Color image encryption based on chaotic shit keying with lossless compression

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 6, December 2020, pp. 5736~5748
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i6.pp5736-5748  5736
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
Color image encryption based on chaotic shit keying with
lossless compression
Ashwaq T. Hashim, Bahaa D. Jalil
Control and Systems Engineering Department, University of Technology-Iraq, Iraq
Article Info ABSTRACT
Article history:
Received Jan 2, 2020
Revised May 7, 2020
Accepted May 20, 2020
In order to protect valuable data from undesirable readers or against illegal
reproduction and modifications, there have been various data encryption
techniques. Many methods are developed to perform image encryption.
The use of chaotic map for image encryption is very effective, since it
increases the security, due to its random behavior. The most attractive feature
of deterministic chaotic systems is the extremely unexpected and
random-look nature of chaotic signals that may lead to novel applications.
A novel algorithm for image encryption based on compression and hyper
chaotic map techniques is suggested. First, the RGB image is broken down
into R, G and B subbands after that each band is compressed using lossless
technique. The generated chaotic sequences from the 3D chaotic system are
employed to code the compressed results by employing the idea of chaotic
shift encoding (CSK) modulation to encode the three bands to generate
the encrypted image. The experiments show that the proposed method give
good results in term of security, feasibility, and robustness.
Keywords:
Chaotic map
Cryptography
CSK
Image compression
Image encryption
Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Bahaa Dhiaa Jalil,
Department of Control and Systems Engineering,
University of Technology-Iraq,
Baghdad, Iraq.
Email: 60042@uotechnology.edu.iq
1. INTRODUCTION
Recently, computer technology has developed rapidly, so digital image processing has its share from
this development and it entered into many life aspects like investigation, industrial detection, communication,
remote sensing, intelligent robots, medicine, meteorology, etc. Therefore, image information entices
widespread awareness. In many fields; especially in military and medical fields, security of image data is
very significant. So a way to protect transmission of digital images is needed which leads to found the image
encryption. Classical encryption algorithms like Advanced Encryption Standard(AES) and Data Encryption
Standard (DES) don’t offer image encryption needs because of the image data characteristics such as the data
amount, the highly redundanc and the strong interrelationship which present low protection and low
efficiency encryption [1].
As a result of high redundancy, data compression is the main thrust in multimedia applications
because with no compression, communication resources and storage will be used inefﬁciently. Due to power
and bandwidth restrictions, low-bit-rate compression is required for power-limited devices and
low-bandwidth communication channels. Furthermore and especially for open-access network, encryption is
needed for integrity and privacy of information. Algorithms of encryption are improved to a particular
kind of data based on many characteristics like power of processing, sensitivity to bit changes and
ciphered speed [2].
Compression contains two approaches which are lossless and lossy. In the case of lossless
compression, the compressed data maintains its original format devoid of losing information, whereas

Int J Elec & Comp Eng ISSN: 2088-8708 
Color image encryption based on chaotic shit keying with lossless compression (Ashwaq T. Hashim)
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compressed data that loses data will lose some of the original information, but the loss is small to noticeable
through a person's sense of eye and ear. Lossless compression is used for critical mission application such
financial document and lossy is for application can be tolerated in slightly loss of information such as
pictures. Compression required algorithm and several prominent compression algorithm techniques such as
the Huffman, Run Length Encoding, arithmetic, and entropy. The main objective of proposed lossless
compression is to reduce the size of image file, maintain quality of the reconstruction image from
compression, and can be managed in available transmission bandwidth and secured during transmission [3].
Encryption algorithms like Blowﬁsh, RC6, and AES which intended for text data encryptions are not
appropriate for image data encryption. Particular encryption techniques are wanted for encryption of image
because of the strong correlation and the redundancy among neighboring pixels. Chaotic map cryptosystems,
compared with the classical techniques of encryption, are more appropriate to encryption of image. With its
high sensibility for both elementary conditions and system parameters like false arbitrariness, non-repetition,
retrograde, and accurately generated and regenerated of chaotic sequences, chaos is particularly appropriate
for ciphered image. Therefore, the chaotic system is used as a base for many image encryption algorithms.
In 1998, American scientist Friedrich introduced alternative architecture for publishing images to encrypt
images [4].
Later, this structure was widely received, and today, most image encryption patterns depend on this
chaotic structure [5-16], but the only using of the low dimensional chaotic system in image encryption
doesn’t present enough security. Compression is on the same importance of encryption, and if these two
processes are separated, the high degree of uncertainty in cipher image length cannot be achieved. By using
both encryption and compression techniques [2, 17-19], secure and efficient image transmission over
non-private network can be guaranteed and that leads to increase the difficulty level that the attackers would
be experienced due to the size of the encrypted image which would be uncertain.
Emad et al., [20], presented a secured image compression system for image satellite communication
based on the fractal compression theory combined with the enhanced hill multimedia cryptosystem (EHMC)
algorithm for encryption. Somaya et al., [21], proposed image-encryption technique by combining two
techniques: encryption and compression. A wavelet transform was used to decompose the image and
decorrelate its pixels into approximation and detail components. The more important component
(the approximation component) is encrypted using a chaos-based encryption algorithm. The remaining
components (the detail components) are compressed using a wavelet transform. Tabash et al., [22],
introduced an image encryption technique based on three chaotic logistic maps and multi-pseudo random
block permutation. The encryption process has been divided mainly into three steps; the first step is to
encrypt the whole image using logistic map, the second step is to divide the image into a random number of
blocks, the third step is to generate a random permutation for these blocks.
Borislav et al., [23], suggested an algorithm for image encryption which stands on two
pseudorandom bit generators, one is based on Chebyshev map and the other on rotation equation.
The Chebyshev map part is for variation while the rotation equation is for replacement. Zhang et al., [24],
proposed a scheme that can simultaneously encrypt and compress a medical image using compressive
sensing (CS) and pixel swapping based permutation approach. Poorani et al., [25], proposed a scheme of
compressing encrypted images with auxiliary information. Some auxiliary information with uncompressed
encrypted image is used for data compression and image reconstruction. Jiaojiao et al., [26], proposed
a sparse decomposition and the Chinese remainder theorem to compress the image, and then chaos map was
used in encryption process. That is done to achieve the joint compression and encryption effect.
Sireesha et al., [27], presented an encryption algorithm of pixel level image based on chaotic
mapping and Chinese remainder theorem. Nasrullah et al., [2], proposed a combined algorithm of image
compression with encryption which is stands on integer wavelet transform (IWT) beside a set of subdivide in
hierarchical trees (SPIHT), Kd-tree and multiple chaotic maps. Shuqin et al., [1], proposed an algorithm for
image encryption that stands on chaos and SHA-256 firstly by surrounding the plaintext image by a hash
value sequence, then scrambling the image, finally adopting the feedback mechanism of the dynamic index.
Saravanan et al., [28], proposed an image encryption algorithm in which discrete wavelet transform (DWT) is
applied and randomly generated 256 bit key is used to create the measurement matrix used in compressive
sensing. Osama et al., [29], proposed an image encryption algorithm, which involves a chaotic block image
scrambling followed by a two–dimensional (2D) discrete linear chirp transform.
This research present a combined image compression and encryption structure which stands on CSK
modulation is offered. The using of 3D chaotic system which is used for the diffusion and permutations of
image pixels is the contribution of the work. In the proposed joint compression and encryption was
performed. Firstly, only lossless compression is used, then 3D chaotic maps are used to perform
the encryption. By comparing the suggested method with the remaining joint image compression and

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Int J Elec & Comp Eng, Vol. 10, No. 6, December 2020 : 5736 - 5748
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encryption methods, it offers high security and much more compression and its effectiveness is clearly
demonstrated by the experimental results which are obtained.
The remains of this paper is organized as follows: In Section 2, related works are discussed,
while section 3 illustrate the proposed structure of the image compression and encryption. Section 4 shows
the experimental results and security analysis of the suggested structure and finally, the conclusions are
discussed in section 5.
2. RELATED WORKS
In this section the related works of the proposed system are reviewed in next two sub sections:
2.1. Hyper-chaotic system and chebyshev map
The system suggested by [1] is employed to generate the three random sequences constructed by
hyper chaotic system and two Chebyshev maps. This approach utilized a hyper-chaotic system of four
dimensional in addition to four initial conditions and ﬁve system parameters which is showed by (1):
𝑑𝑥
𝑑𝑡⁄ = 𝑎(𝑦 − 𝑥) + 𝑤
𝑑𝑦
𝑑𝑡
⁄ = 𝑑𝑥 − 𝑥𝑧 + 𝑐𝑦
𝑑𝑧
𝑑𝑡⁄ = 𝑥𝑦 − 𝑏𝑧
𝑑𝑤
𝑑𝑡⁄ = 𝑦𝑧 − 𝑒𝑤 (1)
The system parameters are a, b, c, d and e. and the system is hyper-chaotic if a=35, b=3, c=12,
d=7 and e∈(0.085, 0.798), and it has two positive Lyapunov exponents, LE1=0.596, LE2=0.154.
So the system is in a hyper-chaotic state. The two Chebyshev maps are designed by (2):
𝑢1(𝑖 + 1) = 𝑐𝑜𝑠 (4 × 𝑎𝑟𝑐𝑜𝑠(𝑢1(𝑖)))
𝑢2(𝑖 + 1) = 𝑐𝑜𝑠 (4 × 𝑎𝑟𝑐𝑜𝑠(𝑢2(𝑖))) (2)
The initial values are u1(1) and u2(1).
After iterated the hyper-chaotic system, four sequences are generated which are signified as
X=[x(i)], Y= [y(i)], Z=[z(i)] and W=[w(i)], respectively, where, i=1, 2, ... On the other hand two Chebyshev
maps with u1(1) and u2(1) as initial values are repeated for constructing U1 and U2 sequences respectively.
Three sequences of real values D1, D2 and D3 are transformed to six chaotic sequences X, Y, Z, W, U1 and U2
to extra enhance sequences complication. The interval of the three sequences is in [0, 1].
By the following Formulas (3)-(5) the D1, D2 and D3 are calculated.
𝐷1 = 𝑐𝑜𝑠2
((𝑋 + 𝑌 + 𝑍)/3) (3)
((𝑊 + 𝑈1 + 𝑈2)/3) (4)
((𝑋 + 𝑍 + 𝑈2)/3) (5)
2.2. Chaotic shift keying
In binary CSK modulation, the binary information is conveyed by chaotic signals which are taken
energies of different bit. By means of transferring one chaotic signal x1(t) or x0(t) at a time, the encoding of
information signal is done. So chaos signal x1(t) will be transferred if the information signal binary bit is "1",
otherwise, x0(t) will be transferred. The modulation and demodulation of CSK are shown in Figure 1.
By using either the same chaos system with different parameters or by two different systems, the two chaotic
signals be obtained. The transmitted signal can be given [30] as describe by the following formula:

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𝑆(𝑡) = {
𝑥1(𝑡) , 1 𝑖𝑠 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑
𝑥0(𝑡) , 0 𝑖𝑠 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑
(6)
Figure 1. Block diagram of the CSK for modulator and demodulator [31]
3. PROPOSED SYSTEM
To improve the degree of security, dual image compression and encryption which stands on hyper
chaotic system is used. The proposed system is divided into two stage at first the image is compressed using
proposed lossless compression method and then encrypted by employing the CSK which is used a hyper
chaotic system. Figure 2 displays the proposed system block diagram.
Figure 2. The proposed system block diagram
3.1. Proposed encryption
Many algorithms of encryption, precisely for digital images, are introduced to maintain the needs of
strong applications for encryption of image. Chaos-based ciphered algorithms among them, which are
became common due to numerous optimal features like unexpected and high sensitivity to initial conditions
and various parameters. The chaotic maps security is influenced by the number of parameters of these chaotic
cryptosystems. To increase the key space of proposed algorithm, a system proposed by [1] and explained in
section (2.1) is used. Algorithm 1 shows the steps of proposed encryption algorithm.

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Algorithm 1. Image encryption
Input : I // RGB color image
W, H // width and height of I
Output : E // Encrypted image
Step 1 : Let the size of the color image I is W × H
Step 2 : Separate the three bands R, G, B of the color image I
Step 3 : The band matrices R, G, and B are converted to a one dimensional vector
R={R(1), R(2),..., R(l)}, G={G(1), G(2),..., G(l)}, B={B(1), B(2),..., B(l)},
where l=W × H
Step 4 : Compressed the three vectors R, G and B separately using algorithm (2) to generate
three binary compressed streams RComp, GComp and BComp
Step 5 : Create the chaotic sequences D1, D2, D3 of length l1, l2, l3 as defined in section
2.1 for encryption.
Step 6 : Convert the range of generated real sequences D1, D2, D3 from [0 1] to [-1 1].
Step 7 : Encoded the compressed streams RComp, GComp and BComp by embedding them in
generated random sequences D1, D2, D3 using formula (6) to generate three real
encoded sequences E1, E2, E3.
For i= 1 to W×H
If RComp (i) =1
E1(i)=D1(i)
Else
E1(i)=- D1(i)
EndIF
EndFor
Step 8 : Repeat step7 for GComp and BComp to generate E2 and E3 respectively.
Step 9 : Convert the three real sequences E1, E2 and E3 to binary using following formula
BinE1=Round (E1 + 0.5)
BinE2=Round (E2+0.5) (7)
BinE3=Round (E3 + 0.5)
where the real numbers less than zero became 0 and the numbers greater than zero
become 1.
Step 10 : Combine BinE1, BinE2 and BinE3 into encrypted image E.
3.2. Proposed lossless image compresion
Lossless compressing is proposed to decrease the redundancy and irrelevance of image data to store
or transfer data in an efficient form. Hence the image compression raises the transmission speed and
decreases the storage requirement. In Lossless technique of image compression, no data get lost while doing
the compression. The steps of Algorithm 2 describe the proposed lossless compression method.
Algorithm 2. Lossless image compression
Input : R,G,B // subands of input image
W, H // width and height of suband
Output : RComp, GComp, BComp, // compressed subands
Step 1 : For each subbands do the following:
Step 1.1 : The subband R is amended by defining the differences between adjacent
pixels using the following formula:
𝑅𝑖= 𝑅𝑖 − 𝑅𝑖−1 for i=1,.., n-1 (8)
where n is the length of subband R (i.e., W×H).
Step 1.2 : Mapping the Ri to positive by this point the coding complexity
resulting from positive/negative values is removed. The modulated
values are converted to be always positive, by performing the
following mapping equation:
𝐶𝑖 = {
2𝑅𝑖 𝑖𝑓 𝑅𝑖 ≥ 0
−2𝑅𝑖 − 1 𝑖𝑓 𝑅𝑖 < 0
(9)
where Ci is the ith
element. According mapping equation all positive
values are converted to even numbers while the negative values are
became positive odd numbers.
Step 1.3 : Huffman Entropy encoding is used to encode the modulated band C to
generate compressed stream RComp
Step 4 : Repeat step1 to generate GComp and BComp

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3.3. Image deciphering
The operation of deciphering for ciphered image is decomposed of two operations. At first
the decompressing is performed for each compressed subbands. Secondly, three sequences are generated
using the same keys of encryption process. These sequences are used as chaotic signals to transmit or decode
decompressed subbands to generate the decrypted image. The steps of decryption algorithm are described
in Algorithm 3.
Algorithm 3. Image decryption
Input : E // Encrypted image
l1, l2, l3 // length of BinE1, BinE2 and BinE3
Output : I // decrypted image
Step 1 : Separate the three encrypted subbands BinE1, BinE2 and BinE3 of the encrypted image E
Step 2 : Produce the required chaotic sequences D1, D2, D3 of length l1, l2, l3 used the same
chaotic parameters used in encryption process.
Step 3 : Convert the range of generated real sequences D1, D2, D3 from [0 1] to [-1 1].
Step 4 : For each encrypted subbands decoded them such as follows:
For I←1.. to l1
H (I)= D1 (I) × Round( (BinE11 (I)+ (- 0.5) ) )
IF H> T) // T is the threshold value
RCompi=1
Else
RCompi=0
EndIf
EndFor
Step 5 : Repeat step4 to generate GCompi and GCompi
Step 6 : decompressed the three vectors RCompi, GCompi and GCompi separately using Algorithm
4 to generate three binary streams R, G and B
Step 7 : Combine the three subbands into decrepted image I
Algorithm 4. Lossless image decompression
Input : RComp, GComp, BComp // Compressed streams
Output : R, G, B // R,G,B subbands
Step 1 : For each compressed subbands RComp, GComp, BComp ;
Step 1.1 : Huffman Entropy deccoding is applied on the compressed stream RCom to
generate C.
Step 1.2 : Mapping to Negative is used for the decoded data resulted from step1
performing the following equation:
𝑅𝑖 = {
𝐶𝑖 𝑑𝑖𝑣 2 𝑖𝑓 𝐶𝑖 𝑖𝑠 𝑒𝑣𝑒𝑛
−(𝐶𝑖 + 1)𝑑𝑖𝑣2 𝑖𝑓 𝐶𝑖 𝑖𝑠 𝑜𝑑𝑑
(10)
where Ri is the ith
element. The previous equation turns the odd values
to negative and the even values to positive.
Example of encryption four pixel of subband R without compression to clarify proposed encryption
algorithm:
- Encryption
- Let four R subband pixels are 107 149 51 88
- In binary
107 = 0 1 1 0 1 0 1 1
149 = 1 0 0 1 0 1 0 1
51 = 0 0 1 1 0 0 1 1
88 = 0 1 0 1 1 0 0 0
- 1D of four binary pixels=0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 0
- Let D1 generated from chaotic map after convert its range to [-1 1]
D1 = -0.5025 0.0000 -1.0000 -0.9899 -0.9699 -0.9301 -0.8509 -0.6933
-0.3797 0.2444 -0.5136 -0.0222 0.9559 0.9022 0.7954 0.5829
0.1601 -0.6815 -0.3561 0.2913 -0.4204 0.1635 -0.6747 -0.3426
0.3182 -0.3668 0.2701 -0.4624 0.0798 -0.8412 -0.6740 -0.3412
- The coded E = 0.5025 0.0000 -1.0000 0.9899 -0.9699 0.9301 -0.8509 -0.6933
-0.3797 -0.2444 0.5136 -0.0222 -0.9559 0.9022 -0.7954 0.5829
-0.1601 0.6815 -0.3561 0.2913 0.4204 -0.1635 -0.6747 -0.3426
-0.3182 -0.3668 -0.2701 -0.4624 0.0798 0.8412 0.6740 0.3412

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- Converted to binary using
BinE=Round (E + 0.5)=1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1
0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1
- Encrypted output in decimal: 212 37 88 15
- Decryption: 212 37 88 15
- Convert to binary
BinE1,= 1 1 0 1 0 1 0 0
0 0 1 0 0 1 0 1
0 1 0 1 1 0 0 0
0 0 0 0 1 1 1 1
- Let D1 generated from chaotic map after convert its range to [-1 1] using the same parameters of encryption
process
D1 = -0.5025 0.0000 -1.0000 -0.9899 -0.9699 -0.9301 -0.8509 -0.6933
-0.3797 0.2444 -0.5136 -0.0222 0.9559 0.9022 0.7954 0.5829
0.1601 -0.6815 -0.3561 0.2913 -0.4204 0.1635 -0.6747 -0.3426
0.3182 -0.3668 0.2701 -0.4624 0.0798 -0.8412 -0.6740 -0.3412
- The output after this formula: G=Round( (BinE11 (I)+ (- 0.5) )
G=1 1 -1 1 -1 1 -1 -1 -1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 -1
- 1 -1 -1 -1 -1 1 1 1 1
H (I)= D1 (I) × G
H= -0.5025 0.0000 1.0000 -0.9899 0.9699 -0.9301 0.8509 0.6933
0.3797 -0.2444 -0.5136 0.0222 -0.9559 0.9022 -0.7954 0.5829
-0.1601 -0.6815 0.3561 0.2913 -0.4204 -0.1635 0.6747 0.3426
-0.3182 0.3668 -0.2701 0.4624 0.0798 -0.8412 -0.6740 -0.34120
- IF H (i) > T ) // T is the threshold value (i.e., T= 0)
RComp (i)=1
Else
RComp (i)=0
RComp= 0 1 1 0 1 0 1 1
1 0 0 1 0 1 0 1
0 0 1 1 0 0 1 1
0 1 0 1 1 0 0 0
0 1 0 1 1 0 0 0
- Converted to decimal: 107 149 51 88
4. EXPERIMENTAL RESULTS
In this paper four bmp color images of size 256×256 are tested as depicted in Figure 3.
Encryption and decryption operations are implemented using Matlab 2018a and (x0, y0, z0, w0) are set to
(0.398, 0.456, 0.784, 0.982) successively. Figure 4 depicts the encrypted test images by proposed system.
Figure 3. Test images
Figure 4. Encrypted images by proposed system

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Table 1 shows the compression ratio (CR) of tested images. The aimed of the compression in
this research to reduce the time that is required for coding the image by CSK. At the same time the type of
compression is lossless there is no effect on the input image quality. Table 2 displays the time consuming of
proposed system for the tested images.
Table 1. The comparison of tested images
Image name Original size Compressed Size CR
A 196608 56008 3.5
Nike 196608 28850 6.8
Peppers 196608 33234 1.48
Lena 196608 120005 1.64
Table 2. The time consuming of tested images
Image name Compression Time in Sec. Coding Time in Sec. Total time in Sec.
A 1.875 1.563 3.438
Nike 1.867 0.851 2.718
Peppers 1.432 3.137 4.569
Lena 1.368 3.922 5.29
4.1. Security analysis
The suggested encryption scheme security is inspect in this section with the RGB color images
as an example.
4.1.1. Histogram analysis
A perfect histogram of an efficiently ciphered image must be uniform and much different from
the original image. For a 24-bit color image, the histogram for red, green, blue channels are drawn
respectively. Thus histograms for red, green, blue channels of Lena and the cipher-image are plotted in
Figure 5. It is notice that the histograms of the cipher image are uniform and fully unlike from the original
image, necessitating that the redundancy of the original image be successfully hidden after the encryption,
and therefore does not provide any valuable information for statistical attacks.
Figure 5. The histogram analysis result, (c)-(e) red, green, blue channel components of plain-image,
(f)-(h) red, green, blue channel components of encrypted image

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4.1.2. Key space
In cryptography, as much as the key space is large, as much as the capability for resisting force
attacks is strong. The keys of the proposed algorithm are represented by the initial values x(0), y(0), z(0),
w(0) of the chaotic system in (1), the parameter e of chaotic system and the Chebyshev maps initial values
u1(1), u2(1) in (2). The x0, y0, z0, w0, u1(1) and u2(1) is precise to 10−15
, while the parameter e for
e∈(0.085, 0.798) is precise to 10−12
, so the size of the key space is (1015
)6
×1012
=10102
≈2339
.
In reference [32], Li mentioned that to avoid brute force attacks, the ciphered system keyspace
shouldexceed 2100
. Consequently, the algorithm key is large adequate to immune the brute force attacks.
Table 3 compare the key space size between the used algorithm and other similar encryption algorithms,
and it is clear that utilized algorithm’s key space size is larger than that of most analogous algorithms.
Table 3. The key space comparisons
Encryption Algorithm Key Space
Wang et al. [33] 2149
Guesmi et al. [34] 2256
Li et al. [35] 2299
Li et al. [36] 2375
Curiac et al. [37] 2128
Curiac et al. [38] 2357
Used System [1] 2339
4.1.3. Correlation analysis
In plain-image, the adjacent pixels have high correlation which attacker use in their attacks,
so the correlation coefficient is always high. Therefore, the correlation coefficient must be significantly
reduced after encryption. By (11), the correlation coefficients of four directions are calculated.
𝑟𝑥𝑦 =
𝑐𝑜𝑣(𝑥,𝑦)
√𝐷(𝑥) ×√𝐷(𝑦)
(11)
where
𝑐𝑜𝑠(𝑥, 𝑦) =
1
𝑁
∑(𝑥𝑖 − 𝐸(𝑥))
𝑁
0
(𝑦𝑖 − 𝐸(𝑦)), 𝐷(𝑥) =
1
𝑁
∑ 𝑥𝑖 − 𝐸(𝑥)2
𝑁
0
, 𝐸(𝑥) =
1
𝑁
𝑥𝑖.
The values of two adjacent pixels of four directions are represented by x, y, and N is image pixels
number. Table 4 lists the correlation coefﬁcients of original images and its encrypted images as well as
the vertical (V), horizontal (H), diagonal (D) directions. Table 4 clearly shows that suggested algorithm can
resist hacker attacks according to the value of the correlation coefficient which is close to 0 of the cipher-
images while it is close to 1 of the plain-images. Figures 6 and 7 show the vertical, horizontal, and diagonal
directions for image ‘A’ and ‘lena’.
Table 4. Horizontal, vertical and diagonal correlation coefﬁcients between original and encrypted images
Image name Correlation of plain image Correlation of ciphered image
Horizontal Vertical Diagonal Horizontal Vertical Diagonal
A R 0.8993 0.9385 0.9014 0.0126 –0.0114 –0.0077
G 0.9936 0.9928 0.9897 −0.0009 0.0003 −0.0002
B 0.9265 0.9192 0.8809 −0.0024 −0.0008 −0.0043
Nike R 0.9808 0.9907 0.9747 0.0017 –0.0042 0.0015
G 0.9855 0.9848 0.9783 −0.0019 −0.0004 0.0003
B 0.9527 0.9527 0.9178 −0.0035 0.0005 −0.0062
Peppers R 0.9704 0.97739 0.9583 –0.0001 –0.0003 –0.0023
G 0.8668 0.7759 0.7432 0.0033 0.0018 0.0003
B 0.9067 0.8844 0.8544 0.0006 0.0004 0.0008
Lena R 0.9753 0.9853 0.9734 −0.0028 0.0046 0.0013
G 0.9666 0.9802 0.9630 0.0004 −0.0009 0.0007
B 0.9334 0.9558 0.9264 −0.0029 −0.0007 −0.0050

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Figure 6. The correlation of the image ‘A’ with the correspondent encrypted image of ‘A’
Figure 7. The correlation of the ‘Lena’ image and the correspondent encrypted image of ‘Lena’

 ISSN: 2088-8708
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4.1.4. Entropy analysis
The ideal value of the information entropy E to an encrypted image which has 256 gray intensities
is 8. The information entropy of natural images and their matching ciphered images-which are encrypted
using proposed system and compared with other algorithms in the literature-are calculated based on (12) and
these data are listed in Table 5. It is noticed that the encrypted images information entropies were totally near
to the perfect value. Furthermore, the encrypted images possessed a perfect feature of randomness and
the unexpectable.
 

n
i
PiPiE
0
2log (12)
where pi is gray value probability
Table 5. The result entropy of information for encrypted images
Images Plain image Cipher image
R G B R G B
A 4.733 4.651 4.021 7.999 7.999 7.999
Nike 3.499 3.444 3.270 7.999 7.999 7.999
Peppers 7.434 7.235 7.057 7.999 7.999 7.999
Lena 5.046 5.457 4.800 7.999 7.999 7.999
Lena in [23] - - - 7.999 7.999 7.999
Lena in [39] - - - 7.991 7.991 7.991
Lena in [40] - - - 7.997 7.997 7.996
Lena in [41] - - - 7.997 7.997 7.997
Lena in [42] - - - 7.997 7.997 7.997
Lena in [43] - - - 7.994 7.994 7.994
4.1.5. Key sensitivity
There are to features are employed to assess the key sensitivity the first one is that the ciphered
image is wholy differed if the same natural image is ciphered with two keys of slightly different. The change
rate of is used to measure the differences of the encrypted images. Second, there is no information available
of the plaintext image in the decrypted image using wrong key, although there is a very slight difference
between the wrong key and the correct key.
The test results of sensitivity are shown in Table 6 and it has been conﬁrmed that the the proposed
algorithm sensitivity to the keys x0, y0, z0, w0 is very high, and can reach more than 10−14
. To assess the key
sensitivity in the second features, the following error keys K1, K2, K3 and K4 are chose to decrypt the original
encrypted Lena image, and the result of decryption is depicted in Figure 8.
K1={x0, y0, z0, w0}=(0.367 + 10−14
, 0.436, 0.766, 0.991),
K2={x0, y0, z0, w0}=(0.367, 0.436 + 10−14
, 0.766, 0.991),
K3={x0, y0, z0, w0}=(0.367, 0.436, 0.766 + 10−14
, 0.991),
K4={x0, y0, z0, w0}=(0.367, 0.436, 0.766, 0.991 + 10−14
).
Table 6. Initial key sensitivity tests
Keys Change Rate
X0 0.9953
Y0 0.9972
Z0 0.9981
W0 0.9967
(a) (b) (c) (d)
Figure 8. The image deciphered with the erroneous keys, (a) image decryption with K1,
(b) image decryption with K2, (c) image decryption with K3, (d) image decryption result of K4

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4.1.6. NPCR and UACI analysis
The satistical tests NPCR and UACI are utilized in the analysis of image by measuring the degree of
sensitivity to image encryption algorithms of plaintext. The NPCR and UACI are calculated using following
formulas [44]:
𝑁𝐶𝑃𝑅 = ∑ ∑
𝑆 𝑖𝑗
𝑀×𝑁
× 100%𝑁
𝑗=1
𝑀
𝑖=1
𝑆𝑖𝑗 = {
1 𝑋(𝑖, 𝑗) ≠ 𝑋′(𝑖, 𝑗)
0 𝑋(𝑖, 𝑗) = 𝑋′(𝑖, 𝑗)
𝑈𝐴𝐶𝐼 = ∑ ∑
|𝑋(𝑖,𝑗)−𝑋′(𝑖,𝑗)|
𝑀×𝑁×255
× 100%𝑁
𝑗=1
𝑀
𝑖=1
where 𝑀×𝑁 is the size of the image and (𝑖,) and 𝑋′(𝑖, 𝑗) denote the pixel values for the positions matching of
plaintext and ciphertext. When the NPCR and UACI of the ciphertext are larger than 99.6% and 33.46% as
shown in Table 7, respectively this shows that the algorithm possesses perfect security. So this algorithm is
more sensible for plaintext and thus, this algorithm is resisted to differential attacks.
Table 7. The NPCR and UACI of encrypted images
Image NPCR UACI
A 99.60 33.51
Nike 99.60 33.47
Peppers 99.62 33.53
Lena 99.63 33.54
5. CONCLUSION
A hyper method of compression and encryption schemes based on CSK is proposed. In the CSK
the multiple chaotic systems is employed. The input color image is compressed using proposed lossless
image compression method. This stage is required for two goals the first one is to speed up encryption stage
and other for enhancing security. The next step is image encryption based on CSK is used. The use of chaotic
map for image encryption is very effective, since it increase the security, due to its random behavior.
The utmost attractive characteristics of deterministic chaotic systems are the greatly unpredictable and
random nature for the chaotic signals which are may guide to unprecedented (engineering) applications.
The sequences of chaotic produced from the hyper chaotic map are utilized for coding the compressed results
by employing the idea of chaotic shift encoding modulation to encode the three bands to generate
the encrypted image. Simulation results manifest that the suggested encryption algorithm possess
good performance.
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