Lower-Complexity Multi-Layered Security Partitioning Algorithm Based on Chaos Mapping-DWT Transform for WA/SNs

Abstract

The resource limitations of Low-Power Wireless Networks (LP-WNs), such as Wireless Sensor Networks (WSNs), Wireless Actuator/Sensor Networks (WA/SNs), and Internet of Things (IoT) outdoor applications, restrict the utilization of the error-performance-enhancing techniques and the use of the powerful and robust security tools. Therefore, these LP-WN applications require special techniques to satisfy the requirements of a low data loss rate and satisfy the security requirements while considering the accepted level of complexity and power efficiency of these techniques. This paper focuses on proposing a power-efficient, robust cryptographic algorithm for the WA/SNs. The lower-complexity cryptographic algorithm is proposed, based on merging the data composition tools utilizing data transforms and chaos mapping techniques. The decomposing tool is performed by the various data transforms: Discrete Cosine Transform (DCT), Discrete Cosine Wavelet (DWT), Fast Fourier Transform (FFT), and Walsh Hadamard Transform (WHT); the DWT performs better with efficient complexity. It is utilized to separate the plaintext into the main portion and side information portions to reduce more than 50% of complexity. The main plaintext portion is ciphered in the series of cryptography to reduce the complexity and increase the security capabilities of the proposed algorithm by two chaos mappings. The process of reduction saves complexity and is employed to feed the series of chaos cryptography without increasing the complexity. The two chaos mappings are used, and two-dimensional (2D) chaos logistic maps are used due to their high sensitivity to noise and attacks. The chaos 2D baker map is utilized due to its high secret key managing flexibility and high sensitivity to initial conditions and plaintext dimensions. Several computer experiments are demonstrated to evaluate the robustness, reliability, and applicability of the proposed complexity-efficient crypto-system algorithm in the presence of various attacks. The results prove the high suitability of the proposed lower-complexity crypto-system for WASN and LP-WN applications due to its robustness in the presence of attacks and its power efficiency.

1. Introduction

With the widespread use of wireless network applications in various fields, the need to overcome constraints is increasing. These constraints decrease the utilization of error control schemes and the robust security techniques [1]. Due to crucial applications such as military, medical, healthcare, and environmental monitoring applications, these applications require the provision of sufficient security level for the network and the transferred information [2,3]. The computational complexity of the security algorithms limits its suitability for the limited resources of wireless networks. Outdoor applications suffer from various challenges due to the resource limitations and the different cyber-attacks. Hence, the suitable security algorithms for the crucial applications must be lower in complexity, flexible in security levels management, and power-efficient [4].

By reviewing the recently published related research papers that focus on the balance between proposing security tools and techniques that are flexible and efficient, and considering the power and computational complexity, it is found that these papers are few, considering the essential issues of complexity and power efficiency in the proposed security techniques for the real-time and outdoor applications of the Object-Oriented Wireless Networks (OOWNs) and Internet of Things (IoT) [5,6,7]. Due to the restrictions of WN applications in the various fields of open environments, such as environmental monitoring, healthcare, and the Internet of Medical Things (IoMT), the side of complexity must be considered in the utilization of data and network security tools as well as the error performance improving tools [8]. The role of security and error control techniques cannot be ignored in the various applications to satisfy the accepted level of data safety and error performance. The computational complexity is defined as the total executed arithmetic and logic operations included in the security algorithms. Hence, the CC is related directly to the power complexity. In the past five years (2019–2024), the researchers’ contributions are not sufficient for this research point [9,10,11,12,13,14,15,16].

The available resources limit the outdoor applications of the Wireless Sensing-based Networks (WSNs) and Internet of Things (IoT). Also, they restrict the utilization of powerful security techniques and error control schemes. Most WSN applications require a long life for the network nodes. The computational complexity of the system is directly related to the amount of consumed power. It is also considered the main utilizing challenge of the channel coding and the powerful security tools in Low-Power Wireless Networks, such as the Object-Oriented Wireless Network (WSN) and Wireless Body Area Network (WBAN), for example [17,18]. This research paper investigates the methods of enhancing the power efficiency of the limited resources of wireless networks, in addition to the balancing of the power efficiency of the proposed security algorithm and achieving a perfect security level to satisfy the requirements and combat various cyber-attacks.

The main tools of power-efficient security algorithms are the data transformation techniques that are used to partition the information into two main portions: the crucial section, which carries the main features, and the second portion, which is the side information [19]. The various data transformation techniques are utilized to evaluate and choose the more suitable techniques based on the results of the preliminary experiments. The features of the proposed algorithm are mentioned in the Main Contributions subsection.

Main Contributions

In this subsection, the main contributions of the presented research paper are presented. The proposed security algorithm is constructed based on chaos mapping and data transforms to achieve the required security level for the classified plaintext and to enhance the power efficiency of the security algorithm. The data transforms are employed to execute the securing processes in different domains and improve the complexity of the algorithm by reducing the amount of the processed plaintext using the decomposing process. The proposed security algorithm provides the optional multi-layered security without increasing the complexity of the algorithm, as clarified in the operation mechanism of the proposed approach. The high flexibility of the proposed algorithm is due to its interaction with the various conditions based on the type of plaintext, the classification degree, the available energy “battery level”, and the environment of the communications.

The existing techniques suffer from some of the limitations and drawbacks. The main limitation of the real-time applications is the longer consumed time of cryptographic algorithms in the encryption and decryption processes [20,21]. Also, the several recent related research works do not consider the time complexity in the evaluation of their proposed algorithms [22,23]. Also, the time complexity is considered a metric through measuring the processing time, which is very essential in real-time applications. The time complexity of the proposed work is compared with the recent related work in an additional table, and real-time IoT applications are considered in [24,25].

The proposed security algorithm achieves security requirements and power/complexity efficiency trade-off via a simple and effective mechanism. In the next generation of security algorithms, the complexity and power of the approach will be the main players in the efficiency of the security techniques, and the power-efficient security algorithms will be the major approaches of Energy-Saving Security Algorithms (ESSAs). The applicability and robustness of the proposed security algorithm are evaluated in the results and experiments using colored and grayscale images considering various attacks. The Gaussian noise, salt and pepper, and speckle attacks are considered in the simulation experiments to evaluate the proposed power-efficient crypto-system algorithm [26]. As clarified in the results, the proposed algorithm has lower complexity and robustness in the presence of various attacks/noise.

Also, the proposed power-efficient security algorithm provides a multi-layered security approach. The security of plaintext is performed in the spatial and frequency domains. The flexible power-efficient security algorithm provides multi-layers based on many conditions such as the available energy resource, the nature of networks and nodes, etc. Also, data transforms are utilized to decrease the complexity, as described in the proposed security algorithm discussion. The power efficiency of the proposed crypto-system is concluded from the decomposing process due to data transform utilization. This decomposition process reduces the original payload/plaintext from a size of 1024 × 1024 to 256 × 256; the complexity of the first dimension is 16 times the last payload size. The security and its levels can be controlled and determined based on the requirements. In the revised manuscript, the computational complexity is considered in a comparison with the recent related work, and the time complexity is added as a metric in the evaluation of the proposed crypto-system, as clarified in the following section. The correlation coefficient (Cr), mean square error (MSE), peak signal-to-noise ratio (PSNR), structural similarity (SSIM), time complexity (TC), and attacks presence are used as metrics for evaluating the proposed crypto-algorithm [27].

The rest of this paper is organized as follows: Section 2 presents the preliminaries to describe the techniques used. Section 3 presents the recent related research works. Section 4 describes the operation mechanism of the proposed power-efficient and lower-complexity multi-layered security algorithm. Section 5 presents the objective metrics that are used for evaluating the proposed technique. Section 6 presents a discussion of the computer simulation experiment results. Section 7 presents various comprehensive comparisons of the proposed algorithm with the existing and related works in different scenarios. The final conclusions are presented in Section 8.

2. Preliminaries

In this section, the utilized techniques for constructing the proposed lower-complexity security algorithm are presented.

2.1. Data Transforms

The data transforms employed in this powerful and robust security algorithm perform two functions: the plaintext decomposition extracts the important portion and reduces the complexity degree. The data transforms are also used to execute the cryptographic process in various spatial and frequency domains, to increase the reliability and robustness of the proposed security algorithm compared to existing approaches, by limiting the complexity due to the multi-layered security [28].

The different data transforms are tested and evaluated to choose the most suitable for achieving the trade-off of security and accepted level of complexity in order to meet the requirements of limited resources of the outdoor applications such as the IoT, WSN, and WBAN [29].

Figure 1 shows the mechanism of DWT for five levels of transformation. Every level/stage can be considered as a complexity reducer and a separate layer of security by unique S_key.

The DCT, WHT, FFT, and DWT are tested due to the complexity of all these data transform techniques being very close, as clarified in Equations (4)–(7). The detailed decomposition of the DWT helps in the construction of the cryptographic algorithm and in eliminating the huge increase in the complexity [17].

Example of algorithm operation and complexity reduction:

The L(ɳ) contains the main information of the plaintext, where ɳ = Ψ/2 and Ψ = M/2.

The H(ɳ), L_Ψ(ɳ), and H_Ψ(ɳ) are the side information of the plaintext. The ciphering of these portions is neglected due to complexity reduction and lower intelligence in these sections.

2.2. Chaos Mapping

This section is devoted to defining and clarifying the second technique, which is employed for constructing the proposed crypto-algorithm. The chaotic encryption is a widely used tool for image encryption; it utilizes the chaotic maps such as baker, logistic, and cat maps to build cryptography algorithms. The chaos mapping term is defined as the cryptographic approach based on one or more chaotic maps. It is used for performing the ciphering process. In the proposed algorithm, there are two chaos maps utilized: the logistic and baker maps. The first map is employed due to its high sensitivity towards any tampering, noise, and attacks. The baker chaos mapping is employed due to its sensitivity to the secret keys and its robustness and resistance to the attacks. It interacts with the multi-layered crypto-system perfectly [30].

The most applicable chaotic maps are the 2D baker and logistic maps. The ciphering based on baker chaos mapping is performed on the plaintext/payload and the per-encrypted portion, while the logistic based ciphering is executed on the n-ciphered text in the last stage of the algorithm [31].

The baker map is defined as a two-dimensional chaotic map. It transforms a square matrix into itself after operations similar to randomization. The baker map can be considered an efficient tool to randomize a square matrix of data. The baker map is described mathematically, as shown in the following Equation (1) [32,33].

$$B\left(x,y\right)=\left\{\begin{array}{c}\left(2x,y/2\right)0\le x<1/2\\ \left(2x-1,y/2+1/2\right)\hspace{1em}\hspace{1em}1∕2\le x<1\end{array}\right.$$

(1)

The generalized form of a baker chaos map is the simplified form, as presented in [34]. The more complex chaos baker map is formulated in 2D, as in Equation (2), as follows:

$$B\left(ɳ,\psi \right)=\left({\displaystyle \frac{N}{n_i}}\left(ɳ-M_i+\psi +mod\left({\displaystyle \frac{M}{m_i}}\right),{\displaystyle \frac{n_i}{N}}\left(\psi -\psi mod\left({\displaystyle \frac{M}{m_i}}\right)\right)\right)+M_i\right)$$

(2)

The generalized and discretized versions are shown in Figure 2a. The discredited map can be represented for an M × M matrix, as shown in Figure 2b, which represents a 2D chaotic encryption of an 8 * 8 matrix. The baker map encryption is dependent on the stretch-and-fold concept. This means that the plain image is randomly distributed in the encrypted image [35].

The logistic map is defined as a chaotic map; it has two formats for application as a tool in data encryption, which are 1D LM and 2D LM. The latter is considered in our research. The 2D logistic map is a discrete dynamic system; it is described and presented as an efficient tool to encrypt the digital images in several research papers, such as in [36,37]. Equation (3) gives the mathematical formula of the 2D logistic map [38]. This chaos map is highly sensitive towards noises and attacks; it is used as a perfect detection tool to detect any tiny tampering in the original data. Due to its sensitivity, the LM chaos-mapping-based ciphering in the proposed algorithm is only performed as a last level of the security layer.

$$L\left(x_{i+1},y_{i+1}\right)=\left\{\begin{array}{c}r\left(3y_i+1\right)x_i\left(1-x_i\right)\\ r(3xi+1+1)y_i(1-y_i)\end{array}\right.$$

(3)

The (x_i, y_i) represents the point at the ith iteration. Further, (x_i, y_i) and r are the initial values and the system parameter of this map, respectively. The previous equation defining the 2D logistic map is complicated, and is a complex dynamical system.

Due to the behavior of chaos mapping, it is suitable to use as an efficient data randomizing tool, as proposed previously in a number of research papers [30,31,32,33,34,35,36,37,38]. This type of chaotic map has high capability to resist the noise and tampering in the cipher version. The different noise/attacks are employed, such as Gaussian noise, salt and pepper, and speckle attacks, for evaluation of the performance of the proposed chaos-mapping- and transforms-based crypto-system in the presence of the various noises/attacks [39,40,41].

2.3. Key Management of Chaos Mapping

The secret key management in the baker mapping case can be presented through its mechanism operation [36]. In Figure 2b, the original plaintext/payload and the encrypted version/cipher text are given for the square matrix of 8 × 8 dimension. The baker map operation depends on the dimension of the input data/payload, which determines the length of the secret key (S_key). Figure 2b gives the operation mechanism of the baker map for 8 × 8 matrixes and the S_key = (2, 4, 2). The secret key is controlled and determined based on the size of the managed plaintext. The degree of confusion effectiveness can be controlled by the contents and elements of the secret key.

The amount of payload/plaintext determines the Skey, and the contents of the Skey control and determine the power of the randomization and encryption process.

The generation steps of secret keys for constructing the keys pool can be expressed as follows:

For the image pixels’ dimensions (m, n, x) for RBG images, the image must be a two-dimensional image and converted to grayscale mode images (M × M), as in Equation (4).

I [M, N] = immersive (I (m, n, x)

(4)

It is reshaped to a square matrix for generalization of the format to a square (Equation (5)).

I(Square) = reshape(I[M, N], Sqrt(M × N)Sqrt(M × N)]

(5)

The key elements must be equal to the Sqrt (M*N):

S_key = (e1, e2, e3, e4, ----------en). =Squar_root(M × N)

(6)

To generate the key automatically, there are two processes: the systematic auto-key, as in Equation (1), and the semi-systematic auto-key generation, as in Equation (7). For the systematic key generation, simple examples are given in Equations (5) and (6).

The systematic auto-key Gen=

$$\mathbf{T}\mathbf{h}\mathbf{e}\mathbf{A}\mathbf{u}\mathbf{t}\mathbf{o}.\mathbf{G}\mathbf{e}\mathbf{n}.\mathbf{S}\mathbf{y}\mathbf{s}.\mathbf{K}\mathbf{e}\mathbf{y}\mathbf{s}=\left[{\displaystyle \frac{\mathbf{s}\mathbf{r}(\mathbf{m}\mathbf{\ast }\mathbf{n})}{\mathbf{z}}},{\displaystyle \frac{\mathbf{s}\mathbf{r}(\mathbf{m}\mathbf{\ast }\mathbf{n})}{\mathbf{z}}},{\displaystyle \frac{\mathbf{s}\mathbf{r}(\mathbf{m}\mathbf{\ast }\mathbf{n})}{\mathbf{z}}},\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots .,{\displaystyle \frac{\mathbf{s}\mathbf{r}(\mathbf{m}\mathbf{\ast }\mathbf{n})}{\mathbf{z}}}\right]$$

(7)

Listed are the employed secret keys (S_keys) that are utilized in this proposed work for encryption of the classified images in the various simulation experiments.

• Camera man (1024 × 1024) secret keys:

S_key1 = [23, 25, 10, 6, 23, 25, 10, 6, 23, 25, 10, 6, 23, 25, 10, 6].

S_key2 = [35, 15, 14, 35, 15, 14, 35, 15, 14, 15, 35, 14].

S_key3 = [32, 16, 4, 8, 8, 4, 64, 8, 16, 32, 32, 16, 16].

S_key4 = [32, 32, 32, 16, 16, 32, 4, 4, 16, 4, 4, 16, 16, 32].

• Girl secret keys:

S_key1 = [64, 32, 32, 32, 32, 64].

S_key2 = [50, 44, 26, 8, 8, 26, 44, 50].

S_key3 = [64, 32, 64, 32, 64].

S_key4 = [25, 25, 5, 73, 73, 5, 25, 25].

• Sailboat secret keys:

S_key1 = [40, 10, 25, 25, 30, 20].

S_key2 = [50, 5, 10, 30, 20, 30, 5].

S_key3 = [20, 5, 15, 10, 35, 15, 50].

S_key4 = [10, 40, 40, 10, 10, 40].

• Cable Car secret keys:

S_key1 = [10, 55, 32, 40, 13].

S_key2 = [35, 5, 10, 10, 15, 25, 50].

S_key3 = [15, 35, 15, 20, 10, 5, 15, 30, 5].

S_key4 = [25, 15, 10, 35, 15, 40, 10].

3. Literature Review

In this section, our survey focuses on the recently published and existing security algorithms that consider the power efficiency of the presented security approaches. Also, similar objectives are considered in the presented comprehensive comparison of the proposed work with the state-of-art related works in Section 7.

As mentioned in the Section 1, the most existing and recent published related works ignore the two important factors, the computational complexity analysis and the power efficiency of the proposed security algorithms, as well as the provided security level and layers. Most of the presented related work focuses on the proposed techniques and their applicability in-the outdoor applications of WSN and IoT. This section of the literature review includes the related works of image/visual data security techniques. In the following are the most closed related security algorithms that consider the two vital issues without enough analysis.

Approaches of securing data on WSNs are proposed in [42,43]. In [42], the proposed approach relies on integrating asymmetric elliptic curve cryptography (ECC) and symmetric advanced encryption system (AES) techniques to provide a high level of security for data on the network. In this approach, the cluster head encrypts the data received from the subnodes based on the encryption keys generated from ECC and symmetric AES techniques. The encrypted data are sent to the main station. The main station decrypts the encrypted data relying on private encryption keys in order to retrieve the original data before the encryption process. Figure 3 illustrates the proposed approach for securing data in the WSNs. In [43], the authors discussed data security in WSNs. The authors presented an evaluation of four different types of algorithms used for data encryption. These algorithms are Rectangle, Fantomas, Camellia, and AES. The evaluations included the performance of the algorithms in execution times, throughput, and energy consumption in encrypting and decrypting data. The results showed that the Rectangle and Fantomas algorithms performed better in WSNs.

This research presents an approach for data encryption in WSNs applications. The proposed approach relies on the dynamic salt key for data encryption. The proposed approach includes three stages: the first stage is the creation of the encryption salt key, the second stage is the encryption of the data using the encryption key, and the third stage is the decryption of the encrypted data at the main station of the network. The proposed approach provides a level of security for the data with low energy consumption and low computational complexity. Figure 4 illustrates the data encryption scheme for the proposed approach [44].

The concepts of combing techniques or multi-layered security tools are presented in [45,46]. In [45], they presented a multi-level encryption system to secure data on WSNs. The proposed system combines symmetric algorithm AES and asymmetric algorithm ECC encryption of data. Data are encrypted at two levels, the first using AES encryption and the second using ECC encryption. The encrypted data are reduced in size using the Lempel–Ziv–Welch (LZW) image compression encoding technique. The proposed system provided time savings for encryption compared to some other systems. In [46], the authors provided data security algorithms for WSNs. The proposed security algorithms were constructed based on the suitability of the encryption data on WSNs. The evaluations included the performance of the algorithms in PDR, throughput, and energy consumption.

In [47], the authors suggested an approach for securing data transfer over the WSN applications. The approach relies on the Exceptional Key-based Node Validation for Secure Data Transmission-asymmetric encryption technique (EKbNV-SDT-AC) to encrypt data on the network. The proposed approach generates secret keys and distributes them on each node in WSNs. Each node encrypts data using a special secret key. The encrypted data are sent to the WSN main station. Figure 5 illustrates the proposed approach scheme for securing data in the WSNs.

The authors in [48] presented an approach to improve the routing and security of the transferred data on WSN application scenarios. The proposed approach relies on the Trust-Analysis-Based Energy Efficient and Safe Routing (TABEESR) protocol for routing network and securing data. Also, the proposed approach relies on public static agreement keys for encrypting data. Figure 6 illustrates the proposed approach for routing and securing data in the WSNs. In [49], the authors presented an evaluation of three different types of algorithms used for encrypting the transferred information. These utilized algorithms are block ciphers, stream ciphers, and hybrid ciphers. The evaluations included the performance of the algorithms in terms of the computational complexity of these techniques.

Securing of the colored images’ transmission over the WSNs utilizing a multi-level of encryption technique was proposed in [50]. The proposed encryption approach integrates three different levels of encryption, relying on three different encryption techniques. The techniques used in the proposed system are One-dimension Empirical Mode Decomposition 1D (EMC), 2D-DWT, and a 1D modified version of the logistic map (1D MVL). The system divides the colored image into three channels. Each channel is encrypted using different encryption levels. The three channels are combined again after the different encryption levels to produce the encrypted image. Figure 7 illustrates the proposed system diagram for encrypting colored images on WSNs, showing the symbol of the XOR logic function in the various processes of the combined cryptographic technique.

A data security approach in a healthcare application was presented in [51], to protect the reading data of the medical monitoring sensors. The proposed approach relies on the integration of different techniques for encrypting sensor data. This integration of various techniques provided a high level of security for the data on the network. The proposed approach combines AES and Rivest–Shamir–Adleman (RSA) techniques to secure data from medical monitoring sensors. Figure 8 illustrates the proposed approach diagram for securing medical sensor data. In [52], the authors presented an approach for securing data for smart home healthcare. The proposed approach combines AES and RSA techniques to secure data for smart home healthcare.

The security of WSNs was considered in [53]. This research discussed an algorithm for securing the transferred information over WSN applications scenarios. The proposed algorithm relies on the management of data routing and encryption on the network. The proposed algorithm uses hybrid energy-efficient distributed protocol for data routing. In the proposed algorithm, encryption keys are generated using a pseudo-random number generator. Data are encrypted on the network through cipher block chaining–Rivest Cipher 5. The proposed algorithm provides a high level of security for data on the network. Figure 9 illustrates the proposed algorithm scheme for securing data.

In [54], the authors provided an encryption approach to enhance the WSN security and provide a wireless secured link. The proposed cryptographic approach relies on the management of data routing and encryption on the network. The proposed approach improved the Low-Energy Adaptive Clustering Hierarchical (LEACH) routing protocol responsible for data routing over the WSNs scenarios. Also, the proposed approach provided data security on the network by managing the distribution of encryption keys among nodes, relying on the elliptic curve cryptography technique. In [55], the authors presented a survey about security, attacks, and security threats in real life based on WSNs. Also, the authors provided a solution to improve security on WSNs by adopting a handshaking mechanism with the alpha method.

4. The Methodology of the Lower-Complexity Crypto-System

The lower-complexity security algorithm based on the data composition and chaos mapping techniques is described in this section. The proposed algorithm is designed for and devoted to the limited-resource wireless network applications due to their resource limitations, such as Wireless Actuator Sensor Networks (WASNs), the outdoor applications of IOT and its medial functions, etc. Figure 10 and Figure 11 clarify the construction and mechanism operation of the algorithm.

4.1. Encryption Algorithm Steps

In the following, the processes and multimedia handling stages are listed to clarify the smoothing and robustness of the proposed crypto-algorithm.

The marking process is described stepwise, and is also described briefly in the block diagram shown in Figure 11.

Notes: In the following steps of the cryptography algorithm, the plaintext term means the original data (original classified image), while the side information/header term means the LH, HL, and HH partitions of the DWT transform technique. These terms are replaced by “payload and “header” terms.

The steps of the encryption process are described as follows in a step-by step manner to be more readable and understandable:

Step#1

• The classified RBG image (I_RGB) is converted to a grayscale image

*Grayscale image is directed processed as input to step two.

I_GR = I_Con (RGB).

• Gr stands for grayscale images and SD stands for square dimensions.

Generating square image I_SD = I_Gr (M*M).

Step#2

• The I_SD decomposition transforms tech as a stage (1) processing.

DWT (I_SD) = {LL₁, LH₁, HL₁, HH₁}.

*LL, LH, HL, and HH are symbols that represent the output of the DWT transform.

L refers to low band, H refers to high band.

1 refers to the stages of decomposition and method of controlling the complexity.

The dimensions refer to the amount of complexity.

The components of LL₁ dimensions (M/2*M/2).

LL₁Dim (M/2, M/2).

• LL_{1_Org} is separated to decompose the process individually.

Org refers to the original main partition of the original classified image.

Step#3

• DWT₂(LL_{1_Org}) = {LL₂, LH₂, HL₂, HH₂}

The LL₂Dim (M/4, M/4).

M: the Dim of the original plaintext.

Step#4

Repetition of Step#3 can be performed for more iterations to increase the reduction in the complexity and extension of secret keys to subsections.

Suppose: after N repetition,

• The LL_NDim(M/2N, M/2N).

Ex: Let the Org. dimensions of payload/plaintext be {Dim (1024 × 1024)} and the number of iterations is two (N = 2).

Therefore, LL₂Dim (256 × 256)—the amount of data will be manipulated by the chaos mapping cryptography in the frequency domain (FD).

If the number of iteration is doubled to four (N = 4):

The LL₄ Dim (64 × 64), as shown the iterations, reduces the original processed payload to one-fourth of the case (N = 2).

Then:

Step#5

LL_nS* = {LL*_n, LH*_n, HL*_n, HH*_n}.

The nS refers to the number of stages.

The components are segmented into two segments.

The main portion/payload = {LL*}.

The inside information/header = {LH*, HL*, HH*}.

• The encryption process can be performed at every stage or the lower dimensions.

Step#6

The encryption process is performed to manipulate the last payload size for ensuring the lower level of complexity.

LL*nS_EncI = BM (LL*nS), using Equation (2).

* The nS refers to the number of stages (nS): the decomposition times by DWT.

*EncI is contained from two sections. Enc is the abbreviation of “encryption”; it refers to the produced encrypted version, and I (number) refers to the number of the encryption process.

Step#7

To increase the confidentiality, the process can be repeated in cascaded behavior with the variations in secret keys.

Repeating the encryption with various Skeys:

Notes:

The accepted number of stages is restricted by the Org. Dim of the plaintext/payload, due to the direct relation of the power and varieties of S_key and the Dim of the plaintext/payload.

Enc-I, Enc-II, Enc-III, etc., denote the stage of encryption, and may equal the decomposing stages or not; this is optional in the algorithm.

The generated S_key is executed based on the new Dim of the processed plaintext.

Stage 2 of the encryption (optional) uses the different S_key or the same one, or relays the encryption to another decomposing process for more simplicity.

Example of the two optional processes:

In the following, description, two optional processes can be used to manipulate the payload for achieving the requirements of security and accepted level of complexity. These two approaches of data manipulation involve the encryption and data transform tools for data decomposition via different roles, as in the following examples: LL*1S_EncI = BM (LL*1Org) First Enc. {this first encrypting process}.

The encrypted payload can be encrypted again (directly) or manipulated by DWT to be decomposed to subpayload; hence, the main payload (produced LL) will be manipulated by the second encryption process only to satisfy the lower complexity in the computation and time.

In the second Enc., there are two ways:

LL*2S_EncII = BM (LL*1S_EncI).

**First type on manipulating (direct encryption of encrypted payload)

OR

DWT (LL*1S_EncI) = {LL_E1, LH_E1, HL_E1, HH_E1} (Decomposition2)

E1 means the production of the 1st encryption stage.

(Decomposing the encrypted payload to decrease its size in FD).

The main produced payload portion (LLE1) will be manipulated in the second encryption process as follows:

LL*2S_EncII = BM (LL {LL*1S_EncI}) (encryption of generated LL_E1).

The repetition is as required.

LL*nS_Enc_O = BM (LL*nS_Enc_n)(Direct encryption) by n times (N refers to the number of repetition process)

OR

LL*_{nS_Enc_O}=BM (LL {LL*(n-1) S_Enc_n-1}) {decomposition and encryption of decomposed payload) n times, where O refers to the order of required open process.

Figure 10 shows the stages of the cryptographic algorithm with the various data transforms merging. Due to the complexity survey of the different data transform techniques, which are utilized in the proposed algorithm to decompose the original plaintext, it is found that the computational complexities of them are close. Hence, based on the preload experiments, the DWT is the most suitable to achieve the high quality extracted decipher text and complexity reduction.

The product of stage 1 in the proposed algorithm will be the data input to the optional next stage, which is given in Figure 10. In this additional stage, there are two powerful points: one is employing the number of rounds after transforming the pre-encrypted data, the second is the round of chaos-based crypto-system containing one or more rounds using highly sensitive logistic map (LM)-based cryptography in the form of one-dimensional (1D) LM and two-dimensional processing 2D LM to catch and detect any tiny tampering.

Figure 11 clarifies the crypto-algorithm complexity utilizing the DWT transform, where a single * refers to the output portions of the decomposing process, and a double ** represents the cascaded cryptographic process on the (LL*) portion only, after the decomposition process. The multi-stage ciphering can be executed on the plaintext with the same complexity order due to the decomposition of the classified plaintext and separation of the main portion from the side information portions. As shown in the previous Figure 9, Figure 10 and Figure 11, the partitioning/decomposition of the plaintext/payload reduces the manipulated number of data to one-fourth of the size. The complexity of the proposed algorithm decreases with the increase in the level of security due to the Skey segmenting and cascaded multi-layered crypto-algorithm. In Section 6, an example of the complexity efficiency of the proposed algorithm is presented in a simple numerical comparison between the classic and proposed approach for manipulating the same image size.

4.2. The Complexity Analysis of the Proposed Algorithm

The different tools of the data transforms are utilized to employ the most suitable one, and the DCT and DWT are commonly used. The DWT is more suitable than the DCT and WHT transforms due to the dimension results of them. Therefore, the DWT-based approach is used for ciphering the digital image and protecting the plaintext from the various attacks, with high power efficiency and reduction in the complexity [56,57,58]. In the following, the complexities of the various data transform techniques are presented in Equation (8).

$$C_{DCT}=O\left(N^2\right)No.A.\&L.Ops$$

(8)

The reduced required operations are calculated using Equation (9) as follows:

$$C_{MDCT}=O\left(Nlog\left(N\right)\right)No.A.\&L.Ops$$

(9)

The computational complexity of DWT is expressed by Equation (10):

$$C_{DWT}=O\left(N^2\right)NumberofOperations$$

(10)

The computational complexity of WHT is expressed by Equation (11):

$$C_{WHT}=O\left(m\ast {log}_{2}m\right)NumberofOperations$$

(11)

As shown, from these previous equations, the complexities of the different techniques are very close, especially the DCT and DWT. Practically, and based on the computerized experiments, the DWT-based power/complexity efficient crypto-system is effective and robust due to the varieties of the side information.

5. The Objective Metrics: Performance Evaluations

The efficiency, reliability, applicability, and complexity measurements of the proposed cascaded lower-complexity crypto-system are performed, evaluating the processing time, quality of the extracted/decrypted image, and number of rounds. Also, the presence of noise/attacks is considered in the evaluation scenario. A special group of computer-based simulation experiments were executed to measure the resistance of the proposed lower-complexity crypto-algorithm and its applicability in the presence of noise/attacks.

This section defines the different performance metrics, which are used for evaluating the robustness and reliability of the proposed cascaded–interactive cryptographic algorithm depending on time complexity, extracted image quality, decrypted image quality, attack resistance, and attack sensitivity. Many metric tools are employed for measuring the similarities of the original image and the extracted/decrypted image. Also, the efficiency of the presented crypto-stego algorithm is evaluated through the classified image quality. The used metrics are described in [27,59,60] as follows:

• Correlation Coefficient (Cr):

It is one of the best metrics to evaluate the degree of closeness between the two functions. This metric can be used to determine the extent to which two images are close to each other, as given in Equation (12).

$$Cr=Corr\left(F\right(x,y),f(X,Y)$$

(12)

Thus, it gives a direct measure of the proposed algorithm efficiency. The most efficient algorithms produce images with correlation ratios closer to unity.

• Mean Square Error (MSE):

MSE is one of the most important image quality evaluation metrics, and it can be defined as the average of the squares of the differences between the intensities of two examined images. It can be mathematically represented as in Equation (13):

$$MSE={\displaystyle \frac{1}{MN}}\sum _{i=1}^M\sum _{j=1}^N(f\left(i,j\right)-f^{\prime }\left(i.j\right){)}^2$$

(13)

where f (i, j) is the original image and f′ (i, j) is the marked image. Higher values of MSE mean that the image is of poor quality.

• Peak Signal-to-Noise Ratio (PSNR):

The PSNR can be formulated mathematically as in Equation (14):

$$PSNR\left(dB\right)=10\log \left({\displaystyle \frac{{255}^2}{MSE}}\right)$$

(14)

A higher value of PSNR is better.

• Structural Similarity (SSIM):

The SSIM is a recently proposed image fidelity measure which has proved highly effective in measuring the fidelity of signals. The human visual system is highly sensitive to structural distortions and easily compensates for nonstructural distortions. The main function of the SSIM is to simulate this functionality; it is calculated as follows:

Let x = {xi|i = 1, 2, ..., N} and y = {yi|i = 1, 2, ..., N} be the original and the test image signals, respectively. Then, the SSIM can be expressed as in Equation (15):

$$SSIM\left(x,y\right)={\displaystyle \frac{\left(2{\mu }_x{\mu }_y+C_1\right)(2{\sigma }_{xy}+C_2)}{\left({\mu }_x^2+{\mu }_y^2+C_1\right)({\sigma }_x^2+{\sigma }_y^2+C_2)}}$$

(15)

• The Computational and Time Complexity (CC&TE):

The fifth metric tool is the complexity of the proposed crypto-system compared to the related and existing security techniques. The complexity term refers to three related concepts: the computational complexity, which deals with the number of operations for executing the crypto-system to encrypt and decrypt the plaintext; the time complexity (TE), which deals with the execution time of the crypto-system algorithms; and the power complexity, which deals with the amount of power required to perform the algorithms of the crypto-system. These three terms are joint and related. In this paper, the time complexity is measured to evaluate the processing time of the encryption algorithms of the proposed lower-complexity crypto-system.

6. Computer Simulation Result Discussion

The different computer-based simulation experiments were performed to demonstrate the performance of the Multi DWT and N-round chaos-based cascaded cryptographic approaches. Simulation tests were run using Windows 10 and MATLAB version 2017.

The simulation experiments were implemented on a set of different images, both in terms of size and grayscale (black and white) and RBG colored images to evaluate the applicability of the proposed technique. Figure 12 illustrates the utilized images in the computer simulation experiments, including the grayscale and RBG images.

The selected testing images for the simulation experiments were chosen to achieve the applicability, where they included the standard and nonstandard images with variations in both two types for evaluating the proposed crypto-algorithm. The WSN and outdoor IOT applications carry the scalar data and images; the proposed crypto-algorithm is suitable for both scalar data and images. The image encryption requires high computation; this issue is manipulated through the decomposition process to reduce the processed payload by 4 times and to decrease the computational complexity by 16 times.

6.1. Preparation of Simulation and Parameter Setting

This section defines the environment of the simulation experiments. The parameter setting of the simulation is defined to help the researchers and readers understand and make logical comparisons.

Table 1. Parameters of the computer-based simulation experiments.

Simulation Experiments Parameter Settings
Parameters	Description
Simulation tool	Matlab Program R2017a
Simulation environment	O.S: windows 10
	Intel(R) Core(TM)
	i5-6200U CPU @ 2.30 GHz 2.40 GHz
	RAM: 6.00 GB
Utilized image signal	Grayscale image: standard and nonstandard
	Color image: nonstandard
Image signal size	Grayscale image: 1024*1024
	Color image: 300*400*3
Security mechanism	Permutations and substitution
Domain	Domain time Frequency domain Merging time and frequency domains
Transforms tools	DWT
Number of secret keys (SK)	12 Skeys
Evaluation metrics	Cr, SSIM, PSNR, and MSE, Tc
Presence noise attacks	Gaussian noise, salt and pepper, speckle, and Poisson noise

tabulates the different parameter settings of the simulation and their values and natures.

Table 1 is added to tabulate the experimental simulation environment. Also, the similar objectives are considered in the presented comprehensive comparison of the proposed work with the state-of-art related works.

6.2. The Applicability Measurement of the Multi DWT and N-Round Chaos-Based Cascaded Cryptographic Approach Using Grayscale Images: Four-Cascaded S_keys (N = 4)

In this section, the experiments are demonstrated to measure the applicability of the Multi DWT and four-cascaded cryptographic algorithm using grayscale images within the four different Skeys. In these experiments, the various images, standard and nonstandard, are utilized, where the different metrics are used to evaluate the quality of the extracted plaintext after the Multi DWT and four-cascaded process.

Table 2. Tabulated results of applicability measurement of the Multi DWT and chaos N-round crypto-algorithm using grayscale images: Four-cascaded Skey (N = 4).

	Image Quality Metrics	Metrics Value
Camera man	Cr Plaintext and Cipher-text	0.0030
	Cr Plaintext and Decrypted text	1
	PSNR	99
	MSE	0
	SSIM	1
Girl	Cr Plaintext and Cipher text	0.0079
	Cr Plaintext and Decrypted text	1
	PSNR	99
	MSE	0
	SSIM	1

and Figure 13 show the results of the simulation experiments on four encryption keys for different images of size 1024 * 1024. The results presented in the table illustrate the robustness of the Multi DWT and N-round chaos-based cascaded cryptographic approach. We observe a significant difference between plaintext and cipher-text in the camera man image and the girl image

In the camera man image, the correlation coefficient between plaintext and cipher-text is 0.0030, while in the girl image, the correlation coefficient between plaintext and cipher-text is 0.0079. These are values less than 1, indicating the robustness of the encryption for Multi DWT and N-round chaos-based cascaded cryptographic approaches.

The results of experiments and the metric values demonstrate the effectiveness of the proposed lossless cascaded cryptographic approach based on decomposition/cryptography techniques in recovering data with the lossless technique. As observed in both images, the Cr between plaintext and decrypted text is 1.

Based on the results of the computerized experiments, it is clarified that the multi-merged secret keys for the 4L-DWT have the same complexity; in the case of reduction of these levels, the complexity is decreased by 25% with every level-DWT reduction. Therefore, based on the circumstances of the data communications on the WA/SN or on the outdoor IOT application scenarios, the amount of suitable complexity can be determined according to the level of DWT utilization.

6.3. Attacks Presence Consideration {Grayscale Images}

In this section, we present the results of the simulation experiments for the Multi DWT and N-round chaos-based cascaded cryptographic approach in the presence of different attacks. The simulation experiments were conducted on a number of different grayscale images.

Two images were used to test the robustness of the algorithm and its resistance of the noise. The noises were applied with various values, as shown in the results.

The three different image attacks, Gaussian noise, salt and pepper, and speckle attacks, were applied with the different values of α 0.1, 0.01, and 0.001. These attacks were applied on the proposed approach. The result samples of the two different deciphered images are tabulated in

Table 3. Deciphered image samples of the Multi DWT/N-round chaos crypto-system with respect to the various image attacks: {Four-cascaded Skey (N = 4) (α = 0.1)}.

	Image Quality Metrics	Different Attacks
		Gaussian Noise α = 0.1	Salt and Pepper Noise α = 0.1	Speckle Noise α = 0.1
Camera man	Cr	0.6671	0.7955	0.8015
	PSNR	39.5958	41.4101	39.6408
	MSE	115.0862	75.7864	113.8985
	SSIM	0.4595	0.5830	0.5727
Girl	Cr	0.4884	0.6957	0.7089
	PSNR	39.6361	41.7914	39.9103
	MSE	114.0219	69.4153	107.0471
	SSIM	0.4313	0.6359	0.6442

,

Table 4. Deciphered image samples of Multi DWT and N-round crypto-chaos algorithm with respect to the presence of various attacks: {Four-cascaded Skey (N = 4) (α = 0.01)}.

	Image Quality Metrics	Different Attacks
		Gaussian Noise α = 0.01	Salt and Pepper Noise α = 0.01	Speckle Noise α = 0.01
Camera man	Cr	0.9397	0.9762	0.9674
	PSNR	40.8252	48.6841	41.6788
	MSE	86.7114	14.1969	71.2391
	SSIM	0.8002	0.9097	0.8731
Girl	Cr	0.8748	0.9588	0.9549
	PSNR	40.8265	49.5830	42.2649
	MSE	86.6855	11.5424	62.2455
	SSIM	0.8229	0.9408	0.9319

and

Table 5. Deciphered image samples of Multi DWT and crypto-algorithm on grayscale images with different attacks: {Four-cascaded Skey (N = 4) (α = 0.001)}.

	Image Quality Metrics	Different Attacks
		Gaussian Noise α = 0.001	Salt and Pepper Noise α = 0.001	Speckle Noise α = 0.001
Camera man	Cr	0.9929	0.9974	0.9964
	PSNR	45.3780	57.1919	47.9450
	MSE	30.3948	2.0017	16.8306
	SSIM	0.9691	0.9893	0.9834
Girl	Cr	0.9849	0.9958	0.9951
	PSNR	45.4493	59.3389	50.0465
	MSE	29.8997	1.2210	10.3741
	SSIM	0.9766	0.9935	0.9923

for α = 0.1, α = 0.01, and α = 0.001, respectively.

As shown in Figure 14 and Table 3, the worst-case result is {α = 0.1}; the ordinary quality metrics mentioned in Section 4 are utilized to evaluate the deciphered images. The Gaussian noise has a worse effect on the images than the salt and speckle noise. Sometimes, the effects of these noises differ from one image to another due to the values of pixels, as shown in the variations between the camera man (Cr = 0.6671) and girl (Cr = 0.4884) for Gaussian noise. For speckle noise, the metrics values are very close, as shown in the tabulated results in Table 3. Therefore, based on these results, it is clear that the proposed algorithm resists the salt and pepper and speckle noise more than the Gaussian noise.

As shown in Table 4 and Table 5, Figure 15 and Figure 16, the deciphered images have been improved, as clarified from the values of the quality metrics. From the tabulated results in Table 4, the deciphered image from the Gaussian noise is affected more, with Cr = 0.9397, compared with the Cr = 0.9762 and Cr = 0.9674 for the salt and speckle noise, respectively, in the same scenario. The effects of these noises differ from one image to another, as shown in the results of experiments, due to the values of pixels, as shown in the variations between the camera man (Cr = 0.9397) and girl (Cr = 0.8748) for Gaussian noise. In the case of salt and pepper noise, the metric values are very close, as shown in the tabulated results in Table 5. Therefore, it is clear that the proposed Multi DWT and N-round chaos crypto-algorithm performs better with the moderate noise existence; the quality of the extracted deciphered classified image is good.

In the presence of lower noise levels, the proposed security algorithm successfully extracts the image with very high quality, as verified by the tabulated results in Table 5.

6.4. The Applicability Measurement of the Multi DWT and N-Round Chaos-Based Cascaded Cryptographic Approach Using RGB Images: Four-Cascaded S_keys (N = 4)

In this section, the experiments are demonstrated to measure the applicability of the Multi DWT and four-cascaded cryptographic algorithm using RGB images within the four different Skeys. In these experiments, the various images are utilized, where the different metrics are used to evaluate the quality of the extracted plaintext after the Multi DWT and four-cascaded process.

Table 6. Tabulated results of applicability measurement of the Multi DWT and chaos N-round crypto-algorithm using RGB images: Four-cascaded Skey (N = 4).

	Image Quality Metrics	Metrics Value
Sailboat	Cr Plaintext and Cipher-text	0.1596
	Cr Plaintext and Decrypted text	1
	PSNR	99
	MSE	0
	SSIM	1
Cable car	Cr Plaintext and Cipher text	0.0571
	Cr Plaintext and Decrypted text	1
	PSNR	99
	MSE	0
	SSIM	1

and Figure 17 show the results of the simulation experiments employing four different encryption secret keys (S_keys) with different four images of size 300 × 400 × 3. The results presented in the table illustrate the strength of the Multi DWT and N-round chaos-based cascaded cryptographic approach. We observe a significant difference between plaintext and cipher-text in the sailboat image and the cable car image.

In the sailboat image, the correlation coefficient between the plaintext and cipher-text is 0.1596, while in the cable car image, the correlation coefficient between plaintext and cipher-text is 0.0571; these values of correlation indicate and prove the robustness of the encryption for the Multi DWT and N-round chaos-based cascaded cryptographic approach.

The results also demonstrate the effectiveness of the Multi DWT and N-round chaos-based cascaded cryptographic approach in recovering the ciphered images. Hence, it can been considered a lossless cascaded cryptographic technique. We observe in both images that the correlation coefficient between the plaintext and decrypted text is 1. This indicates the efficiency of the Multi DWT and N-round chaos-based cascaded cryptographic approach in recovering data without any loss.

The computer-based experiments were demonstrated to evaluate the applicability of the proposed lower-complexity chaos-DWT cryptographic algorithm utilizing the different RBG and grayscale images. As clarified in Section 2, which presents a description of the proposed approach, and confirmed in the preliminary experiments, the main portion of the decomposed plaintext represents 25% of the entire decomposed file and carries the most important data of the plaintext. Therefore, the series of the chaos mapping series cryptography algorithm can be performed on the plaintext four times without extending the complexity. Also, the complexity and consumed power can be limited/reduced by decreasing the levels/times of decomposition of the plaintext. For example, supposing the decomposing level is 16 DWT, the complexity of the processes of the proposed algorithm reduces if the cryptography is executed in a series in the last four stages of the decomposed files. In this proposed scenario, the complexity of the chaos mapping cryptography algorithm can be calculated by the following Equation (16):

$$C_{Dec.16}=O(OriginalAlg.)/2^L$$

(16)

where L represents the number of level decomposition; it can also express the amount of complexity reduction.

According to the previous results and analysis, the proposed chaos mapping decomposition crypto-system can be applied for the hashing environment applications of the IoT and LP-WN, such as WSNs, WBANs, and WA/SNs, due to the variations of the application’s scenarios based on the nature of the application environment.

6.5. Attacks Presence Consideration {RBG Images}

In the following, the previous computer experiments are repeated for evaluation of the performance of the algorithm utilizing the RBG classified images. The results of these experiments are tabulated in

Table 7. Multi DWT and chaos N-round crypto-algorithm on RGB images with different attacks: Four-cascaded Skey (N = 4) (α = 0.1).

	Image Quality Metrics	Different Attacks
		Gaussian Noise α = 0.1	Salt and Pepper Noise α = 0.1	Speckle Noise α = 0.1
Sailboat	Cr	0.5737	0.7551	0.8295
	PSNR	35.1615	37.0602	35.7496
	MSE	109.6856	70.8400	95.7960
	SSIM	0.4249	0.5985	0.6750
Cable car	Cr	0.7275	0.8390	0.8962
	PSNR	35.1791	36.6259	35.4335
	MSE	109.2425	78.2904	103.0262
	SSIM	0.3262	0.4534	0.5530

,

Table 8. Multi DWT and chaos N-round crypto-algorithm on RGB images with different attacks: Four-cascaded Skey (N = 4) (α = 0.01).

	Image Quality Metrics	Different Attacks
		Gaussian Noise α = 0.01	Salt and Pepper Noise α = 0.01	Speckle Noise α = 0.01
Sailboat	Cr	0.9121	0.9688	0.9756
	PSNR	36.3195	44.0207	38.6215
	MSE	84.0149	14.2639	49.4482
	SSIM	0.7845	0.9090	0.9172
Cable car	Cr	0.9556	0.9806	0.9833
	PSNR	36.2930	42.2072	38.1504
	MSE	84.5290	21.6564	55.1144
	SSIM	0.6777	0.8245	0.8192

and

Table 9. Multi DWT and chaos N-round crypto-algorithm on RGB images with different attacks: Four-cascaded Skey (N = 4) (α = 0.001).

	Image Quality Metrics	Different Attacks
		Gaussian Noise α = 0.001	Salt and Pepper Noise α = 0.001	Speckle Noise α = 0.001
Sailboat	Cr	0.9876	0.9946	0.9953
	PSNR	40.6685	49.4520	45.4799
	MSE	30.8640	4.0842	10.1932
	SSIM	0.9540	0.9814	0.9810
Cable car	Cr	0.9920	0.9952	0.9953
	PSNR	40.0027	45.1766	42.7429
	MSE	35.9779	10.9305	19.1433
	SSIM	0.8917	0.9343	0.9263

and Figure 18, Figure 19 and Figure 20.

As clarified from the results of the proposed multi DWT and crypto-system on the RBG images, the presence of noise has a weak effect on the extracted deciphered images due to the greater values of the metrics compared to the values in the previous experiments with the same scenarios of testing and noise type presence.

In Figure 21, the quality of decrypted grayscale/RBG images is inspected in the presence of Poisson attacks. As clarified in the metrics values, the proposed crypto-system performs better in the presence of Poisson attacks than the previous attacks, as tabulated in Table 9 and

Table 10. The proposed N-round chaos/transform crypto-system and the related works comparison with respect to Cr, SSIM, PSNR, MSE, and the methodology/utilized technique (no attacks considered).

Ref	Cr Orig&Enc	Cr Orig&Dec	SSIM	PSNR	MSE	Methodology/Utilized Techniques
Nasr, M. [34]	0.0044	0.3787	0.04756	11.5565	-	Henon + Arnold
Wanqing, W. [37]	0.0074	_	_	_	_	FRFT transform+2D Logistic map+2D-Baker map
Razaq, A. [61]	0.0047	_	_	_	_	S-box
Yasser, I. [62]	0.004	_	_	_	_	Novel chaotic maps
Gaffar, A. [63]	_	_	0.9719	31.7289	5.6789	2D-LCG, silver ratio, and Galois field
Dai, L. [64]	_	_	0.9383	33.3145	_	Improved GAN and Hyper Chaotic
Proposed Crypto-graphic Algorithm	0.0030	1	1	99	0	N-round chaos/transform crypto-system

. As shown in the results of this experiment, the metrics of the deciphered grayscale images are Cr = 0.9999, PSNR = 63.36, SSIM = 0.9995, and MSE = 0.4833 for the camera man image; and Cr = 1, PSNR = 76.29, SSIM = 1 and MSE = 0.0246 for the girl image. For the results of the RBG images, the metrics’ values are PSNR = 50.920, Cr = 0.9976, SSIM = 0.9904, and MSE = 2.9088 for the sailboat image. The metrics of the deciphered sailboat image are as follows: PNR = 45.752, Cr = 0.9970, SSIM = 0.9508, and MSE = 9.5736. The results prove the superiority of the proposed crypto-technique and its reliability for ciphering the grayscale and RBG images in the presence of attacks. The grayscale images perform better in the presence of Poisson attacks than the colored images.

Therefore, the results of the previous experiments conclude the robustness of the crypto-system with the grayscale and RBG images, while it performs better with colored images. Also, the presence of different noises does not prevent the successful extraction of the deciphered image after several rounds of encryption. Hence, the proposed Multi DWT-N-round crypto-system is robust, reliable, and shows good resistance to noise and attacks.

The proposed crypto-system manipulates the complexity of the existing and recent related works through consideration of the real-time application requirements. It presents a flexible manner based on the decomposition process to reduce the amount of payload. The computational complexity is affected by the amount of payload and is related directly to the time consumption and the power complexity. In the following example, the complexity efficiency is presented.

For example, suppose that the plaintext is in an image with Dim (1024*124) pixels:

The complexity due to the chaos mapping = O (N*Φ).

N is the number of data elements (size of image as an example), and Φ is the number of operation due to the ciphering process. Hence, the number of operations = ${\mathbf{O}\left(\mathbf{10}\right(\mathbf{2}}^{\mathbf{10}}\ast {\mathbf{2}}^{\mathbf{10}}\left)\right)={\mathbf{O}(\mathbf{2}}^{\mathbf{21}})$; if the Φ = 10 operations only, one round is required by one Skey.

With the proposed algorithm:

Suppose that the level = 4 only, so the processed plaintext Dim (1024/4, 1024/4) = (256*256).

Therefore, when applying the ciphering only on the level 4:

The complexity = $\mathbf{O}\left(\mathbf{10}\left({\mathbf{2}}^{\mathbf{8}}\mathrm{\ast }{\mathbf{2}}^{\mathbf{8}}\right)\right)={\mathbf{O}(\mathbf{2}}^{\mathbf{17}})$, and the complexity is decreased to one-fourth of the value compared to the previous.

Let us consider the ciphering applied on the plaintext in level 3 of the DWT and level 4. The 2-ciphering process will cost the complexity half the original processing of the plaintext ciphering.

7. Comprehensive Comparison

This section presents the comprehensive comparison of the proposed algorithm within the different scenarios with respect to the existing techniques and related works. The presented comparison considers and includes the recent related works that propose the security techniques for the real-time applications of the IOT and WSNs.

In the first scenario of comparison, the different metrics are considered and the utilized techniques are tabulated in Table 10. As clarified in the tabulated results, our proposed algorithm has high-quality decrypted images and it is superior to those of the related research papers in terms of the encryption algorithm performance.

In the second scenario of comparison, the utilized metrics in our work are considered in the presence of attacks, as tabulated in

Table 11. Comparison of N-round chaos/transform crypto-system with the related works with respect to the presence of various attacks.

Ref	Image Quality Metrics	Different Attacks
		Gaussian Noise α = 0.1	Gaussian Noise α = 0.01	Gaussian Noise α = 0.001	Salt and Pepper Noise α = 0.1	Salt and Pepper Noise α = 0.01	Salt and Pepper Noise α = 0.001	Speckle Noise α = 0.1	Speckle Noise α = 0.01	Speckle Noise α = 0.001
Razaq, A. [61]	PSNR	_	_	_	_	24.76	_	_	_	_
Ustun, D. [65]	PSNR	_	_	_	14.6180	24.6022	34.5396	_	_	_
Kumar, S. [66]	PSNR	_	_	_	18.3675	_	_	_	_	_
Mohamed, A. [67]	PSNR	_	_	_	18.3045	_	_	_	_	_
Qin, X. [68]	PSNR	_	_	_	_	25.8941	_	_	_	_
Singh, D. [69]	PSNR	_	_	_	19.0380	_	_	_	_	_
	SSIM	_	_	_	0.6882	_	_	_	_	_
Souici, I. [70]	PSNR	_	_	_	23.84	_	29.89	_	_	_
Singh, D. [71]	PSNR	_	_	_	12.7136	19.0145	30.0487	_	_	_
Sharma, V. [72]	PSNR	19.1547	_	_	18.6230	_	_	_	_	_
Raghuvanshi, K. [73]	PSNR	_	_	_	18.45	_	_	_	_	_
Al-Muhammed, M. [74]	PSNR	_	_	24.253	_	22.177	_	_	_	_
	MSE	_	_	244.219	_	393.895	_	_	_	_
Pandey, K. [75]	PSNR	_	_	_	18.3613	_	_	_	_	_
Proposed crypto-algorithm metrics	Cr	0.6671	0.9397	0.9929	0.7955	0.9762	0.9974	0.8015	0.9674	0.9964
	PSNR	39.5958	40.8252	45.3780	41.4101	48.6841	57.1919	39.6408	41.6788	47.9450
	MSE	115.0862	86.7114	30.3948	75.7864	14.1969	2.0017	113.8985	71.2391	16.8306
	SSIM	0.4595	0.8002	0.9691	0.5830	0.9097	0.9893	0.5727	0.8731	0.9834

. As clarified in the tabulated results, our proposed algorithm performs better in the presence of different attacks and it is superior to those of the related research papers in terms of evaluation procedures, as clear from the utilized performance metrics.

In the last scenario of comparison, the time complexities of the proposed crypto-algorithm and the related works are considered and tabulated in

Table 12. Comparison of N-round chaos/transform crypto-system with the related works with respect to the time complexity of encryption and decryption algorithms.

Ref.	Encryption Time	Decryption Time	Methodology/Utilized Techniques
Shabana, U. [42]	2.5	1.71	ECC + AES
Elamurugu, V. [44]	0.841	0.037	Salt key
Ramadevi, P. [46]	73	_	IKEC
Bhanu, P. [47]	12	11	EKbNV-SDT-AC model
Satheesh, M. [48]	3.8	2.3	PSKAC
Nester, M. [51]	4	4	Hybrid encryption algorithm
Proposed crypto-graphic algorithm	2.1379	1.5717	N-round chaos/transform crypto-system
	2.6318	1.6654
	4.7546	1.5610
	5.0286	1.5769

. Figure 22 gives a brief overview of the consumed time for the encryption process and the decrypting process of the proposed chaos-DWT crypto-algorithm for the utilized images. Our proposed algorithm has lower time complexity than the related works due to the amount of time consumed in the encryption and decryption processes, as shown in Table 12.

Practical Limitations and Future Directions

This section is devoted to a brief description of the practical limitations and drawbacks of the proposed power-efficient crypto-algorithm, along with suggested solutions. The suggested solutions will be considered in future research works.

The main limitations of our proposed work rely on the amount of processed data and the degree of secret classifications, which determine the number of iterations in the proposed works. On the other hand, the available resources in the nodes must be considered. The resources and complexity due to the security trade-off is a challenge in the proposed technique. This challenge will be considered in future work through proposing algorithms to manage the required security level with respect to the available resources and overhead computation.

8. Conclusions

This paper presents an efficient and robust cryptographic algorithm for the limited-resource LP-WNs such as WA/SNs and outdoor IOT applications. The proposed security algorithm is constructed based on a combination of the decomposing tool and chaos mapping techniques. The lower-complexity cryptographic approach utilizes the plaintext decomposition to reduce the complexity through exclusion of the side information portions of plaintext. The various data transform techniques were employed to choose the superior tool. The DWT-chaos cryptographic algorithm gives lower complexity and high power efficiency. The chaos mapping is used to perform the ciphering process in a series of stages. The 2D logistic is used due to its high sensitivity; it encrypts the main plaintext portion in the last crypto-series. The 2D chaos baker mapping is used due to its secret keys management and its sensitivity to initial conditions. The experimental results revealed that the complexity is decreased by than 50%. Also, many computer experiments were demonstrated to evaluate the robustness, reliability, and applicability of the proposed complexity-efficient crypto-system algorithm in the presence of various attacks, using RBG and grayscale images. The results prove the high suitability of the proposed lower-complexity crypto-system for WASN and LP-WN applications due to its robustness in the presence of attacks and its power efficiency. As also clarified from the results, the time complexity is lower than the related works. Hence, the proposed chaos mapping-DWT crypto-algorithm is suitable for real-time applications.