculated and compared with each other. The results of correlation co
efficient are shown in the Table 4.1 for various plain, cipher images and maps
based correlation co efficient.
Table 4.1 Horizontal, Vertical and Diagonal Correlation coefficients of
Cipher Image
Original Image
Horizontal Correlation
Verticalcorrelation
DiagonalCorrelation
Cipher image with Maps and
scrambling Knee 0.2254 0.4400 0.0012 -0.00070115
Chest -0.0515 -0.0241 -0.0084 0.00010436
Human Head 0.5930 0.5759 -0.0646 -0.00094391
Lena 0.5254 -0.0241 0.0028 0.00095436
Correlation analysis of Scanning Pattern: The correlation coefficient is
found for the various directions of scanning patterns employed as presented in
section 3.2.6. The results as correlation co efficient for raster and zigzag
scanning are shown in Table 4.2.
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Table 4.2 Horizontal Correlation Co-efficient for Raster Scanning and Zigzag Scanning
IMAGE Raster Scanning zigzag Scanning
Knee 0.0539 -0.00139
Chest -0.0535 -0.00590
Human Head 0.0174 -0.00230
Lena -0.0635 -0.00980
The observation shows from the task that the zigzag scanning is
more efficient than the raster scanning. In addition, the cipher image with
multiple maps is more resistant to crypt by the analyst attacks. The correlation
for plain and cipher image is shown in Table 4.3.
Table 4.3 Correlation Coefficient in Plain Image and Cipher Image
Direction of Adjacent Pixels Plain Image
Cipher image using Bernoulli
Map
Cipher Image with Maps and
Scrambling Horizontal 0.9670 0.0781 0.00887
Vertical 0.9870 0.0785 0.00923
Diagonal 0.9692 0.0683 0.00893
PSNR and Speed Analysis: The peak signal to noise (Krishnamoorthi and
Sheba Kezia Malarchelvi 2008, Jiri and Karel 2009) ratio of encrypted image
and original image is computed as mentioned in section 3.1.4. In the present
scheme of encryption, higher the visual quality of the cipher image, lesser are
the number of changed pixels and larger the value of PSNR it is around
9.3158 for the chest image, 9.0061for the knee image and 9.2709 for the head
image mentioned in the tables and shown in the Table 4.4.
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Table 4.4 Encryption Speed
Image Size Speed (seconds)
PSNR
(dB)
Knee 256x256 0.1143 9.11
64x64 7.3168 9.32
8x8 117.06 9.26
Lena 256x256 0.1293 9.09
64x64 8.2722 9.31
8x8 132.35 9.20
Sensitivity Analysis : In differential attacks (Ahmed et al 2007) , to test the
influence of one-pixel change on the whole image encrypted by the present
algorithm, two common measures are NPCR and UACI as mentioned in the
section 3.1.4. The NPCR and UACI are calculated for knee, chest and Human
head and shown in the Table 4.5.
Table 4.5 NCPR AND UACI for Cipher Image
Image NPCR (%) UACI(%)
Knee 99.993 -0.00077
Chest 99.843 -0.00546
Human Head 98.430 -0.00839
Lena 98.80 -0.00330
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4.2 A TWO CHAOTIC IMAGE ENCRYPTION USING PIXEL
SCRAMBLING
4.2.1 Introduction
In the previous section chaotic image encryption based on simple
scrambling and logical operation is discussed. However, always there is a
scope for improvement in the speed and security measures. Hence a new
chaotic image encryption based on simple scrambling and logical operation is
introduced. The present techniques is analyzed and its performances are evaluated
by statistical measures such as histogram, cross correlation, entropy, PSNR
,scrambling distance ,speed and key sensitivity analysis are discussed
4.2.2 The Present Novel Method for Image Security System Use of
Two Chaotic Image Encryption using Pixel Scrambling
4.2.2.1 The Present Image Encryption Method
The present encryption method is shown as a flow diagram in
Figure 4.5. Basically it uses pixel scrambling and XOR operation performed
in the present novel method. In the present work the key stream is generated
by PMMLCG and logistic chaotic maps.
In the first part of the algorithm which performs row and column
scrambling based on prime modulus linear congruential generator
(PMMLCG) chaotic map and then XOR operation is performed for scrambled
image with PMMLCG map. The scrambled image is again row and column
scrambling based on logistic map and then XOR operation performed for
scrambled image with logistic map.
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Figure 4.5 Flow Diagram of the Present Novel Method
PMMLCG
Column scrambling
{ , , … , … }
{ , , … , … }
XOR pixels in adjacent rows
XOR pixels in adjacent columns
Scramble each pixel
Plain image{M ×N}
Chaos map
Column scrambling
Row scrambling
{ , , … , … }
{ , , … , … }
XOR pixels in adjacent rows
XOR pixels in adjacent columns XOR pixels in each row with chaos map
Cipher Image
Row scrambling
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4.2.2.2 Key Stream Generator
The key stream is generated by two chaotic maps and the present
novel work uses PMMLCG and logistic map.The random sequence is
generated using PMMLCG. Linear Congruential Generators (LCG) are one of
the oldest and most studied random number generator (RNGs). A LCG is
parameterized by three integers , and .
Its basic form is
= ( + ) (4.1)
A special kind of LCG is called PMMLCG. Its parameters are
= 0 and being a prime. The advantage of PMMLCG is that eliminates an
addition which has an almost full period (of length ( 1)) and can be
subjected to the Spectral test. PMMLCG generate a random sequence by
using the above equation. PMMLCG is a secret key for the first part of the
algorithm and it is used for row, column scrambling and key XOR operations.
In the second part the algorithm uses logistic map as a secret key
and it is generated as follows. A random sequence from the logistic map has
been generated with secret key as mentioned in equation (3.3).
For (0,1) and (3.9876543210001,4) and are the
system control parameter and initial condition respectively. A secret key
value is , its typical value is 0.9876543219991. Depending on the value
of , the dynamics of the system could be changed dramatically.
The choice of in the equation above guarantees the system is in a
chaotic state and the output chaotic sequences have perfect randomness.
The Logistic map (Dachselt and Schwarz 2001, Parker and Chua 1995) has a
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secret key for the second part of the algorithm and it is used for row, column
scrambling and key XOR operations.
4.2.2.3 The Algorithm for Present Novel Method
Step 1.1: Read an input plain image.
For the Gray scale image of size × pixels, can have an
arbitrary chaotic iteration
= ( ) , (4.2)
to generate two chaotic sequences of real numbers of lengths and
respectively. The initial seed value is derived from the secret key for one of
the sequence, and from the previous sequence for the other set.
Step 1.2: Similarly, generate two PMMLCG sequences of real numbers of
lengths M and N respectively as given by,
= (4.3)
The initial seed value is derived from the secret key for one of
the sequence and from the previous sequence for the other set.
Step 2: Permute the row of the image with the row obtained from
one of the PMMLCG sequences generated in step 1.2, and the column
with column obtained from the other sequence for all values of from
1 and from1 .
Step 3: If = and = , XOR adjacent pixels and end the iteration.
Otherwise, increment i and k and Repeat the previous step.
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Step 4: Scramble each pixel ( , ) in the image to a position ( , )
determined from the random sequence generated in the earlier steps.
Step 5: Permute the row of the image with the row obtained from
one of the Chaotic sequences generated in step 1.1, and the column with
column obtained from the other sequence for from 1 and
from1 .
Step 6: If = and = , XOR adjacent pixels and end the iteration.
Otherwise, increment i and k and Repeat the previous step to produce double
encrypted cipher image.
Pseudo code
READ plain image and key.
GENERATE two PMMLCG sequences defined by
x = ax mod q, using an initial seed derived from the key.
PERMUTE ROWS of the plain image with
WHILE i!=M
I(i,j) I(xi,j)
I(i,j)= I(i,j) I(i+1,j).
PERMUTE COLUMNS of the resulting image
WHILE k!=N
I(i,j) I(i,xk)
I(i,j)= I(i,j) I(i,j+1).
SCRAMBLE Each Pixel in the Image
WHILE (i!=M && k!=N)
I(i,j) I(xi,xk).
GENERATE two Chaos sequences defined by
x = f( x ), using an initial seed derived from the key.
PERMUTE ROWS of the plain image with
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WHILE i!=M
I(i,j) I(xi,j)
I(i,j)= I(i,j) I(i+1,j)
PERMUTE COLUMNS of the resulting image
WHILE k!=N
I(i,j) I(i,xk)
I(i,j)= I(i,j) I(i,j+1).
XOR pixels in each row with the chaos map.
WRITE the cipher image.
4.2.2.4 The Various Transformation of Pixel in the Plain Image during
Scrambling and flow Diagram of Present Image Encryption
Method
The image has been represented as 2D box and pixels of the plain
image are demonstrated by blue color shading. The scrambled image pixels
are represented by red color. After scrambling, the image is XORéd with
Logistic map, it is represented by grey color.
Stage I: Applying PMMLCG’s to transpose rows, columns and every
individual pixel in the image:
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PMMLCG generator equation: z = ( z )mod q
where, a - multiplier q - Large Prime number
( , )
( , )
Stage II: Applying Logistic map to transpose rows and columns in the image:
Logistic map equation: x = ( x ) ( x )where – multiplier
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4.2.3 The Analysis and Evaluation of Present Method for Security
System to Two Chaotic Map based Image Encryption using
Pixel Scrambling
In the present novel method of encryption the analysis of security
was also performed through the following types. Histogram analysis,
correlation co efficient analysis, key space analysis, PSNR and speed
analysis, average moving distance of scrambling, entropy and key sensitivity
analysis.
Histogram Analysis: The histograms of the several encrypted images as
well as its original images that have widely different content are analyzed as
mentioned in section 3.1.4. One typical example among them is shown in Figure
4.6 (b) as below.
CIPHER IMAGEEX-OR
Logistic Map
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(a) (b) (c)
Figure 4.6 (a) Original Image (b) Histogram of Original Image (c) Histogram of Cipher Image
The histogram of a plain image contains large spikes, such spikes
correspond to gray values that appear more often in the plain image. The
histogram of the cipher image is shown in Figure 4.6 (c), is uniform,
significantly different from that of the original image and bears no statistical
resemblance to the plain image.
It is clear from the above that the histogram of the encrypted image
is fairly uniform and significantly different from the respective histograms of
the original image and hence does not provide any clue to employ any
statistical attack on the present novel method of image encryption procedure.
Correlation Coefficient Analysis : The cross–correlation coefficient
(Shubo et al 2009, Patidar et al 2009, Jiankun and Fengling 2009, Fishawy and
Zaid 2007, Zhang et al 2007) between the plain image A and the cipher image
B are calculated as presented in section 3.1.4.
The algorithm for present novel method produces highly
uncorrelated cipher text images with cross correlation values (horizontal,
vertical and diagonal correlations) that are lower than earlier chaos-based
image encryption schemes. The difference in correlation of plain and cipher
images obtained for other methods and present method is shown in the
Table 4.6
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 50 100 150 200 250
0
2000
4000
6000
8000
10000
12000
0 50 100 150 200 250
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Table 4.6 The cross correlation analysis of the present algorithm
Image
Correlation between plain and cipher image Ahmed et al (2007), Xiangdong et al
(2008), Shubo et al (2009), Jiankun and Fengling (2009), Ismail et al (2007)
chaos based method
Present novel method
Lena.tif -0.00012303 -0.000061326Baboon.tif 0.00029386 0.000852120 Einstein.tif 0.00179810 -0.000423850Airplane.tif 0.00047238 -0.000291900Peppers.tif 0.00276760 -0.000651910
The statistical parameter of Vertical correlation, Horizontal
correlation and Diagonal correlation co efficient are obtained for other chaos
based method and present novel method for various pictures (Images).The
difference in values are shown in the Table 4.7.
Table 4.7 The Statistical Parameter Obtained for other Chaos based Method and Present Method
Statistical parameters
Images
Lena.tif Baboon.tif Airplane.tif
Vertical Correlation
Other chaos based techniques Ismail
et al (2007) 0.00054724 -0.00096242 -0.00005729
Our present technique 0.00007429 -0.000008235 0.001656900
Horizontal Correlation
Other chaos based technique
Ismail et al (2007)-0.0003686 -0.004313800 -0.00082698
Our present technique 0.00056377 -0.000774680 0.000563420
Diagonal Correlation
Other chaos based technique
Ismail et al (2007)0.0026055 0.001244600 0.003412100
Our present technique 0.0030529 0.002380700 0.000932380
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Key Sensitivity Test with Several Slightly Different Keys : The key
sensitivity (Patidar et al 2009, Chang et al 2001, Kocarev and Jakimovski
2001) test have been performed through the following key sensitivity tests:
Decryption key sensitivity, Encryption key sensitivity and Key space analysis.
In decrypted lena.tif image is as shown in Figure 4.7(a) and 4.7(b)
with a wrong decryption key differing from the original private key by one
bit. In the present case the novel method has high degree of key sensitivity as
shown in the Figure 4.8 (a) and 4.8 (b). This confirms that an adversary
cannot retrieve the plaintext with a wrong key.
Figure 4.7 (a) Plain Image and Histogram of Plain Image
Figure 4.7(b) Cipher Image and Histogram of Cipher image
Figure 4.8 (a) Decrypted Image and Histogram of Cipher Image with Wrong Key
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
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Encryption key sensitivity: The parametric changes between
encrypted image of lena.tif with two keys differing by 1 bit and found the
resultant as in Table 4.8. The present method provides the difficulty of a
related key attack.
Table 4.8 Quantitative Analysis of Sensitivity Tests
Analysis CAB NPCR(%) UACI(%)
Encryption key sensitivity
0.0011 99.6124 18.4749
Plain text sensitivity 0.0015 99.3347 22.4449
Key Space Analysis: The key space for a good cryptosystem should be
sufficiently large to make the brute-force attack infeasible. Key spaces imply
the total number of different keys which can be used for the purpose of
encryption and decryption. With respect to the speed of computers today, the
key space should be more than 2100 = 1030 in order to avoid brute-force attacks
(Pisarchik and Zanin 2008). The present novel method uses a 256 bit key as
the result the key space would become 2256 -1. Consequently, the sensitivity
of the algorithm to the key is significantly improved.
The present algorithm is highly sensitive to changes even in the
least significant bit of the key as demonstrated in the process of decryption
using wrong key varying by only one bit from the original key as in the
Figure 4.7(a) and 4.7(b).
PSNR and Speed Analysis : PSNR (Krishnamoorthi and Sheba Kezia
Malarchelvi 2008, Jiri and Karel 2009) of encrypted image and original image
are obtained as given by equation (3.8).
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Table 4.9 Comparison of PSNR’s for the PS based, BFTCGH based, Integrated Imaging PS based and Present Novel Method with 85% Data Loss as Index
PS-based dB
BFT CGH-based
dB
Integral imaging and PS – based
dB
presentmethod
dBPSNR 5.58 9.45 17.11 16.98
Apart from the security consideration, running time and speed is
also an important on image encryption. The simulator for the present novel
method is implemented using the MATLAB 7.6 and the performance has
been measured on a 2.2 GHz Pentium IV with 1 GB of RAM running in
Windows XP.
Table 4.10 shows the performance evaluation (Marwa et al 2008) of
the present scheme. The analysis has been done by selecting 12 images each
one is of different sizes (1.5, 9, 24, 44 and 72 MB etc) having different
contents and using 10 randomly chosen secret keys for each image. Some of
the performance evaluation to present novel method and other methods are
shown in the Table 4.10
Table 4.10 Time of Image Encryption and Algorithms
Algorithm Lena(seconds)Combinational Permutation (Mitra et al 2006)
0.33
CKBA (Yen and Guo 2000) 1.05Encryption using SCAN pattern (Maniccam and Bourbakis 2004)
2.54
ECKBA (Socek et al 2005) 1.84Present Technique 1.72
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Average Moving Distance of Scrambling :The average moving distance of
scrambling (Xiangdong et al 2008) is defined as
| | = ( ) + ( ) (4.4)
where , represents the pixel coordinate of a point in original image and
( , ) represents the pixel coordinate of that point in scramble image. The
statistical results are evaluated for moving distance of pixel. The results from
other chaos based method and present novel method is shown in the
Table 4.11. From the table, the larger the average moving distance of the
scrambling method less relation between the original image and the scramble
image and the increases the efficiency of the method.
Table 4.11 Statistical Results of Average Moving Distance of Present Algorithm
Image Average moving distance of pixel
Other chaos based techniques (Xiangdong et al 2008)
Our present technique
Lena.tif 85.2564 135.0582
Peppers.tif 85.0564 135.5139
Entropy: Entropy (h) (Mohammad and Jantan 2003) is calculated as given by
equation (3.7). The maximum h an 8–bit image can attain is 8. The average of
present novel method gives 7.99. Hence a statistical attack is too difficult to
make.
Sensitivity Analysis: The sensitivity analysis (Ahmed et al 2007) could be
performed through net pixel change rate and unified average change in
intensity as given by equation (3.9) and (3.10). The sensitivity analysis is
obtained as above for LENA image. The results are shown in the Table 4.12.
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Table 4.12 Key Sensitive Analysis on LENA Image
Analysis CAB NPCR(%) UACI(%)
Encryption key sensitivity 0.0011 99.6124 18.4749
Plaintext sensitivity 0.0015 99.3347 22.4449
Ciphertext sensitivity 0.0064 99.9298 19.2178
4.3 A CHAOTIC MAP BASED IMAGE ENCRYPTION USING
INTEGRATED PIXEL SCRAMBLING WITH DIFFUSION
4.3.1 Introduction
In the previous section CSDP based image scrambling technique is
presented. The CSDP based techniques take more time for encryption of the
image but it has very high key space. Hence, always there is a scope for
improvement in the speed and security measures. Therefore, a new chaotic
image encryption based on simple scrambling and logical operation is
introduced.
The present novel method is analyzed and its performances are
evaluated by statistical measures such as histogram, cross correlation,
entropy, PSNR, scrambling distance, speed and key sensitivity analysis.
4.3.2 Chaotic Map
The chaos (Parker and Chua 1995, Wu and Rulkov 1993) can be
generated by using various chaotic maps. In the present method chaotic map
is used to produce the chaotic sequence which is used to control the
encryption process.
89
Logistic Map
A simple and well-studied example from (Dachselt and Schwarz
2001, Parker and Chua 1995) of a 1D map that exhibits complicated behavior
is the logistic map from the interval [0,1] in to [0,1], parameterised by :
( ) = ( ) (4.5)
where 0 4. This map constitutes a discrete-time dynamical system in
the sense that the map : [0,1] [0,1] generates a semi-group through the
operation of composition of functions.
The state evolution is described by ( ) = ( ) and denote
( ) = ( ) (4.6)
For all [0,1], a “discrete-time” trajectory{ } , where
= ( ), can be generated. The set of points { , … . } [0,1] is
called the (forward) orbit of . A periodic point of is a point [0,1]
such that = ( ) for some positive integer . The least positive integer n
is called the period of . A periodic point of period 1 is called a fixed point.
For differentiable g, a periodic point x with period n is stable if
( ) < 1 and unstable if ( ) > 1 ,
where = ( ). In the logistic map, as is varied from 0 to 4, a period-
doubling bifurcation occurs. In the region [0,3], the map possesses
one stable fixed point. As is increased, the stable fixed point becomes
unstable and two new stable periodic points of period 2 are created.
90
As is further increased, these stable periodic points in turn
become unstable and each spawns two new stable periodic points of period 4.
Thus the period of the stable periodic points is doubled at each bifurcation
point.
Each period-doubling episode occurs in a shorter “parameter”
interval, decreasing at a geometric rate each time. Moreover, at a finite , the
period-doubling episode converges to an infinite number of period doublings
at which point chaos is observed.
4.3.3 The Present Novel Method for Image Security System to the
Chaotic Map based Image Encryption using Pixel Scrambling
with Diffusion
In the present novel method, the security system is discussed
through key stream generator and design of encryption, decryption. For the
same algorithm, IISPD technique for image encryption analysis of IISPD is
also performed.
4.3.3.1 Key Stream Generator
The random sequence from the logistic map with secret key has
been generated as mentioned in equation (3.3).
For [0,1] and ( , 3.987653210001,4), and are the system control
parameter and initial condition. A secret key value is whose typical value
is 0.9876543219991. Depending on the value of , the dynamics of the
system can change dramatically. The choice of in the equation above guarantees
the system is in chaotic state and output chaotic sequences have perfect
randomness (Abdulkarim et al 2010, Raynel et al 2009). There are two
91
logistic maps generated for the above purpose based on one integer number
and two floating point numbers.
The integer number is height / width of the image. The first chaotic
logistic map is said to be and second chaotic logistic map is said to be .
For the first logistic map two floating point numbers are secret keys, and
integer number, which is size of the image. Similarly, second logistic map is
generated based on two floating point number are secret key (which is passed
as parameter obtained from the first chaotic logistic map), and integer
number, which is size of the image. Then the values generated by both the
maps are converted in to decimal.
4.3.3.2 Design of Encryption and Decryption Model
The encryption is simple. First the adjacent pixels of an image in a
row is bitwise XOR’ ed with its neighbor pixels and based on chaotic key
the pixels are scrambled. This process is repeated for all the rows until it
creates a row scrambling. Similarly the adjacent pixel of an image in a
column is bitwise are XOR’ed with its neighbor pixels and based on chaotic
key the pixels are scrambled as process.
This process is repeated for all the columns until it creates a column
scrambling. The combination of both row and column scrambling would form
a cipher image1. Further, the diffusion process is carried out by bitwise
XOR‘ing cipher image1 and chaotic key , generates a cipher image2 as
shown in the Figure 4.9.
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Figure 4.9 The Present Novel Method of Encryption
Cipher 1
Secret Key Initialization
Logistic Map XK / Row
Logistic Map Y/Col
Yk/col
For all row’s
For all Column’s
Column Scrambling
RowScrambling
Adjacent pixels in rows Bit XOR’ed
Adjacent pixels in column’s Bit XOR’ed
Pixel values are XOR’ed with
Chaotic sub key
Original image
Transmit through
unsecured channel
Cipher 2
93
Decryption operation is performed in a similar manner as to the
encryption. The differences to are that the key is traversed in the reverse
direction and the rotations based on the key bits. The key bits are used to
rotate the pixel in the opposite direction to the one used in encryption. For
example, in the encryption the row was rotated right-ward, in for decryption it
will be rotated left-ward and in order to retain the correct sequence of
rotation, the key is traversed in the reverse direction in all the rotation loops.
4.3.3.3 The Present Algorithm used in the Present Novel Method for Reading of (plain) Original Image (OI)
The original image is converted to gray scale if it is color image.
= , , where and , and are height and width of
the original image in pixel respectively.
The Secret Key
The secret key in the present method of encryption technique is a
set of two floating point numbers and one integer = ( , , ), where mu
is whose typical value is 3.9876543210001, is initial value of the
chaotic map i.e key where typical value is 0.9876543219991 and is width
of the image.
= ( , ( ), )
where mu is whose typical value is 3.9876543210001, ( ) is last value of
map and column is Width of the image. = the logistic map is generated
with the value said above and X is multiplied with number of rows and fixed
as row.
Ykey = the logistic map is generated with the value said above and Y
is multiplied with the number of columns and fixed as Column.
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Row Scrambling
Step 1: First the pixel values are XOR’ ed with its adjacent pixel values
XOR with Adjacent Pixels
FOR i = 1 to row
FOR j=1 to column-1
OI (i,j+1) =OI(I ,j) OI(i,j+1)
END
END
Step 2:
The ROW Scrambling is done as follows
FOR i = 1 to ROW
v = OI(x Key(i),All column);
OI(Xkey(i),All column) = OI(i,All Column);
OI(i,All Column) = v;
END
Step 3:
Similarly for column scrambling the pixel values of the adjacent
pixel values are XOR’ed.
XOR with Adjacent Pixels
FOR i = 1 to column
FOR j=1 to row-1
OI(j+1,i) = OI(j,i) OI(j+1,i)
END
END
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Step 4: The Scrambling of Columns is done as follows
FOR i = 1 to Y key
v = OI (All rows,Y Key(i));
OI(All rows,Y Key(i)) = OI(All rows,i);
OI(All rows,i) = v; END
Step 5: Then chaotic key value Y key is XOR’ed with image.
FOR i=1 to row y=(mu,x(i),col)
y = y * column;
Y key = integer(y) FOR j=1 to column
OI(i,j) = OI(i,j) Y key( j)
END END
Step 6: The current pixel value of the Original image is XOR’ed with its
neighbors as follows :
XOR with Next pixel FOR i = 1to row
FOR j to 1:col-1
OI(i,j+1) = OI(i,j) OI(i,j+1) END
END
96
4.3.3.4 The Various Transformation of Pixel in the Plain Image during
Scrambling and Flow Diagram of Present Image Encryption -
IISPD
The image has been represented as 2D box and pixels of the plain
image are demonstrated by blue color shading. The scrambled image pixels
are represented by red color. After scrambling the image is XORéd with
Logistic map, it is represented by grey color.
Stage1: Adjacent pixels of values are XOR’ ed with its adjacent pixel values
before Row scrambling for all individual pixel in the image.
Stage 2: Applying Logistic map to scramble Column for every individual
pixel in the image.
Logistic Map equation: 1 ( )n nx g xwhere,
: [0,1] [0,1]g0 4.
thjColum nOI 1
t h
jC o l u m nO I
[ ] t h
k e y c o l u m niX [ ] t ha l l c o l u m nX i
97
Stage 3: Adjacent pixels of values are XOR’ ed with its adjacent pixel values
before Column Scrambling for all individual pixel in the image.
Stage4: Applying Logistic map to scramble Row for every individual pixel in the
image. Logistic Map equation:
1 ( ( ))n keyy g nX where, : [0,1] [0,1]g
0 4.
Stage5: The Scrambled Row and Column of the image XOR ‘ed with
Logistic maps every individual pixel in the image and called Cipher image -I.
th
irowO I
1t hi r o wO I
[ ] t hA l l r o w siY
[ ] t h
k e y r o wiY
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Logistic Map equation: = ( ( ))
Stage 6: Finally, the current pixel value of the Cipher image-I is XOR’ed
with its neighbors as follows
4.3.4 Analysis and Evaluation of Security Problem for Chaotic Map
based Image Encryption using Integrated Pixel Scrambling
with Diffusion
Histogram Analysis: An image histogram illustrates (Shubo et al 2009,
Patidar et al 2009, Jiankun and Fengling 2009, Fishawy and Zaid 2007) how
pixels in an image are distributed by graphing the number of pixels at each
color intensity level as presented in section 3.1.4. One typical example among
them is shown in Figure 4.10(b).
EX-OR
CIPHER IMAGE-I
thj Colum nOI 1
t h
j C o l u m nO I
CIPHER IMAGE-I
CIPHER IMAGE-II
LogisticMap
99
(a) (b) (c)
Figure 4.10 (a) Original Image (b) Histogram of Original Image (c) Histogram of Cipher Images
The histogram of a plain image contains large spikes. These spikes
correspond to gray values that appear more often in the plain image. The
histogram of the cipher image is shown in Figure 4.10(c), is uniform significantly
different from that of the original image and bears no statistical resemblance
to the plain image. Therefore, it does not provide any clue to employ any
statistical attack on the present image novel method of encryption procedure.
Correlation Coefficient Analysis: For a plain image having definite visual
scene, each pixel is highly correlated with its adjacent pixels either in
horizontal, vertical direction and diagonal direction. In ideal case an image
encryption scheme should produce a cipher image with no such correlation in
the adjacent pixels as shown in the Figure 4.11(b).
Figure 4.11 (a) The Correlation of Original Image (b) The Correlation of Cipher Image
100
The horizontal, vertical and diagonal correlations of the adjacent
pixels in plain image and cipher images (Shubo et al 2009, Patidar et al 2009,
Jiankun and Fengling 2009, Fishawy and Zaid 2007, Ahmed et al 2007,
Krishnamoorthi and Sheba Kezia Malarchelvi 2008, Zhang et al 2007) as
shown in the Table 4.13.The correlation coefficients for the original and
encrypted images are calculated by using the equation (3.4)-(3.6) as
mentioned in section 3.1.4 and shown in the Table 4.14. It is clear that the
two adjacent pixels in the original image are highly correlated, but there is
negligible correlation between the two adjacent pixels in the encrypted image.
Table 4.13 The Average Values of Various Cross Correlation Values between Plain Images and their Corresponding Cipher Images Produced by using 100 Randomly Chosen Secret Keys
S.No Image Size Direction of Adjacent Pixels CC V CCH CCD
1 Lena 512×512 -0.0000137 0.0014838 0.00193042 Man 1024× 1024 0.0001455 -0.0020267 0.00191733 Truck 512×512 0.0002895 -0.0002960 0.00579024 Girl 256× 256 0.0009585 -0.0530100 0.00859725 House 512× 512 0.0039037 -0.0078371 0.01279306 Tree 256×256 -0.0019082 0.0056540 0.00184377 Jelly beans1 256×256 0.0096442 -0.0099263 -0.00138508 Jelly beans2 256×256 0.0002329 -0.0119130 0.02032909 Splash 512×512 0.0042977 -0.0037865 0.000743710 Girl (Tiffany) 512×512 0.0026670 -0.0118100 0.004214411 Mandrill 512×512 -0.0023210 -0.0010998 0.006324212 Airplane (F-16) 512×512 -0.0012490 -0.00097192 0.006207613 Sailboat on lake 512×512 0.0048180 -0.0022361 0.006014314 Peppers 512×512 0.0003603 0.0017060 0.006155815 Aerial 256×256 -0.0039220 0.0118920 -0.002707516 Airplane 256×256 0.0042030 -0.0096231 0.016641017 Clock 256×256 -0.0041880 0.0106830 0.014376018 Resolution chart 256×256 -0.0008446 -0.0048259 0.011594019 Chemical plant 256×256 -0.0021289 -0.0042305 0.016563020 Couple 512×512 0.0005150 -0.0031021 0.0027036
101
The schematic diagrams as 3D bar chart is shown below to compare
the present method to the existing method (Ismail et al 2007) in Horizontal
and vertical correlations in Figures 4.12 and 4.13.
.Figure 4.12 Compares Present Method with AES Image Encryption
Method in Terms of Horizontal Correlation Co efficient
Figure 4.13 Compares Present Method with AES Image Encryption Method in Terms of Vertical Correlation Co efficient
102
Table 4.14 Correlation Co efficient of the Cipher Image for Encryption Quality (Ismail et al 2007)
Image AES
(Buchholz Jörg 2001)
Ismail et al Gun et al Chen et alPresent method
Lena 0.0029048 -0.0001046 0.0090000 0.0089000 -0.00070495
Ship 0.0049048 0.0000425 0.0042000 0.0022000 -0.00008723
Penguin 0.0099048 0.0005917 0.0114000 0.0100000 0.000106790
PSNR and Speed Analysis: PSNR (Ramana Reddy et al 2009) of encrypted
image and original image are obtained by using the equation (3.8) as
presented in section 3.1.4. From the statistics in Table 4.16, from the table the
higher the visual quality of the encrypted image, the lesser the number of
changed pixels will be, and the larger the values of PSNR with less time cost
are indentified. The PSNR for PS based, BFTCGH based, Integrated imaging
PS based and present novel method with 85% data losed are calculated. The
calculated values are compared with PSNR obtained for the present novel
method. The differences are shown in the Table 4.16.
Table 4.15 Comparison of PSNR’s for the PS based, BFTCGH based, Integrated Imaging PS based and Present Novel Method with 85% Data Loss As Index
PS-based BFT CGH-based
Integral Imaging and PS – based
Present method
PSNR(dB) 5.58 9.45 17.11 12.8
Apart from the security consideration, running time and speed
(Marwa et al 2008) are also important on image encryption.
103
In Table 4.17 shows the performance evaluation of the present
scheme. The analysis has been done by selecting 12 images each one is of
different sizes (1.5, 9, 24, 44 and 72 MB etc) having different contents and
using 10 randomly chosen secret keys for each image. Some of performance
evaluation to present novel method and (Marwa et al 2008) other methods are
shown in the Table 4.17
Table 4.16 Time of Image Encryption and Algorithms (seconds)
Algorithm Lena Goldhill
Combinational Permutation (Mitra et al 2006) 0.3300 0.9800
CKBA (Yen and Guo 2000) 1.0500 2.2700
Encryption using SCAN pattern
(Maniccam and Bourbakis 2004)
2.5400 4.7700
ECKBA (Socek et al 2005) 1.8400 2.8600
Present Technique 0.2926 0.4277
Key Sensitivity Test and Evaluation Analysis with Several Slightly different Keys
The key sensitivity test (Ahmed et al 2007) has been performed
through the following key sensitivity tests. The encryption scheme should be
key-sensitive meaning that a smallest change in the key will cause a
significant change in the output. In the present method, used the fixed initial
value = 0.123456789, = 0.265200000, changing the system parameter
with a single bit (Shubo et al 2009, Patidar et al 2009, Etemadi Borujeni et al
2009, Ismail et al 2007).
104
The system parameter can be any value in the finite area
3.569945< 4, thus and can provide (1) and (2) with the same value.
The key sensitivity test is performed in detail according to the
following steps:
(1) First, a 256×256 image is encrypted by using the test
key1 = 0.123456789 and its corresponding encrypted image is
referred as encrypted image A as shown in Figure 4.14(a).
(2) The least significant bit of the key is changed, so that the
original key becomes key2. Key2 = 0.123456788, which is
used to encrypt the same image, and its corresponding
encrypted image is referred as encrypted image B as shown in
Figure 4.14(b).
(3) Again, the same image is encrypted by the key3 = 0.123456787
and its corresponding encrypted image is referred as encrypted
image C as shown in Figure. 4.15(c).
Image A: cipher image of key1; Image B: cipher image of key2; Image C:
cipher image of key3.
Figure 4.14 (a) Cipher Image with Key 1 and its Histogram
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Figure 4.14 (b) Cipher Image with key 2 and its Histogram
Figure 4.15 (a) Cipher Image with Key1 (b) Cipher Image with Key 2 (c) Cipher Images with Key3 and (d) Difference Image with Key1 and KEY2
(4) Finally, the above three encrypted images A, B and C,
encrypted by the three slightly different keys, are compared as
given below in Table 4.15.
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Table 4.17 Key Sensitivity test with Several Slightly different Keys
Image Encrypted Image1
Encrypted image2
Pixel Difference
Present MethodCorrelation Coefficient
Man Image A
Image C
Image B
Image B
Image A
Image C
99.60
99.61
99.61
-0.00030842
-0.00020265
-0.00011947
Tree Image A
Image C
Image B
Image B
Image A
Image C
99.60
99.59
99.62
0.00460000
-0.00330000
0.00110000
Airplane
(F-16)
Image B
Image C
Image B
Image A
Image A
Image C
99.62
99.61
99.59
0.00190000
0.00070425
0.00290000
Average Moving Distance of Scrambling: The average moving distance of
scrambling (Xiangdong et al 2008) is calculated as mentioned in equation (4.4).
The statistical results are evaluated for moving distance of pixel. The results
from other chaos based method and present novel method is shown in the
Table 4.18. From the table, the larger the average moving distance of the
scrambling method less relation between the original image and the scramble
image and the increases the efficiency of the method.
Table 4.18 Statistical Results of Average Moving Distance of Present row Scrambling Algorithm with Randomly Choosing 1000 Keys for a 256×256 Image
Average Moving Distance Maximum Minimum Average
LENA 141.2014 118.1848 130.4608
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Entropy: The Entropy (Fishawy and Zaid 2007) is calculated as mentioned in
equation (3.7). The average of present novel method gives 7.99. Hence a
statistical attack is too difficult to make. In Table 4.19 compares Cross
Correlation and Entropy for various images, it shows that the present model is
highly secured.
Table 4.19 Comparison of Cross Correlation Efficient (CC) and Entropy
S.No Image Size CC Entropy
1 Lena 512 x 512 -0.00070495 7.9993
2 Man 1024 x 1024 -0.00070225 7.9998
3 Truck 512 x 512 -0.00118770 7.9993
4 Girl 256 x 256 0.00219600 7.9970
5 House 512 x 512 -0.00033701 7.9973
6 Tree 256 x 256 0.00051871 7.9970
7 Jelly beans1 256 x 256 0.00295000 7.9969
8 Jelly beans2 256 x 256 -0.00056896 7.9978
9 Splash 512x512 -0.00260560 7.9993
10 Girl (Tiffany) 512x512 0.00158940 7.9992
11 Mandrill 512x512 0.00008723 7.9993
12 Sailboat on lake 512x512 0.00010679 7.9992
13 Peppers 512x512 -0.00058102 7.9993
14 Aerial 256x256 0.00105870 7.9974
15 Airplane 256x256 0.00184570 7.9972
16 Resolution chart 256x256 -0.00055520 7.9973
17 Chemical plant 256x256 0.00102370 7.9974
18 Couple 512x512 0.00241990 7.9993
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Sensitivity Analysis: The present encryption novel method uses three
different chaotic maps, with different initial values and they are used in row
scrambling, column scrambling and XOR operation. Therefore, the present
method provides a choice of using three different keys.
Hence, larger keys space of iterations (logistic map) to skip before
the actual encryption/decryption starts. The key key-sensitive analysis is
tabulated in Table 4.16, the complete key space for the present encryption
/decryption technique is ~1045, i.e., the effective key of log 2[(10.558)3
X 1045] ~ 157 bits, which is sufficient enough to resist the brute-force attack.
The sensitivity analysis (Ahmed et al 2007) could be performed
through net pixel change rate and unified average change in intensity as
mentioned in equation (3.9) and (3.10). The NPCR (Fishawy and Zaid 2007)
value of the difference image is as follows: NPCR of AB = 99.6002, NPCR
of BC = 99.6239 and NPCR of CA = 99.6140. The present novel method
gives encryption scheme reaches an average UACI of 15-22%.
The Chaos theory has already proved that it is an excellent
alternative to provide a fast, simple, and reliable image encryption scheme
and has a high enough degree of security. From an engineer’s perspective,
chaos-based image encryption technology is very promising for real-time
security of a still image and video communications in military, industrial, and
commercial applications. In the first present work, an image encryption
scheme is present based on CSDP based scrambling technique using two
chaotic maps have been described in detail.
The system is a block cipher based architecture and its
effectiveness is tested. In the second present work, a new image encryption
algorithm with a large pseudorandom permutation which is computed from
chaos logistic maps and PMMLCG generators. The initial condition of chaos
109
logistic map and PMMLCG can be selected easily. In the third present work,
a chaos based image encryption with integrated scrambling technique has
been discussed. A detailed statistical analysis is given above and the
experimental results shows that it outperforms the existing techniques, both in
terms of speed and security.
Analysis of the statistical information of encrypted images in the
experimental tests, shows that the present algorithm provides reasonable
security against statistical cryptanalysis. In the next chapter a design of a new
image encryption technique and effect of diffusion technique in an image
encryption technique is explored.