Multilayer Convolutional Processing Network Based Cryptography Mechanism for Digital Images Infosecurity

Abstract

Digital images can be easily shared or stored using different imaging devices, storage tools, and computer networks or wireless communication systems. However, these digital images, such as headshots or medical images, may contain private information. Hence, to protect the confidentiality, reliability, and availability of digital images on online processing applications, it is crucial to increase the infosecurity of these images. Therefore, an authorization encryption scheme should ensure a high security level of digital images. The present study aimed to establish a multilayer convolutional processing network (MCPN)-based cryptography mechanism for performing two-round image encryption and decryption processes. In the MCPN layer, two-dimensional (2D) spatial convolutional operations were used to extract the image features and perform scramble operations from grayscale to gray gradient values for the first-image encryption and second-image decryption processes, respectively. In the MCPN weighted network, a sine-power chaotic map (SPCM)-based key generator was used to dynamically produce the non-ordered pseudorandom numbers to set the network-weighted values as secret keys in a sufficiently large key space. It performs the second and first encryption processes using the diffusion method, modifying the image pixel values. Children’s headshots and medical images were used to evaluate the security level by comparing the plain and cipher images using the information entropy, number of pixel change rate, and unified averaged changed intensity indices. Moreover, the plain and decrypted images were compared to verify the decrypted image quality using the structural similarity index measurement and peak signal-to-noise ratio.

1. Introduction

Digital images contain several types of information which represent original images in a set of pixel numbers and can be processed and stored using digital computer and storage devices in multimedia files, such as static images, audio, and video. These files can be widely shared and transmitted through computer networks or wireless communication networks (internet) to the desired destinations. These visual data are visible and accessible to specific users, catering to telemedicine, video-conference, video-on-demand, monitoring in a cloud computing intelligent transportation system (ITS), and medical images in an internet of medical things (IoMT) system [1,2,3,4]. However, these digital images may be easily duplicated or modified by their unauthorized distribution and illegal copying. Thus, ensuring digital image infosecurity, including data confidentiality, data integrity, and data availability, is a crucial task in open public communication channels so as to protect them from unauthorized individuals. For example, the users of mobile-phone digital cameras may protect their private pictures such as their headshots on online image-processing applications [5,6], ensuring image privacy on these applications. The cloud computing ITS acquires and processes images from various motorway sectors for car navigation, traffic-signal control, number-plate recognition, and speed-monitoring applications; thus, it requires a security protocol to protect the drivers’ private information, including license-plate numbers, location, and driving habits [1,7]. In addition, an IoMT system [2,3,8] allows for secure communication between the computer network and different medical devices to collect patients’ information using smart sensors or medical imaging equipment and, subsequently, analyzes it using artificial intelligence-based interpretation methods [2,8,9,10]. However, the IoMT is currently facing security and privacy concerns, such as medical record and image thefts or ransomware attacks in the healthcare sector [11]. Hence, the primary concern of online image-processing websites is to improve protection technologies to circumvent possible attacks. The goal of the proposed image encryption method is to apply a cryptography mechanism for restricting unauthorized users and protecting private information from theft, modification, or loss.

The cryptography scheme utilizes an encryption method to secure information by concealing the digital image contents. When encrypted, an image is only accessible to the specific authorized users using the secret keys, including asymmetric and symmetric cryptography methods. To protect security and privacy for digital images, previous studies [12,13,14,15,16,17,18,19,20,21] have designed the symmetric cryptography scheme to perform permutation, substitution, or shift operations for the encryption and decryption tasks, such as the permutation method (PM), the diffusion method (DM), or the combination of both methods, which have been used for digital signals and images encryption processes. In the PM-based encryption algorithms, the Arnold map and one-dimensional (1D) and multi-dimensional chaotic maps [12,13,14,15,16,17,19,22,23,24] are well-known cryptography schemes to support symmetrical encryption processes. The Arnold map, as a scrambling operator, uses the Arnold transform [12,13,14,15,25] to produce pseudorandom sequence numbers to rearrange the image pixel matrix, which randomly permutates the image pixel positions for producing a shuffled image; moreover, its inverse transform is used to decrypt the cipher image. Its chaotic permutation is produced by line mapping while also controlling two positive-integer parameters as secret keys or extending the control parameters to enlarge the secret key space [14,15,16]. However, the encryption processes are performed by the same keys and cannot affect the frequency of image pixel values. Hence, this method can be easily broken by statistical attacks (with frequency counting or statistical analysis) or brute force attacks.

In the DM-based encryption algorithms, the 1D and multi-dimensional chaotic maps are used to produce the pseudorandom sequence numbers as secret keys, replacing the image pixel values without rearranging their pixel positions. Their cryptography scheme’s secret keys are generated by using the chaotic map functions, as the so-called chaotic key generator (CKG), for image encryption, such as the logistic, sine, cosine, circle, tent, and Chebyshev maps [3,14,17,22,26,27]. Moreover, their scrambling operator can produce oscillation and chaotic behaviors by setting an initial condition and adjusting the control parameters in the specific range with the iteration computations. To increase the chaotic-complexity levels, from three-dimensional (3D) to five-dimensional (5D) chaotic maps, such as Euler equations and Hamiltonian conservative chaotic systems [2,18,28,29], are also used to establish a multi-dimensional scrambling operator, which can produce hyperchaotic behaviors, allowing pseudorandom numbers to exhibit probability and fractional-dimension distribution in random-number seed space. These chaotic operators can perform both PM- and DM-based methods to change the image pixel positions and image pixel values in digital color-scale (red, green, and blue) or grayscale images. However, the CKG-based cryptography mechanism is sensitive to the initial conditions and control parameters, and also selects secret keys in a fixed range of the random-number seed. Hence, the CKG needs to enlarge the secret key space to defend against different attacks.

Additionally, deep-learning (DL)-based network models, such as the convolutional neural network (CNN) [2,18], DL-based image encryption and decryption network (DeepEDN), and conditional generative adversarial network models, have been used to encrypt and decrypt digital images, and owing to their complex structure and the large key space, they exhibit excellent potential for digital image infosecurity. Traditional DL-based models have promising capabilities to perform the feature extraction and classification tasks, such as face recognition and disease or cancer diagnosis [17,19,27,29,30,31,32], which use multi convolutional and polling computations with multi convolutional windows to extract a hierarchy of feature patterns from incoming images [31,32,33]. Hence, their multilayer model can perform scrambling operations to produce shuffled images, which are different from the plain images, for also defending against statistical and differential attacks. Hence, the DL-based method, an image-to-image transformation technique which uses multi convolutional operations, can also be used to realize the cryptography mechanism and is sensitive to change in secret keys [2].

Therefore, based on the DM-based method, we intend to establish a multilayer convolutional operation-based cryptography mechanism, consisting of two convolutional layers and a weighted network (WN) to perform image encryption and decryption processes, as seen in Figure 1. In the two convolutional layers, the two fractional-order convolutional windows (FOCWs) are used to perform two-dimensional (2D) spatial convolutional operations in order to scramble pixel values from grayscale values to gray gradient values. The FOCW-based operator with the adjustable fractional-order parameters (∈[0, 1]) are used to scramble image pixel values using a 3 × 3 sliding window (sliding stride = 1) [29,34] over the plane image in the horizontal and vertical directions, which allows for the combination of the convolutional weight calculations and scrambled pixel values. The FOCW-based window also has a rotation-invariant ability [33,35] (rotating the angle 45° clockwise in eight directions from 0° to 315°) and can capture the same feature pattern in a 2D image. Before any cipher image transmission, the authorized person can reset the weighted values of FOCWs by adjusting the fractional-order parameter, and the connecting weighted values in the WN are produced by using the sine-power chaotic map (SPCM)-based key generator [17]. Thus, two-round convolutional operations are used to perform the first encryption process. In the WN, the SPCM-based key generator [17,26] generates the non-ordered pseudorandom numbers to set the connecting weighted values of the network, as a large number of secret keys are used to enhance the security level for the second encryption process. Hence, the cipher images are obtained through image-to-image transformation; moreover, the inverse processes, with the WN and two-round convolutional operations, are used to decrypt the cipher image. Through experimental validation with children’s headshots (Facial Expression Image Database) [36] and medical images (self-created hand X-ray images and National Institutes of Health (NIH) chest X-ray database), the security level is evaluated by using the information entropy (IE), the number of pixel changing rate (NPCR), and the unified averaged changed intensity (UACI) for the image encryption process [2,15,17,18,27,37]; the structural similarity index measurement (SSIM) and peak signal-to-noise ratio (PSNR) [15,38,39] are used to evaluate the quality of the decrypted image for the decryption process.

The remainder of this article is organized as follows: Section 2 describes the methodology, including the MCPN design, differential (security level) evaluation, and decrypted-image quality evaluation. Section 3 describes the experimental setup, digital image encryption and decryption tests, and performance evaluation using the NPCR, UACI, IE, SSIM, and PSNR indices. Section 4 concludes the paper.

2. Methodology

2.1. First-Image Encryption Using Fractional-Order Convolutional Processes

A conventional CNN typically contains convolutional, pooling, and fully-connected layers [2,31,33], with more than one convolutional layer for extracting feature maps, enabling the recognition of these features in the images. The pooling layer receives the specific features from a convolutional layer and compresses them using the maximum or average pooling processes. The fully-connected layer is employed to acquire the reduced feature maps for prediction, object recognition, or classification applications. In the CNN, the convolutional process is employed to constantly extract and compress the image features. Herein, it functioned to control the scrambling operations in the image encryption process against the active hacker attacks. Thus, the fractional-order convolutional process [29,30] is used to perform the 2D spatial convolutional operations in both the x horizontal and y vertical directions, which compute the gray gradient of a plain image, I₀ (I_xy = I₀), and can be expressed as follows [29,30]:

$${\mathit{ECI}}_{\mathit{xy}}^{\mathit{c}}=C^c(I_{xy},M,v), c=1, 2, \dots$$

(1)

$$\begin{gathered} M_x=\left[\begin{array}{ccc}{c}_0& c_1& c_2\\ c_1& c_1& 0\\ c_2& 0& c_2\end{array}\right], M_y=M_x^T, \mathrm{subject} \mathrm{to} \det (M_x)\ne 0 \mathrm{and} \\ \det (M_y)\ne 0 \end{gathered}$$

(2)

Elements in matrix M_x and M_y [29,30]:

$$c_n=\frac{\mathrm{\Gamma }(n-v)}{(n)!\mathrm{\Gamma }(-v)}, n=0, 1, 2, ..., \mathrm{subject} \mathrm{to} {\displaystyle \sum _{n=0}^{\infty }{c}_n\ne 0}$$

(3)

where C^c(•) is the fractional-order convolutional operator at the cth-round convolutional operation; I_xy ∈ [0, 255] is the grayscale pixel value at location (x, y) in a 2D image, where N × M is the size of the image, x = 1, 2, 3, …, N, and y = 1, 2, 3, …, M; ECI_xy^c is the convolution result by the matrix multiplication operation at location (x, y); v is the fractional-order parameter, v ∈ [0, 1]; M_x and M_y are the FOCWs, which are derived from the Grünwald–Letnikov (G-L) derivative in fractional calculus [30,31], and are used to perform the convolutional operations both in the horizontal and vertical directions, respectively. In this study, we select the 3 × 3 convolutional window, as seen in Equations (2) and (3).

Hence, three parameters, c₀, c₁, and c₂, were used to set the elements of the FOCW in the x and y directions. As seen in Figure 1, we defaulted the two-round convolutional operations (two convolution layers) with two 3 × 3 FOCWs, padding and passing an N × M matrix through two convolutional windows. The 2D convolutional process can be performed using a window, M_x, in the x direction and subsequent convolution using a window, M_y, in the y direction, which can transform the grayscale values to gray gradient values and also serves as a filter for edge detection and feature extraction. Hence, after each 2D spatial convolutional process, the result of the convolutional operation can be represented in a normalized value as follows [34]:

$${\mathit{ECI}}_{{}_{\mathit{xy}}}^{\mathit{c}}\cong \frac{|{\mathit{ECI}}_{\mathit{x}}^{\mathit{c}}|+|{\mathit{ECI}}_{\mathit{y}}^{\mathit{c}}|}{255}, c=1, 2, \dots$$

(4)

where ECI_x^c and ECI_y^c are the convolutional values in both the x and y directions for the first encryption processes, respectively. Equation (4) shows the values from the grayscale values [0, 255] to the normalized values [0, 2]. After the multi-round convolutional processes (c = 2 for two-round operation in this study), the first encrypted image could be obtained. This DM-based method with the fractional-order convolutional operation is a flexibility-encryption mechanism by controlling the fractional-order parameters for enhancing the security level.

2.2. Second-Image Encryption Using the Weighted Network

As seen in Figure 1, the first WN maps the ECI_xy to the second encrypted image, EI_xy, using the connecting network-weighted values. These connecting weighted values function as secret keys, which are used to construct both the encryption and decryption networks for the secondencryption process and first decryprion process, respectively, with the number of parameters for each network being N × M. The network-weighted values are obtained using the SPCM-based key generator [17,26] to set the secret keys (SKs) as follows:

$$c_{h+1}={\sin }^2(\sqrt{|c_h|})+2(1-r)|c_h|(1-2|c_h|), h=0, 1, 2, \dots , N_c$$

(5)

where r is the control parameter, c₀ is the initial condition, as 0 < c₀ < 1, and N_c = N × M is the number of SKs, as key space for the second encryption. We can compute the unsigned non-ordered integer numbers, sk_xy, sk_xy ∈ [1, 255], using the following equation [16,18]:

$$s{k}_{xy}=\mathrm{mod}(round(255\cdot |2c_h|){,}_{}255), h=0, 1, 2, \dots , N_c$$

(6)

where round(•) is the operator to return the nearest integer number, and mod(•) is the modulo operator. Hence, the pseudorandom numbers, sk_x, can be used to set the SKs at location (x, y). Further, the second encryption process can be calculated as follows:

$${\mathit{EI}}_{\mathit{xy}}={\mathit{ECI}}_{xy}\cdot s{k}_{xy}$$

(7)

where I₁ = EI_xy is the cipher image transmitted from a data-emitter end to a data-receiver end via a computer network (IEEE 802.3 standard or IEEE 802.15 standard [16,40]).

2.3. First-Image Decryption Using the Weighted Network

As seen in Figure 1, the second WN uses the symmetric SK to decrypt the cipher image using the following equation:

$${\mathit{DI}}_{\mathit{xy}}={\mathit{ECI}}_{xy}\cdot \frac{1}{s{k}_{xy}}, \mathrm{subject} \mathrm{to} s{k}_{xy}\ne 0$$

(8)

where DI_xy is the first decrypted image. In the proposed second encryption and first decryption processes, the key space contains N × M SKs, ensuring that the encryptor’s key space is sufficiently large and sensitive to the SKs, which are randomly distributed between values of 1 and 255. Thus, these multi-SKs can be dynamically readjusted at any time by using the SPCM-based key generator [17,26] to prevent the active hacker attacks.

2.4. Second-Image Decryption Using Fractional-Order Convolutional Processes

In the second decryption process, we used the 2D spatial convolutional operations to decrypt the DI_xy with the inverse matrix, M⁻¹, which can be expressed as follows:

$${\mathit{DCI}}_{\mathit{xy}}^{\mathit{c}}=C^c(\mathit{D}{I}_{xy},M^{-1},v), c=1, 2, \dots$$

(9)

$$M_x^{-1}=inv(\left[\begin{array}{ccc}{c}_0& c_1& c_2\\ c_1& c_1& 0\\ c_2& 0& c_2\end{array}\right]), M_y^{-1}={(M_x^{-1})}^T, \mathrm{subject} \mathrm{to} \det (M_x^{-1})\ne 0 \mathrm{and} \det (M_y^{-1})\ne 0$$

(10)

where inv^c(•) is the inverse matrix operator. Hence, after the two-round convolutional operations, the cipher image can be recovered by using Equations (9) and (10), and the final result of the convolutional operation can be represented as follows:

$${\mathit{DCI}}_{\mathit{xy}}^{\mathit{c}}\cong \frac{|{\mathit{DCI}}_{\mathit{x}}^{\mathit{c}}|+|{\mathit{DCI}}_{\mathit{y}}^{\mathit{c}}|}{255}, c=1, 2, \dots$$

(11)

where DCI_x^c and DCI_y^c are the convolutional values in both the x direction and y direction for the decryption processes, respectively.

Then, the decrypted image, I₂, can be computed by

$${\mathit{I}}_2\cong \frac{255\cdot {\mathit{DCI}}_{\mathit{xy}}^{\mathit{c}}}{\max (DC{I}_{xy}^c)}$$

(12)

where operator max(•) is the function for finding the maximum value in DCI_xy^c (c = 2 in this study).

2.5. Differential Evaluation between the Plain and Cipher Images

In general analysis, the graph of a histogram analysis is preliminary to evaluate the robustness of the image-cryptography mechanism, which indicates frequency distributions in grayscale pixel values within an image [15,18], as seen in the number of pixels distribution and the correlation analysis in Figure 2, respectively, where the green color represents the plian image, the blue color represents the cipher image and plain image versus cipher image, and the red color represents the plain image versus the decrypted image. Hence, we used a 227 × 227-sized (N = 227, M = 227, and N_c = 51,529 grayscale pixels for key space) digital image (resolution of 96 × 96 dots per inch and 24 bits per pixel (colored image)) to perform the encryption process and demonstrate the frequency distributions among the plain, cipher, and decrypted images. The plain and decrypted images exhibit the right-skewed distributions, whereas the histogram plot of the cipher image is uniform and nearly flat (plateau distribution), and exhibits significantly different behavior of the cipher image compared to the plain image as regards offering a secure encryption process. This also indicates that the proposed encryption model can change the distribution relationship in pixel values between the plain and cipher images for the statistical attack (frequency counting analysis). Additionally, for correlation analysis with the linear regression method, a good cipher image exhibits low adjacent correlation between the plain and cipher images, as evidenced by the adjacent location (x + 1, y) versus the location (x, y) in Figure 2, where the correlation coefficient (CC) of the plain image versus the cipher image is 0.1022 (blue coloring plot) and that of the plain image versus the decrypted image is 0.8126 (red coloring plot). The adjacent pixels in the cipher image exhibit extremely low correlation at CC = 0.0284 (blue coloring plot).

The IE is also an index to evaluate the level of randomness distribution in a cipher image [17,24,37,41]. The complexity and chaotic encryption processes can increase the IE level. For an 8-bit encrypted image, the ideal IE level is 8.00, as the larger the IE, the more confusing the information in the cipher image is. The IE index can be defined as follows [17,24,37,41]:

$$\mathit{IE}(q)={\displaystyle \sum _{j=0}^{Q-1}P(q_j){\log }_2(\frac{1}{P(q_j)})}, {\displaystyle \sum _{j=1}^{Q}P(q_j)=1}, j=0, 1, 2, \dots , Q-1$$

(13)

where Q is the total number of grayscale pixels, j is the grayscale pixel value (Q = 2⁸ = 256 in this study) in a cipher image, q_j is the jth grayscale value, and P(q_j) is the emergence probability of q_j. The IE value indicates that the same SKs can generate different diffusion images for different images. To evaluate the security level, the NPCR and UACI [2,15,17,18,27,37,42] are used to quantify the confidentiality between the plain image, I₀, and the cipher image, I₁, as follows:

$$\mathit{NPCR}=\frac{{\displaystyle \sum _{x=1,y=1}^{N,M}D(x,y)}}{N\times \mathit{M}}\times 100\%$$

(14)

$$D(x,y)=\left\{\begin{array}{l}0, if {\mathit{I}}_0(x,y)={\mathit{I}}_1(x,y)\hfill \\ 1, if {\mathit{I}}_0(x,y)\ne {\mathit{I}}_1(x,y)\hfill \end{array}\right.$$

(15)

$$\mathit{UACI}=\frac{{\displaystyle \sum _{x=1,y=1}^{N,M}|{\mathit{I}}_0(x,y)-{\mathit{I}}_1(x,y)|}}{N\times M}\times 100\%$$

(16)

where I₀ and I₁ represent the size of the N × M images; x= 1, 2, 3, …; N and y = 1, 2, 3, …, M; and I₀(x, y) and I₁(x, y) are the grayscale pixel values of plain and encrypted images, respectively. The NPCR index indicates the pixel change rate in a plain image after the encryption process, and the UACI index indicates the degree, which is used to measure the pixel differences between the plain and cipher images. For an ideal condition, the values of NPCR = 99.59% and UACI = 33.46% [37] yield the best performance for encryption processing.

2.6. Decrypted Image Quality Evaluation and Similarity Level Calculation between the Plain and Decrypted Images

After the image decryption process, the SSIM index is used to measure the recovery quality of a decrypted image and the similarity level between the plain image, I₀, and the decrypted image, I₂. The SSIM uses three comparison measurements, the luminance (L), contrast (C), and structure (S) [15,38,39]:

$${\mathit{L}(\mathit{I}}_0{,\mathit{I}}_2)=\frac{2{\mu }_{I_2}{\mu }_{I_0}+d_1}{{\mu }_{I_2}^2+{\mu }_{I_0}^2+d_1}, {\mathit{C}(\mathit{I}}_0{,\mathit{I}}_2)=\frac{2{\sigma }_{I_2}{\sigma }_{I_0}+d_2}{{\sigma }_{I_2}^2+{\sigma }_{I_0}^2+d_2}, \mathrm{and} {\mathit{S}(\mathit{I}}_0{,\mathit{I}}_2)=\frac{{\sigma }_{I_2{I}_0}+d_3}{{\sigma }_{I_2}^{}{\sigma }_{I_0}^{}+d_3}$$

(17)

$$d_1={(0.01l)}^2, d_2={(0.03l)}^2, \mathrm{and} d_3=\frac{1}{2}{d}_2$$

(18)

$$SSIM({\mathit{I}}_0,I_2)=L{(I_0,I_2)}^{\alpha }C{(I_0,I_2)}^{\beta }S{(I_0,I_2)}^{\gamma }$$

(19)

where ${\mu }_{I_2}$ and ${\mu }_{I_0}$ represent the mean values of the decrypted and plain images (I₂ and I₀), respectively; ${\sigma }_{I_2}$ and ${\sigma }_{I_0}$ are the standard deviations of the plain and decrypted images, respectively; ${\sigma }_{I_2{\mathit{I}}_0}$ is the covariance of images, I₂ and I₀; parameter, l, is the dynamic range of the pixel values (l is the maximum value in an image, that is, 255 for an 8-bit grayscale image); d₁ and d₂ are constants used to maintain the stability; parameters, 0.01 and 0.03 [15,17,39], are small constants; and the values of parameters, α, β, and γ, are set to 1. Hence, the SSIM offers a quantitative indication for evaluating the recovery quality and can be represented as follows [15,38,39]:

$$SSIM({\mathit{I}}_2,I_0)=\frac{(2{\mu }_{I_2}{\mu }_{I_0}+d_1)(2{\sigma }_{I_2{I}_0}+d_2)}{({\mu }_{I_2}^2+{\mu }_{I_0}^2+d_1)({\sigma }_{I_2}^2+{\sigma }_{I_0}^2+d_2)}, SSIM(I_2,I_0)\in [0,1], SSIM(I_2,I_0)\ge 0.95$$

(20)

The value of SSIM lies between 0 and 1. A value closer to 1 or greater than 0.95 indicates higher similarity (good recovery quality) between the plain and decrypted images, whereas a value of 0 indicates the absence of structural similarity. This index is also a human perception of recovery quality. The larger the SSIM value, the smaller the loss, which means that the proposed decryptor exhibits a good recovery quality without any active hacker attack.

In addition, the PSNR is an index to quantify the recovery quality level in image decryption [18,43], which measures the image distortion level by using the mean squared error (MSE) between the plain and decrypted images as follows:

$$MSE=\frac{1}{\mathit{NM}}{\displaystyle \sum _{i=1}^{\mathit{N}}{\displaystyle \sum _{j=1}^{\mathit{M}}{[I_2(i,j)-I_0(i,j)]}^2}}$$

(21)

$$PSNR\left(\mathit{dB}\right)=10{\log }_{10}(\frac{{MAX}_I^2}{MSE})$$

(22)

where I₀(x, y) and I₂(x, y) represent the plain and decrypted images, respectively, and MAX_I is the maximum pixel value in image I₂, where each point is represented by 8 bits, and the maximum value may be 255. The PSNR is a nonnegative index, which is used to evaluate the difference between the plain and decrypted images. This index has a smaller value for evaluating the encrypted image and performs better; the larger the index value, the smaller the distortion after the decryption process.

3. Experimental Results and Discussion

For the validated proposed MCPN-based cryptography mechanism, in experimental tests, the digital images were collected from headshots of 100 children (facial expression image database [36]) and 10 medical images (hand X-ray images, self-created), as seen in Figure 3 and Figure 4, respectively. Each digital image in joint photographic experts group (JPEG) format was digitized to a resolution of 96 × 96 dots per inch and 24 bits per pixel, with each image sized 227 × 227 pixels (N = 227, M = 227, and N_c = 51,529 represents KS), where the row numbers were x = 1, 2, 3, …, 227, and the column numbers were y = 1, 2, 3, …, 227. The proposed MCPN-based cryptography mechanism was designed on a tablet PC (Intel^® Xeon^®, CPU E5-2620, v4, 2.1 GHz and 64 GB of RAM) using MATLAB 9.0 version software (MathWorks, Natick, MA, USA), with a graphics processing unit (GPU: NVIDIA Quadro P620, 64-bit Windows 10.0 operating system) used to process digital images. Herein, we used a 2D FOCW with the fractional-order parameters v ∈ [0, 1] (using Equation (3)) [29,30] to perform the first encryption process; for example, the fractional-order parameter v = 0.02 was set, and then the FOCW and its inverse FOCW in both the horizontal and vertical directions were represented as follows:

$$M_x={\mathit{M}}_{\mathit{y}}^{\mathit{T}}=\left[\begin{array}{ccc}1.0000& -0.0200& -0.0098\\ -0.0200& -0.0200& 0\\ -0.0098& 0& -0.0098\end{array}\right] \mathrm{and} M_x{}^{-1}={({\mathit{M}}_{\mathit{y}}^{\mathit{T}})}^{-1}=\left[\begin{array}{ccc}0.9711& -0.9711& -0.9711\\ -0.9711& -49.0289& 0.9711\\ -0.9711& 0.9711& -101.0698\end{array}\right]$$

In the WN, the SPCM-based key generator was used to produce the pseudorandom numbers with the initial condition c_h=0 = 0.0 and control parameter r ∈ [3.3510, 4.0000] [17], and, further, 51,529 non-ordered pseudorandom numbers could be selected to set the SKs for image encryption and decryption using Equations (5) and (6), as seen in Figure 5a,b, respectively.

Table 1. Related formula and parameters for setting MCPN-based encryption mechanism.

Task	Method	Parameter Assignment
First Image Encryption	Two-round 2D spatial convolutional operations (two convolution layers) in the x and y directions [29,30] ${\mathit{ECI}}_{\mathit{xy}}^{\mathit{c}}=C^c(I_{xy},M,v)$, c = 1, 2 $M_x=\left[\begin{array}{ccc}{c}_0& c_1& c_2\\ c_1& c_1& 0\\ c_2& 0& c_2\end{array}\right]$, $M_y=M_x^T$$c_0=1$, $c_1=-v$, $c_2=\frac{v^2-v}{2}$, v ∈ [0, 1]. The results of the convolutional operations are normalized by using Equation (4). ${\mathit{ECI}}_{{}_{\mathit{xy}}}^{\mathit{c}}\cong \frac{|{\mathit{ECI}}_{\mathit{x}}^{\mathit{c}}|+|{\mathit{ECI}}_{\mathit{y}}^{\mathit{c}}|}{255}$	The fractional-order parameter, v, is set by the authorized persons, v ∈ [0, 1].
Second Image Encryption	The 2nd image encryption is performed by using ${\mathit{EI}}_{\mathit{xy}}={\mathit{ECI}}_{xy}\cdot s{k}_{xy}$	The secret keys, skxy, are produced by SPCM based key generator [17]. $c_{h+1}={\sin }^2(\sqrt{|c_h|})+2(1-r)|c_h|(1-2|c_h|)$, ch=0 = 0.0, r ∈ [3.3510, 4.0000]. $s{k}_{xy}=\mathrm{mod}(round(255\cdot |2c_h|){,}_{}255)$
First Image Decryption	The 1st image decryption is performed by using ${\mathit{DI}}_{\mathit{xy}}={\mathit{ECI}}_{xy}\cdot \frac{1}{s{k}_{xy}}$, subject to $s{k}_{xy}\ne 0$.
Second Image Decryption	Two-round 2D spatial convolutional operations in the x and y directions. ${\mathit{DCI}}_{\mathit{xy}}^{\mathit{c}}=C^c(\mathit{D}{I}_{xy},M^{-1},v)$, c = 1, 2 $M_x^{-1}=inv(\left[\begin{array}{ccc}{c}_0& c_1& c_2\\ c_1& c_1& 0\\ c_2& 0& c_2\end{array}\right])$, $M_y^{-1}={(M_x^{-1})}^T$, subject to $\det (M_x^{-1})\ne 0$ and $\det (M_y^{-1})\ne 0$$\det (M_y^{-1})\ne 0$. The decrypted image is computed by ${\mathit{DCI}}_{\mathit{xy}}^{\mathit{c}}\cong \frac{|{\mathit{DCI}}_{\mathit{x}}^{\mathit{c}}|+|{\mathit{DCI}}_{\mathit{y}}^{\mathit{c}}|}{255}$, ${\mathit{I}}_2\cong \frac{255\cdot {\mathit{DCI}}_{\mathit{xy}}^{\mathit{c}}}{\max (DC{I}_{xy}^c)}$	The fractional-order parameter, v, is set by the authorized persons, v ∈ [0, 1].

shows the related formula and parameters for setting MCPN-based encryption mechanism. Finally, through experimental tests using children’s headshots and medical images (hand X-ray and chest X-ray images), the difference between the plain and cipher images, as the so-called “security level”, could be evaluated by IE, NPCR, and UACI indexes after the encryption process; and the SSIM and PSNR (dB) indexes were used to evaluate the “quality of decrypted images” after the decryption process, as seen in the flowchart in Figure 6, including secret keys generation, image encryptor and decryptor establishment, image encryption and decryption processes, and security level and decrypted image quality evaluations, respectively.

In experimental tests, the digital images, including children’s headshots and medical images, were used to validate the proposed MCPN-based cryptography mechanism. From 100 children’s headshots, we randomly selected five images, as seen in Figure 7; the correlation analysis showed the relationships of two horizontally adjacent grayscale pixel values (location (x + 1, y) versus location (x, y)) for the plain images and cipher images (green and blue coloring plots) and the plain images versus decrypted images (red coloring plots), respectively. For example, as seen in the headshot in the first row in Figure 6, after encryption processing with the linear regression method, the CC was 0.0129 in the cipher image, which was extremely small, and small relationships were observed between the adjacent grayscale pixel values. It was challenging to restructure the relationship between the cipher and plain images. Hence, the proposed encryption mechanism was able to effectively shuffle the plain images against frequency counting, statistical, and entropy hacker attacks. For differential evaluation, the IE, NPCR, and UACI indices could also be used to evaluate the security levels for image encryption between the plain and cipher images.

As seen in

Table 2. Experimental results for differential evaluation and decrypted-image quality evaluation.

Digital Image	NO.	Security Level Evaluation			Decrypted Image Quality Evaluation
		IE	NPCR%	UACI%	SSIM	PSNR (dB)
	1	7.7936	100.00	80.24	0.9406	105.2513
	2	7.7864	100.00	75.45	0.9371	105.2513
	3	7.6396	100.00	65.33	0.8715	105.2513
	4	7.6338	100.00	67.24	0.8946	105.2513
	5	7.9286	100.00	87.72	0.9405	105.4591
	1	6.8112	100.00	34.60	0.9162	105.2704
	2	6.9452	100.00	37.86	0.9066	105.4208
	3	6.5357	100.00	28.29	0.9194	105.2513
	4	6.7082	100.00	32.02	0.9025	105.2513
	1	7.2054	100.00	45.11	0.9279	104.4977
	2	7.7354	100.00	60.87	0.9244	104.4977
	3	7.7686	100.00	60.87	0.9244	104.4977
	4	7.6144	100.00	58.66	0.9492	104.5395
	5	7.3966	100.00	46.17	0.9392	104.5205
	6	6.9366	100.00	39.54	0.9264	104.4977

, Equations (13)–(16) were used to compute the values of the IE, NPCR, and UACI indices; for example, for the headshot (No. 1) in first row in Figure 6, the NPCR% = 100.00% and UACI% = 80.24% were obtained to estimate the number of changing grayscale pixels and the number of averaged changed intensity, respectively; the IE index was used to quantify the randomness, disorder, and unavailable information using the probability, and it exhibited higher values and better performance for image encryption. As seen in Table 2, their IE values were greater than 7.5000 (very close to 8 [43]). Hence, the proposed encryption mechanism could produce random SKs to protect the digital images, and the promising quality of random number generation could contribute to the higher security value of the secret key. Additionally, with Equations (17)–(20), the SSIM index, as a value range of 0–1, was used to measure the similarity level between the decrypted and plain images. Their average value was greater than 0.9000, which indicated that the cipher images had been effectively recovered after the decryption process; otherwise, the similarity level of the cipher images was extremely low. The PSNR index (average value = 105.2928 dB) exhibited a higher value and also indicated that the proposed cryptography mechanism could meet the criteria for image recovery. Therefore, for five of the children’s headshots, the proposed MCPN-based cryptography mechanism could effectively resist differential attacks (with an average IE of 7.7564, average NPCR of 100.00%, and average UACI of 75.19%). The proposed cryptography mechanism took an average CPU time of 0.065 s and 0.107 s to perform the image encryption and decryption tasks, respectively.

For the medical images, the hand X-ray images were low-radiation exposure images, which are used to detect fractures, bone tumors, degenerative bone conditions, and osteomyelitis [44,45]. As evident from the four hand X-ray images in Figure 8, the hand X-rays were used to determine the bone age of children so as to circumvent the problem of impaired growth in children. Hence, they also contained patients’ private information and thus required protection. In Figure 8, in the plain images and decrypted images, the correlation between the adjacent pixels was extremely high (average CC = 0.9125, as seen in the blue and purple coloring plots); in contrast, the correlation between the adjacent pixels of the cipher image was extremely low (average CC = 0.1058, as seen in the green coloring plots). For the four randomly selected hand X-rays, an average IE, NPCR, and UACI of 6.7500, 100.00%, and 33.19%, respectively, were obtained to evaluate the encryption performance, and an average SSIM and PSNR of 0.9112 and 105.2985 dB, respectively, indicated the decryption performance for the quality evaluation of decrypted images. For these decrypted images, they exhibited sufficient quality to evaluate the bone age using DL-based computer-aided diagnosis methods [44,45].

Furthermore, six chest X-ray (CXR) images were selected from the Nation Institutes of Health Chest X-ray Database (Nation Institutes of Health, Clinical Center, Bethesda, MD, USA) [46,47,48] for validating the proposed cryptography mechanism (Table 2). Six images were labeled as representing normal condition, pneumonia, fibrosis, pleural effusion, emphysema, and pneumothorax, respectively, and each image in portable network graphics (PNG) format was digitized to a resolution of 96 × 96 dots per inch and 24 bits per pixel (colored image), and was a 1024 × 1024-pixel image. They were resized from 1024 × 1024 pixels to 227 × 227 pixels in JPEG format. As seen from the results of the correlation and histogram analyses in Figure 9, the linear regression method showed a low correlation in the cipher image, being CC = 0.9063 for the plain image in Figure 9a and CC = 0.1338 for the cipher image in Figure 9c, respectively; the histograms were significantly different for the cipher and plain images (Figure 9b,d). The average NPCR, UACI, and IE of 100.00%, 51.87%, and 7.4428, respectively, could be obtained to indicate the significant potential of the proposed method for CXR image encryption. In the decryption process, the average SSIM and PSNR of 0.9319 and 104.5048 dB, respectively, were obtained to measure the recovery quality of the decrypted images, offering promising recovery quality for the existing medical imaging examinations of cardiopulmonary diseases and lung cancers. The experimental results of the six selected CXR images are shown in Table 2. Additionally, with a standard digital image (512 × 512 pixels in tagged image file format, 96 × 96 dots per inch and 24 bits per pixel) from the University of Southern California-Signal and Image Processing Institute (USC-SIPI) Image Dataset [48,49], Figure 10 indicates the satisfactory encryption performance of the proposed method using correlation and histogram analyses. With 100 children’s headshots [36], 10 hand X-rays, 20 CXR images [46,47,50], and 10 standard images [49],

Table 3. Experimental results for encryption and decryption evaluations using IE, NPCR, UACI, SSIM, and PSNR.

Image Type	Security Level (Differential) Evaluation			Decrypted Image Quality Evaluation
	Average IE	Average NPCR%	Average UACI%	Average SSIM	Average PSNR (dB)
100 Children’s Headshots [36]	7.7900 ± 0.1553	99.99 ± 0.02	78.01 ± 9.27	0.9400 ± 0.0124	105.2532 ± 0.0083
10 Hand X-ray Images	6.7292 ± 0.1507	100.00 ± 0.00	32.88 ± 3.96	0.9039 ± 0.0127	104.6487 ± 0.8096
20 CXR Images [46,50]	7.4491 ± 0.2984	99.69 ± 0.69	56.01 ± 11.37	0.9363 ± 0.0092	104.5053 ± 0.0152
10 Standard Images [49]	7.4692 ± 0.1930	99.89 ± 0.02	53.88 ± 8.85	0.9013 ± 0.0012	112.3162 ± 0.0015

shows the experimental results for the image encryption and decryption evaluations. The experimental results validated the performance of the proposed cryptography mechanism and its encryption and decryption abilities. In

Table 4. Comparison of different cryptography mechanisms for digital image encryption.

Literature	Image Database	Method	Promising Result
[2]	Image Database from U.S. National Library of Medicine, Department of Health and Human Services in the USA and Shenzhen No. 3 People’s Hospital in China [47].	Deep-Learning-based Image Encryption and Decryption Network (DeepEDN) with Backpropagation Algorithm	Average IE = 7.96, Average SSIM = 0.014 for Encryption, Average SSIM = 0.913 for Decryption, Average PSNR = 36.35 dB
[16]	Standard 512 × 512 Pixels Images from SIPI Database [48] (Boats, Bridge, Baboon, Sailboat, Airplane, Peppers)	Cascading 1D Logistic-Chebyshev and 1D Logistic-Sine Maps.	Average IE = 7.9995 (Global), Average NPCR = 99.62%, Average UACI = 33.47%, and Average PSNR = 8.2123 dB for Image Encryption
[17]	NIH CXR Image Database (100 PA CXR Images) [46,50]	Chaotic Map and Quantum based Key Generator + GRA based Image Encryptor and Decryptor	Average IE = 7.55, Average NPCR = 99.45%, and Average UACI = 31.92% for Image Encryption,
[18]	Standard 256 Grayscale Images (Pepper, Butterfly, Architecture, Boat)	Logistic Map + 5D Conservative Hyper-Chaotic System + CNN	Average IE = 7.9983, Average NPCR = 99.61%, Average UACI = 33.45%, Average MSE = 8,315.6, and Average PSNR = 8.6125 dB for Image Encryption;
[26]	USC-SIPI Image Dataset [49], including 256 × 256, 512 × 512, and 1024 × 1024 Pixels Images (Miscellaneous Database)	2D Logistic-Modulated-Sine- Coupling-Logistic Chaotic Map	Average ISE (Local Shannon Entroy) = 7.9020, Average NPCR = 99.6096%, Average UACI = 33.4629% for Image Encryption;
[51]	PEIR (Pathology Education Informational Resource) Digital Library Image Database [51] (Medical Images)	Logistic Map based Key Generator + Perceptron Neural Network based Encryption System	Average PSNR=4.82 dB, Average IE = 7.98, Average NPCR = 99.88%, Average UACI = 24.54% for Image Encryption,
Proposed Method	100 Children’s Headshots [36] 10 Hand X-ray Images (self created) NIH CXR Image Database (20 CXR Images) [46,50] USC-SIPI Image Dataset [49] (10 Standard Images)	MCPN based Cryptography Mechanism (2D Spatial Fractional-Order Convolutional Operations + SPCM based Key Generator) [17,27,29,30]	As seen Experimental Results in Table 3

is shown comparison of different cryptography mechanisms for digital image encryption.

As is evident from the literature in Table 4 [2,16,17,18,26,51], DeepEDN [2], chaotic map-based key generator [16,26], and chaotic map-based key generator + neural network-based encryption systems [17,18,52] have been implemented for digital image encryption and decryption processes. For example, a previous study [16] used cascaded 1D logistic-Chebyshev and 1D logistic-sine maps to permute the plain image and substitute the permuted image, respectively. With the standard 512 × 512 pixel-images from SIPI Database (boats, bridge, baboon, sailboat, airplane, and peppers) [48], the experimental results, having an average IE = 7.9995 (Global), average NPCR = 99.62%, average UACI = 33.47%, and average PSNR = 8.2123 dB, showed the effectiveness of the cascading chaotic map-based cryptosystem for image encryption. Moreover, in a previous report [18], the 5D conservative hyperchaotic system was used to establish a multi-dimensional key generator with a strong pseudorandomness scheme to produce pseudorandom numbers for a large key space, and, further, the CNN was used to generate the chaotic pointer to control the scrambling operations for image encryption. With 256 standard grayscale images (pepper, butterfly, architecture, and boat), an average IE, NPCR, UACI, MSE, and PSNR of 7.9983, 99.61%, 33.45%, 8,315.6, and 8.6125 dB, respectively, were obtained to validate the feasibility of the cryptography mechanism in the digital encryption channel. Dridi et al. [52] used the combined cryptography mechanism as a “logistic map-based key generator + perceptron neural network (PNN)” to generate cipher images with sufficiently large key space (>2¹⁰⁰) to resist brute-force attacks. With medical images from the Pathology Education Informational Resource digital library image database [53], average PSNR, IE, NPCR, and UACI values of 4.82 dB, 7.98, 99.88%, and 24.54%, respectively, showed that the PNN with chaotic map could enhance the cryptography technique for statistical and differential attacks. Ding et al. [2] and Lin et al. [17] demonstrated promising results for image encryption in medical images using the DL-based cryptography mechanism [46,50]. Through the experimental tests utilizing the standard image database [37,46,47,49], the proposed cryptography mechanism indicated the following advantages for digital image encryption:

• The FOCW was a flexible encryptor to perform the first-image encryption and second-image decryption processes, which could control the scrambling operations by adjusting the multiscale fractional-order parameters.
• The SPCM-based key generator was used to produce the non-ordered pseudorandom numbers as SKs to perform second-image encryption and first-image decryption processes in the WN.
• The proposed cryptography mechanism presented a simple structure to scramble image pixel values using two-round 2D spatial convolutional operations and diffusion processes.
• Using the children’s headshots [36], medical image database [46,50], and standard digital image database [49], the security level (differential evaluation) could be verified using the IE, NPCR, and UACI indices.
• The decrypted image quality could be evaluated using the SSIM and PSNR indices.

4. Conclusions

In this study, an MCPN-based cryptography mechanism was proposed to ensure online digital image infosecurity in a computer network, an ITS, an IoT, or an IoMT system [53,54,55]. The proposed MCPN consisted of two 2D spatial convolutional layers and a WN to perform the image encryption and decryption processes. In the two convolutional layers, two FOCW-based operators were used to scramble image pixel values for the purpose of, first, encrypting the plain image and, second, in WN, to produce the cipher image, the SPCM-based key generator produced the non-ordered pseudorandom numbers as SKs. With 100 children’s headshots and 10 hand X-rays, the IE, NPCR%, and UACI% indices were used to validate the security level of the proposed cryptography mechanism against statistical and differential attacks. For image decryption processes, the reciprocal numbers in WN and 2D spatial convolutional operations with a FOCW inverse matrix were used to decrypt the cipher images. The SSIM and PSNR, used to revaluate the recovery quality, indicated a satisfactory decryption performance. Hence, the proposed MCPN-based cryptography mechanism offers promising capabilities to protect the data confidentiality, data recoverability, and data availability of digital images. In future works, we can combine the artificial intelligence (AI)-based classifiers for online applications in face recognition or disease and cancer diagnosis (lung cancer, cardiopulmonary-related diseases, or bone tumors) to extend its applications in the ITS, IoT, and IoMT systems, and continually integratenew secure communication techniques, such as blockchain or discrete fractional fourier fransform methods, to enhance the security level in the physical layer for data transmission and sensing or imaging data fusion between heterogeneous devices.