Chaotic Block Image Scheme using Large Key Space and Message Digest Algorithm

Fahmi Nasser Ali & Mussa Mohamed Ahmed
International Journal of Computer Science and Security (IJCSS), Volume (13) : Issue (4) : 2019 135
Chaotic Block Image Scheme using Large Key Space and
Message Digest Algorithm
Fahmi Nasser Ali fahminasser_88@yahoo.com
Department of information technology
University of Aden
Aden, Yemen
Mussa Mohamed Ahmed mussa_m7@yahoo.com
Department of electronics and communication
University of Aden
Aden, Yemen
Abstract
In this paper, chaotic block image scheme using large key space and message digest algorithm.
Cat map intended for confusion and 2D-Sine Tent Composite map (2D-STCM) key generator
intended for diffusion. Confusion is implemented by 2D Cat map with arbitrary block size. In the
first tendency, 2D cat map use for local shuffling of indexes inside blocks, while in the second
tendency, 2D cat map used for global shuffling of whole image indexes. The designed algorithm
executes two confusions and one diffusion in each iteration. To increase the security level, the
message digestion algorithm is used as a fingerprint for the plain image that creates the initial
value of the key. After that 2D-STCM generates a large key stream. Diffusion implementation
takes place by XOR operation; between a key stream and confused image. Experimental
results, show that security level increases due to integration of confusion and diffusion. On the
other side large key space and the high sensitivity of secret keys have been given a guarantee
for the performance of the security. Performance measures reach to the top value among those
in the similar researches. To verify the obtained results, authors implemented inverse chaos.
All the tests are processed by MATLAB 2015a.
Keywords: Image Encryption, 2D-STCM, Cat Map, MD5, Confusion, Diffusion.
1. INTRODUCTION
The converting of information image, video, audio and text from insecure form into secure form
and transmitting it over the insecure network is known as cryptography [2]. In cryptography,
there are many traditional encryption schemes such as Advanced Encryption Standard (AES),
Data Encryption Standard (DES), 3DES and Rivest-Shamir-Adleman algorithm (RSA) etc. [2-
3]. Traditional encryption schemes are not suitable for image encryption because there are
inherent features in image like bulk data capacity, correlation among adjacent pixels and high
redundancy so the image encryption differs from text encryption.
System Chaos is the best in encryption and decryption for multimedia. Chaos system was
discovered by Edward Lorenz in 1963 [5]. Chaos system properties are pseudo-random, non-
periodicity, ergodicity and highly sensitive to system parameters and initial conditions [6]. Chaos
systems are based on initial condition and control parameter. Therefore, a little change in initial
condition or control parameter cause a completely change. Chaotic maps can be categorized
into two groups: 1D chaotic maps such as Logistic map, Sine map and Tent map etc. and a
high-dimensional chaotic map such as Arnold map, Exponential map and Henon map etc. The
combining of chaotic theory and cryptography are important fields in multimedia security to
achieve high security. Therefore, the level of security is high when it achieves grouping of
confusion and diffusion [7]. The concept of confusion is to change the pixel's position of plain
image and diffusion is to change the gray level value of confused image.
Rest of the paper is discussed as follows. Section 2 explores the related work in the area of
chaotic block Image scheme using large key space and message digest algorithm, discuss

Arnold Cat Map, MD5 and 2D-STCM. Section 3 represents a detail description of proposed
designed scheme. Section4 introduces the experimental results, compares varies image
encryption techniques and discusses the outcomes from several algorithms. Section5 is
conclusion and future work.
2. RELATED WORK
There are many researches in digital image encryption based on chaotic maps and key stream
generators. In [8], cat map and significant bit-planes are executed. The cat map is used to
scramble the positions of image pixels and the significant bit-planes can diffuse the image
pixels, but is not robust against differential attack because NPCR is not approaching to
100%and UACI is not approaching to 33% In [9], Arnold cat map and 1D Logistic map are
applied. The Arnold cat map is used to shuffle the pixels' positions of image and the 1D Logistic
map diffused the image pixels to get encrypted image, but is not robust against brute-force
attack because key space of encryption algorithm is not large. In [10], the three-dimensional
Henon chaotic map and the Cat chaotic map are executed. The cat chaotic map is used to
confuse the positions of image pixels and the three-dimensional Henon chaotic map can diffuse
the image pixels. Then, repeat the confusing and diffusing process to increase the resistance
to statistical and related attacks. The disadvantages of this method are the low encryption
speed. In [11], the 2D-sine tent composition map (2D-STCM) and the chaotic circular pixel
shuffling (CCPS) are applied. 2D-STCM is used to generate a key sequence and CCPS is used
to shuffle the pixels' positions of image based on 2D-STCM. In [12], algorithm based on one-
time keys and robust chaotic maps. Generate pseudo-random key sequence by a piecewise
linear chaotic map. The initial conditions were generated by the MD5 of the mouse positions.
This method is robust against brute-force attack because key space of encryption algorithm is
very large, but is not strong in resisting statistical attack because correlation coefficients of
ciphered image is not good. In [16], created new chaotic maps based on Beta function. It
executes three phases: permutation, diffusion and substitution. In [17], new chaotic map, strong
S-boxes and permutation function are implemented. It executes four phases: diffusion,
substitution, diffusion and permutation. The diffusion process is based on a new chaotic map.
The substitution process is based on a strong S-boxes. The permutation process is based on
a permutation function. In [19], cat map, logistic and tent maps are applied. The cat map is used
to permutation process, and then the logistic and tent maps diffused the image pixels to get the
encrypted image, but is not robust against statistical attack because correlation coefficients of
ciphered image is not good. In [20], combined 2-D Sine Logistic modulation map, derived from
the Logistic and Sine maps with a chaotic magic transform, aim was to resist various attacks
but, without mention target or specific types. In [22], logistic map, cat map, SHA-3 hash function
and auto-updating system are executed. Algorithm acts like one-time pad. The logistic map and
SHA-3 hash function are used to permutation process, and then the cat map and SHA-3 hash
function diffused the image pixels to get the encrypted image, but it is not strong against
statistical attack because correlation coefficients of ciphered image are not too low.
In this paper, the idea of encryption scheme proposes to achieve confusion and diffusion. First,
the whole image is divided into blocks, random change of block size in each iteration. Then,
Arnold cat map is Implemented to obtain confused image. Second, the key stream is generated
by 2D-STCM. Then, implement bit-XOR operation between key stream of 2D-STCM and
confused image. the previous steps are repeated two or more times to obtain the final encrypted
image.
Below Arnold Cat Map, MD5 and 2D-STCM Key are analyzed.
2.1 Arnold Cat Map
Arnold Cat Map [9] is two-dimensional discrete map. This map is used to shuffle the pixel's
positions of image.
[X′
Y′
] = [
1 a
b ab + 1
] [
X
Y
] mod(N) (1)
The Arnold cat map uses two parameters (a, b); the a, b are control parameters which change
the pixels' positions in image, where (a, b) are positive integers stand for the control parameters,
(x, y) are the old pixel position and (x', y') are the new pixel position.

The disadvantage of Arnold map, that the same original image appears after several iterations;
which concludes that Arnold map has periodic behavior. To solve this, issue the parameters (a,
b) are generated randomly by using 2D-STCM or manual change of parameters (a, b) in each
iteration.
2.2 Message Digest Algorithm
The message digest algorithm (MD5) takes any arbitrary length as input data, and produces
output of 128-bit (32-digit hexadecimal) as fingerprint [15]. Each message produces a special
MD5. It has been widely used to verify data or image integrity. As can be seen, in proposed
scheme Fig.2, MD5 produces initial value. More details, explanations and applications of MD5
are given in section 3.1.
2.3 Two Dimensional-Sine Tent Composite Map
The 2D-Sine Tent composite map [11] is a discrete-time dynamical system. It is built from 1D
Sine map and 1D Tent map defined in equations (3) and (4) respectively:
𝑥 𝑛+1 = 𝜇 × sin(𝜋𝑥 𝑛) (3)
𝑥 𝑛+1 = {
𝑟𝑥 𝑛 . 0 ≤ 𝑥 < 0.5
𝑟(1 − 𝑥 𝑛) . 0.5 ≤ 𝑥 ≤ 1
(4)
Here μ and r are control parameters lies in the range (0, 4] [11]. To overcome the limitations of
1D chaotic map, combined Sine and Tent maps. It can be defined as:
𝑥 𝑛+1 =
{
((sin( 𝜋𝑦𝑛) + 3) ×
𝑥 𝑛
2
) 𝑚𝑜𝑑 1. 𝑥𝑖 < 0.5
((sin( 𝜋𝑦𝑛) + 3) ×
(1−𝑥 𝑛)
2
) 𝑚𝑜𝑑 1 𝑥𝑖 ≥ 0.5
(5)
𝑦 𝑛+1 =
{
((sin( 𝜋𝑥 𝑛) + 3) ×
𝑦 𝑛
2
) 𝑚𝑜𝑑 1. 𝑦𝑖 < 0.5
((sin( 𝜋𝑥 𝑛) + 3) ×
(1−𝑦 𝑛)
2
) 𝑚𝑜𝑑 1. 𝑦𝑖 ≥ 0.5
(6)
A trajectory of 2D-Sine Tent composite map is excellent chaotic behavior. Figure 1 compares
the trajectories of 2D-STCM, 2D-SLMM and 2D-LM [11]. From trajectory figure1(a) of 2D-STCM
covers a large region compared with other two. So, it proves that the proposed chaotic function
has better ergodicity and randomness property.
(a) (b) (c)
FIGURE 1: Trajectories of (a) 2D-STCM Map; (b) 2D-SLMM Map and (c) 2D-Logistic Map [11].

3. PROPOSED DESIGNED SCHEME
The proposed image encryption scheme has two or more iterations, in each iteration there is
group of confusion and diffusion processes. In first confusion process, an Image of size N×N is
random decomposed into M×M block, 2D-cat map is used for local shuffling of indexes inside
blocks. In second confusion process, 2D-cat map is used for global shuffling of whole image
indexes. In diffusion process, XOR operation between key stream {Ki} of 2D-STCM and
confused image is implemented.
3.1 Initial Value (X) Generation using MD5
Steps to generate the initial value (x): First, extract the value of MD5 hexadecimal from plain
image. Second, convert the hexadecimal MD5 value to a decimal value. Third, use the
summation operation to sum decimal values to obtain a single value. Finally, convert the
decimal value to a fractional value by dividing by 1000.
Let's take a look at this example, on a system that has an image called " Lena.TIF " the MD5
hash would look as follows:
Image name Hash Value
C: Lena.TIF 5649b212f4f9e5c781a9e4f8c75208e5
Hexadecimal Value Decimal Value
5649b212f4f9e5c781a9e4f8c75208e5
5.6.4.9.11.2.1.2.15.4.15.9.14.5.12.7.8.
1.10.9.14.4.15.8.12.7.5.2.0.8.14.5
Sum (Decimal Value) = 243. Initial value (x) = 243/10000 = 0.0243.
As shown in Fig.2 y as second initial value could be given by user directly or by using indirect
different methods from given image.
3.2 Key Sequence Generation using 2D-STCM
The equations (5) and (6) of 2D-STCM are repetitive for generate two key sequences {K1} and
{K2} which as original image size. The initial values (x, y) are a fractional value which passes
to the 2D-STCM equations to generate two keys sequences. In the next iteration, we change
the initial values (x, y). The random change of initial values (∆x, ∆y) in each iteration increasing
the key space that resist brute-force attack. In [14], shows preprocessing of fractional key to
obtain integer key with 8 bits suitable for image encryption as following:
xn = (floor (xn × 232))mod 256. xn = k1 (7)
yn = (floor (yn × 232))mod 256. yn = k2 (8)
where Floor (𝑥 𝑛, 𝑦𝑛) returns the values of (𝑥 𝑛, 𝑦𝑛) to the nearest integer and mod (𝑥 𝑛, 𝑦𝑛) returns
the rest of the division. Preprocess leads to a better distribution.
3.3 Image Encryption Process
In this section, the proposed image encryption process is explained.
Step 1: Read two dimensional 8-bit gray scale image {𝐼𝑖×𝑗} of size N×N, where N = (256, 512
or 1024).
Step 2: Decompose the whole image {𝐼𝑖×𝑗} into the M×M size blocks, where M = (64, 16,128…).
Step 3: Apply a 2D-cat map with each block using the control parameters (𝑎𝑖 , 𝑏𝑖) to shuffle the
pixel's positions with each block and perform this step two or more times to get first confused
image I1(𝑖×𝑗)
.

Step 4: Apply the 2D-cat map with first confused image {I1(𝑖×𝑗)
} using the control parameters
(𝑎𝑖 , 𝑏𝑖) to shuffle the pixel's positions of first confused image and perform this step two or more
times to get a second confused image {I2(𝑖×𝑗)
}.
Step 5: In diffusion process. The 2D-STCM keys stream {𝑘1, 𝑘2} are converted to two
dimensions { k1(𝑖×𝑗)
, k2(𝑖×𝑗)
} as the size of confused image. Then select one key used in the
diffusion process. Final, apply a bit-XOR operation between one key stream { k1 𝑜𝑟 2(𝑖×𝑗)
} from
2D-STCM and the second confused image {I2(𝑖×𝑗)
}, to get the final encrypted image.
{𝐸(𝑖×𝑗)} = {I2(𝑖×𝑗)
} ⊕ { k1 𝑜𝑟 2(𝑖×𝑗)
} (9)
Step 6: In the next iterations, the previous steps are repeated to obtain the encrypted image.
3.4 Image Decryption Process
In this section decryption process of the encrypted image is explained.
Step 1: In diffusion process. 2D-STCM keys stream {𝑘1, 𝑘2} are converted to two dimensions
{ k1(𝑖×𝑗)
, k2(𝑖×𝑗)
} as the size of encrypted image. Then chose the same key that was used in the
encryption process, it should be used in the decryption process. Apply bit-XOR operation
between key stream { k1 𝑜𝑟 2(𝑖×𝑗)
} from 2D-STCM and the encrypted image {𝐸(𝑖×𝑗)}, to get the
second confused image {I2(𝑖×𝑗)
}.
In diffusion process. The 2D-STCM keys stream {𝑘1, 𝑘2} are converted to two dimensions {
k1(𝑖×𝑗)
, k2(𝑖×𝑗)
} as the size of confused image. Then select one key used in the diffusion process.
Final, apply a bit-XOR operation between one key stream { k1 𝑜𝑟 2(𝑖×𝑗)
} from 2D-STCM and the
second confused image {I2(𝑖×𝑗)
}, to get the final encrypted image.
{I2(𝑖×𝑗)
} = {𝐸(𝑖×𝑗)} ⊕ { k1 𝑜𝑟 2(𝑖×𝑗)
} (10)
Step 2: Apply the 2D-cat map with second confused image {I2(𝑖×𝑗)
} using the control parameters
(𝑎𝑖 , 𝑏𝑖) to shuffle the pixel's positions of second confused image and perform this step two or
more times to get a first confused image {I1(𝑖×𝑗)
}.
Step 3: Decompose the first confused image I1(𝑖×𝑗)
into the M×M size blocks, where M = (64,
16,128,).
Step 5: Apply a 2D-cat map with each block using the control parameters (𝑎𝑖 , 𝑏𝑖) to shuffle the
pixel's positions with each block and perform this step two or more times to get a decrypted
image.
Step 6: In the next iterations, the previous steps are repeated to obtain original image.
Looking at the left-hand side of the figure 2, we can see that the processing of the key in three
phases. First, put an initial value (x, y) as a fractional value. Second, random change of the
initial values (x, y) in each iterate. Finally, the initial values (x, y) enter to 2D-STCM equations
which generate a two sequence keys as the size of the encryption image. These keys are used
in the cat map and diffusion process. The right-hand portion of the figure 2, shows the
encryption steps in four phases. First, divided the whole image into the blocks. Second, Apply
a 2D-cat map with each block. Third, apply a 2D-cat map with whole image. Finally, implement
a bit-XOR operation between key stream {Ki} of 2D-STCM and confused image.

FIGURE 2: Block Diagram of The Proposed Encryption Scheme.
4. EXPERIMENTAL RESULT
The algorithm proposal encrypts the original image through confusion and diffusion using
multiple steps. The algorithm is implemented using the MATLAB 2015a simulation program,
several gray images from University of Southern California - Signal and Image Processing
Institute (USC-SIPI) and system configuration Intel® core™ i3 CPU M330- @2.13 GHz and 4
GB RAM, operating system 64 bits. A comparison is done with the many other algorithms in
[16, 17, 18, 19, 20, 21]. The results showed that our algorithm performs better or similar than
other algorithms.
4.1 Key Space
The key space of encryption algorithm should be large enough to resist brute-force attack.
Diffusion Key has five parameters (x. y. ∆x. ∆y. n); four parameters (x, y, ∆x, ∆y) represented by
a double data type, each parameter is 64 bits and parameter (n) is real number represented by
Plain
image
4. Divide image
into M*M blocks
(64,16.128,..)
5. Confusion with
each block by cat
map
7. Confusion with
whole image by
cat map
8. Diffusion by
bit-XOR
cipher
image
Put
Initial
value y
1. random change of
initial values (x, y) in
each iteration
3. 2D-
STCM
generate
(a, b) key
use with cat
map
2. 2D-
STCM use
to generate
a two keys
stream
Two or more
iteration.
Two or more
iteration.
Two or more
iteration.
Get
MD5
Get Initial
value x

8 bits. Diffusion key space size in this paper is 2264
and it is large enough to resist brute-force
attack.
In addition, there are confusion keys in this paper represented by key (a, b) of cat map, number
of internal iterations and block size change, they are longer than 240
. Total key space is longer
than 2304.
4.2 Key Sensitivity
A small change in security key causes large change in cipher image and a small change in
security key can't be recover an original image as show in figures below.
Encryption Key 1: x0=0.0058052, y0=0.0352572, ∆x = 0.01, ∆y = 0.01, n=5.
Decryption Key 2: x0=0.0058052, y0=0.0352571, ∆x = 0.01, ∆y = 0.01, n=5.
FIGURE 3: An Original Image Encryption by Key 1 and Decryption by Key 2.
4.3 Histogram
The histogram plots the occurrences frequency of image pixel value that show statistical
features of images. Y-axis represents number of image pixels and X-axis represents intensity
level. The histogram of plain image is not distributed uniformly, this means statistically pixels
can be predicted, but histogram of cipher image is distributed uniformly, this means statistically
pixels can't be predicted. Analyzed histograms of three plain images and their ciphered images.
Figure 4 gives the plain images of ‘Cameraman’, ‘Lena’, ‘Couple’, and their histograms,
respectively. Figure 5 gives the ciphered images of ‘Cameraman’, ‘Lena’, ‘Couple’, and their
histograms respectively. The results shown in Figures 4 and 5 [images from USC-SIPI] indicate
that our algorithm resists statistical attack.
FIGURE 4: Plain images of ‘Cameraman’, ‘Lena’, ‘Couple’, and their histograms respectively.

FIGURE 5: Ciphered images of ‘Cameraman’, ‘Lena’, ‘Couple’, and their histograms respectively.
4.4 Pixel Correlation
This analysis is used to study the correlation between two adjacent pixels in a plain image and
a cipher image. In the plain image, the correlation between adjacent pixels are high, but in the
cipher image should be low correlation between the adjacent pixels to resist statistical attacks.
The below equations calculate the correlation coefficient as follows:
Ex =
1
N
∑ xi
n
i=1 . (11)
Dx =
1
N
∑ (xi
n
i=1 − EX)2
. (12)
cov(x, y) =
1
N
∑ (xi
n
i=1 − EX)(yi − Ey) . (13)
rxy =
cov(x,y)
√Dx√Dy
. (14)
In the above equations, in equation (11) calculates mean, in equation (12) calculates stander
division, in equation (13) calculates covariance and in equation (14) calculates correlation
coefficient. In below Table 1 illustrates correlation coefficient values of the plain image and its
cipher image.
4.5 Information Entropy
Entropy is a statistical measure that use to randomness test in the plain image and ciphered
image. The information of entropy is given by equation (15):
H(X) = − ∑ Pr(2N
i=1 xi) log2 Pr(xi) (15)
Here H(X) is the entropy value, Pr(xi) is the probability of symbol xi, and N is the number of
bits to represent a symbol xi. When H(X) = N this ideal entropy value. The results shown in
Tables 2 indicate that our algorithm resists entropy attack.
4.6 NPCR and UACI Tests
NPCR (Number of pixels change rate) and UACI (Unified average changing intensity) are used
in plain image sensitivity tests. NPCR is approaching to 100%, when changing one pixel in the
plain image, resulting in a complete change to the cipher image. Let's take a look at this
example. I1 is a plain original image, we change one pixel to get another plain image I2, the
result after the encryption process is two completely different C1 and C2 ciphered images.

Arithmetically, the value of the bipolar array D(i,j) can be calculated as follows:
D(i.j) = {
0. if C1(i.j) = C2(i.j)
1. if C1(i.j) ≠ C2(i.j)
(16)
Then NPCR can be calculated as follows:
NPCR =
1
N×M
∑ ∑ D(i.j) × 100% (17)N
j=1
M
i=1
plain image sensitivity is better when the NPCR value is close to 100%. UACI measures the
average intensity between the C1 and C2 ciphered images, obtained from plain images I1 and
I2. It can be defined as follows:
UACI =
1
N×M
[∑ ∑
C1(i.j)− C2(i.j)
255
N
j=1
M
i=1 ] × 100% (18)
plain image sensitivity is better when the UACI value is close to 33%. The results shown in
Tables 3.4 indicate that our algorithm resists differential attack.
4.7 Comparison of Various Image Encryption Techniques
Comparison is done on the basis of; direction, plain image and encrypted image of our scheme
with various image encryption algorithms
Image Direction
Plain
image
Encrypted image
Our
scheme
Ref.
[16]
Ref.
[17]
Ref.
[18]
Ref.
[19]
Ref.
[20]
Ref.
[21]
Airplane Horizontal 0.957 0.0075 0.0033 −0.0002 0.0011 −0.0164 0.0004 0.0045
Vertical 0.9365 -0.001 0.0002 −0.0090 −0.0035 −0.0181 0.0061 −0.0215
Diagonal 0.8926 0.0037 −0.0019 −0.0066 −0.0029 0.0004 −0.0079 −0.0015
Airport1 Horizontal 0.9099 -0.0018 −0.0021 −0.0275 0.004 −0.0061 0.0094 −0.0142
Vertical 0.9033 0.0008 0.0002 −0.0154 −0.0174 −0.0079 −0.0107 −0.0141
Diagonal 0.859 -0.0006 0.0003 −0.0187 −0.0135 −0.0001 −0.0007 0.0002
Barbara Horizontal 0.8953 0.0005 0.0033 −0.0033 −0.0052 −0.0212 −0.0187 0.0037
Vertical 0.9588 -0.0004 0.0032 −0.0269 −0.0067 −0.0161 −0.0016 −0.0202
Diagonal 0.883 0.0015 0.0025 −0.0121 0.0068 −0.0110 0.0001 0.0046
Boat Horizontal 0.9381 0.0005 0.0025 −0.0100 −0.0054 −0.0189 −0.0295 −0.0138
Vertical 0.9713 -0.0026 0.0018 −0.0124 −0.0009 0.0003 −0.0150 −0.0199
Diagonal 0.9221 0.0022 0.0005 −0.0185 0.0026 −0.0204 −0.0224 −0.0057
Camera
man
Horizontal 0.9334 0.0035 0.0047 −0.0095 −0.0211 0.0063 −0.0047 −0.0009
Vertical 0.9592 -0.0002 −0.0054 −0.0170 −0.0103 −0.0142 −0.0195 −0.0223
Diagonal 0.9086 -0.0025 0.0016 −0.0119 0.0054 0.0168 0.0279 0.0025
Chemical
plant
Horizontal 0.9466 -0.0014 −0.0030 −0.0134 −0.0073 −0.0069 −0.0091 0.0072
Vertical 0.8984 0.0025 −0.0019 −0.0005 −0.0073 −0.0100 −0.0029 −0.0015
Diagonal 0.8529 -0.004 −0.0063 −0.0033 −0.0115 −0.0078 −0.0092 −0.0040
Clock Horizontal 0.9564 0.0078 0.0008 0.0024 −0.0140 −0.0248 −0.0143 −0.0123
Vertical 0.974 0.0059 0.0013 −0.0246 −0.0139 −0.0172 0.0097 −0.0041
Diagonal 0.9389 0.0017 −0.009 −0.0081 −0.0175 −0.0025 0.012 −0.0027

Couple Horizontal 0.937 0.0007 0.0012 −0.0251 −0.0178 −0.0122 −0.0236 −0.0106
Vertical 0.8926 -0.0034 0.0011 −0.0213 −0.0025 0.0262 −0.0045 −0.0047
Diagonal 0.8558 0.0022 0.0013 −0.0078 0.0001 −0.0257 0.0016 0.0262
Lena Horizontal 0.9719 0.0009 −0.0047 −0.0048 −0.0086 −0.0066 0.0011 −0.0063
Vertical 0.985 -0.0009 0.0015 −0.0112 −0.0102 −0.0089 0.0098 0.0098
Diagonal 0.9593 -0.0027 0.003 −0.0045 −0.0125 0.0424 −0.0227 −0.0154
Man Horizontal 0.9774 0.0004 −0.0010 −0.0155 −0.0190 −0.0083 0.0022 −0.0100
Vertical 0.9812 0.00004 0.0029 −0.0276 −0.0095 −0.0180 −0.0226 −0.0027
Diagonal 0.9671 -0.0019 −0.0005 −0.0157 −0.0141 0.025 0.006 −0.0195
Moon
surface
Horizontal 0.902 0.0018 −0.0061 −0.0062 −0.0288 −0.0065 −0.0212 −0.0063
Vertical 0.9389 0.0013 0.0001 −0.0075 −0.0194 0.0063 −0.0166 0.0142
Diagonal 0.9037 0.0011 0.0021 −0.0044 −0.0137 0.0135 0.0138 −0.0091
Tank Horizontal 0.9456 -0.0012 0.0033 −0.0202 0.0049 −0.0185 −0.0383 −0.0159
Vertical 0.932 0.0012 0.0002 −0.0200 −0.0128 −0.0119 −0.0362 −0.0114
Diagonal 0.9017 -0.0005 −0.0019 −0.0013 −0.0011 −0.0249 0.022 0.0126
Average Horizontal 0.002 0.003 0.0115 0.0114 0.0127 0.0143 0.0088
Vertical 0.0009 0.0016 0.0161 0.0095 0.029 0.0129 0.0122
Diagonal 0.0026 0.0025 0.0094 0.0084 0.0158 0.0121 0.0086
TABLE 1: Comparing the correlation coefficient of our algorithm with other algorithms.
Image name
Our
scheme
Ref. [16] Ref. [17] Ref. [18] Ref. [19] Ref. [20] Ref. [21]
Airplane 7.997 7.9998 7.996 7.9966 7.9966 7.9969 7.9957
Airport 7.9998 7.9972 7.9974 7.9965 7.9926 7.9954 7.9966
Barbara 7.9992 7.9993 7.9978 7.9964 7.9937 7.9957 7.9964
Boat 7.9993 7.9993 7.998 7.9979 7.996 7.9959 7.9985
Camera man 7.9975 7.9972 7.9985 7.9966 7.9955 7.9964 7.999
Chemical
plant
7.9971 7.9971 7.9964 7.9986 7.9947 7.999 7.994
Clock 7.9975 7.9975 7.9992 7.9974 7.9984 7.9956 7.9977
Couple 7.9991 7.9993 7.9976 7.9987 7.9951 7.998 7.9956
Lena 7.9993 7.9991 7.9963 7.9991 7.9951 7.9965 7.9964
Man 7.9998 7.9998 7.9975 7.9974 7.999 7.9965 7.9949
Moon
surface
7.9972 7.9975 7.9987 7.9979 7.9951 7.9954 7.9969
Tan 7.9992 7.9994 7.9969 7.999 7.9976 7.9965 7.9997
Average 7.999 7.998542 7.997525 7.997675 7.995783333 7.99648333 7.99678333
TABLE 2: Comparing the information entropy of our algorithm with other algorithms.

Image name
Our
scheme
Airplane 99.62 99.5849 99.615 99.6107 99.5662 99.618 99.6201
Airport 99.5984 99.6459 99.6083 99.6077 99.5565 99.6231 99.5499
Barbara 99.6307 99.6215 99.6092 99.6162 99.5227 99.6402 99.5178
Boat 99.6074 99.6227 99.6102 99.6281 99.5609 99.6209 99.5743
Camera man 99.6154 99.6124 99.6205 99.6292 99.5749 99.6105 99.6216
Chemical plant 99.617 99.62 99.6121 99.6131 99.5325 99.6258 99.6185
Clock 99.62 99.5727 99.6102 99.6218 99.591 99.6126 99.5728
Couple 99.612 99.6185 99.6399 99.6292 99.5606 99.6312 99.5468
Lena 99.5914 99.6253 99.6228 99.6146 99.5511 99.6092 99.6231
Man 99.6057 99.6189 99.607 99.6084 99.5417 99.6211 99.5514
Moon surface 99.6429 99.6276 99.6139 99.6168 99.5684 99.6172 99.6033
Tank 99.6059 99.6307 99.629 99.6131 99.5794 99.6687 99.6078
Average 99.6139 99.61676 99.61650833 99.6174083 99.55882 99.624875 99.58395
TABLE 3: Comparing the NPCR of our algorithm with other algorithms.
Image name
Our
scheme
Airplane 33.4188 33.6829 33.5625 33.6632 33.3716 33.6183 33.5961
Airport 33.4354 33.4188 33.5359 33.4143 33.4063 33.5817 33.664
Barbara 33.4914 33.4691 33.7431 33.5776 33.389 33.6714 33.5052
Boat 33.4665 33.5137 33.5367 33.6145 33.4176 33.6018 33.3975
Camera man 33.4165 33.6551 33.7786 33.705 33.3691 33.6862 33.7326
Chemical
plant
33.3856 33.4291 33.6068 33.8543 33.3872 33.3825 33.5831
Clock 33.4893 33.4444 33.582 33.4836 33.4147 33.5793 33.9272
Couple 33.522 33.3615 33.8085 33.6446 33.3723 33.7252 33.8911
Lena 33.4699 33.4807 33.7041 33.5561 33.3461 33.6322 33.8144
Man 33.4834 33.4815 33.7905 33.6744 33.3684 33.472 33.6949
Moon surface 33.2323 33.4408 33.6898 33.5333 33.3758 33.6993 33.8063
Tank 33.4714 33.5212 33.9213 33.7155 33.4045 33.5224 33.7415
Average 33.4402 33.49157 33.68831 33.6197 33.3852 33.59769 33.6961
TABLE 4: Comparing the UACI of Our Algorithm with Other Algorithms.
5. CONCLUSION AND FUTURE WORK
This paper supports a set of confusion and diffusion methods, and avoids poor key
management processes to achieve high security. The process of confusion deals with changing
the position of the pixel by applying a chaotic map (the cat). The diffusion process deals with
changing the pixel value by performing a bit-XOR operation between the 2D-STCM and the
confused image. In the algorithm, confusion and diffusion pass through two or more iterations,
in each iteration new key sequences are created by 2D-STCM. Therefore, the total key space
is long enough to resist brute-force attack and increase security level.

From experimental results the key space analysis, key sensitivity analysis, histogram,
correlation coefficient, information entropy, NPCR and UACI show very good result. As a result,
the encryption algorithm is resistant to attacks such as statistical and differential attacks. The
cipher image has a high security level not only because of confusion and diffusion methods,
but also any key should only be used once. After comparison it is found that in our paper
correlation coefficient was reduced and reach 29% fewer than the results of similar references
in contrast, entropy information is higher than the listed papers (tends to 8) and NPCR is similar
or higher than the listed papers. The obtained results show that the submitted image information
becomes random. Future work will deal with color encryption schemes using different methods
of image fusion.
6. REFERENCES
[1] F. Nasser and M. Mohamed. “Improvement of Images Encryption Based on Multiple
Chaotic Maps and 2D-STCM Key Space,” presented at the 3rd
Int. Conf. Computer
Science and Engineering Information technology, Aden, Yemen, 2019.
[2] W. Stallings. Cryptography and Network Security Principles and Practice, 4th ed. USA:
Prentice Hall, 2006, pp.1-210.
[3] B. Schneier. Applied Cryptography, Protocols, Algorithms, and Source Code, second ed.
New York: John Wiley & Sons, Inc., 1996, pp. 370-642.
[4] S. Lian. “A Block Cipher Based on Chaotic Neural Networks.” Elsevier, Neuro
computing, vol. 72, pp. 1296-1301, Nov. 2009.
[5] M. Billal Hossain, M. Toufikur Rahman, S. Rahman and S. Islam. "A New Approach of
Image Encryption Using 3D Chaotic Map to Enhance Security of Multimedia
Component," presented at the 3rd Int. Conf. Communication Engineering Department,
Bangladesh, 2014.
[6] M. Mishra, P. Singh and C. Garg. “A New Algorithm of Encryption and Decryption of
Images Using Chaotic Mapping.” International Journal of Information and Computation
technology, Vol. 4, pp. 741-746, 2014.
[7] C.E. Shannon. Communication theory of secrecy systems. Bell. Syst. Tech. 1949, pp.
656-715.
[8] K. Naik and A. Kumar Pal. "An Image Cryptosystem based on Diffusion of Significant Bit-
planes of a Scrambled Image with Generated Binary Key Matrices," Proceedings of
IEEE (ICCICR), 2013, pp. 15.
[9] S. Som and A. Kotal. "Confusion and Diffusion of Grayscale Images Using Multiple
Chaotic Maps," Proceedings of IEEE (NCCCS), 2012, pp. 15.
[10] Z. Lv, L. Zhang, and J. Guo. “A Symmetric Image Encryption Scheme Based on
Composite Chaotic Dispersed Dynamics System,” in Proc. ISCSCT, 2009, pp.191-194.
[11] S. Agarwal. “Secure Image Transmission Using Fractal and 2D-Chaotic Map.” The
International Journal of Imaging, pp. 17, Jan. 2018.
[12] L. Hongjun and W. Xingyuan. "Color Image Encryption based on One-Time Keys and
Robust Chaotic Maps." The International Journal of Computers and Mathematics with
Applications, pp. 3320–3327, Mar. 2010.
[13] S. Agarwal, G. Srivastava and A. Negi. " Dynamics of Mandelbrot set with
transcendental function." The International Journal of Advanced Computer Science and
Applications, Vol. 3, No.5, pp. 142-146, 2012.

[14] X. Tong, Y. Liu, M. Zhang, H. Xu and Z. Wang. “Image Encryption Based on
Hyperchaotic Liu System Algorithm.” The International Journal of Eng. & Tech. Journal,
Vol.33, No.17, pp.181-196, Jan. 2015.
[15] R. Rivest. “MD5.” Internet: https://en.wikipedia.org/wiki/MD5, May. 29, 2019.
[16] R. Zahmou, R. Ejbali and M. Zaied. “Image Encryption Based on New Beta Chaotic
Maps.” The International Journal of Opt. Lasers Eng., Vol.96, pp. 39–49, Apr. 2017.
[17] A. Belazi, A. Abd El-Latif and S. Belghith, “A Novel Image Encryption Scheme Based on
Substitution-Permutation Network and Chaos.” The International Journal of Signal
Process pp.41, Mar. 2016.
[18] X. Wang, L. Teng and X. Qin. “A Novel Colour Image Encryption Algorithm Based on
Chaos.” The International Journal of Signal Process, pp.1101–1108, Oct. 2011.
[19] X. Wang, L. Liu and Y. Zhang. “A Novel Chaotic Block Image Encryption Algorithm
Based on Dynamic Random growth Technique.” The International Journal of Opt. Lasers
Eng., Vol.66, pp.10–18. Aug. 2014.
[20] Z. Hua, Y. Zhou, C. Pun and C.L. Philip Chen. “2D Sine Logistic Modulation Map for
Image Encryption.” The International Journal of Inf. Sci. Vol.297, pp.80–94, Nov, 2015.
[21] XY. Wang, L. Yang, R. Liu and A. Kadir. “A Chaotic Image Encryption Algorithm Based
on Perceptron Model.” The International Journal of Nonlinear Dyn, pp. 615–621, Jun,
2010.
[22] G. Ye* and X. Huang. "A secure Image Encryption Algorithm Based on Chaotic Maps
and SHA-3." Security and Communication Networks, pp. 2015–2023, Feb. 2016.

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