mathematics-11-01769

mathematics
Article
Neural Attractor-Based Adaptive Key Generator with DNA-Coded
Security and Privacy Framework for Multimedia Data in
Cloud Environments
Hemalatha Mahalingam 1 , Padmapriya Velupillai Meikandan 2 , Karuppuswamy Thenmozhi 3 ,
Kawthar Mostafa Moria 4 , Chandrasekaran Lakshmi 3 , Nithya Chidambaram 3, * and Rengarajan Amirtharajan 3, *
1
2
3
4
*
Citation: Mahalingam, H.; Velupillai
Meikandan, P.; Thenmozhi, K.;
Moria, K.M.; Lakshmi, C.;
Chidambaram, N.; Amirtharajan, R.
Neural Attractor-Based Adaptive
Key Generator with DNA-Coded
Security and Privacy Framework for
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University,
Jeddah 22254, Saudi Arabia; [email protected]
Department of Computer Sciences, Marquette University, Milwaukee, WI 53233, USA;
[email protected]
School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur 613401, India;
[email protected] (K.T.); [email protected] (C.L.)
Department of Computer Science, Faculty of Computing and Information Technology, King Abdulaziz University,
Jeddah 22254, Saudi Arabia
Correspondence: [email protected] (N.C.); [email protected] (R.A.)
Abstract: Cloud services offer doctors and data scientists access to medical data from multiple
locations using different devices (laptops, desktops, tablets, smartphones, etc.). Therefore, cyber
threats to medical data at rest, in transit and when used by applications need to be pinpointed and
prevented preemptively through a host of proven cryptographical solutions. The presented work
integrates adaptive key generation, neural-based confusion and non-XOR, namely DNA diffusion,
which offers a more extensive and unique key, adaptive confusion and unpredictable diffusion
algorithm. Only authenticated users can store this encrypted image in cloud storage. The proposed
security framework uses logistics, tent maps and adaptive key generation modules. The adaptive key
is generated using a multilayer and nonlinear neural network from every input plain image. The
Hopfield neural network (HNN) is a recurrent temporal network that updates learning with every
plain image. We have taken Amazon Web Services (AWS) and Simple Storage Service (S3) to store
encrypted images. Using benchmark evolution metrics, the ability of image encryption is validated
against brute force and statistical attacks, and encryption quality analysis is also made. Thus, it is
proved that the proposed scheme is well suited for hosting cloud storage for secure images.
Multimedia Data in Cloud
Environments. Mathematics 2023, 11,
1769. https://doi.org/10.3390/
Keywords: chaos key generator; adaptive key generator; DNA encoding; image ciphering; neural
networks; cloud storage
math11081769
Academic Editor: Catalin Stoean
MSC: 94A60
Received: 8 March 2023
Revised: 30 March 2023
Accepted: 3 April 2023
1. Introduction
Published: 7 April 2023
In recent decades, the world of computing has grown tremendously. The revolution
in modern gadgets is completely rebuilding information sharing and storing in the public
sector. In reflection, the security and privacy of information sharing have become a challenge [1]. Additionally, the incremental impact of data storage platforms such as cloud [1],
fog [2], edge [3], etc., has led to development in the field of information technology (IT).
The rapid increase in Internet of Things-centric engineering applications also demands
platforms such as cloud and edge [4,5]. However, information security is a significant
concern during transit, and the rest of the multimedia data are shared in the public domain.
Confidentiality, integrity, authentication and nonrepudiation are security components that
structure the security solutions to share and store multimedia data. The cloud paradigm
has recently enabled worldwide organisations to host and run their business applications
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Mathematics 2023, 11, 1769. https://doi.org/10.3390/math11081769
https://www.mdpi.com/journal/mathematics
Mathematics 2023, 11, 1769
2 of 23
and IT services in cloud environments (public, private and hybrid). The consistent growth
of the cloud paradigm makes it a cornerstone for efficient and affordable multimedia data
storage for various applications. Owing to the multitenant nature of the cloud, addressing
the security and privacy concerns of multimedia data is essential. Authentication is one
solution to ensure the tightest security for confidential and customer data. Images are
a significant segment of multimedia data. Multimedia data are captured and transmitted to
geographically distributed cloud environments. One such solution is proven and potential
image encryption.
Cloud computing plays a commendable role in shaping the IT infrastructure [6]. Cloud
computing is the consolidated, centralised/federated, automated and shared computing
model representing IT industrialisation. Due to the shared environment, anybody can
access cloud services globally to host their data. The pay-per-usage model has created
a string of newer possibilities and opportunities for business houses, IT service providers,
governments and other establishments across the globe.
The cloud environment offers infrastructure, a platform and storage as a service.
Storage is the superior service and backbone for e-commerce and online finance applications
(e.g., Salesforce CRM and Netflix) [7]. However, security and privacy are unbeatable
challenges for the cloud storage environment, particularly for images as multimedia data.
In addition, tamper resistance and data protection are significant challenges [8]. The
new shape for image encryption schemes is vital in this concern. Ciphering images is
the solution to protect the images in the public cloud storage area. The art of the image
encryption approach is to make the image unreadable by unauthorised users. Due to the
uniqueness of the image, such as high correlation among neighbouring pixels, conventional
crypto solutions cannot be advised for image ciphering [9].
Chaos theory supports image encryption to break neighbouring pixels’ correlation
after encryption. Chaotic maps [10], attractors [11], etc. have specific properties such
as periodicity, greater keyspace, sensitivity to initial parameters, etc. [12], which played
a commendable role in the substitution and transposition process of image encryption [13].
Ponuma et al. proposed compressive sensing-based image encryption with the key matrix
generated from the chaotic measurement approach [14].
2. Related Works
The confusion process using a chaotic Arnold’s cat map (ACM) has a flaw: the specific
number of rotations fetches the original image again [15]. Along with ACM, the diffusion
process using chaotic nature keys increases impulsiveness [16]. Belazi et al. proposed
a new 1D map for a permutation-substitution network attained through chaotic linear fractional transformation (LFT) along with the interleaved diffusion process [17]. Huang et al.
suggested plain image-dependent encryption through N-dimensional chaotic maps [18].
Broumandnia experimented with image ciphering using multidimensional nonlinear chaos
equations to enhance the keyspace [19]. Finally, Chen et al. proposed an image ciphering
technique which tolerates brute-force attacks. Nonlinear fractional Tchebyshev moments
are used to achieve the fractal permutation to enrich the security level of a colour image [20].
DNA blended image encryption has become a remarkable strategy for data privacy [21]. Substitution rules of DNA coding agree that chaos offers better diffusion in
image encryption, which increases the keyspace and entropy, and the correlation results
are meagre [22]. Hu et al. suggested a spatiotemporal chaos system constructed using
a logistic-sine system (LSS) in the coupled map lattice (CML) for diffusion and DNA-based
shuffling in the encryption process and obtained good entropy [23]. Chai et al. experimented with the DNA blended chaos-based grey image encryption where 1D chaotic
maps and cipher block chaining approaches are used to obtain near-zero correlation
and maximum entropy [24]. Enayatifar et al. proposed DNA XORing for diffusing the
image followed by confusion through three-dimensional logistic maps. Still, the diagonal
correlation of the encrypted image is near zero compared to the vertical and horizontal correlation of the same. Additionally, the entropy value needs to be improved [25].
Mathematics 2023, 11, 1769
3 of 23
A multidimensional hyperchaotic system generates the random key for colour image
encryption blended with a DNA-based diffusion process at block and bit levels [26,27].
Wenjie et al. experimented with plaintext-specific key generation for image encryption.
The SHA-512 hash value is generated for every plain image as a random key for bit-level
scrambling and diffusion [28]. Pavithran et al. suggested DNA-based image encryption
using a hyperchaotic key generator [29]. Yousif et al. experimented with an image encryption algorithm comprising bit-level permutation and diffusion using DNA addition to
improve the resistivity against known attacks in the cryptosystem [30].
Qin et al. suggested a fully homomorphic encryption (FHE) scheme for image encryption linked with cloud storage where complexity and overhead are very high, even for
small images [31]. Chidambaram et al. proposed the DNA blended chaos-based image
encryption to offer a secure image repository in the public cloud. Due to coupled chaos
and cipher block chaining approaches, the image entropy after encryption was increased,
but the keyspace was small, which may not be entertained [32].
Zhang et al. proposed an image encryption algorithm for the Internet of Multimedia
Things (IoMT), a combination of Arnold transform-based scrambling followed by XORbased diffusion using the key generated through cascade chaotic maps [33]. The neuralbased works have concluded that it is well suited for all images, namely grey, colour and
medical images, which are more feasible for cloud-based storage. In cloud storage, the user
is not restricted from uploading these types of images. In addition, neural-based works
contribute metrics equivalent to the chaos and attractors [34–37].
It is observed from the literature that the image encryption approaches [38–53] linked
with cloud storage have become essential, and there are few such algorithms in the literature.
Utility-specific algorithms to offer multimedia security to cloud storage demand cloud
computing. This proposed algorithm can be a solution for secure image storage in the
public cloud network. This security framework experimented with DNA coding blended
with chaotic maps to cipher grey images before storing them in a public repository. Any
authenticated user can download the decrypted image from the cloud. Later, with the
valid keys, the image is decrypted to attain the original image, with confidentiality and
authentication. The proposed algorithm is an enhanced approach for managing cloud
repositories with utmost image security.
From the survey, offering security for sharing information in the public domain is
essential. The uniqueness of the proposed encryption scheme has been enriched with
adaptive key generation and chaos key generation for image encryption. As all multimedia
data are unique, including their dimensions, value range, nature of the value, properties
of the data, randomness and redundancy, at the same time, the key should be random,
and it should not be predicted easily. With consideration, the proposed scheme has been
inaugurated with adaptive key generation using the back propagation neural (BPN) model,
which should be a supervised learning model. As the input of the neural network should be
extracted from the features of the multimedia data, such as images and outputs, the initial
seed has limited chaotic range. Future prediction is an inherent property of the artificial
neural network. The BPN model includes precise selection for the adaptive key generation;
during the training, BPN can learn about the randomness and redundancy nature of the
image from the extracted image features. After the training, BPN can adapt to any image,
producing the adaptive key. The proposed security framework mainly focuses on securely
sharing and storing images in the cloud. The significant contributions of the proposed
solution are:
1.
2.
3.
4.
5.
6.
Neural–DNA–chaos permutation-based image encryption.
Adaptive key generation based on plain image.
Neural-based confusion of grey image.
Establishment of a public cloud interface with the security framework.
Validation of user authenticity to access the cloud-ciphered image.
Improved protection for image sharing in multimedia communication.
Mathematics 2023, 11, 1769
4 of 23
3. Pre-Requisites
3.1. DNA Approach
Nucleic acid bases A (adenine), C (cytosine), G (guanine) and T (thymine) form a DNA
sequence. It produces a DNA-coded value for every two-bit binary value, i.e., 00, 01, 10, 11.
Based on Watson and Crick’s complementary rule, A complements T and G complements
C. Thus, the possible combinations of DNA coding and operations result in 24 DNA rules
in which only 8 rules are appropriate for image encryption, as shown in Table 1.
Table 1. DNA encoding rules.
Binary Stream (DNA Rules)
00
01
10
11
I
II
III
IV
V
VI
VII
VIII
A
A
T
T
C
C
G
G
C
G
G
C
A
T
A
T
G
C
C
G
T
A
T
A
T
T
A
A
G
G
C
C
In DNA space, addition, subtraction and XORing operations are carried out to offer
diffusion. DNA XORing reflects the binary XOR operation rule in DNA space. DNA
addition and subtraction are performed as follows:
DNAX(OUT) = mod((DNAX(IN1) + DNAX(IN2)), 4)
DNAX(OUT) = DNAX(IN1) − DNAX(IN2); if DNAX(IN1) − DNAX(IN2)
= (4 + DNAX(IN1)) − DNAX(IN2); else
DNAX(OUT) is the output DNA value in the ruleset X after addition/subtraction.
DNAX(IN1) and DNAX(IN2) are the input values in DNA space at the rule set X.
3.2. Chaotic System
The chaotic system offers a good impact in ciphering the images due to its properties
of ergodicity, keyspace and chaotic behaviour. The proposed work used 1D logistic and
tent chaotic maps. The initial parameters for the chaotic maps X0 and Y0 vary from 0 to
1. The control parameter for the 1D logistic map is 3.57 ≤ α ≤ 4 and, for the tent map,
2 ≤ µ ≤ 4. The chaotic equations for a 1D logistic map and tent map are expressed through
(1) and (2).
F (α, Xn+1 ) = (α × Xn ) × (1 − Xn )
(1)
 
 µYn ; Yn < 0.5


2
F (µ, Yn+1 ) =
 µ(1 − Yn )


; Yn ≥ 0.5

2
(2)
The Suitability of Chaotic Sequences for the Image Encryption Algorithm
The chaotic system consistently exhibits disordered behaviour due to chaos properties.
In addition, it shows a direct relation with properties expected for cryptographic functions,
namely confusion and diffusion [38]. Even if there is a slight change in the initial condition
value, the chaos sequences will diverge to the extreme after some iteration. The ergodicity
property in the diverged sequences will give uncorrelated neighbouring values, making the
chaos system genuinely dynamic. Regarding the property of sensitivity to initial condition
value, two very close initial condition values, such as 0.949 and 0.950, have been taken as
input and iterated 20 times, as illustrated in Figure 1.
condition value, the chaos sequences will diverge to the extreme after some iteration. The
ergodicity property in the diverged sequences will give uncorrelated neighbouring values, making the chaos system genuinely dynamic. Regarding the property of sensitivity
to initial condition value, two very close initial condition values, such as 0.949
and
5 of
23 0.950,
have been taken as input and iterated 20 times, as illustrated in Figure 1.
Mathematics 2023, 11, 1769
Chaotic values
Random series for two different initial conditions
Initial condition = 0.949
Initial condition = 0.950
Iterations
Figure 1.
Random
series for
two for
different
initial conditions.
Figure
1. Random
series
two different
initial conditions.
3.3. Hyperchaotic HNN
3.3. Hyperchaotic HNN
The presented work employed a four-node HNN. All the nodes are interconnected
The presented work employed a four-node HNN. All the nodes are interconnected
with all others, along with self-connection. Every node produces the output based on its
with all others, along with self-connection. Every node produces the output based on its
previous state and the external bias input. The connection paths between the nodes are
previous state and the external bias input. The connection paths between the nodes are
weighted, and the updated weights depend on the Hebb rule with a hyperbolic activation
weighted, and the updated weights depend on the Hebb rule with a hyperbolic activation
function, which exhibits the desired chaotic behaviour. Since the proposed HNN has four
function, which exhibits the desired chaotic behaviour. Since the proposed HNN has four
nodes, there are 16 weight values, namely W1 –W16 (3).
nodes, there are 16 weight values, namely W1–W16 (3).


w1 w2 w3 w4
w
w4 


w w
 w5 w61 w7 2 w8  3


Wij = 
(3)
 w ww w w

w8 
105
11 6 12  7
 w9 w


(3)
Wijw=
13 w14 w15 w16
 w 9 w 10 w 11 w 12 
 compared to the
Converged weight values decide the accuracy of obtained output
w
w
w
w

 integer/floating
13
14
15
16
actual output. Based on the activation function, the weight values can be
decimal values.
The HNN
generates
random
sequences
chaoticoutput
behaviour
using to the
Converged
weight
values decide
the
accuracy with
of obtained
compared
Equations
(4)
and
(5).
actual output. Based on the activation function, the weight values can be integer/floating
4
decimal values. The HNNx generates
random sequences with chaotic behaviour
(4) using
i+1 = −ci xi + ∑ wij vj
Equations (4) and (5).
j=1
vix= tanh
= −(xci )x
i +1
i
4
i
+  w ij v j
j=1
(5)
(4)
where Ci is constant and C1 = C2 = C3 = 1; C4 = 100; Xi is the previous state and wij is the
weight matrix.
vi = tanh (xi )
(5)
Nonlinearity analysis of HNN
The proposed hyperchaotic HNN weight matrix is given below:
where Ci is constant and C1 = C2 = C3 = 1; C4 = 100; Xi is the previous state and wij is the


weight matrix.
1
0.5
−3 −1
Nonlinearity analysis ofHNN

 0 2+p 3
0 
The proposed hyperchaotic
HNN weight matrix
 is given below:
wij = 
 3
−3
1
0 


100
0
0 170
where p is the control parameter.
 3
100

−3
1
0
0
0 
170
where p is the control parameter.
6 of 23
The weight matrix must be asymmetrical, and the control parameter p = 0.3 is fixed
to achieve the chaotic behaviour. With control parameter p = 0.3, the chaotic behaviour is
The weight matrix must be asymmetrical, and the control parameter p = 0.3 is fixed
depicted using Figure
2. The chaotic behaviour shown in Figure 2 depends on the initial
to achieve the chaotic behaviour. With control parameter p = 0.3, the chaotic behaviour is
seed Xi, weight values
andusing
theFigure
control
parameter
p. shown in Figure 2 depends on the initial
depicted
2. The
chaotic behaviour
Mathematics 2023, 11, 1769
seed Xi , weight values and the control parameter p.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 2. Chaotic
behaviour
with
p = 0.3.
(a–c) Between
nodes
all other
three
nodes.
Figure 2. Chaotic behaviour
of HNN
withofpHNN
= 0.3.
(a–c)
Between
nodes
X1Xand
other
three
1 andall
(d,e) Between nodes X2 with X3 and X4 . (f) Between nodes X3 and X4 .
nodes. (d & e) Between
nodes X2 with X3 and X4. (f) Between nodes X3 and X4.
4. Proposed Approach
4. Proposed ApproachThe proposed approach consists of transposition followed by two DNA-based diffusion
process stages. For the confusion and diffusion processes, keys are vital. In this proposed
The proposedframework,
approach
consists
of transposition
followed
bythetwo
diffutwo
key generator
modules are available
to generate
keys,DNA-based
which are random
is to changeand
the pixels’
positionprocesses,
in an image, and
theare
othervital.
is to change
the prosion process stages.sequences.
For theOne
confusion
diffusion
keys
In this
pixel’s value. A neural attractor-based key is generated specifically for the images, so no two
posed framework, non-identical
two key generator
modules are available to generate the keys, which
images have the same key for transposition. A chaotic-based key generation
are random sequences.
One
to change
pixels’
an image,
and the other is
generates
the is
random
numbersthe
through
whichposition
image pixelin
values
are diffused.
First,
the
adaptive
key
is
generated
through
neural
networks
for
the
confusion
process.
to change the pixel’s value. A neural attractor-based key is generated specifically
for the
Second, features extracted from the plain image influence the key generation. Hence,
images, so no two generated
non-identical
haveThe
the
same key
transposition.
A chaotickeys are images
image specific.
advantage
is thatfor
cryptanalysis
cannot guess
the
key without
knowing
image features
and features
unique
to theimage
images. pixel
Third, the
based key generation
generates
thethe
random
numbers
through
which
values
Hopfield neural network confuses the image irrespective of the modality or pixel intensity
are diffused.
of the plain image; the knowledge database of the confusion model is updated to the plain
First, the adaptive
isimage-specific
generated confusion
throughis carried
neuralout;
networks
for the redundancy
confusionis proimage. key
Hence,
as a result, interpixel
removed,
which
enhances
the
resistance
against
statistical
attacks.
cess. Second, features extracted from the plain image influence the key generation. Hence,
generated keys are image specific. The advantage is that cryptanalysis cannot guess the
key without knowing the image features and features unique to the images. Third, the
Hopfield neural network confuses the image irrespective of the modality or pixel intensity
of the plain image; the knowledge database of the confusion model is updated to the plain
Mathematics 2023, 11, 1769
is removed, which enhances the resistance against statistical attacks.
Adaptive key generation can be implemented with supervised learning, the BPN
model. The model training data set is considered a significant feature of the image and
required range of chaotic seeds. The proposed model enhances security using artificial
intelligence. Firstly, adaptive key generation using the BPN model and image confusion
7 of 23
with the Hopfield neural attractor are carried out. The BPN model is a multilayer feedforward architecture that can be learned through back propagating the error and with the
gradient descent method. The Hopfield neural attractor is a recurrent random auto-assokey generation
canneural
be implemented
with supervised
learning,
thethen
BPN
ciatorAdaptive
architecture.
The Hopfield
attractor is stimulated
with initial
inputs,
model.
Theremoved
model training
data set is
considered
feature
of the
image
and
inputs are
and the attractor
moves
towardsa asignificant
stable state.
With the
initial
input,
required
range
of chaotic
seeds.
proposed
enhances security
artificial
the Hopfield
neural
attractor
has The
a finite
numbermodel
of pseudo-random
states.using
The pseudointelligence.
key process
generation
using the
model
and image
confurandom statesFirstly,
govern adaptive
the confusion
adaptively.
TheBPN
proposed
method
is a hybrid
sion
with the
Hopfield
attractor
are carried out.
The
BPN model
is a multilayer
technique
which
creates neural
artificial
intelligence-assisted
DNA
blended
security.
feedforward
that can
be block
learned
through
backpixels
propagating
the error
and
Diffusionarchitecture
stages are called
cipher
chaining,
where
are ciphered
sequenwith
method.
The
Hopfield
attractor
a recurrent
random
tially.the
Thegradient
diffusiondescent
operation
uses the
random
keysneural
generated
by theischaos
key generator.
auto-associator
architecture.
Theinto
Hopfield
neural
is in
stimulated
with
initial
inputs,
The encrypted image
is pushed
a storage
areaattractor
available
the public
cloud
environthen
areberemoved
theoriginal
attractor
moves
a stablekey(s).
state. With
the initial
mentinputs
and can
retrievedand
as the
only
withtowards
the encryption
The proposed
input,
the Hopfield
neural
attractor
a finite
number
pseudo-random
framework
establishes
secure
storage has
of grey
images
in theofcloud,
as shown instates.
FigureThe
3.
pseudo-random
states govern
the confusion
process adaptively.
proposed
method
The proposed security
framework
for the cloud-based
grey imageThe
repository
consists
ofis
avarious
hybridphases
technique
which
creates
artificial
intelligence-assisted
DNA blended security.
in the
image
encryption
process,
namely,
Diffusion
stages are
cipher block chaining, where pixels are ciphered sequenPhase I: Adaptive
keycalled
generator.
tially.Phase
The diffusion
uses the random keys generated by the chaos key generator.
II: Chaosoperation
key generator.
The encrypted
image is neural
pushednetwork-based
into a storageconfusion
area available
in the public cloud environPhase III: Hopfield
process.
mentPhase
and can
retrieved
the original only
with the
encryption key(s). The proposed
IV: be
Cipher
blockas
chaining-based
diffusion
process.
framework
establishes
grey images
in the cloud, as shown in Figure 3.
Phase V:
Interfacingsecure
cloudstorage
and theof
security
framework.
The proposed
framework for theblock
cloud-based
image repository consists of
Phase VI: security
Image decryption—cipher
chaining grey
process.
various
phases
the image
encryption process, namely,
Phase
VII: in
Image
decryption—Hopfield-based
reassembling.
Figure
Proposed Security
Security Framework.
Framework.
Figure 3.
3. Proposed
Phase I: Adaptive key generator.
4.1. Image Ciphering and Deciphering Process
Phase II: Chaos key generator.
The various
phases neural
incorporated
in the image
ciphering
and deciphering process are
Phase
III: Hopfield
network-based
confusion
process.
givenPhase
below:
IV: Cipher block chaining-based diffusion process.
Phase V: Interfacing cloud and the security framework.
Phase VI: Image decryption—cipher block chaining process.
Phase VII: Image decryption—Hopfield-based reassembling.
4.1. Image Ciphering and Deciphering Process
The various phases incorporated in the image ciphering and deciphering process are
given as Algorithms 1–4 below:
Mathematics 2023, 11, 1769
8 of 23
Algorithm 1: Adaptive random sequence generation using discrete Hopfield attractor
Input: Multiplicative identity matrix (B)[4,4] , sampling rate Tw , random initiator h[1,4]
Output: Nonlinear random sequence Ω
Initialise wij ← [w w/2 σ − w; Ψ 2w 3w 0; 3w φ w 0; mw 0 0 nw] ← [1 0.5 −5 −1; −0.37 2 3 0; 3
−13 1 0; 100 0 0 170]
Update the wij with new σ, Ψ, φ
Get H(0) ← [h]T
Repeat
f ( H (r )) = tanhH (r )H(r + 1) = (1 − BTw ) H(r ) + Tw w f (H(r ))
Dh = |(H(r + 1) − b |H(r + 1)| c ) |
Set r ← r + 1
Until r ≤ (Image size/4)
Initialise Ω ← {}
for f ← 1 to 16,384
for i ← 1 to 4
Ω ((4 × (f − 1)) + i) = Dh(i)
end
end
Return (Ω)
Algorithm 2: Chaos key generator
Input: Initial parameters (KLD (0), KT (0)) control parameters (γ, µ) and image size N
3.4 ≤ α2 ≤ 4; 0 ≤ γ ≤ 2; 0 ≤ KLD (0) and KT (0) ≤ 1
Output: Chaos sequence KLDM and KTM as key for size N and DNA rule selectors R1 , R2
1D tent map-based sequence as key for Diffusion I
Initialise KTM = { }; θ = 1/2
for i ← 1 to N do
if KT (i − 1) ≥ θ then Set KT (i) ← (µ × (1 − KT (i − 1)))
else Set KT (i) ← (µ × KT (i − 1))
Set KTM (i) ← mod (KT × 1014 , 256)
end
Return (KTM )
1D logistic map-based sequence as key for Diffusion II
Set KLD (1) ← (γ × KLD (0)) × (1 − KLD (0))
Initialise KLDM = { }
for i ← 2 to N do
Set KLD (i) ← (γ × KLD (i −1)) × (1- KLD (i − 1))
Set KLDM (i) ← mod (KLD × 1014 , 256)
end
Return (KLDM )
Algorithm 3: Image encryption—Hopfield based permutation
Input: Original image I of size (X) [M, N], Nonlinear random sequence Ω
Output: Scrambled image matrix C
Get [ R, ∀] ← sort (Ω , ‘ascend’)
where R is the ascending order of key stream Ω;
∀ is the index of the sorted key stream Ω
Repeat
Set C ( j) ← I (∀( j))
Set j ← j + 1
Until j < (M × N)
Return (C)
Mathematics 2023, 11, 1769
9 of 23
Algorithm 4: Image encryption—cipher block chaining process
Input: Shuffled image C, Key sequences KTM , KLDM , rule for DNA encoding R1 , R2 and 8-bit
secret key K1
Output: Encrypted image E
Set E(1) ← C(1) ⊕ K1
for i← 2 to N do
Cd (i) ← C(i) ⊕ E(i − 1)
Diffusion Stage I:
R
1
Set CdDNA (i) ←−
DNAEncode (Cd (i))
R
1
Set KTMDNA (i) ←−
DNAEncode (KTM (i))
Set List ← [0, 2, 4, 6]
for j ← 1 to 4 do
Set n ← List[j]
Set Cd1 (i)[n:n + 1] ← mod ((CdDNA (i) [n:n + 1] + KTMDNA (i) [n:n + 1]), 4);
end
Diffusion Stage II:
R
2
Set Cd1DNA (i)←−
DNAEncode (Cd1 (i))
R
2
Set KLDMDNA (i) ←−
DNAEncode (KLDM (i))
Set List ← [0, 2, 4, 6]
for j ← 1 to 4 do
Set n ← List[j]
Set E(i)[n:n + 1] ← Cd1DNA (i) [n:n + 1] ⊕ KLDMDNA (i) [n:n + 1]
end
end
Return (E)
The aim is to store the secure image in a public repository called the cloud. So, the
ciphered images are uploaded into the private storage area allotted by Amazon’s public
cloud, availed with access privileges and credentials. Algorithm 5 pseudo-code describes
the security framework and cloud storage interface. First, the authenticity verification
process is carried out with invalid credentials.
Algorithm 5: Authenticated cloud access process
Input: Encrypted image E of size X, login credentials of AWS, identity and access management
(IAM) key pairs
Output: Uploaded encrypted image E in the cloud storage
Set AWS login credentials: username ← “username” and password←“password”
emphSet IAM key pairs:
access key ← “AAAAAAA” and secret key ←
“SSSSSSS”
if (username = “username” && password = “password”) then
if (access key = “AAAAAAA” && secret key = “SSSSSSS”) then
captcha = randomgen (captcha) and user expect to type it on the screen
if captcha matched then
Access = “Access Granted”
Push S3: Bucket ← Encrypted images
else Return (“Invalid CAPTCHA”)
else Return (“Invalid Credentials”)
else Return (Access = “Access Denied”)
The cloud is accessed to download the ciphered images with valid credentials. Then,
the ciphered images are decrypted using the algorithms described in Algorithms 6 and 7.
Mathematics 2023, 11, 1769
10 of 23
Algorithm 6: Image decryption—cipher block chaining process
Input: Encrypted image of size (E) [M, N], key sequences KTM , KLDM , rule for DNA encoding R1 ,
R2 and 8-bit secret key K1
Output: Shuffled image C
Diffusion Stage I:
R
2
Set EDNA (i) ←−
DNAEncode (E(i))
R
2
Set KLDMDNA (i) ←−
DNAEncode (KLDM (i))
Set List ← [0, 2, 4, 6]
for j ← 1 to 4 do
Set n ← List[j]
Set Cd1 (i)[n:n + 1] ← EDNA (i) [n:n + 1] ⊕ KLDMDNA (i) [n:n + 1]
end
Diffusion Stage II:
R
1
Set Cd1DNA (i) ←−
DNAEncode (Cdi (i))
R
1
Set KTMDNA (i) ←−
DNAEncode (KTM (i))
Set List ← [0, 2, 4, 6]
for j ← 1 to 4 do
Set n ← List[j]
Set Cd (i)[n:n + 1] ← mod ((Cd1DNA (i) [n:n + 1] − KTMDNA (i) [n:n + 1]), 4)
end
Set C(1) ← Cd (1) ⊕ K1
for i ← 2 to N do
Set C(i) ← Cd (i) ⊕ Cd (i − 1)
end
Return (C)
Algorithm 7: Image decryption—Hopfield-based reassembling
Input: Scrambled image matrix C of size (X) [M, N], nonlinear random sequence Ω
Output: Original image I
Get [R, A] ← sort (Ω, “ascend”)
where R is the ascending order of key stream Ω;
A is the index of the sorted key stream Ω
Repeat
Set I (A(j)) ← C(j)
Set j ← j + 1
Until j < (M × N)
Return (I)
4.2. Security Framework Interface with Public Cloud
In this proposed approach, the S3 service from Amazon Web Services (AWS) is used
as a public repository to store the grey images in encrypted form. The proposed approach
offers third-level authentication because one of the contributions of the work is improved
protection for image sharing in multimedia communication over public repositories. A user
registers with AWS to obtain the S3 service and credentials as a cloud user. Every registered
user is provided with a username and password as a level 1 authentication credential.
At level 2 authentication, the secret key pairs validate the user’s identity. Third-level
authentication employs CAPTCHA verification. During data access, the user’s authenticity
is verified. If the credentials fail to be correct at any level of authentication, the user access
is denied with the warning “Invalid credentials”. The interface between the proposed
framework and the AWS is illustrated in Figure 4a. Figure 4b illustrates the uploading
process of cipher images into AWS S3 storage. The view of the S3 bucket with uploaded
ciphered images is shown in Figure 5.
Mathematics 2023, 11, 1769
level authentication employs CAPTCHA verification. During data access, the user’s au
thenticity is verified. If the credentials fail to be correct at any level of authentication, th
user access is denied with the warning “Invalid credentials”. The interface between th
proposed framework and the AWS is illustrated in Figure 4a. Figure 4b illustrates the up
of 23
loading process of cipher images into AWS S3 storage. The view of the S311bucket
wit
uploaded ciphered images is shown in Figure 5.
(a)
(b)
Mathematics 2023, 11, x FOR PEER REVIEW
12 o
Figure
4. (a)
Block
diagram
Storingciphered
ciphered
image
S3 bucket.
(b) diagram
Block diagram
view
Figure
4. (a)
Block
diagram view:
view: Storing
image
in S3inbucket.
(b) Block
view:
Retrieving
ciphered
S3bucket
bucket
with
three-tier
authentication.
Retrieving
cipheredimage
imagefrom
from S3
with
three-tier
authentication.
5. Viewimage
of thein
ciphered
in AWS S3 bucket.
Figure 5. View of Figure
the ciphered
AWS S3image
bucket.
5. Results and Discussion
5. Results and Discussion
The performance
ofperformance
the proposedofencryption
approach
wasapproach
analysedwas
using
different
The
the proposed
encryption
analysed
using diffe
grey images of size
[256,
256]
with
the
Waterloo
image
databases
(https://links.uwaterloo.
grey images of size [256, 256] with the Waterloo image databases (https://links.uwa
ca/Repository.html
(accessed on 8 December
2022)).
It was implemented
using
the Lab- using
loo.ca/Repository.html
(accessed
on 8 December
2022)). It was
implemented
VIEW platformLabVIEW
on an Intel
Core
i5
system
configured
with
a
2.5
GHz
CPU,
500
GBCPU,
of 500 G
platform on an Intel Core i5 system configured with a 2.5 GHz
main memory and 4 GB of RAM. The ability of the encryption approach against atta
such as brute force, statistical and chosen plaintext was analysed. The proposed sche
is influenced by adaptive key generation using the BPN model, which generates the ad
tive key based on the randomness and redundant nature of the images. Furthermore,
Mathematics 2023, 11, 1769
12 of 23
main memory and 4 GB of RAM. The ability of the encryption approach against attacks
such as brute force, statistical and chosen plaintext was analysed. The proposed scheme is
influenced by adaptive key generation using the BPN model, which generates the adaptive
key based on the randomness and redundant nature of the images. Furthermore, the
security framework resists known plaintext attacks due to image-specific key generation
for transposition. In addition, encryption quality analyses were carried out to prove the
fitness of the proposed image encryption algorithm for secure image storage in the cloud.
5.1. Brute Force Attack
5.1.1. Keyspace Analysis
According to Kerckhoff’s cipher principle, the key must be vital and secure even if
the encryption algorithm is public access. Keeping a longer key for the encryption process
increased the key searching space, increasing the time to find the correct key [25]. In this
security framework, six keys were generated adaptively with a precision of 1014 . Hence,
10112 is the keyspace for keys generated through the HNN. For the diffusion process, three
different keys, K1, K2 and K3, are used of which two keys have chaotic behaviour, requiring
four initial parameters, with precision of 1014 and one key is a fixed 8-bit key. Thus, the
total keyspace is 102 × 1014 × 1014 × 1014 × 1014 × 10112 = 10170 . In our earlier research
on DNA blended chaos-based image encryption [24], the keyspace was 1086 . Compared
to earlier work, this proposed approach exhibits greater keyspace, making the brute force
attack even more complex.
5.1.2. Key Sensitivity Analysis
Chaotic sequence generators such as a hyperchaotic HNN and logistic and tent maps are
used in the proposed security framework because they are sensitive to the initial conditions.
Furthermore, an independent and adaptive key for each image makes the key search
complex. Image features used to generate the adaptive keys through the HNN make the
search even more complex. For example, a change in one bit out of 256 × 256 × 8 bits in the
diffusion stage II key produces an entirely different image due to the chaotic behaviour of
the key generated through the 1D logistic map. This is evident for the anti-brute force attack
Mathematics 2023, 11, x FOR PEER REVIEW
of 23 before and
approach of the proposed security algorithm. Figure 6 shows the Lena13image
after encryption with correct and incorrect keys as evidence of the key sensitivity analysis.
(a)
(b)
(c)
(d)
(e)
(f)
Figure
6. Key
sensitivity
analysis
through
various various
images: (a)
Plain; (b)
(E1);
(c) ciphered
Figure
6. Key
sensitivity
analysis
through
images:
(a)ciphered
Plain; (b)
ciphered
(E1); (c) ciphered
(one-bit change in original key) (E2); (d) E1 XOR E2; (e) decrypted E1 with correct key; (f) decrypted
(one-bit
change
in
original
key)
(E2);
(d)
E1
XOR
E2;
(e)
decrypted
E1
with
correct
key;
(f) decrypted
E1 with an incorrect key.
E1 with an incorrect key.
5.2. Statistical Attack Analysis
Images with statistical properties are subject to vulnerability when stored in public
environments such as the cloud. The images before their storage are expected to have zero
correlation to avoid such a security breach. The resistivity of the encryption algorithm
against statistical attacks is tested through histogram, correlation and entropy analysis.
(d)
Mathematics 2023, 11, 1769
(e)
(f)
Figure 6. Key sensitivity analysis through various images: (a) Plain; (b) ciphered (E1); (c) ciphered
(one-bit change in original key) (E2); (d) E1 XOR E2; (e) decrypted E1 with correct key; (f) decrypted
E1 with an incorrect key.
13 of 23
5.2. Statistical Attack Analysis
with
statistical
5.2.Images
Statistical
Attack
Analysisproperties are subject to vulnerability when stored in public
environments
suchstatistical
as the cloud.
The images
before
storage when
are expected
have zero
Images with
properties
are subject
to their
vulnerability
stored intopublic
correlation
to
avoid
such
a
security
breach.
The
resistivity
of
the
encryption
algorithm
environments such as the cloud. The images before their storage are expected to have zero
against
statistical
attacks
through
correlation
and entropy
analysis.
correlation
to avoid
suchisa tested
security
breach.histogram,
The resistivity
of the encryption
algorithm
against statistical attacks is tested through histogram, correlation and entropy analysis.
5.2.1. Histogram Analysis
5.2.1. Histogram Analysis
The intensity of pixels in the greyscale must be distributed uniformly over the image
The intensity of pixels in the greyscale must be distributed uniformly over the image
plane for any encrypted image. However, due to the proposed DNA diffusion process,
plane for any encrypted image. However, due to the proposed DNA diffusion process, the
the
histogram obtained for the test images is flat in response. Thus, an image’s unpredicthistogram obtained for the test images is flat in response. Thus, an image’s unpredictability
ability
is proved.
The histogram
analysis
the test
images
of the
proposed
method is
is proved.
The histogram
analysis for
the testfor
images
of the
proposed
method
is illustrated
illustrated
in
Figure
7.
Figure
7
shows
that
the
pixels
are
uniformly
distributed
in Figure 7. Figure 7 shows that the pixels are uniformly distributed after encryption, after
and encryption,
andofhistograms
of plain
andare
cipher
imagesdifferent.
are completely different.
histograms
plain and cipher
images
completely
Plain
Hist(Plain)
Cipher
Hist(Cipher)
Figure 7. Representation of Histogram for Plain and Cipher images.
5.2.2. Neighbouring Pixel Correlation Analysis
The co-located pixels in the original image are extremely correlated. Ideally, the correlation is zero for an encrypted image, i.e., a near-zero correlation [25]. After employing
the proposed encryption algorithm on the images, the randomness of co-occurring pixels is high. Randomness in the encrypted images is calculated using a relation among
co-located pixels. The dependency among the pixels is measured using the following
expressions ((6)–(8)):
covariance Yi , Yj
Corr Yi , Yj =
(6)
σYi × σYj
where standard deviation σEi is obtained by
σYi
v
u
u
=t
1 M×N
(Yi -mean(image))2
M × N i∑
=1
(7)
Co-variance of an image is computed by
Co-variance Yi , Yj
=
1 M×N
(Yi -mean(image)) × Yj -mean(image)
M × N i∑
=1
(8)
Barbara
Mathematics 2023, 11, 1769
House
Test Image (Lena)
Ref. [25]
0.0198
0.0132
0.0032
Plain
0.8319
0.9483
0.7880
Proposed
−0.0072
0.0002
0.0088
Ref. [12]
−0.0187
−0.0016
0.0001
Ref. [16]
−0.0212
−0.0161
−0.0110 14 of 23
Ref. [17]
−0.0033
−0.0269
−0.0121
Plain
0.9782
0.9529
0.9361
where Yi and Yj are two nearby
pixel values of the ciphered
Proposed
0.0062
−0.0014 image. The correlation
0.0074 among
neighbouring
pixels
in
all
three
directions
of
plain
and
encrypted
images
is
illustrated in
Ref. [12]
−0.0339
0.0186
−0.0001
Figure
8.
Figure
8
reveals
that
the
correlation
with
the
adjacent
pixel
values
of
the ciphered
Ref. [13]
0.01659
0.01531
0.00034
image is very low. Thus, the proposed neural-based adaptive key generation used for
Ref. [16]
0.0023
−0.0187
−0.0225
confusion offers near-zero correlation among the neighbouring pixels compared to other
Ref. [17]
−0.0095
−0.0259
−0.0094
state of the art works shown in Table 2, which proves the ability of attack mitigation in the
spatial domain.
Horizontal Correlation
Diagonal
Correlation
Vertical Correlation
Plain
Cipher
Figure 8. Pixel distribution in horizontal, vertical and diagonal directions.
Table 2. Correlation analysis of Proposed versus Existing methods.
Correlation Direction
Test Images
Method
Lena
Plain
Proposed
Ref. [12]
Ref. [13]
Ref. [16]
Ref. [17]
Ref. [19] Arnold Cat Map
Ref. [19] 2D Modular Chaotic Map
Ref. [19] 3D Modular Chaotic Map
Ref. [25]
Ref. [28]
Ref. [39]
Ref. [40]
Ref. [41]
Ref. [42]
Ref. [43]
Ref. [44]
Ref. [45]
Ref. [46]
Ref. [47]
Ref. [48]
Horizontal
Vertical
Diagonal
0.9106
0.0003
0.0011
0.00352
−0.0066
−0.0048
0.0003
0.0287
0.0269
0.0023
0.0028
−0.0287
0.0054
− 0.0126
0.0070
−0.0042
−0.002153
0.0090266
−0.0067
0.001348
0.0018
0.9507
0.0042
0.0098
0.00648
−0.0089
−0.0112
0.0145
0.0217
0.0038
0.0019
−0.0027
0.0071
−0.0073
− 0.0048
−0.0180
-0.0028
−0.0000901
−0.0059255
−0.0038
0.00016
0.0028
0.8849
−0.0049
−0.0227
0.00355
0.0424
−0.0045
0.0841
0.0179
0.0094
0.0011
−0.0032
0.0007
0.0021
0.0054
−0.0033
0.0027
−0.0006059
0.0055227
0.0063
0.002236
0.0016
Mathematics 2023, 11, 1769
15 of 23
Table 2. Cont.
Test Images
Correlation Direction
Method
Horizontal
Vertical
Diagonal
Ref. [49]
Ref. [50]
Ref. [51]
Ref. [52]
Ref. [53]
0.0049
0.0015
0.0016
0.0003
0.000033
−0.0022
−0.0021
−0.0034
−0.0021
−0.000295
−0.0042
−0.0020
−0.0032
−0.0030
−0.000085
Baboon
Plain
Proposed
Ref. [13]
Ref. [14]
Ref. [25]
0.8423
0.0050
0.00083
0.0003
0.0059
0.8213
0.0022
0.00660
−0.0162
0.0041
0.7408
−0.0048
0.00159
0.0134
0.0028
Cameraman
Plain
Proposed
Ref. [12]
Ref. [13]
Ref. [16]
Ref. [17]
Ref. [25]
0.9303
−0.0055
−0.0047
0.00954
0.0063
−0.0095
0.0198
0.9590
0.0073
−0.0195
0.01908
−0.0142
−0.0170
0.0132
0.9048
−0.0072
0.0279
0.00568
0.0168
−0.0119
0.0032
Barbara
Plain
Proposed
Ref. [12]
Ref. [16]
Ref. [17]
0.8319
−0.0072
−0.0187
−0.0212
−0.0033
0.9483
0.0002
−0.0016
−0.0161
−0.0269
0.7880
0.0088
0.0001
−0.0110
−0.0121
House
Plain
Proposed
Ref. [12]
Ref. [13]
Ref. [16]
Ref. [17]
0.9782
0.0062
−0.0339
0.01659
0.0023
−0.0095
0.9529
−0.0014
0.0186
0.01531
−0.0187
−0.0259
0.9361
0.0074
−0.0001
0.00034
−0.0225
−0.0094
The neighbouring correlation values in Table 2 prove that the neural-based confusion
model breaks the correlation between the adjacent pixels and the desired level. Due
to neural-based adaptive confusion, all the images are equally confused, and pixels are
dislocated repeatedly until the expected correlation is achieved.
5.2.3. Information Entropy
After encryption of an image, robustness and randomness are analysed using information
entropy [25]. Global Shannon entropy E(s) is obtained using the following expression (9):
256
E(s) = − ∑ I(si ) log2 I(si )
(9)
i=1
where I(Si ) is the probability of symbol (Si ). The pixel bit depths for grey images are
always 8, so the entropy exists in the range [0 to 8]. For an ideally encrypted image, the
entropy is always 8 [25]. This proposed neural-assisted DNA-based image encryption
algorithm makes the pixel distribution over an image plane highly random. Therefore, the
entropy value of an encrypted image is very close to 8. If the entropy value is less than
8 or close to 0 then the randomness effect in the encrypted image is significantly less and
the vulnerability to attack is high. Table 3 shows that the proposed neural-based image
encryption algorithm results in an entropy of almost eight, irrespective of the input image.
The entropy value of the proposed encryption is compared with other state of the art works
and exhibits the maximum unpredictability of the plain image.
Mathematics 2023, 11, 1769
16 of 23
Table 3. Entropy Analysis of Proposed versus Existing methods.
Test Images
Lena
Peppers
Baboon
Boat
Cameraman
Barbara
House
Plain
7.48183
7.9970
7.9965
7.99802
7.9951
7.9975
NA
7.9975
7.9973
7.9914
7.60129
7.9973
7.9958
7.99852
7.9965
7.9958
NA
7.9972
7.9972
NA
7.23399
7.9976
NA
7.99712
NA
7.9938
7.9972
NA
7.9972
7.9914
7.26437
7.9972
7.9959
NA
7.9960
7.9941
7.9962
NA
7.9972
NA
7.12881
7.9977
7.9964
7.99662
7.9955
7.9939
7.9972
7.9973
7.9974
NA
7.51504
7.9973
7.9957
NA
7.9937
NA
7.9969
NA
7.9972
NA
6.49614
7.9973
7.9952
7.99781
7.9978
NA
NA
7.9973
7.9970
7.9914
Cipher
Proposed
Ref. [12]
Ref. [13]
Ref. [16]
Ref. [25]
Ref. [28]
Ref. [31]
Ref. [32]
Ref. [39]
* NA—Not Available.
5.3. Encryption Quality Analysis
5.3.1. Chi-Square Test
The chi-square test measures pixel distribution in ciphered images [18]. The variation
in the histogram is quantitatively obtained using a statistical metric called chi squared (χ2 ),
which is expressed as follows:
(PI(i) − 256)2
256
i=0
255
χ2 = ∑
(10)
where PI is the pixel intensity value in the interval of 0 to 255. “i” is the intensity value
in the encrypted pixels. The chi-square values that were found for encrypted images are
verified with the distribution probability for 1% and 5% significance levels. The critical
values for the 1% and 5% significance level with a degree of freedom of 255 are 310.457 and
293.2478, respectively. Therefore, the χ2 value must be lower than the critical values for the
ideally encrypted image. Table 4 reveals the uniform distributions of pixels in an encrypted
image through low chi-square values compared to essential values.
Table 4. Chi-square test: Pixel distribution test.
Plain
Test Image
Airplane
Baboon
Barbara
Boat
Cameraman
Girl
House
Lena
Peppers
Splash
Cipher
χ2 Value
H0 Test
χ2 Value
H0 Test
168,463
58,247.8
35,001.2
85,621.8
97,215.8
93,817.1
300,852
37,973
30,024.6
86,407.1
Fail
Fail
Fail
Fail
Fail
Fail
Fail
Fail
Fail
Fail
258.172
213.781
242.57
255.305
212.992
240.836
242.477
276.633
248.867
269.953
Pass
Pass
Pass
Pass
Pass
Pass
Pass
Pass
Pass
Pass
5.3.2. Histogram Maximum Deviation
The histogram maximum deviation is a measure of diffusion efficiency and encryption
quality. Histogram maximum deviation is the difference in histogram values between the
ciphered and plain image at every pixel intensity [17]. For an ideally encrypted image,
the value must be close to the total size of the image. A histogram maximum deviation
Mathematics 2023, 11, 1769
17 of 23
value close to the size of an image proves the randomness of pixel distribution through the
encryption process. Histogram maximum deviation (HM) is obtained using the following
Equation (11):
HM =
254
dif(0) + dif(255)
+ ∑ dif(j)
2
j=1
(11)
where dif(j) is the difference between the plain and cipher image histogram at the jth index.
After encryption, the histogram deviation between the plain and cipher image is high, as
shown in Table 5. From Table 5, it is proven that the strength of the encryption algorithm
is well suited for secure image sharing and storing compared to other state of the art
works. This is because, after ciphering the image, its statistical properties do not reveal any
significant detail about the plain image.
Table 5. Histogram Maximum Deviation.
Histogram Maximum Deviation
Test Image/Method
Proposed
Ref. [12]
Ref. [16]
Ref. [17]
Ref. [28]
Ref. [31]
Barbara
Boat
Cameraman
Lena
Peppers
40,694.5
17,944
19,384
18,148
NA
158,258
53,452.5
25,367
25,193
25,442
NA
148,597
60,413
16,674
16,803
18,007
64,119
64,300
40,921.5
20,811
19,931
21,339
41,458
NA
36,169
22,648
22,966
22,935
36,391
NA
* NA—Not Available.
5.3.3. Irregular Deviation
Encryption quality is analysed using irregular deviation. The linearity of the pixel
distribution may be reflected in a differential attack. In any image encryption algorithm,
the pixel intensities are expected to be uniformly distributed in the cipher image [17]. The
irregular deviation is calculated through Equations (12)–(14), given below:
d = imhist(abs((P) − (C)))
(12)
The mean for the histogram of the difference in pixel intensities between the plain and
cipher images (d) is calculated through the following expression:
Md =
1 255
di
256 i∑
=0
(13)
where di is the ith element in the array d.
Irregular deviation (HI ) is obtained using Equation (14).
255
HI = ∑ |di − Md |
(14)
i=0
Table 6 reveals that the proposed encryption algorithm distributes the pixel intensities
uniformly without bias in the plain image.
Mathematics 2023, 11, 1769
18 of 23
Table 6. Irregular Deviation.
Test Image/Method
Proposed
Ref. [12]
Ref. [16]
Ref. [17]
Ref. [28]
Ref. [31]
Irregular Deviation
Barbara
Boat
Cameraman
Lena
Peppers
43,446
42,556
43,014
42,708
NA
129,765
46,218
36,124
36,220
36,226
NA
137,793
39,020
39,380
39,414
39,244
38,959
39,668
44,748
40,820
40,768
40,480
44,465
NA
41,394
34,824
34,706
35,088
41,184
NA
5.3.4. Deviation from Ideality
Deviation from ideality must be minimal after encryption to prove the algorithm is
promising for attacks [17]. Deviation of the originally encrypted image histogram from
ideally encrypted images is estimated by the following Equation (15):
HDI =
∑255
i=0 |imhist(Idealcipher)i − imhist(Originalcipher)i |
M×N
(15)
where M × N is the total size of the image.
Near-zero HDI proves the quality of the encryption algorithm. Table 7 depicts the
existence of a very low deviation from ideality between plain and ciphered images. Thus,
the proposed encryption algorithm produces low deviation from ideality compared to the
existing literature, as shown in Table 7.
Table 7. Deviation from Ideality.
Test Image/Method
Proposed
Ref. [12]
Ref. [16]
Ref. [17]
Ref. [28]
Ref. [31]
Deviation from Ideality
Barbara
Boat
Cameraman House
Lena
Peppers
0.04834
0.0928
0.1012
0.0976
NA
0.0522
0.05002
0.0985
0.0995
0.0958
NA
0.0528
0.04437
0.092
0.1065
0.0942
NA
0.0502
0.05182
0.0934
0.1001
0.0994
0.0468
NA
0.04916
0.0977
0.0979
0.0917
0.0496
NA
0.04889
0.0994
0.1141
0.0882
0.0485
NA
5.4. Chosen Plaintext Attack
Diffusion employed in the encryption through XOR alone as an operation is subject to
a chosen plaintext attack. The chosen plaintext attack results in the key used for diffusion;
the encryption algorithm is compromised. Any encryption algorithms against the chosen
plaintext attack need to satisfy the following condition:
P1 ⊕ P2 6= E1 ⊕ E2
Any two plain grey images, as P1 and P2, are XORed. Similarly, the encrypted
versions of P1 and P2 as E1 and E2 are XORed. If both the XORed values are equal, it is
vulnerable to chosen plaintext attack. Otherwise, breaking the image encryption algorithm
is impossible, and its fitness against the chosen plaintext attack is proved. The ability
of this security algorithm is analysed and it is shown that the DNA diffusion approach
acts against the chosen plaintext attack. Figure 9a shows the XORed result of two plain
images; the encrypted version of the same plain images is XORed, as shown in Figure 9b.
Figure 9a,b are not identical, which indicates that the proposed diffusion process is not
vulnerable to the chosen plaintext attack. A known plaintext attack becomes unviable in
the proposed security framework due to the image-specific adaptive key generation using
a neural network.
Mathematics 2023, 11, 1769
ity of this security algorithm is analysed and it is shown that the DNA diffusion approach
acts against the chosen plaintext attack. Figure 9a shows the XORed result of two plain
images; the encrypted version of the same plain images is XORed, as shown in Figure 9b.
Figure 9a,b are not identical, which indicates that the proposed diffusion process is not
vulnerable to the chosen plaintext attack. A known plaintext attack becomes unviable in
19 of 23
the proposed security framework due to the image-specific adaptive key generation using
a neural network.
(a)
(b)
Figure
Figure9.9.(a)
(a)P1
P1⊕
⊕P2;
P2;(b)
(b)E1
E1⊕
⊕ E2.
E2.
5.5.Bit
BitDistribution
DistributionAnalysis
AnalysisatatPlane
PlaneLevel
Level
5.5.
Thepotency
potencyofofthe
thediffusion
diffusionprocess
processisisfurther
furtheranalysed
analysedusing
usingthe
theequality
equalitytest
testover
over
The
every
bit
plane.
For
any
encrypted
image,
the
distribution
of
zeros
and
ones
in
each
bit
every bit plane. For any encrypted image, the distribution of zeros and ones in each bit
plane
must
be
equal,
i.e.,
50%
of
zeros
and
ones
must
be
present
in
each
plane
to
prove
plane must be equal, i.e., 50% of zeros and ones must be present in each plane to prove
theunpredictability
unpredictabilityofofthe
theplain
plainimage
imageafter
afterencryption.
encryption.The
Thediffusion
diffusionstrategy
strategyproposed
proposed
the
in
the
algorithm
outfit
for
the
image
encryption
are
shown,
where
the
bits
1
and
an
in the algorithm outfit for the image encryption are shown, where the bits 1 and 00ofofan
encrypted
image
are
equally
distributed
and
tabulated
in
Table
8.
Table
8
shows
the
bit
encrypted image are equally distributed and tabulated in Table 8. Table 8 shows the bit
“1” percentage in each plain and encrypted test image’s bit plane. Table 8 shows that each
“1” percentage in each plain and encrypted test image’s bit plane. Table 8 shows that each
plane’s bit “1” in an encrypted image is equally distributed. So, the proposed DNA-based
plane’s bit “1” in an encrypted image is equally distributed. So, the proposed DNA-based
diffusion offers strong enough image encryption.
diffusion offers strong enough image encryption.
Table 8. Bit distribution analysis at plane level.
Table 8. Bit distribution analysis at plane level.
PlanesTest
Test Images
Planes
Images
P P
Airplane
Airplane
E E
11
50.383
50.383
50.191
50.191
22
49.817
49.817
50.134
50.134
33
49.355
49.355
49.817
49.817
44
51.842
51.842
50.22
50.22
55
53.865
53.865
49.763
49.763
66
24.394
24.394
50.531
50.531
77
78.969
78.969
50.034
50.034
88
81.544
81.544
49.969
49.969
Baboon
P
E
50.247
49.834
50.075
50.006
50.378
50.09
50.563
49.844
53
50.102
55.841
50.092
44.63
49.715
53.096
49.782
Barbara
P
E
49.928
50.041
49.916
50.259
50.075
49.825
50.272
50.356
48.856
50.066
48.956
49.71
47.932
49.623
35.727
50.128
Boat
P
E
49.924
49.889
50
50.281
49.974
49.783
49.364
50.168
50.856
49.977
39.584
49.974
22.548
49.911
67.471
49.98
Cameraman
P
E
49.841
50.145
49.379
49.895
50.844
49.931
52.199
49.965
42.644
49.867
50.958
50.336
18.71
49.782
60.005
50.058
Girl
P
E
50.175
49.586
50.787
49.832
50.722
49.916
49.904
49.887
46.37
49.77
50.824
50.003
26.7
50.111
8.197
49.713
House
P
E
50.035
49.921
49.631
50.359
52.985
50.259
65.085
49.77
67.981
49.988
71.492
50.05
52.217
49.829
48.505
50.122
Lena
P
E
50.009
50.247
50.108
49.968
49.728
49.486
49.901
49.768
49.777
50.113
50.337
50.005
41.794
50.536
51.187
50.444
Peppers
P
E
49.979
49.925
49.715
50.201
49.796
49.954
49.933
50.281
53.462
49.966
46.248
49.78
44.778
50.204
47.327
50.194
P—Plain image; E—Encrypted image.
Mathematics 2023, 11, 1769
20 of 23
5.6. Computational Complexity
The overhead of the proposed security framework includes significant operations
called key generation, confusion and DNA-based diffusions. The greyscale image used in
this research is of size [M, N], where M = N = 256. The random number generated using
the HNN takes the complexity of O {n(M × N)}. The transposition process complexity is
O {M × N}. The proposed algorithm contains two DNA-based diffusion stages, which
take O {4(M × N)}. So, the total computational complexity of the proposed framework
takes O {(n + 5)(M × N)}. Table 9 compares the proposed system and other state of the art
works with various aspects such as system configuration, tool used for implementation,
the approach suggested and execution time. This proposed work has been implemented
using the LabVIEW platform on an Intel Core i5 system configured with a 2.5 GHz CPU,
500 GB of main memory and 4 GB of RAM. Total execution time taken by this proposed
approach, including key generation and cipher block chaining encryption, is calculated as
219.5 ms, comparable with Ref. [32]. The file is pushed into the AWS S3 bucket via a Wi-Fi
network with 144.4 Mbps speed, which takes an uploading time of 0.4056 sec. Network
speed influences propagation delay, which means they are inversely proportional.
Table 9. Computational complexity comparison with existing literature.
Parameters
Tool Used for
Implementation
System Configuration
Proposed Approach
Execution
Time (s)
Ref. [17]
MATLAB
Intel Core i3-3227U
1.9 CPU and 4 GB
of RAM
LFT-based S-box using a new
chaotic map, P-S network
0.095
Ref. [18]
MATLAB R2011b
Intel(R) Core (TM)
i3–2350, 2.30 GHz CPU
Plain image-dependent keystream
using 2D logistic map
0.0343
Ref. [19]
MATLAB R2017a
Intel Core i7–7500 U,
3.5 GHz CPU, 4GB RAM
3D modular chaotic map
permutation process for
image encryption
0.8271
Ref. [25]
MATLAB 8
Intel Core i7, 2.3 GHz
CPU, 8 GB RAM
Logistic chaos system, DNA
encoding and operations.
0.281
Ref. [30]
MATLAB 2013a
Intel Core i3, 2.4 GHz
CPU and 4 GB RAM
Bit-level permutation and diffusion
using DNA addition
0.54
Ref. [32]
Virtual
instrumentation
tool
Core i5, 2.5 GHz CPU,
4 GB RAM
Chaos-based key generation system,
DNA encoding and operations for
secure image storage in the cloud
0.2188
Ref. [33]
MATLAB2011b
AMD A6-3420M and
2 GB RAM
Secure sampling through cascade
chaotic map followed by confusion
using Arnold transform and
single-stage XOR-based diffusion
1.663661
Proposed
Virtual
instrumentation
tool
Core i5, 2.5 GHz CPU,
4 GB RAM
Neural attractor-based
image-specific key generation
and chaos key generation for
image scrambling and
DNA-based diffusion
0.2195
Existing Work
5.7. Discussion
The proposed algorithm is tested with ten test images of size [256, 256]. The algorithm achieves average entropy of 7.996098 and offers better entropy when compared to
Refs. [12,16,39] and is comparable with [40–53]. The near-zero correlation offered by the
proposed algorithm is better than the previous works, which is also given in the findings.
The obtained average bit distribution at the plane level for the test images is 50.00364 and
shows that the encrypted images are highly randomised. Therefore, the proposed image
Mathematics 2023, 11, 1769
21 of 23
encryption is cryptographically efficient and can withstand statistical and chosen plaintext
attacks. Furthermore, the presented work can restore useful images from captured versions
of images under various environmental conditions. The suggested methodology is the best
for analysing an image across a wireless medium and is sufficiently robust to interference.
6. Conclusions
Cloud storage is trendy and inevitable in many applications. However, data stored in
the cloud are always under threat due to their multitenancy. So, it is essential to construct
a security solution to ensure the security of cloud-hosted data. The proposed Hopfield
attractor-based permutation blended DNA diffusion provides tightened security for grey
images hosted in public cloud storage during when at rest, in transit and used by other
applications. The proposed security framework exhibits greater potency to defend against
various attacks. This proposed work uses a Hopfield attractor and chaotic maps, resulting
in the keyspace of 10170 . The key generated for the confusion process is adaptive and
image specific; hence, attackers cannot find the key using a chosen plaintext attack and
a known plaintext attack. The proposed security algorithm yielded an average entropy
value of 7.9973 and an average correlation value of 0.0008; hence, attackers cannot find the
plain image using a statistical attack. This framework can be enhanced in future by using
a reconfigurable hardware platform.
Author Contributions: Conceptualisation, H.M., N.C. and R.A.; methodology, C.L., N.C. and P.V.M.;
software, C.L., N.C. and P.V.M.; validation, P.V.M., K.M.M. and K.T.; formal analysis, K.M.M. and
P.V.M.; investigation, N.C., P.V.M. and K.M.M.; resources, P.V.M.; data curation, N.C., P.V.M. and K.T.;
writing—original draft preparation, H.M., K.T. and R.A.; writing—review and editing, H.M., K.M.M.
and R.A.; visualisation, P.V.M.; supervision, R.A. and K.T.; project administration, H.M., K.T. and
R.A.; funding acquisition, HM and R.A. All authors have read and agreed to the published version of
the manuscript.
Funding: Institutional Fund Projects under grant no. IFPIP: 965-144-1443. Ministry of Education and
King Abdulaziz University, DSR, Jeddah, Saudi Arabia.
Data Availability Statement: Not applicable.
Acknowledgments: The authors gratefully acknowledge the technical and financial support provided
by the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Singh, A.; Chatterjee, K. Cloud security issues and challenges: A survey. J. Netw. Comput. Appl. 2017, 79, 88–115. [CrossRef]
Yang, R.; Xu, Q.; Au, M.H.; Yu, Z.; Wang, H.; Zhou, L. Position based cryptography with location privacy: A step for Fog
Computing. Future Gener. Comput. Syst. 2018, 78, 799–806. [CrossRef]
Shahzadi, S.; Iqbal, M.; Dagiuklas, T.; Qayyum, Z.U. Multi-access edge computing: Open issues, challenges and future perspectives. J. Cloud Comput. 2017, 6, 30. [CrossRef]
Huh, J.H.; Seo, Y.S. Understanding edge computing: Engineering evolution with artificial intelligence. IEEE Access 2019, 7,
164229–164245. [CrossRef]
Eom, S.; Huh, J.H. The opening capability for security against privacy infringements in the smart grid environment. Mathematics
2018, 6, 202. [CrossRef]
Tao, M.; Ota, K.; Dong, M. Ontology-based data semantic management and application in IoT- and cloud-enabled smart homes.
Future Gener. Comput. Syst. 2017, 76, 528–539. [CrossRef]
Asadi, S.; Nilashi, M.; Husin, A.R.C.; Yadegaridehkordi, E. Customers perspectives on adoption of cloud computing in banking
sector. Inf. Technol. Manag. 2017, 18, 305–330. [CrossRef]
Singh, S.; Jeong, Y.S.; Park, J.H. A survey on cloud computing security: Issues, threats, and solutions. J. Netw. Comput. Appl. 2016,
75, 200–222. [CrossRef]
Kumari, M.; Gupta, S.; Sardana, P. A Survey of Image Encryption Algorithms. 3D Res. 2017, 8, 37. [CrossRef]
Wang, B.; Xie, Y.; Zhou, C.; Zhou, S.; Zheng, X. Evaluating the permutation and diffusion operations used in image encryption
based on chaotic maps. Optik 2016, 127, 3541–3545. [CrossRef]
Alsaedi, M. Colored image encryption and decryption using multi-chaos 2D quadratic strange attractors and matrix transformations. Multimed. Tools Appl. 2017, 76, 24527–24547. [CrossRef]
Mathematics 2023, 11, 1769
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
22 of 23
Hua, Z.; Zhou, Y.; Pun, C.M.; Chen, C.L.P. 2D Sine Logistic modulation map for image encryption. Inf. Sci. 2015, 297, 80–94.
[CrossRef]
Diaconu, A.V. Circular inter-intra pixels bit-level permutation and chaos-based image encryption. Inf. Sci. 2016, 355–356, 314–327.
[CrossRef]
Ponuma, R.; Amutha, R. Compressive sensing based image compression-encryption using novel 1D-chaotic map. Multimed. Tools
Appl. 2018, 77, 19209–19234. [CrossRef]
Abbas, N.A. Image encryption based on Independent Component Analysis and Arnold’s Cat Map. Egypt. Inform. J. 2016, 17,
139–146. [CrossRef]
Wang, X.; Liu, L.; Zhang, Y. A novel chaotic block image encryption algorithm based on dynamic random growth technique. Opt.
Lasers Eng. 2015, 66, 10–18. [CrossRef]
Belazi, A.; Abd El-Latif, A.A.; Belghith, S. A novel image encryption scheme based on substitution-permutation network and
chaos. Signal Process. 2016, 128, 155–170. [CrossRef]
Huang, X.; Ye, G. An image encryption algorithm based on irregular wave representation. Multimed. Tools Appl. 2018, 77,
2611–2628. [CrossRef]
Broumandnia, A. Designing digital image encryption using 2D and 3D reversible modular chaotic maps. J. Inf. Secur. Appl. 2019,
47, 188–198. [CrossRef]
Duan, C.F.; Zhou, J.; Gong, L.H.; Wu, J.Y.; Zhou, N.R. New color image encryption scheme based on multi-parameter fractional
discrete Tchebyshev moments and nonlinear fractal permutation method. Opt. Lasers Eng. 2022, 150, 106881. [CrossRef]
Zhang, Q.; Liu, L.; Wei, X. Improved algorithm for image encryption based on DNA encoding and multi-chaotic maps. AEU Int.
J. Electron. Commun. 2014, 68, 186–192. [CrossRef]
Wang, X.Y.; Zhang, Y.Q.; Bao, X.M. A novel chaotic image encryption scheme using DNA sequence operations. Opt. Lasers Eng.
2015, 73, 53–61. [CrossRef]
Hu, T.; Liu, Y.; Gong, L.H.; Guo, S.F.; Yuan, H.M. Chaotic image cryptosystem using DNA deletion and DNA insertion. Signal
Process. 2017, 134, 234–243. [CrossRef]
Chai, X.; Chen, Y.; Broyde, L. A novel chaos-based image encryption algorithm using DNA sequence operations. Opt. Lasers Eng.
2017, 88, 197–213. [CrossRef]
Enayatifar, R.; Abdullah, A.H.; Isnin, I.F.; Altameem, A.; Lee, M. Image encryption using a synchronous permutation-diffusion
technique. Opt. Lasers Eng. 2017, 90, 146–154. [CrossRef]
Wang, S.; Peng, Q.; Du, B. Chaotic color image encryption based on 4D chaotic maps and DNA sequence. Opt. Laser Technol. 2022,
148, 107753. [CrossRef]
Alarood, A.A.; Alsolami, E.; Al-Khasawneh, M.A.; Ababneh, N.; Elmedany, W. IES: Hyper-chaotic plain image encryption scheme
using improved shuffled confusion-diffusion. Ain Shams Eng. J. 2022, 13, 101583. [CrossRef]
Zhou, W.; Wang, X.; Wang, M.; Li, D. A new combination chaotic system and its application in a new Bit-level image encryption
scheme. Opt. Lasers Eng. 2022, 149, 106782. [CrossRef]
Pavithran, P.; Mathew, S.; Namasudra, S.; Srivastava, G. A novel cryptosystem based on DNA cryptography, hyperchaotic
systems and a randomly generated Moore machine for cyber physical systems. Comput. Commun. 2022, 188, 1–12. [CrossRef]
Yousif, S.F.; Abboud, A.J.; Alhumaima, R.S. A new image encryption based on bit replacing, chaos and DNA coding techniques.
Multimed. Tools Appl. 2022, 81, 27453–27493. [CrossRef]
Qin, Z.; Weng, J.; Cui, Y.; Ren, K. Privacy-Preserving Image Processing in the Cloud. IEEE Cloud Comput. 2018, 5, 48–57. [CrossRef]
Chidambaram, N.; Raj, P.; Thenmozhi, K.; Rajagopalan, S.; Amirtharajan, R. A cloud compatible DNA coded security solution for
multimedia file sharing & storage. Multimed. Tools Appl. 2019, 78, 33837–33863.
Zhang, Y.; He, Q.; Xiang, Y.; Zhang, L.Y.; Liu, B.; Chen, J.; Xie, Y. Low-Cost and Confidentiality-Preserving Data Acquisition for
Internet of Multimedia Things. IEEE Internet Things J. 2018, 5, 3442–3451. [CrossRef]
Bigdeli, N.; Farid, Y.; Afshar, K. A robust hybrid method for image encryption based on Hopfield neural network. Comput. Electr.
Eng. 2012, 38, 356–369. [CrossRef]
Lakshmi, C.; Thenmozhi, K.; Rayappan, J.B.B.; Amirtharajan, R. Hopfield attractor-trusted neural network: An attack-resistant
image encryption. Neural Comput. Appl. 2020, 32, 11477–11489. [CrossRef]
Lakshmi, C.; Thenmozhi, K.; Venkatesan, C.; Seshadhri, A.; Rayappan, J.B.B.; Amirtharajan, R. Mutated cleavages of images for
stealth disclosure: A hopfield neural network attractor (HNNA) approach. Neural Process. Lett. 2021, 53, 907–928. [CrossRef]
Lakshmi, C.; Thenmozhi, K.; Rayappan, J.B.B.; Rajagopalan, S.; Amirtharajan, R.; Chidambaram, N. Neural-assisted imagedependent encryption scheme for medical image cloud storage. Neural Comput. Appl. 2021, 33, 6671–6684. [CrossRef]
Dhall, S.; Pal, S.K.; Sharma, K. A chaos-based probabilistic block cipher for image encryption. J. King Saud Univ. Comput. Inf. Sci.
2022, 34, 1533–1543. [CrossRef]
Patel, S.; Thanikaiselvan, V.; Pelusi, D.; Nagaraj, B.; Arunkumar, R.; Amirtharajan, R. Colour image encryption based on
customised neural network and DNA encoding. Neural Comput. 2021, 33, 14533–14550. [CrossRef]
Jiang, Z.; Liu, X. Image Encryption Algorithm Based on Discrete Quantum Baker Map and Chen Hyperchaotic System. Int. J.
Theor. Phys. 2023, 62, 22. [CrossRef]
Wang, W.T.; Sun, J.Y.; Zhang, H.; Zhang, J. Quantum cryptosystem and circuit design for color image based on novel 3D
Julia-fractal chaos system. Quantum Inf. Process. 2023, 22, 64. [CrossRef]
Mathematics 2023, 11, 1769
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
23 of 23
Wang, H.K.; Xu, G.B.; Jiang, D.H. Quantum grayscale image encryption and secret sharing schemes based on Rubik’s Cube.
Physica A Stat. Mech. Its Appl. 2023, 612, 128482. [CrossRef]
Hao, W.; Zhang, T.; Chen, X.; Zhou, X. A hybrid NEQR image encryption cryptosystem using two-dimensional quantum walks
and quantum coding. Signal Process. 2023, 205, 108890. [CrossRef]
Mahalingam, H.; Veeramalai, T.; Menon, A.R.; S., S.; Amirtharajan, R. Dual-Domain Image Encryption in Unsecure Medium—A Secure
Communication Perspective. Mathematics 2023, 11, 457. [CrossRef]
Zhu, S.; Deng, X.; Zhang, W.; Zhu, C. Image Encryption Scheme Based on Newly Designed Chaotic Map and Parallel DNA
Coding. Mathematics 2023, 11, 231. [CrossRef]
Song, X.; Chen, G.; Abd El-Latif, A.A. Quantum Color Image Encryption Scheme Based on Geometric Transformation and
Intensity Channel Diffusion. Mathematics 2022, 10, 3038. [CrossRef]
Zhong, H.; Li, G.; Xu, X.; Song, X. Image Encryption Algorithm Based on a Novel Wide-Range Discrete Hyperchaotic Map.
Mathematics 2022, 10, 2583. [CrossRef]
Mansoor, S.; Sarosh, P.; Parah, S.A.; Ullah, H.; Hijji, M.; Muhammad, K. Adaptive Color Image Encryption Scheme Based on
Multiple Distinct Chaotic Maps and DNA Computing. Mathematics 2022, 10, 2004. [CrossRef]
Mfungo, D.E.; Fu, X.; Wang, X.; Xian, Y. Enhancing Image Encryption with the Kronecker xor Product, the Hill Cipher, and the
Sigmoid Logistic Map. Appl. Sci. 2023, 13, 4034. [CrossRef]
Chen, C.; Zhu, D.; Wang, X.; Zeng, L. One-Dimensional Quadratic Chaotic System and Splicing Model for Image Encryption.
Electronics 2023, 12, 1325. [CrossRef]
Chen, X.; Wang, Q.; Fan, L.; Yu, S. A Novel Chaotic Image Encryption Scheme Armed with Global Dynamic Selection. Entropy
2023, 25, 476. [CrossRef] [PubMed]
Chang, H.; Wang, E.; Liu, J. Research on Image Encryption Based on Fractional Seed Chaos Generator and Fractal Theory. Fractal
Fract. 2023, 7, 221. [CrossRef]
Zhao, J.; Wang, S.; Zhang, L. Block Image Encryption Algorithm Based on Novel Chaos and DNA Encoding. Information 2023, 14, 150.
[CrossRef]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual
author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to
people or property resulting from any ideas, methods, instructions or products referred to in the content.