Multilayer Convolutional Processing Network Based Cryptography Mechanism for Digital Images Infosecurity

Round 1

Reviewer 1 Report

In this manuscript, the authors propose an algorithm for image encryption. Their algorithm involves CNNs and encryption stages. The authors aim to provide an algorithm with a general purpose, so they test it on different image datasets. This is not very common in the literature and I do not particularly like it. The paper, as a whole, is not very easy to read and understand. Furthermore, it does not seem intentionally written for the community of image encryption scientists and engineers.

 

I do not believe that the manuscript is ready for publication in its current form. I suggest its authors would attend to the following comments:

 

1.     In lines 104 to 130, a brief is given about the proposed methodology. This is then written in full in Section 2. This is a little confusing, since the earlier provided brief on the methodology is not easy to understand.

2.     “Grünwald–Letnikov” is the correct name of the scientist, not what is written in line 161.

3.     The coloring of the correlation coefficient (CC) plots in Figure 2, Figure 6 and Figure 7 are done in red, green and blue. This is very misleading, as it gives the idea that the CC plots are for the RGB color channels of the same image, which is not true as described over each plot.

4.     The authors have decided to test their encryption scheme with images obtained from various datasets, other than the standard SIPI database. While this could be justified as their paper is geared towards medical images, nevertheless, it makes it hard to carry out a comparative analysis with the computed performance evaluation metrics. This leads to the authors both presenting their computed results in a strange way (as in Table 3), as well as comparing their computed results with the literature also in a strange way. When I say “strange way” here, I mean in a manner that is rather different than that utilized by most authors who publish articles on image encryption.

5.     While most of the references are recent, a few ones (dating as back as 2009) could definitely be replaced by more recent ones

6.     Overall, this manuscript needs a proof-reading by a native speaker of the English language to improve its writing style and fix the numerous punctuation errors.

Author Response

In this manuscript, the authors propose an algorithm for image encryption. Their algorithm involves CNNs and encryption stages. The authors aim to provide an algorithm with a general purpose, so they test it on different image datasets. This is not very common in the literature and I do not particularly like it. The paper, as a whole, is not very easy to read and understand. Furthermore, it does not seem intentionally written for the community of image encryption scientists and engineers. I do not believe that the manuscript is ready for publication in its current form. I suggest its authors would attend to the following comments:

Response: Thank you for review’s comments. The point-to-point responses to all the referees are shown below.

1. In lines 104 to 130, a brief is given about the proposed methodology. This is then written in full in Section 2. This is a little confusing,since the earlier provided brief on the methodology is not easy to understand.

Response: Thank you for reminding us. Some sentences have been added in Introduction, Pages#2 and #3.

Introduction, Pages#2 and #3

… The cryptography schemes 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 [12-21] have designed the symmetric cryptography scheme for performing the permutation, substitution, or shift operations for the encryption and decryption tasks, such as permutation method (PM), diffusion method (DM), or the combination of both methods 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 [12-17, 19, 22-24], are well-known cryptography schemes to support symmetrical encryption processes. The Arnold map, as a scrambling operator, uses the Arnold transform [12-15, 25] to produce the 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 with controlling two positive-integer parameters as secret keys or extending the control parameters to enlarge the secret key space [14-16]. However, the encryption processes are performed  by the same keys and cannot affect the frequency of image pixel values. Hence, this manner can be easily broken by statistical attacks (with the 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 its pixel positions. Its 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, 17, 22, 26-28]. Moreover, its scrambling operator can produce oscillation and chaotic behaviors by setting initial condition and adjusting the control parameters in the specific range with the iteration computations. To increase the chaotic-complexity levels, three-dimensional (3D) to five-dimensional (5D) chaotic maps, such as Euler equations and Hamiltonian conservative chaotic systems [2, 18, 29-30], are also used to establish a multi-dimensional scrambling operator, which can produce the hyperchaotic behaviors, allowing pseudorandom numbers to exhibit the 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, blue) or grayscale images. However, the CKG - based cryptography mechanism is sensitivity 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 for against different attacks.

Additionally, deep-learning (DL)-based network models, such as convolutional neural network (CNN) [2, 18], DL-based image encryption and decryption network (DeepEDN), and conditional generative adversarial network, have been used to encrypt and decrypt the digital images, owing to their complex structure and the large key space and hence 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, 31-34], which use multi convolutional and polling computations with multi convolutional windows to extract a hierarchy of feature patterns from the incoming images [32-34]. Hence, its multilayer model can perform the scrambling operations to produce the shuffled images different from the plain images for also against the statistical and differential attacks. Hence, the DL-based method, an image-to-image transformation technique with the multi convolutional operations, can also be used to realize the cryptography mechanism and will be sensitive to change in secret keys [2].

Therefore, basedon 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 to scramble pixel values from grayscale values to gray gradient values. The FOCW-based operator with the adjustable fractional-order parameters (Î [0, 1]) are used to scramble image pixel values using a 3 ´ 3 sliding window (sliding stride = 1) [30-31] over the plane image in the horizontal and vertical directions, which allows the combination of the convolutional weight calculations and scrambled pixel values. The FOCW-based window also has a rotation-invariant ability [35-36] (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 with 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 headshots (Facial Expression Image Database) [37] 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 image encryption process [2, 15, 17-18, 27, 38]; the structural similarity index measurement (SSIM) and peak signal-to-noise ratio (PSNR) [15, 39-40] are used to evaluate the quality of the decrypted image for the decryption process. …

 

2. “Grünwald–Letnikov” is the correct name of the scientist, not what is written in line 161.

Response: Thank you for reminding us. Some sentences have been added in Section 2, 2.1, Page#5.

 Section 2, 2.1, Page#5

… which are derived from the Grünwald–Letnikov (G-L) derivative in fractional calculus [31-32], and are 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 (02) and (03). …

 

3. The coloring of the correlation coefficient (CC) plots in Figure 2, Figure 6 and Figure 7 are done in red, green and blue. This is very misleading, as it gives the idea that the CC plots are for the RGB color channels of the same image, which is not true as described over each plot.

Response: Thank you for reminding us. Some sentences have been added in Section 2, 2.5 and Section 3, Pages#7, #11, and #14.

 Section 2, 2.5, Page#7

… which indicates frequency distributions in grayscale pixel values within an image [15, 18], as seen the number of pixels distribution and the correlation analysis in Figure 2, respectively, where green color for plian image, blue color for cipher image and plain image versus cipher image, and red color for plain image versus 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 that frequency distributions among the plain, cipher, and decrypted images. 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 for 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 evident from the adjacent location (x+1, y) versus location (x, y) in Figure 2, where the correlation coefficient (CC) of the plane image versus cipher image is 0.1022 (blue coloring plot) and that of the plane image versus 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). …

 Section 3, Page#11

… , 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. …

 Section 3, Page#14

… 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 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 green coloring plots). …

 

4. The authors have decided to test their encryption scheme with images obtained from various datasets, other than the standard SIPI database. While this could be justified as their paper is geared towards medical images, nevertheless, it makes it hard to carry out a comparative analysis with the computed performance evaluation metrics. This leads to the authors both presenting their computed results in a strange way (as in Table 3), as well as comparing their computed results with the literature also in a strange way. When I say “strange way” here, I mean in a manner that is rather different than that utilized by most authors who publish articles on image encryption.

Response: Thank you for reminding us. Some sentences have been added and Table 3 has also been modified in Section 3, Page#9.

 Section 3, Page#9

… 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 “security level”, could be evaluated by IE, NPCR and UACI indexes after the encryption process; and the SSIM and PSNR(dB) indexes were used evaluate the “quality of decrypted images” after the decryption process, as seen the flowchart in Figure 6, including cipher code generation, image encryptor and decryptor establishment, image encryption and decryption processes, and security level and decrypted image quality evaluations, respectively. …

 

5. While most of the references are recent, a few ones (dating as back as 2009) could definitely be replaced by more recent ones

Response: Thank you for reminding us. Some references have been cited.

 

14. Linqing Huang, Shuting Cai, Mingqing Xiao, and Xiaoming Xiong, “A simple chaotic map-based image encryption system using both plaintext related permutation and diffusion, ”Entropy, vol. 20, no. 7, 2018, pp. 1-18.
15. Xuejing Kang, Xuanshu Luo, Xuesong Zhang, and Jing Jiang, “Homogenized chebyshev-Arnold map and its application to color image encryption, ”IEEE Access, vol. 7, 2019, pp. 114459-114471.
16. Ahmad Alanezi, Bassem Abd-El-Atty, Hoshang Kolivand, Ahmed A. Abd El-Latif, Basma Abd El-Rahiem, Syam Sankar, and Hany S. Khalifa, “Securing digital images through simple permutation-substitution mechanism in cloud-based smart city environmen, ”Security and Communication Networks, vol. 2021, no. 6615512, 2021, pp. 1-17.
17. Pi-Yun Chen, Xuan-Hao Zhang, Jian-Xing Wu, Ching Chou Pai, Jin-Chyr Hsu, Chia-Hung Lin, and Neng-Sheng Pai, “Automatic breast tumor screening of mammographic images with optimal convolutional neural network, ”Applied Sciences, vol. 12, 2022, pp. 1-23.
18. Ahmad Alanezi, Bassem Abd-El-Atty, Hoshang Kolivand, Ahmed A. Abd El-Latif, Basma Abd El-Rahiem, Syam Sankar, and Hany S. Khalifa, “Securing digital images through simple permutation-substitution mechanism in cloud-based smart city environmen, ”Security and Communication Networks, vol. 2021, no. 6615512, 2021, pp. 1-17.
19. Hong Wen, Jie Tang, Jinsong Wu, Huanhuan Song, Tingyong Wu, Bin Wu, Pin-Han Ho, Shu-Chao Lv, and Li-min Sun, “A Cross-layer Secure Communication Model Based on Discrete Fractional Fourier Fransform (DFRFT), ”IEEE Transactions on Emerging Topics in Computing, vol. 3, no. 1, 2015, pp. 119-126.

57. Ruby Dwivedi, Divya Mehrotra, and Shaleen Chandrac, “Potential of Internet of Medical Things (IoMT) applications in building a smart healthcare system: a systematic review, ”J. Oral Biol Craniofac Res., vol. 12, no. 2, 2022, pp. 302–318.

58. Sung-Jung Hsiao and Wen-Tsai Sung, “Enhancing cybersecurity using blockchain technology based on IoT data fusion, ”IEEE Internet of Thing Journal, vol. 10, no. 1, 2023, pp. 486-498.

6. Overall, this manuscript needs a proof-reading by a native speaker of the English language to improve its writing style and fix the numerous punctuation errors.

Response: Thank you for reminding us. Correct as suggestion.

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

1- Flowchart / Pseudocode and algorithm steps need to be added in more details.
2- Discussion and Limitation sections need to be added.

3- Time spent need to be measured in the experimental results.

Author Response

1- Flowchart / Pseudocode and algorithm steps need to be added in more details.

Response: Thank you for reminding us. Some sentences and Figure 6 have been added in Section 3, Pages#9 and #10.

Section 3, Pages#9 and #10

… 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 “security level”, could be evaluated by IE, NPCR and UACI indexes after the encryption process; and the SSIM and PSNR(dB) indexes were used evaluate the “quality of decrypted images” after the decryption process, as seen the flowchart in Figure 6, including cipher code generation, image encryptor and decryptor establishment, image encryption and decryption processes, and security level and decrypted image quality evaluations, respectively. …

2- Discussion and Limitation sections need to be added.

Response: Thank you for reminding us. Some sentences have been added in Conclusion, Page#17.

 Conclusion, Page#17

… In future works, we can combine the artificial intelligence-based classifiers for on-line applications in face recognition or disease and cancer diagnosis (lung cancer, cardiopulmonary-related diseases, or bone tumors) for extending its applications in the ITS, IoT, and IoMT systems, and continually integrates new secure communication techniques, such as blockchain or discrete fractional fourier fransform methods, to enhance security level in physical layer for data transmission and sensing or imaging data fusion between heterogeneous devices..

 3- Time spent need to be measured in the experimental results.

Response: Thank you for reminding us. Some sentences have been added in Section 3, Page#14.

 Section 3, Page#14

… The proposed cryptography mechanism took average CPU time of 0.065 s and 0.107 s to perform the image encryption and decryption tasks, respectively. …

 

Author Response File: Author Response.pdf

Reviewer 3 Report

This submission aims to establish a 19 multilayer convolutional processing network (MCPN)-based encryption 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 the scramble operations from grayscale to gray gradient values for the first-image encryption and second-image decryption processes, respectively. In the MCPN weighted network, the 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.

1.This submission has not sufficiently clarified the novelty of the proposed approach. 

2. This submission misses discussing a few relevant works, such as

 “A Cross-layer Secure Communication Model Based on Discrete Fractional Fourier Fransform (DFRFT)”, IEEE Transactions on Emerging Topics in Computing,  vol. 3 , no. 1, pp. 119-126, Mar. 2015

 

 

Author Response

1. This submission has not sufficiently clarified the novelty of the proposed approach. 

Response: Thank you for reminding us. Some sentences have been added in Introduction, Pages#2 and #3.

 Introduction, Pages#2 and #3

… The cryptography schemes 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 [12-21] have designed the symmetric cryptography scheme for performing the permutation, substitution, or shift operations for the encryption and decryption tasks, such as permutation method (PM), diffusion method (DM), or the combination of both methods 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 [12-17, 19, 22-24], are well-known cryptography schemes to support symmetrical encryption processes. The Arnold map, as a scrambling operator, uses the Arnold transform [12-15, 25] to produce the 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 with controlling two positive-integer parameters as secret keys or extending the control parameters to enlarge the secret key space [14-16]. However, the encryption processes are performed  by the same keys and cannot affect the frequency of image pixel values. Hence, this manner can be easily broken by statistical attacks (with the 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 its pixel positions. Its 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, 17, 22, 26-28]. Moreover, its scrambling operator can produce oscillation and chaotic behaviors by setting initial condition and adjusting the control parameters in the specific range with the iteration computations. To increase the chaotic-complexity levels, three-dimensional (3D) to five-dimensional (5D) chaotic maps, such as Euler equations and Hamiltonian conservative chaotic systems [2, 18, 29-30], are also used to establish a multi-dimensional scrambling operator, which can produce the hyperchaotic behaviors, allowing pseudorandom numbers to exhibit the 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, blue) or grayscale images. However, the CKG - based cryptography mechanism is sensitivity 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 for against different attacks.

     Additionally, deep-learning (DL)-based network models, such as convolutional neural network (CNN) [2, 18], DL-based image encryption and decryption network (DeepEDN), and conditional generative adversarial network, have been used to encrypt and decrypt the digital images, owing to their complex structure and the large key space and hence 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, 31-34], which use multi convolutional and polling computations with multi convolutional windows to extract a hierarchy of feature patterns from the incoming images [32-34]. Hence, its multilayer model can perform the scrambling operations to produce the shuffled images different from the plain images for also against the statistical and differential attacks. Hence, the DL-based method, an image-to-image transformation technique with the multi convolutional operations, can also be used to realize the cryptography mechanism and will be sensitive to change in secret keys [2].

     Therefore, basedon 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 to scramble pixel values from grayscale values to gray gradient values. The FOCW-based operator with the adjustable fractional-order parameters (Î [0, 1]) are used to scramble image pixel values using a 3 ´ 3 sliding window (sliding stride = 1) [30-31] over the plane image in the horizontal and vertical directions, which allows the combination of the convolutional weight calculations and scrambled pixel values. The FOCW-based window also has a rotation-invariant ability [35-36] (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 with 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 headshots (Facial Expression Image Database) [37] 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 image encryption process [2, 15, 17-18, 27, 38]; the structural similarity index measurement (SSIM) and peak signal-to-noise ratio (PSNR) [15, 39-40] are used to evaluate the quality of the decrypted image for the decryption process. …

 

2. This submission misses discussing a few relevant works, such as

“A Cross-layer Secure Communication Model Based on Discrete Fractional Fourier Fransform (DFRFT)”, IEEE Transactions on Emerging Topics in Computing,  vol. 3 , no. 1, pp. 119-126, Mar. 2015.

Response: Thank you for reminding us. The reference has been cited.

56. Hong Wen, Jie Tang, Jinsong Wu, Huanhuan Song, Tingyong Wu, Bin Wu, Pin-Han Ho, Shu-Chao Lv, and Li-min Sun, “A Cross-layer Secure Communication Model Based on Discrete Fractional Fourier Fransform (DFRFT), ”IEEE Transactions on Emerging Topics in

    Computing, vol. 3, no. 1, 2015, pp. 119-126.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Thank you! The authors have satisfied my earlier comments.

 

Reviewer 2 Report

Accept.