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607 | P a g e
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Hybrid Image Encryption using Non-Adjacent Bits
Dynamic Encoding DNA with RSA and Chaotic
Systems
Marwa A. Elmenyawi1, Nada M. Abdel Aziem2
Benha Faculty of Engineering, Benha University Benha, Egypt1
Arab Academy for Science, Technology and Maritime Transport - Arab League1, 2
Abstract—Image encryption is a crucial aspect that helps to
maintain the images' confidentiality and security in diverse
applications. Ongoing research is focused on improving the
efficiency and effectiveness of encryption. Image encryption has
many practical applications in today's digital world, such as
securing confidential images transmitted over networks,
protecting sensitive personal information stored in images, and
ensuring the privacy of medical images. The suggested work
represents a breakthrough in image encryption by proposing a
model that leverages the power of DNA, RSA, and chaos. This
model has three phases: key generation, confusion, and diffusion.
The key generation phase employs a hash function and
hyperchaotic technique to generate a strong key. During the
confusion phase, the positions of pixels are rearranged, either at
the image level or within blocks, using the Duffing chaotic map.
Once the scrambling level is determined, each pixel undergoes
two successive scrambling steps, with Henon and Arnold's
chaotic map to change its location. During the diffusion phase,
the encryption model employs a two- approach to ensure
maximum security. Firstly, it utilizes dynamic DNA
cryptography for non-adjacent bits, followed by robust RSA
cryptography. The experimental results indicate that the model
possesses a strong security level randomness and can withstand
different attacks.
Keywords—Cryptography; image encryption; hash function;
chaotic map; DNA encoding; DNA operations; RSA algorithm
I. INTRODUCTION
In today's digital era, digital images are widely used for
personal, professional, or commercial purposes. Therefore,
these images require protection from unauthorized access.
Image encryption and information hiding are the two basic
approaches for securing digital images. Image encryption
prevents hackers from recognizing the images by employing
complex mathematical operations to transform image data into
an unreadable form. Therefore, the hacker's attempts are
wasted. There is a need to design and implement an algorithm
characterized by its security and efficiency to succeed in
withdrawing the different attacks. There are two phases in
image encryption: diffusion and scrambling. The pixel
positions are altered during the scrambling phase, whereas the
pixel values are changed during the diffusion phase.
Various methods are employed during the confusion phase.
Some of these works used the Arnold transform [1-3], Zigzag
transformation [4,5], Fisher-Yates [6], and Josephus traversal
[7]. Other works implemented scrambling over two steps, such
as L-shape and Arnold transforms as in [8], new filling curve
design and Josephus traversal [9].
In terms of diffusion, S. Wang. et al. [10] suggested using
the DNA sequence in the diffusion phase. Four sequences were
derived from a 4D chaotic system and utilized to select the
rules for encoding, computing, and decoding. They utilized
higher dimensional chaos to offer a large key space. J. Yu et al.
[11] began with the diffusion phase. They encoded the three
matrices of RGB image using DNA sequence where a chaotic
system chooses the rule. A new operation, known as DNA
triploid mutation, was introduced to achieve cryptographic
translation of DNA bases. Finally, they permuted the image
using row-column permutation. C. Zou et al. [12] utilized two
types of DNA strands: long and short. The image was
permuted using two short DNA strands, while the long DNA
strand was used in the diffusion stage. If the DNA sequence
follows the property of the Watson-Crick base pairing, the
XOR operation of DNA is performed; otherwise, the DNA
addition operation is used.
B. Jasra and A. Moon [13] split the color image into three
planes and encoded each plane using a DNA sequence based
on the chosen row-level. A substitution algorithm relies on
elliptic curves to accomplish effective encryption and
authentication. J. Wang et al. [1] suggested a new type of
chaos; Logistic-Sine self-embedding. They proved this type's
chaotic features and adopted a 0-1 test to find the chaos's
presence in the time series. They encrypted the plain image
using a Logistic-Sine self-embedding chaotic system.
Similarly, X. Li [14] introduced another chaotic sequence,
which was 5D, and they showed that the 5D chaotic did not
have a prominent Lyapunov exponent yet possessed several
good characteristics. The 5D chaotic sequence was utilized to
choose the DNA encoding, computing, and decoding.
The encryption model presented in [15] depended on a
fused magic cube produced by fusing two magic cubes. The
cipher image's pixels value was obtained from the plain
image's pixels value by employing the fuse magic cube. J.
Zheng and Q. Zeng [16] constructed an S-box using the
obtained key from the Logistic map, generating a 16 x 16
matrix ranging from 0 to 255 with no repeated values. The
image was diffused by traversing the scrambled image in order
according to the generated keys.
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A technique for encrypting color images was introduced in
[17], which employs 3D chaos, RSA, DNA, and LSB. The
image is initially encrypted using a DNA method and Lorenz
chaotic map. The secret key is then encrypted employing RSA
and hidden within a cipher image using LSB. In another
approach proposed by M. Liu and G. Ye [18], image
encryption is achieved by utilizing dynamic DNA alongside a
hyperchaotic system. The dynamic DNA coding selects DNA
rules in a randomized manner, guided by the employed chaotic
map. This study also incorporates RSA to protect the secret
key's confidentiality during transmission and management. U.
Mir et al. [19] introduced an encryption method for color
images using RSA and chaos in the domain of Hartley. The
image is first ciphered utilizing RSA and then transformed
from the time to frequency domain using a Hartley domain.
K. Jiao et al. [20] introduced an encryption approach
combining RSA and a generalized Arnold chaotic map. The
RSA algorithm obtains the map parameters, generating the
keystream for a diffusion operation on the plaintext image. The
confusion operation is then employed to conceal the image data
and produce the cipher image. Babu M et al. [21] used chaotic
Maps, RSA, and DNA sequences to encrypt images. This paper
divided the plain image into several blocks. Secondly, different
encryption schemes were utilized on each block, such as
Secure Force, DNA Sequence, Arnold Map, and RSA
encryption. Thirdly, a discrete cosine transformation algorithm
was applied to the merged blocks, after which an XOR
operation was conducted with a randomly generated key to
produce the encrypted image.
This paper aims to enhance image encryption security by
minimizing pixel correlation, maximizing randomness and
unpredictability, and withstanding various types of attacks. The
proposed encryption approach has three phases: key
generation, confusion, and diffusion. The integration of
different chaotic maps leads to a substantial expansion of the
key space and makes encryption impervious to brute-force
attacks. A robust key generation process achieves cryptosystem
robustness against various attacks. Chaos and hash functions,
SHA and MD5, produce the encryption key. The advantages of
the SHA function are its irreversibility and a one-time pad key,
while the chaos is characterized by randomness and
unpredicted ability. The final encryption key is obtained by
applying these hash functions to the user-specified key and the
plaintext image. The encryption security approach is
strengthened by utilizing the plaintext image and the user key.
Scrambling a pixel's locations can be done over the whole
image or the divided blocks of the whole image, depending on
the Duffing chaotic map. Moreover, two levels of confusion
are implemented using Arnold and Henon's chaotic maps. The
scrambling phase achieves high randomness between the pixels
and decreases the correlation between the pixels to the
minimum compared to the previous research, as illustrated by
the results of the suggested method. The final phase is
diffusion, implemented over two steps: DNA and RSA. In the
DNA algorithm, the pair of bits to be replaced with the DNA
sequence is not successive as customary in state-of-the-art
research. The proposed algorithm incorporates dynamic DNA
to select various rules for each pixel and DNA computations to
improve its efficiency. The encoding, computation, and
decoding rules are determined using a 4D hyperchaotic
sequence.
The second diffusion level is to implement the RSA
algorithm, which is different from the state-of-the-art research
where most of the paper used RSA along with DNA utilized
RSA outputs as the initial values of chaotic sequences. Despite
using multiple steps and various types of chaotic maps, we
tried to keep the algorithm's runtime comparable to previous
research. We conducted experimental testing and analysis to
demonstrate the proposed approach's superiority and
feasibility, showcasing its resilience against multiple attacks
such as differential, plaintext, brute-force, occlusion, and noise
attacks. Moreover, the correlation is lower than in the most
recent research.
The paper's structure is as follows: the second section
provides an overview of chaos and DNA cryptography. The
third section outlines the suggested approach for image
encryption/decryption, followed by the fourth section
thoroughly explores the results, conducts in-depth analysis, and
compares them with similar research. Lastly, the fifth section
introduces the paper's conclusion.
II. BACKGROUND
A. Chaotic
Chaotic systems are characterized by unique features
appropriate in encryption, like sensitivity to initial conditions,
irregular behavior, and unpredictability. Therefore, using the
chaotic sequence in the encryption system can give a high-
security degree and robustness against attacks. Our suggested
algorithm employs various types of chaotic systems at different
stages to increase the key space and enhance security.
The 1D logistic map [22] generates chaotic dynamics in a
discrete-time system. The Logistic chaotic map provides high
speed, low arithmetic operations, and low computational
overhead. It is a nonlinear recursive function defined by Eq.
(1). (1)
Where r is a parameter that determines the map behavior. x0
should be ϵ[0,1]and r has to be within interval 0<r≤4 to
produce the chaotic behavior.
The Henon Chaotic Map [19] refers to a discrete-time
dynamical map in 2D. Eq. (2) and (3) define the equations of
the Henon map:
(2)
(3)
To attain chaotic behavior in the Henon Chaotic Map, the
control parameters a and b need to be assigned the values (1.4,
0.3).
The Arnold Chaotic Map [23] is often employed to
scramble and alter pixel locations. It is described in Eq. (4) and
(5). (4)
(5)
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The "mod m" operation ensures that the coordinates do not
exceed the image size.
Quantum Chaotic Map [24] is a classical dynamical system
that is described to develop the function for solving computing
of the quantum. It is used to generate many random numbers.
The quantum map mathematical expression is given in Eq. (6)-
(8). (6)
(7)
(8)
Where x ϵ [0,1], y ϵ [0, 0.1], z ϵ [0, 0.2], r ϵ [0,4], β ϵ [6, ∞)
,and are complex conjugates of x and z.
Duffing Chaotic [23] produces chaotic dynamics in a
discrete-time system. The Eq. (9) and (10) represent this map.
It can be utilized to design damped oscillators.
(9)
(10)
Its control parameters, a and b, should be 2.75 and 0.2 to
maintain chaotic behaviour in the Duffing Chaotic system.
B. DNA
Images are encrypted using nucleic acid bases via a DNA
encryption system, which subsequently carries out several
additional DNA operations. The four nucleic acid bases
identified by the Watson-Crick basic pairing principles are C
(Cytosine), A (Adenine), T (Thymine) and G (Guanine). Every
two bases complement each other; A is the complement of T
and likely C and G. These four bases can be represented in
binary using the numbers 00, 01, 10, and 11. There are 24
possible combinations for the DNA bases represented in
binary. However, only eight satisfy the Watson-Crick
complementary rule. Table I lists these eight coding principles.
An illustration of the encoding process is as follows: Suppose a
pixel value of 90 is represented in binary as 01011010. This
number is then encoded as the AATT sequence if rule 4 is
applied. There are a different number of operations according
to the binary system. The operations used in this paper are
addition, subtraction, multiplication, XNOR, XOR, right rotate
and left rotate [10].
TABLE I. THE RULES OF DNA
Rule
1
2
3
4
5
6
7
8
A
00
00
01
01
10
10
11
11
T
11
11
10
10
01
01
00
00
C
01
10
00
11
00
11
01
10
G
10
01
11
00
11
00
10
01
III. PROPOSED CRYPTOSYSTEM APPROACH
This section will showcase the construction of our
suggested algorithm, which comprises three phases: key
generation, confusion, and diffusion. The complete layout of
our suggested algorithm is introduced in Fig. 1, and each phase
will be elaborated in further detail in the preceding subsections.
Our suggested approach is applicable to both grayscale and
color images. For a color image with a size of MxNx3, the
three colors are separated into three matrices with an M x N
size, and each matrix is processed as a plain image.
A. Key Generation
The immunity of the cryptosystem to various attacks is
based on producing a solid key. The suggested algorithm
employs the hash functions and chaotic sequence to generate
the encryption key. The hash function has the advantage of its
irreversibility and is a one-time pad key, while the chaos is
characterized by randomness and unpredictability.
We chose to use MD5 and SHA-256 as the hash functions.
The MD5 is faster than the SHA-256, but the SHA-256 is more
complex than MD5. A hash value is generated based on
combining the original image and a random user-specified key.
Generating the key from the original image enables the system
to withstand chosen/known-plaintext attacks. The final key
value, consists of 32 bits decimal.
The final key is used to generate the second input of DNA
operation using the hyperchaotic map, Eq. (11)-(14). To
enhance the approach's resistance to brute force attacks, we
opted for the hyperchaotic map, which offers a large key space.
The hyperchaotic initial values are calculated according to Eq.
(15)-(18) and utilizing the final key, . The matrix M x N
constitutes the representation of the second input, possessing
identical dimensions to those of the original image.
Fig. 1. The proposed image encryption approach's block diagram.
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(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
Where is XOR between the generated hash value and the
initial secret key.
B. Confusion Stage
This stage aims to change the pixel locations. Two
alternatives were presented to achieve this goal: either process
each pixel across the entire image or partition the image into
blocks and rearrange the position of pixels within each block.
The option number is calculated by Eq. (19), where y is
determined from Duffing chaos in Eq. (9) and (10). Eq. (20)-
(23) are utilized to compute the Duffing map's initial values
and control parameters.
(19)
(20)
(21)
(22)
(23)
If the option number is one, we will change the pixel
locations on the image's level depending on two chaotic
systems: Arnold and Henon maps. The first step is to convert
the original location, i and j, of each pixel to and locations
using Henon, as shown in Eq. (24) and (25). The final
locations, and , are generated using Arnold chaotic using
the generated locations from the previous step, as illustrated in
Eq. (26) and (27).
(24)
(25)
(26)
(27)
The other alternative is to modify the pixel location at the
block level. The initial step involves partitioning the image into
four blocks and shuffling their positions. Then, the pixel
location within the block is rearranged by applying the same
procedures as in the first method.
C. Diffusion Stage
The confusion stage alone did not meet the encryption
security requirements, necessitating the addition of a diffusion
stage. The diffusion stage effectively conceals the original
image information and increases attack resistance. In our
proposed system, this stage consists of two steps, DNA and
RSA, to offer more security to the cryptosystem.
1) DNA: In the DNA step, the encryption algorithm
converts each pixel into its corresponding binary
representation. Then, every pair of bits is substituted with a
DNA sequence of four bases based on one of the eight DNA
encoding rules shown in Table I. The DNA rule choice is
made dynamically and calculated from Eq. (28), depending on
the quantum map. The generated key is employed to obtain
the quantum sequence's initial values, as shown in Eq. (29)-
(31). The number of the generated quantum sequences equals
the number of pixels to confuse the attacker, which rule is
chosen and makes the cryptographic system unpredictable.
Unlike the previous research, we did not replace the adjacent
bits in each pixel; instead, we constitute a pair from the bit i
and bit i+2, not i+1. (28)
(29)
(30)
(
(32)
An illustration of the encoding process is as follows:
Suppose a pixel value of 90 is represented in binary as
01011010. This number is then encoded using rule 4 as the
GCCG sequence, not AATT. Here, the first A is determined
using the first and third bit, which gives pair 11, equivalent to
A according to rule 4.
After the encoding step, we apply a DNA operation on the
encoded DNA sequence and the generated input from the
previous stage to obtain another DNA sequence. The DNA
operation,, is selected based on the quantum sequence, as
shown in Eq. (32). Finally, we perform the DNA decoding,
which is the encoding reverse. The DNA sequence is converted
to its equivalent binary using the rules in Table I. The rule is
selected according to the quantum sequence shown in Eq. (28).
The corresponding binary bits are reordered in odd and even
positions, not as successive bits. For example, if the sequence
is ATCG and the used rule is 8, the binary equivalent is
11001001, then it is reordered to 10101001. Finally, the
decimal equivalent of the binary number is produced to use as
the input of the RSA step.
2) RSA: The RSA step involves generating random prime
numbers p and q using a Logistic chaotic map. The public and
private keys are then calculated based on the result generated
from the Logistic chaotic map, as shown in Algorithm (1).
Afterwards, image encryption is achieved using the public
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key, and decryption using the private key is illustrated in
Algorithm (2).
Algorithm (1) Public and private key generation
Input: The prime numbers (p, q)
Output: Public key (PU), Private key (PR)
x=q*p
⏀(x)=(q-1)*(p-1)
Choose e in condition that 1<e<⏀(x) and gcd(⏀(x),e)=1
d ≡ e-1 (mod(⏀(x))
PU= {x,e}
PR={x,d}
Algorithm (2) Encryption/Decryption of the image
Input: Public key (PU), Private key (PR)
Output: Cipher image (C), Plain image(P)
C=Pe mod x
P=Cd mod x
D. Image Decryption
In the decryption phase, the encrypted image is converted
back to its initial form, and the decrypted image reproduces the
original image. This process follows a pattern inverse to that of
encryption. The encrypted image first undergoes the diffusion
phase, utilizing RSA followed by DNA techniques. Next, it
enters the confusion phase, where Arnold and Henon chaotic
maps are used, and the key generated from chaotic and hash
functions, MD5 and SHA-256, is applied. The final output of
this process is the original image.
IV. EXPERIMENTAL RESULTS AND ANALYSIS
The effectiveness and robustness of the suggested
algorithm through various security tests are demonstrated in
this section. Using MATLAB R2021a, the algorithm was
simulated on a computer with an Intel(R) Core (TM) i5-6200U
CPU @ 2.3GHz 2.4GHz and 8 GB of memory. There are
different colors and grey images with different sizes utilized
for testing. The grey images used in testing are Male 1024
x1024, Lena 512x512, Barbara 512x512, Lake 512x512,
Cameraman 256x256, and Kitten 256x256. The color images
are Shreveport 1024x1024, Lena 512x512, Baboon 512x512,
Lena 256x256, and Couple 256x256. Most of the images used
in the study were sourced from the USC-SIPI database.
Illustrations depicting the plaintext, cipher, and decrypted
images are presented in Fig. 2 and Fig. 3 (a, c, and e). The right
keys can be utilized to restore all images during the decryption
tests. Any change in the secret keys, even if slight, leads to
incorrect image decrypting, as will be proved in the following
subsections. According to [25], there are four categories to
estimate the proposed algorithm's performance.
The visual perception evaluation
This category aims to generate an uncorrelated cipher
image from the plain image. The performance metrics included
in this category are PSNR, MSE, Correlation, Entropy, and
Histogram analysis. Another test carried out within this
category is the similarity test using the SSIM performance,
which is adopted to evaluate the matching degree between the
plaintext and cipher images.
The high-performance evaluation
The goal of this category is to evaluate the diffusion
characteristics. The tests to accomplish this goal are NPCR and
UACI.
The processing time.
The strength of the cryptosystem evaluation
The cryptosystem strength is measured through key space,
key sensitivity, and attack resistance.
A. The Visual Perception Evaluation
1) Histogram analysis: The distribution of tones inside an
image, made up of pixels with various grey values, is
essential. The histogram, which can adequately depict the
amount of each pixel value, represents the tonal distribution of
an image. An image's histogram gives statistical information
that can be used to assess how strong an encryption system
stands up to statistical attacks. Any plain image's histogram is
covered by an angled or curved bar. There is much
information in this bar. Hackers can use this bar to further
their harmful goals. The cipher's task is to modify the pixel
intensity values to produce a histogram with a uniform bar
above it. Any information leaking in the image is greatly
discouraged by the histogram's uniformity of the bar.
Additionally, it intimidates hackers and prevents them from
succeeding with histogram attacks. Fig. 2 and 3(b,d) introduces
the plain and encrypted images histogram. Apparently, the
pixel distribution in cipher images is relatively uniform across
all channels, but plain images have several peaks.
2) PSNR and MSE: Several measures are used to evaluate
image quality, including PSNR and MSE, which quantify the
level of difference between the original and cipher images.
Equations (33-34) provide the mathematical expressions for
PSNR and MSE.
(33)
(34)
The maximum pixel value, represented by 8 bits, is denoted
by p = 255. The plaintext and cipher images are denoted by
O(i,j) and C(i,j). The higher MSE and lower PSNR values
determine the method's efficiency and security. Table II
presents the PSNR and MSE values for grayscale and color
image channels. As elaborated in Table II, the suggested
algorithm achieves low PSNR and high MSE values, indicating
its strong security and efficiency. Moreover, Table III
compares the suggested algorithm's performance with previous
research, pointing to its better performance relative to other
techniques concerning both PSNR and MSE.
3) SSIM: SSIM is a test used to indicate how much the
cipher image is similar to the plaintext image depending on
the amount of structural information modification of the
plaintext image. The SSIM is obtained as indicated in Eq.
(35). A decrease in the similarity index indicates a decrease in
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the match between the original and encrypted images and an
increase in the degree of changed structural information.
The calculated values of the SSIM index are introduced in
Table II. Table III shows that lower SSIM values close to zero
indicate the lower similarity of the suggested algorithm.
Moreover, the suggested algorithm gives better results than the
other research, meaning the proposed algorithm offers less
similarity to the other research, as indicated in Table III.
(35)
Where the and are the original and cipher images
mean. and are the plaintext and cipher image variance.
The original and cipher images covariance is denoted by .
L is set to 255, while and are set to 0.01 and 0.03,
respectively.
(a)
(b)
(c)
(d)
(e)
Fig. 2. The results of grayscale images (a) plain image (b) plain image histogram (c) cipher image (d)) cipher image histogram (e) decrypted image.
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(a)
(b)
(c)
(d)
(e)
Fig. 3. The results of color images (a) plain image (b) plain image histogram (c) cipher image (d)) cipher image histogram (e) decrypted image.
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TABLE II. THE MSE, PSNR, MAE, AND SSIM PERFORMANCE
Image
Color
MSE
PSNR
SSIM
Male 1024 x1024
Grey
10475
7.9293
0.0001
Barbara512 x 512
Grey
8589.41
8.7912
0.0002
Lake 512 x 512
Grey
10893.21
7.7592
-0.0004
Kitten 256 x256
Grey
9685.53
8.2696
0.0005
Cameraman256 x
256
Grey
11675.60
7.4580
-1.3E-05
Shreveport 1024 x
1024
R
6463.01
10.0265
0.0005
G
6151.77
10.2408
-0.0002
B
9052.82
8.5630
-0.0001
Baboon 512 x 512
R
8627.04
8.7722
0.00097
G
7902.03
9.1534
0.0006
B
9950.34
8.1524
0.0003
Lena 256 x 256
R
10666.34
7.8506
-0.0006
G
9048.21
8.5652
-0.0004
B
7025.62
9.6640
0.0030
Couple 256 x 256
R
14092.71
6.6409
-0.0007
G
15923.85
6.1103
-4.40354E-05
B
16261.35
6.0192
0.0002
4) Correlation analysis: Correlation analysis is a measure
of how closely two variables are related. In plaintext images,
adjacent pixels tend to be highly correlated, which can be
utilized to attack the image. If the neighboring pixels
correlation is excessively high, it makes it easier for attackers
to predict the next pixel value. By breaking the correlation
between pixels, statistical attacks can be prevented. As the
correlation between pixels approaches zero, it becomes
progressively more challenging for a potential attacker to
deduce any insights into the original plaintext image. The
correlation values mathematical formulas in three directions
are computed by Eq. (36). In Table IV, the correlation
coefficients between the original and cipher images are
depicted for all three directions. As depicted in the table, the
original image coefficients are near one, meaning a solid
correlation between pixels.
(36)
Where the pixel total number is denoted by N, the values of
the neighboring pair are x and y. The variance, mean, and
covariance are V(x), E(x), and Cov(x,y), respectively.
The correlation values within the encrypted images
approach zero, indicating a minimal correlation among pixels.
Moreover, Table V shows that the correlation values for the
proposed algorithm outperform the previous methods, which
satisfies our objective of minimizing the correlation. In Fig. 4,
the correlation distribution among adjacent pixels is depicted
for the three directions of the 512 x 512 color Lena image. The
figure shows the equal cipher image distribution, meaning the
correlation between pixels is low. Moreover, scrambling over
pixels on the block's level gives better results than scrambling
pixels on the image's level, as introduced in Table VI.
TABLE III. COMPARISON OF MSE, PSNR, AND SSIM
Image
Ref.
MSE
PSNR
SSIM
Grey Lena
512
Ours
9236.99
8.4755
-0.000208231
[26]
7797.7
9.2111
0.0350
R
G
B
R
G
B
R
G
B
Color Lena
512 x 152
Ours
10492.31
9218.75
7207.19
7.9221
8.4841
9.5531
0.0008
0.0005
0.0003
[26]
10,637
7.8625
0.0331
[17]
8828.6
8.6719
0.0200
TABLE IV. CORRELATION COEFFICIENTS
Image
Plaintext Image
Encrypted Image
V
H
D
V
H
D
Male
Grey
0.9813
0.9774
0.9671
-0.0002
-0.0003
-0.0008
Barbara
0.9589
0.8954
0.8830
0.0021
-0.0002
-0.0004
Lake
0.9679
0.9545
0.9395
-0.0001
-0.00056
0.0012
Kitten
0.9228
0.9505
0.8840
-0.00095
-0.0031
-5.6E-05
Cameraman
0.9549
0.9196
0.8962
-0.0015
0.0033
-0.0078
Shreveport
R
0.8231
0.8295
0.7621
-0.00086
-1.34999E-05
0.00046
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G
0.8207
0.8245
0.7621
0.0006
-0.0002
0.0004
B
0.8617
0.8646
0.8188
-0.00057
0.00086
0.0002
Baboon
R
0.8595
0.9105
0.8474
-0.0001
-0.0003
0.0001
G
0.7755
0.8594
0.7434
0.0004
0.00075
0.0037
B
0.8697
0.8953
0.8296
0.0007
-0.0006
-0.0013
Couple
R
0.9562
0.9493
0.9176
0.00099
0.0005
0.0084
G
0.9534
0.9308
0.9002
-0.0058
-9.03962E-05
0.0023
B
0.9442
0.9178
0.8880
-0.0004
-0.0053
-0.0001
TABLE V. COMPARISON OF CORRELATION COEFFICIENTS
V
H
D
Grey Lena
512 x 512
Ours
0.0001
-0.0004
0.0014
[26]
−0.0113
−0.0215
0.0089
[18]
0.0014
-0.0011
s0.0043
R
G
B
R
G
B
R
G
B
Color Lena
512 x 512
Ours
-0.0009
0.0006
0.00002
-0.00007
0.0007
0.0014
0.0002
0.0006
0.0029
[26]
−0.0027
0.0007
−0.0104
[17]
0.0197
-0.0043
0.0032
Color Lena
256
Ours
0.0004
0.0003
-0.0048
0.0004
0.0036
0.0033
0.0004
0.0012
-0.0006
[11]
0.0098
0.0000
-0.0004
-0.0044
-0.0013
-0.0061
-0.0013
0.0042
-0.0093
[28]
0.0019
0.0020
-0.0025
[27]
0.003
-0.004
-0.0008
0.0003
0.001
-0.0009
0.0008
0.002
0.002
[29]
0.0063
-0.0023
0.0087
-0.0015
0.0035
0.0053
0.0043
-0.0081
0.0011
[19]
−0.0002
−0.0051
0.0016
0.0019
0.0024
0.0007
0.0008
0.0018
−0.0019
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 4. Distribution of correlation values between original and cipher images in different directions for 512 x 512 color Lena image (a) original image's horizontal
correlation (b) original image's vertical correlation (c) original image's diagonal correlation (d) cipher image's horizontal correlation (e) cipher image's vertical
correlation (f) cipher image's diagonal correlation.
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TABLE VI. COMPARISON BETWEEN THE SCRAMBLING ON THE IMAGE'S LEVEL AND THE BLOCK'S LEVEL
V
H
D
R
G
B
R
G
B
R
G
B
Grey Lena
512 x 512
Block
0.0001
-0.0004
0.0014
Pixel
0.0014
0.0015
-0.0024
Color Lena
512 x 512
Block
-0.0009
0.0006
0.00002
-0.00007
0.0007
0.0014
0.0002
0.00055
0.0029
Pixel
0.0015
-0.0024
-0.0009
-0.0009
-0.0009
-0.0013
0.00198
0.0022
-0.0006
Color Lena
256
Block
0.0004
0.0003
-0.0048
0.0004
0.0036
0.0033
0.00036
0.0012
-0.0006
Pixel
-0.008
0.0051
-0.0063
-0.0100
0.0021
-0.00085
-0.0002
-0.0038
-0.0024
5) Entropy: Entropy is a metric that indicates an image's
level of randomness and unpredictability. The entropy can be
calculated as given in Eq. (37).
(37)
Where the probability of x is P(x).
An entropy value of approximately eight is considered the
ideal value for a cipher image [30]. Table VII presents the
entropy value of the suggested algorithm, while Table VIII
compares it with the recent work. The comparison reveals that
the proposed method gives a better or similar result than the
recent work, which satisfies our goal of maximizing the
randomness and unpredictability of the image.
TABLE VII. THE ENTROPY, NPCR, AND UACI VALUES FOR THE
SUGGESTED ALGORITHM
Image
Color
Entropy
NPCR
UACI
Male
Grey
7.99985
99.60
33.58
Barbara
Grey
7.99936
99.60
33.52
Lake
Grey
7.99936
99.60
33.56
Kitten
Grey
7.99752
99.62
33.48
Cameraman
Grey
7.99785
99.60
33.48
Shreveport
R
7.99983
99.61
33.48
G
7.99984
99.61
33.52
B
7.99983
99.60
33.48
Baboon
R
7.99926
99.62
33.60
G
7.99922
99.61
33.62
B
7.99933
99.60
33.63
Couple
R
7.99715
99.62
33.57
G
7.99744
99.58
33.56
B
7.99741
99.60
33.59
B. The High-Performance Evaluation
In a differential attack, an attacker aims to uncover the
differences between encrypted images produced from two
slightly varied versions of the original image. The attacker
looks for non-random areas in the encrypted images and then
looks for changes in these areas that would conclude the key
used in image encryption. In slight alterations to the original
image, the encryption procedure produces two cipher images:
one for the original image and a second for the modified
version. If a single-bit change in the original image causes the
encrypted images to differ by at least 50%, then the differential
attack cannot decrypt the cipher images. Two performance
metrics are utilized, UACI and NPCR, to estimate the
algorithm's resistance to differential attacks. The mathematical
expressions for these two metrics are in Eq. (38) and (39).
(38)
(39)
Where and are two encrypted images of
the same original image, but only one pixel value is changed.
D(x,y) is calculated as follows:
Table VII showcases the NPCR and UACI values obtained
through the proposed algorithm, whereas Table VIII provides a
comparative evaluation of its performance against state-of-the-
art methods. The NPCR and UACI values, approaching
99.6094% and 33.4635%, respectively, are considered close to
the ideal benchmarks. The two metric values achieved by the
suggested algorithm are in close proximity to the ideal values,
demonstrating the suggested method's robustness against
differential attacks.
C. The Processing Time
Time evaluation is necessary in assessing the efficacy of
cryptographic systems, with efficient systems expected to
exhibit minimal encryption processes. To assess the time
efficiency of our suggested algorithm, we conducted time
measurements for each encryption step of the Kitten image, as
shown in Fig. 5. The most consumable time is the key
generation stage, as introduced in Fig. 5. Table IX displays a
comparison of the encryption time consumed by the suggested
approach with that of other approaches. The results show that
our suggested method gives better time encryption for Lena
with size 512. However, in the case of Lena's image with size
256, the results are higher than the two works as these works
did not treat each color channel as a separate matrix as in our
case.
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TABLE VIII. THE ENTROPY, NPCR, AND UACI COMPARISON WITH PREVIOUS WORK
Entropy
NPCR
UACI
Grey Lena
512 x 512
Ours
7.9992
99.61
33.67
[26]
7.9993
99.61
33.701
[18]
7.9994
99.61
33.47
R
G
B
R
G
B
R
G
B
Color Lena
512 x 512
Ours
7.9993
7.9992
7.9994
99.60
99.59
99.60
33.63
33.52
33.53
[13]
7.9924
99.61
33.78
[26]
7.9994
99.63
33.03
[17]
-------
99.62
30.45
Color Lena 256
Ours
7.9971
7.9973
7.9976
99.64
99.63
99.66
33.69
33.49
33.49
[11]
7.9968
7.9973
7.9974
99.60
99.61
99.61
33.53
33.38
33.67
[10]
7.9974
7.9975
7.9973
99.63
99.62
99.62
33.51
33.32
33.46
[27]
7.9892
7.9902
7.9896
99.61
32.95
[29]
7.9973
7.9973
7.9973
99.61
99.60
99.60
33.48
33.46
33.36
[19]
7.9956
7.9954
7.9962
100
100
100
33.45
33.43
33.56
TABLE IX. COMPARISON OF ENCRYPTION TIME
Our
[27]
[29]
[19]
[11]
[26]
[17]
Lena 256
2.318
4.455
0.375
0.282
Lena 512
6.968
14.966
-------
------
12.117
2.0179
80.05
Fig. 5. The execution time of each stage in the encryption approach for the
Kitten image.
D. The Strength of the Cryptosystem Evaluation
1) Key space analysis: There are different types of attacks
to obtain the original image. One type of attack that hackers
can use is Brute force, where they try to decrypt the cipher
image by employing all possible keys until the correct one is
found. A key space with a large size can be a good defense
against brute-force attacks, which refers to the entire set of
keys used for image encryption. The researchers have
determined that a minimum key space of 2100 [31] is required
to resist brute-force attacks. The image cryptosystem's secret
key was generated using 24 parameters from different chaotic
maps in the suggested method—additionally, the hash
function used 256 bits.
Following the IEEE 754 floating-point standard (double),
the substantial precision amounts to 53 bits, necessitating 15
decimal digits for representation. Consequently, the key space
of the proposed system stands at 10437, demonstrating
resilience against brute-force attacks by surpassing the
threshold of 2100.
2) Key sensitivity: A cryptosystem is considered effective
if it is extremely sensitive to keys. Key sensitivity means any
minor change in key value results in a significant change in
output. There are two ways to test key sensitivity. The first is
by making a faint change in the key value; the result should be
two different encrypted images. The other way is that the
slight change in key-value results in not retrieving the original
image correctly from the encrypted one. In this paper, we test
the key sensitivity in two ways. In the first test, we changed
the key slightly and then encrypted the plain image to get
another cipher image using two different keys. We change the
initial value of x and y in the hyperchaotic used to generate the
final key by adding to each value 10-14. The results illustrated
in Fig. 6 show the robustness of the suggested algorithm
regarding the slight change in key as parts c and e show the
difference between the cipher image generated from the valid
key and the cipher image produced from the modified keys.
The alternative approach for conducting the key sensitivity
test encompasses encrypting the original image with the
accurate key and decrypting the resulting cipher image using
an altered key. Fig. 7 illustrates the distinction between the
decrypted image derived from the correct key and the
decrypted image obtained from the two adjusted keys. The
difference between the two images proves the suggested
algorithm's high sensitivity against a minor key change. Based
on the two test results, the suggested method can resist brute-
force and statistical attacks.
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(a)
(b)
(c)
(d)
(e)
Fig. 6. Testing key sensitivity in encryption stage (a) image ciphered by the original key (b) image ciphered by the first modified key 1(x0+10-14) (c) difference
between a and b (d) image ciphered by the second modified key 2(y0+10-14) (e) difference between c and d.
(a)
(b)
(c)
Fig. 7. Testing key sensitivity test in decryption (a) original image (b) decrypted image utilizing the first modified key (x0+10-14) (c) decrypted image utilizing the
second modified key (y0+10-14).
3) Classical attacks: Classical attacks include four attack
types: chosen-plaintext, known-plaintext, chosen-ciphertext
and ciphertext-only attack. The most harmful attacks are
chosen and known plaintext attacks. In these two attacks, the
attacker has access to plaintext and encrypted images and tries
to deduce the keys. If the cryptographic system can withstand
these attacks, it would be immune to the other two types.
The cryptographic system would be immune to the known
and chosen plaintext attacks if it is sensitive to the key change,
which is proved in subsection 2 of section D. Moreover, the
suggested system is a one-time pad system that utilizes the
SHA-256 function to produce the key. Another test in
measuring the immunity to the attacks of known and chosen
plaintext is to use all black and all-white images as the original,
as shown in Fig. 8( a) and (d). The corresponding cipher
images for these two images and their histogram are displayed
in Fig. 8 (b-c) and (e-f). The entropy and correlation values of
the black and white images are depicted in Table X. From the
results, the suggested algorithm shows strong immunity to the
attacks of chosen and known plaintext attacks.
4) Image processing attacks resistance: During
transmission, the cipher image may be exposed to several
disruptions, and some attacks on cipher images will result in
data loss. The decryption of a corrupted cipher image may
thus lead to distorted or even unnoticeable results. The most
famous image processing attacks are data and noise loss
attacks. Minimizing the impact of data and noise loss attacks
on the restored image is crucial for achieving an efficient
image encryption algorithm.
The effectiveness of the proposed algorithm in
withstanding noise attacks was assessed by introducing various
levels of salt and pepper noise (0.5, 0.05, and 0.005) and then
calculating the PSNR values between the original images and
their decrypted counterparts. The results, presented in
Table XI, affirm that the proposed algorithm effectively resists
salt and pepper attacks.
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 8. Classical attack test(a-c) black image, its cipher, and its cipher
histogram (d-f) white image, its cipher, and its cipher histogram.
TABLE X. THE ENTROPY AND CORRELATION OF THE WHITE AND BLACK
IMAGES
image
Entropy
Correlation
V
H
D
White
plain
-0.000000
-
-
-
cipher
7.9993
-0.00005
-0.0034
-0.00199
Black
plain
0.0012
-
-
-
cipher
7.99938
0.00088
0.0011
-0.0033
Furthermore, the algorithm's ability to withstand occlusion
attacks was assessed by applying varying masks to the cipher
images (1/16, 1/8, and 1/4). The decrypted images resulting
from this masking process are displayed in Table XI,
showcasing the algorithm's robustness against cropping attacks.
Despite occlusion attempts, the algorithm demonstrates its
capability to recover a portion of the image's information.
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TABLE XI. THE PSNR VALUE OF THE PLAINTEXT IMAGES AND THEIR
DECRYPTED IMAGES AFTER APPLYING NOISE AND DATA LOSS ATTACKS
Attack
Parameters
PSNR
R
G
B
Salt and pepper
0.005
27.3081
27.8380
27.8922
0.05
20.3436
20.8994
21.9327
0.5
10.8365
11.5345
12.5723
Cropping
1/16
19.1520
20.9261
21.9408
1/8
16.3463
17.9376
18.8688
1/4
13.4978
14.8659
15.8419
V. CONCLUSION
The suggested technique in this paper employs DNA, RSA,
and chaotic maps to produce an extremely robust and secure
image encryption method. The approach encompasses three
phases: key generation, confusion, and diffusion. The hash
function and hyperchaotic are used to generate a robust key as
the hash function is a one-time pad and chaotic produces
unpredictable and random numbers. The suggested algorithm
uses the original image and a user-defined key to generate the
encryption key, thereby preventing the chosen/known-plaintext
attack. In the confusion phase, there are two options to change
the pixel's locations, either changing the location on the
image's level or the block's level based on the Duffing map.
After that, each pixel is subjected to two consecutive confusion
steps: Henon and Arnold map. In the diffusion phase, the
confusion phase output undergoes two successive diffusion
steps: DNA followed by RSA cryptography. Using two steps in
each phase maximizes the security and unpredictability of the
suggested approach. Moreover, the suggested approach can
withstand different attacks. Various security tests demonstrate
the approach's effectiveness in withstanding attacks and
achieving low correlation between neighboring pixels.
In future research, we will explore multi-model image
encryption by combining color, texture, and depth data.
Additionally, we aim to integrate machine learning techniques
to optimize encryption parameters and enhance security.
Another priority is reducing encryption time.
Use of AI tools declaration: The authors have not used
Artificial Intelligence (AI) tools in creating this article.
Funding Statement: The authors received no specific
funding for this study.
Conflicts of Interest: The authors declare no conflicts of
interest to report regarding the present study.
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