A Multilayered Audio Signal Encryption Approach for Secure Voice Communication

Round 1

Reviewer 1 Report

Please revised it as explained in the attached file. 

Comments for author File: Comments.pdf

Author Response

Authors Response for reviewer 1 Comments

The authors would like to thank the reviewer for his/her efforts in reviewing the paper. The notifications of the reviewer have been considered in the revised version.

1. Page 1, lines: 8-15 in the abstract should be moved to the beginning of the introduction section. Hence, the abstract should be started as" This paper proposes three cryptosystems for encrypting audio....."

 Response 1: we modified abstract as mentioned in the comment it is found in (page. 1) lines 9-28

2. Page 2, lines: 82-84, the word “section" should be” Section" . Please, check if there are other places having such an issue.

Response 2: we modified it in page 2 from line 80 to 83 .

3. Page 3, line 96, "Block by block encryption for.wav files" should be corrected.

Response 3: we modified it, it becomes (Block by block encryption for audio files) in page 3 line 110.

4. Page 3, line 138, "The main contributions of this study are briefly summarized here," should be "The main contributions of this study are briefly summarized in the following section".

Response 4: we modified it in page 3 line 163.

5. Page 4, line 161, "Fig. 1" should be " Figure 1", since in many places in the paper you used the word "Figure", so try to make them in one form that is " Figure..." instead of " Fig", see e.g. lines 184 and 186. Similarly, page 5, line 192

Response 5: we modified it as mentioned in the comment as shown in page 4 line 212.

6. Page 5, line 214, “as shown in Figure (3)." should be “as shown in Figure 3"

Response 6: we modified it as mentioned in the comment as shown in page 6 line 248.

7. Page 6, Figure 3, the " Audio Signal" should be "Audio signal".

Response 7: we modified it as mentioned in the comment.

8. Page 7, equations (2), (3), (5) and (6) should be ended with a comma ",", and equation (4) with a period ".".

Response 8: we modified it as mentioned in the comment.

9. Page 8, line 289, "Table3" should be "Table 3".

Response 9: we modified it as mentioned in the comment in page 8 line 337.

10. The references should be written in one form since they are not, like " Family name, initials, title, place of publication, volume and issue numbers, year of publication, doi". They should be ordered alphabetically. Also, reference [20] Pages 155-170,ISSN 0165-1684,https://doi.org/10.1016/j.sigpro.2016.03.021, what is that?

Response 10: we modified it as mentioned in the comment as shown in page 15 line 467 to 472.

Authors Response for reviewer 1 Comments

The authors would like to thank the reviewer for his/her efforts in reviewing the paper. The notifications of the reviewer have been considered in the revised version.

1. Page 1, lines: 8-15 in the abstract should be moved to the beginning of the introduction section. Hence, the abstract should be started as" This paper proposes three cryptosystems for encrypting audio....."

 Response 1: we modified abstract as mentioned in the comment it is found in (page. 1) lines 9-28

2. Page 2, lines: 82-84, the word “section" should be” Section" . Please, check if there are other places having such an issue.

Response 2: we modified it in page 2 from line 80 to 83 .

3. Page 3, line 96, "Block by block encryption for.wav files" should be corrected.

Response 3: we modified it, it becomes (Block by block encryption for audio files) in page 3 line 110.

4. Page 3, line 138, "The main contributions of this study are briefly summarized here," should be "The main contributions of this study are briefly summarized in the following section".

Response 4: we modified it in page 3 line 163.

5. Page 4, line 161, "Fig. 1" should be " Figure 1", since in many places in the paper you used the word "Figure", so try to make them in one form that is " Figure..." instead of " Fig", see e.g. lines 184 and 186. Similarly, page 5, line 192

Response 5: we modified it as mentioned in the comment as shown in page 4 line 212.

6. Page 5, line 214, “as shown in Figure (3)." should be “as shown in Figure 3"

Response 6: we modified it as mentioned in the comment as shown in page 6 line 248.

7. Page 6, Figure 3, the " Audio Signal" should be "Audio signal".

Response 7: we modified it as mentioned in the comment.

8. Page 7, equations (2), (3), (5) and (6) should be ended with a comma ",", and equation (4) with a period ".".

Response 8: we modified it as mentioned in the comment.

9. Page 8, line 289, "Table3" should be "Table 3".

Response 9: we modified it as mentioned in the comment in page 8 line 337.

10. The references should be written in one form since they are not, like " Family name, initials, title, place of publication, volume and issue numbers, year of publication, doi". They should be ordered alphabetically. Also, reference [20] Pages 155-170,ISSN 0165-1684,https://doi.org/10.1016/j.sigpro.2016.03.021, what is that?

Response 10: we modified it as mentioned in the comment as shown in page 15 line 467 to 472.

Author Response File: Author Response.docx

Reviewer 2 Report

1. The language is poor and should be polished.

2.  The paper structure should be rearranged to make it reasonable.

Author Response

Authors Response for reviewer 2 Comments

The authors would like to thank the reviewer for his/her efforts in reviewing the paper. The notifications of the reviewer have been considered in the revised version.

1. The language is poor and should be polished.

Response 1: we modified language as mentioned in the comment.

2. The paper structure should be rearranged to make it reasonable.

Response 2: we modified structure as possible according to what mentioned in the comment.

Author Response File: Author Response.docx

Reviewer 3 Report

The paper considers several approaches for media encryption using chaos-based techniques. The considered topic is relatively hot in nonlinear science and communications design.
The paper is a bit sloppy and requires some polishing prior to publication. My specific comments are:
1. The abstract should be completely rewritten. First, it should not report a well-known fact about media encryption. Second, there should be no typos, e.g. "This paper introduces The proposed technique introduces" and thereafter.
2. "The proposed cryptosystems are 21 contrasted with the 1-D logistic map-based encryption method." - with all respect to the Authors, the logistic-map-based encryption method is far from state-of-the-art solutions in the field. I recommend considering several recently reported approaches, including minimal digital chaotic maps, adaptive discrete chaotic maps, fractional-order maps, finite-precision-based approaches, etc.
3. The problem statement is to be clarified. If "security and privacy pose a serious problem", the data is usually not transmitted through "unsecured communication channels". In other words, modern encryption standards like AES satisfy almost all the needs in regular data transmissions. Speaking of chaos-based encryption - dozens (if not hundreds) of new algorithms were proposed recently. Thus, the question arises - why does one need another chaos-based cryptographic technique? The statements connected with the specifics of audio encryption are not persuasive - in current radio systems the audio signals can be pretty well encrypted, and many successful commercial solutions are known in the field.
4. The proposed cryptosystems should be compared not between themselves, but with other solutions in the field. I suggest expanding the comparison section with recent cryptographic approaches, for example, the encryption schemes based on 1D coupled hyperbolic tangent chaotic map with delay, one dimensional piecewise chaotic map, or bit level cubic shuffling.
5. More statistical attack methods should be taken into consideration.
6. Does your approach suggest concealed transfer? If yes, some techniques for discovering chaos-based communications can be discussed.
7. "High levels of security are present in the proposed cryptosystems" - this statement is to be more thoroughly proven.
8. I recommend expanding the Conclusions section with more discussion on chaos-based encryption.

Nevertheless, I like the study and believe it can be published after relatively major revisions.

Author Response

Authors Response for reviewer 3 Comments

The authors would like to thank the reviewer for his/her efforts in reviewing the paper. The notifications of the reviewer have been considered in the revised version.

1. The abstract should be completely rewritten. First, it should not report a well-known fact about media encryption. Second, there should be no typos, e.g. "This paper introduces The proposed technique introduces" and thereafter.

Response 1: we modified abstract as mentioned in the comment, it is shown in (page. 1) lines 9-28

2. "The proposed cryptosystems are 21 contrasted with the 1-D logistic map-based encryption method." - with all respect to the Authors, the logistic-map-based encryption method is far from state-of-the-art solutions in the field. I recommend considering several recently reported approaches, including minimal digital chaotic maps, adaptive discrete chaotic maps, fractional-order maps, finite-precision-based approaches, etc.

Response 2: we compare our technique to other methods as mentioned in the comment, as shown in page 13 .

4.3 Performance Comparison of Audio Encryption Algorithms

The objective of this comparison is the audio encryption techniques. Table 6 displays the statistical and security analyses, including correlation coefficient analysis and SNR.

                                  Table 6 .Comparison based on statistical analysis

Table 6's findings demonstrate that all correlation studies of the suggested algorithms satisfy zero co-correlation, making it evident that a statistical attack by an intruder cannot reveal any valuable data. On the other hand, all algorithms' SNR results are low, which suggests that the proposed algorithms have a lot of noise, making them more attack-resistant.

.

3. The problem statement is to be clarified. If "security and privacy pose a serious problem", the data is usually not transmitted through "unsecured communication channels". In other words, modern encryption standards like AES satisfy almost all the needs in regular data transmissions. Speaking of chaos-based encryption - dozens (if not hundreds) of new algorithms were proposed recently. Thus, the question arises - why does one need another chaos-based cryptographic technique? The statements connected with the specifics of audio encryption are not persuasive - in current radio systems the audio signals can be pretty well encrypted, and many successful commercial solutions are known in the field.

Response 3: we try to increase the level of security using more layers of encryption techniques to make it difficult to attacker to hack the signal.

4. The proposed cryptosystems should be compared not between themselves, but with other solutions in the field. I suggest expanding the comparison section with recent cryptographic approaches, for example, the encryption schemes based on 1D coupled hyperbolic tangent chaotic map with delay, one dimensional piecewise chaotic map, or bit level cubic shuffling.

Response 4: we compare our technique to other methods as mentioned in the comment, as shown in page 13 .

4.3 Performance Comparison of Audio Encryption Algorithms

The objective of this comparison is the audio encryption techniques. Table 6 displays the statistical and security analyses, including correlation coefficient analysis and SNR.

                                  Table 6 .Comparison based on statistical analysis

Table 6's findings demonstrate that all correlation studies of the suggested algorithms satisfy zero co-correlation, making it evident that a statistical attack by an intruder cannot reveal any valuable data. On the other hand, all algorithms' SNR results are low, which suggests that the proposed algorithms have a lot of noise, making them more attack-resistant.

5. More statistical attack methods should be taken into consideration.

Response 5: I respect your opinion, but we apply some examples of attacks.

6. Does your approach suggest concealed transfer? If yes, some techniques for discovering chaos-based communications can be discussed.

Response 6: Yes we suggest concealed transfer.we try to apply some attacks like noise cropping in order to study the effect of them in recovering the original audio after decryption.

7. "High levels of security are present in the proposed cryptosystems" - this statement is to be more thoroughly proven.

Response 7: Yes we agree with your opinion so we compare our results to different techniques and it is found it is close to the results of other techniques.

8. I recommend expanding the Conclusions section with more discussion on chaos-based encryption.

. Response 8: we modified the conclusion according to the comment as shown in page 13 line 391 to 403

Author Response File: Author Response.docx

Reviewer 4 Report

1. Abstract issues. Rewrite the following "This paper introduces The proposed technique introduces.."

2. Where is the evidence to support the following abstract statement: "The cryptosystems operate on 19 audio sample values rather than using encoding and decoding algorithms, which saves a lot of time and makes them more resistant to hacking and noisy conditions"

3. The abstract conclusion is very vague. Provide some experimental metrics to justify the statements. 

4. Line 1385: Main contributions are missing. 

5. Table 1 is missing

6. Use a better title for Figure 4. 

7. What should I understand from the images in Table 2. Please explain in the image title. 

Author Response

Authors Response for reviewer 4 Comments

The authors would like to thank the reviewer for his/her efforts in reviewing the paper. The notifications of the reviewer have been considered in the revised version.

1. Abstract issues. Rewrite the following "This paper introduces The proposed technique introduces.." Response 1: we modified abstract as mentioned in the comment it is found in (page. 1) lines 9-28
2. Where is the evidence to support the following abstract statement: "The cryptosystems operate on 19 audio sample values rather than using encoding and decoding algorithms, which saves a lot of time and makes them more resistant to hacking and noisy conditions"

Response 2: we apply our technique to different audio signals. As shown in page 15

4.4. Signal to noise ratio between plain and encrypted audio files

Because measures show low SNR, it is clear from Table (7) that all test findings lead to the audio encryption technique being secure. According to Table 7, all of the observed SNR values are negative, indicating that the encrypted files are extremely noisy and that the encryption approach has entirely destroyed the clear signal in the plain audio files.

Table 7 . Objective evaluation for four audio samples.

3. The abstract conclusion is very vague. Provide some experimental metrics to justify the statements. 

Response 3: we modified abstract as mentioned in the comment it is found in (page. 1) lines 9-28

4. Line 1385: Main contributions are missing. 

Response 4: I can’t find line 1385,

5. Table 1 is missing

Response 5: It is modified. It is found in page 9 line 365

Table 1. Comparison between the results of different encrypted schemes.

Table 2. Evaluation metrics for the comparison between original and encrypted signals

6. Use a better title for Figure 4. 

Response 6: It is modified, the title becomes:

Figure 4. Original audio (a) Audio signal in time domain (b) Audio Spectrogram in frequency domain (c) Histogram of audio signal.

In page 9, line 354-355

7. What should I understand from the images in Table 2. Please explain in the image title. 

Response 7: Table 2. Evaluation metrics for the comparison between original and encrypted signals.

Author Response File: Author Response.docx

Reviewer 5 Report

The article deals with audio encryption with the use of chaotic mappings.

The topic of the article is interesting and up-to-date. However, the description and presentation of the methods (or rather the lack of them) leave a lot to be desired. Moreover, the results are not compared with other similar methods. The article still needs much work. Below are some selected comments:

1) Abstract: correct the sentence: "This paper introduces The proposed technique introduces three cryptosystems for….". The abstract is too broadly written. In addition, no specific numerical values ​​showing the usefulness of the discussed technique are included, e.g., SNR values.

2) The literature review is in lines 65-76 and in chapter two.

3) Introduction: highlight the novelty of the article. In addition, there is no reference to the fact that audio encryption is considered here in the context of chaos theory.

4) All symbols should be explained on first use, e.g., DWT.

5) Chapter 3.1 - steps appear describing the encryption method - some introduction to this method is missing.

6) The authors use a logistic map for encryption. However, no details about it appear in the text.

7) The equations could be written better.

8) Tables and figures should appear in the vicinity of the text that mentions them for the first time.

9) The results could be presented better. The selected measures are described briefly. Sometimes it is not even known which formula describes a given measure, e.g., the correlation is given by the formula (6) marked as r. However, instead of r, CR appears in further description.

10) There is no comparison with other similar works mentioned by the authors in Chapter 2.

11) Conclusions probably concern a different work, e.g., the authors write something about a random permutation using Baker map - this is not in the text.

Author Response

Authors Response for reviewer 5 Comments

The authors would like to thank the reviewer for his/her efforts in reviewing the paper. The notifications of the reviewer have been considered in the revised version.

1. Abstract: correct the sentence: "This paper introduces The proposed technique introduces three cryptosystems for….". The abstract is too broadly written. In addition, no specific numerical values ​​showing the usefulness of the discussed technique are included, e.g., SNR values.

Response 1: we modified abstract as mentioned in the comment it is found in (page. 1) lines 9-28

2. The literature review is in lines 65-76 and in chapter two.

Response 2: it is modified and added to the literature review. Page 2 line 86- 100

3) Introduction: highlight the novelty of the article. In addition, there is no reference to the fact that audio encryption is considered here in the context of chaos theory.

Response 3: we cleared it in page 2 line 71 to 79

4) All symbols should be explained on first use, e.g., DWT.

Response 4: it is fixed, and we explain the DWT in page 4 line 181.

5) Chapter 3.1 - steps appear describing the encryption method - some introduction to this method is missing.

Response 5: It is modified. We add ( The proposed algorithm for audio signal encryption based on random projection in the DWT domain is illustrated in Figure 1 .The suggested block diagram is combining the 1-D DWT of the audio signal with a random signal. )

6) The authors use a logistic map for encryption. However, no details about it appear in the text.

Response 6: It is modified, we add

3.4 The logistic maps

In this part, we provide a shuffle approach based on a chaotic map with variable parameters. Perhaps the simplest mathematical objects that exhibit chaotic behavior are one-dimensional maps (Lasota and Mackey 1994). One type of one-dimensional map that was introduced in May (1976) and is already commonly utilized in image encryption is the logistic map.

7) The equations could be written better.

Response 7: we modified  it.

8) Tables and figures should appear in the vicinity of the text that mentions them for the first time.

Response 8: we modified it,

9) The results could be presented better. The selected measures are described briefly. Sometimes it is not even known which formula describes a given measure, e.g., the correlation is given by the formula (6) marked as r. However, instead of r, CR appears in further description.

Response 9: It is modified, we make all as r.

10) There is no comparison with other similar works mentioned by the authors in Chapter 2.

Response 9: We modify that part and adding comparison:

4.3 Performance Comparison of Audio Encryption Algorithms

The objective of this comparison is the audio encryption techniques. Table 6 displays the statistical and security analyses, including correlation coefficient analysis and SNR.

                                  Table 6 .Comparison based on statistical analysis

Table 6's findings demonstrate that all correlation studies of the suggested algorithms satisfy zero co-correlation, making it evident that a statistical attack by an intruder cannot reveal any valuable data. On the other hand, all algorithms' SNR results are low, which suggests that the proposed algorithms have a lot of noise, making them more attack-resistant.

11) Conclusions probably concern a different work, e.g., the authors write something about a random permutation using Baker map - this is not in the text.

Response 11: It is modified; it means the 2-D chaotic map

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The paper has been restructed and the language has been polished. I think it can be considered for publication at present form.

Author Response

The authors would like to thank the reviewer for his/her efforts in reviewing the paper.

Thanks a lot for your feedback

 No Comments

No Responses

Author Response File: Author Response.docx

Reviewer 3 Report

Thank you for providing a revised version of your paper. Despite the impressive amount of work done during the revisions, I still believe the literature review is incomplete. Please, refer to some recent papers on chaos-based encryption.

Second, more proofreading is needed. Please, find below a list of potential typos and stylistic imperfectnesses:

1. "analogue" - please, decide if your manuscript is written in American English or British English. You simultaneously use both forms in the text, which confuses the readers.

2. "is based on a narrative that combines henon and economic maps" - please, write the proper nouns correctly and capitalized, e.g. "Hénon map"

3. At lines 106-110, the sentence is repeated: "the audio signal is transformed into data using a lifting wavelet methodology in a new encryption method, and it is then encrypted using a chaotic dataset and a hyperbolic function the audio signal is transformed into data using a lifting wavelet methodology in a new encryption method;". Please, fix this issue.

4. "Block by block encryption for audio files use" - uses

5. Please, properly define the abbreviation in this case: "On (2 dimension discrete wavelet transform) 2-D DWT"

6. "practice by the multiplication" - by multiplication

Nevertheless, I believe the manuscript requires only minor revisions before acceptance.

Author Response

We thank the editor and the reviewers for their time and effort in evaluating the manuscript. We greatly appreciate all of the insightful comments and ideas which helped us improve the manuscript's quality. We have carefully considered the comments and made every effort to address each one.

Below we provide the point-by-point responses. All modifications in the manuscript were highlighted in green.

Comment

Thank you for providing a revised version of your paper. Despite the impressive amount of work done during the revisions, I still believe the literature review is incomplete. Please, refer to some recent papers on chaos-based encryption.

Response: we addressed this comment by adding some recent papers on chaos-based encryption. It is shown in (page. 4) lines 158-182

The study described in [20] proposes a new chaotic one-dimensional map. The second hyperbolic tangent term in this connection is delayed to prevent dynamical degradation. The map's consistent chaotic behavior for practically all parameter values is demonstrated by computing its bifurcation diagrams and Lyapunov exponent diagrams. The suggested map is then used to construct a high keyspace pseudo-random bit generator. Then, using this generator as a foundation, a proposed password generator application is built. The goal of this program is to develop an algorithm that takes a user-supplied, easy-to-remember key as input and generates a strong password suitable for website security or file security.

The authors of [21] propose a brand-new, straightforward chaotic one-dimensional map. The chaotic properties have been declared using Lyapunov exponent analysis and bifurcation analysis. They also propose a new picture encryption scheme based on this novel chaotic map. The shuffling algorithm and the substitution method both use this map. According to numerous statistical tests and security analyses, this approach has outstanding security performance and can compete with certain other recently presented picture encryption algorithms.

Authors of [22] investigates the problem of chaos-based image encryption. The first step is to create and investigate a generalization of the one-dimensional chaotic map proposed by Talhaoui et al. in The Visual Computer. The generalized map, like the original image, depicts areas of persistent chaos. Using the new map, a statistically safe pseudo-random bit generator is created and used in the encryption procedure. To introduce an image encryption technique based on rearranging the bit levels of an image, the bits are first organized into a three-dimensional matrix, and then a three-level shuffling is applied to each individual row, column, and bit level of the 3D matrix. After the bits have been shuffled, they are subjected to an exclusive OR operation.

With References:

1. [20] Kafetzis, I., Moysis, L., Tutueva, A. et al. A 1D coupled hyperbolic tangent chaotic map with delay and its application to password generation. Multimed Tools Appl (2022). https://doi.org/10.1007/s11042-022-13657-7
2. [21] Liu, L., Miao, S. A new simple one-dimensional chaotic map and its application for image encryption. Multimed Tools Appl 77, 21445–21462 (2018). https://doi.org/10.1007/s11042-017-5594-9
3. [22] Moysis, L., Kafetzis, I., Tutueva, A., Butusov, D., Volos, C. (2022). Chaos-Based Image Encryption Based on Bit Level Cubic Shuffling. In: Abd El-Latif, A.A., Volos, C. (eds) Cybersecurity. Studies in Big Data, vol 102. Springer, Cham. https://doi.org/10.1007/978-3-030-92166-8_7

Comment:

Second, more proofreading is needed. Please, find below a list of potential typos and stylistic imperfectnesses .

1. "analogue" - please, decide if your manuscript is written in American English or British English. You simultaneously use both forms in the text, which confuses the readers.

Response 1: We replaced (analogue ) by (analog) throughout the paper.

2. "is based on a narrative that combines henon and economic maps" - please, write the proper nouns correctly and capitalized, e.g. "Hénon map"

Response 2: We modified word (henon) to be (Hénon) in all text.

3. At lines 106-110, the sentence is repeated: "the audio signal is transformed into data using a lifting wavelet methodology in a new encryption method, and it is then encrypted using a chaotic dataset and a hyperbolic function the audio signal is transformed into data using a lifting wavelet methodology in a new encryption method;". Please, fix this issue.

Response 3: We modified it as shown in page 3 at lines 105-108.

4. "Block by block encryption for audio files use" – uses

Response 4: We modified it as shown in page 3 at line 107.

5. Please, properly define the abbreviation in this case: "On (2 dimension discrete wavelet transform) 2-D DWT"
   Response 5: We modified it as shown in page 5 at line 205.
6. "Practice by the multiplication" - by multiplication

Response 6: We modified it as shown in page 5 at line 225.

Author Response File: Author Response.docx

Reviewer 4 Report

Thank you for addressing comments.

Author Response

The authors would like to thank the reviewer for his/her efforts in reviewing the paper.

Thanks a lot for your feedback

No Comments

No Responses

Author Response File: Author Response.docx

Reviewer 5 Report

Thanks to the authors for their responses to my comments. The article has improved in quality but still requires a lot of work. Some of the issues requiring attention are as follows:

1) Some methods, such as chaotic permutation, are only mentioned in the text. The description of the methods should be in the form of pseudocode or numbered steps. Currently, the methods are either described too general or not explained at all.

2) the logistic mapping should be much better described, e.g., give the formula and properties

3) the equations still look terrible. In addition, authors should note the use of math mode for math symbols appearing in the text. Moreover, in the formulas, attention should be paid to the spelling of the function, i.e. not log but log.

4) Part 4 (Simulation Results and Discussions) lacks details (e.g., parameter values) for the obtained signal examples.

5) In Conclusions, the authors still describe something that does not exist in the earlier sections ("Then, it employs the 2-D chaotic map to produce permutations.").

Author Response

Authors Response for reviewer 5 Comments

We thank the editor and the reviewers for their time and effort in evaluating the manuscript. We greatly appreciate all of the insightful comments and ideas which helped us improve the manuscript's quality. We have carefully considered the comments and made every effort to address each one.

Below we provide the point-by-point responses. All modifications in the manuscript were highlighted in green.

Comment:

• Some methods, such as chaotic permutation, are only mentioned in the text. The description of the methods should be in the form of pseudocode or numbered steps. Currently, the methods are described either too general or not explained at all.

Response 1: We added a description to backer chaotic map in page 7 lines 286-294.

The Baker map is the third tool used in the suggested cryptosystems. It is a two-dimensional chaotic map that shifts each square matrix element [24]. The purpose of using these maps is to nonlinearly randomize the square matrix's components in a framework that is sensitive to the starting conditions. Cryptosystems must be highly sensitive to initial conditions in order to achieve confusion and diffusion. The chaotic Baker map has two main characteristics that can be summarized as follows:

1. Its output is highly random, unpredictable, and correlated little with the input.
2. It is highly dependent on the input parameters, starting values, and early conditions.

Baker maps are classified into two types: generalized Baker maps and discretized Baker maps. The discretized map is better suited to data blocks. It employs a mapping technique to transfer elements from one location to another [24]. Given k selected integers, u₁, u₂,……, and u_k,  the discretized map is represented as a square matrix B where each element B(r,s) is mapped according to the following Equation 2:

  (2)

 Where 0 ≤ s ≤ Z, Z_i ≤ r ≤ Z_i + u_i, Z_i = u₁ + …… + u_i and each integer u_i divides Z [24].

Comment:

2) The logistic mapping should be much better described, e.g., give the formula and properties

Response 2: We modified the logistic mapping by adding formula as shown in page 8 lines 301-316

The logistic map is one of the traditional chaotic maps that can be used to generate keys for an encryption scheme. It serves as a comparison point in this essay.

The following is a representation of the 1-D logistic map:

                                      (3)

where h is a constant with values ranging from 0 to 4, and x m has a value range of 0 to 1. The value of h determines how the logistic map behaves. As the repetitions become entirely chaotic, h is chosen for encryption purposes to be 3.57. Due to the 1-D logistic map's limitations, a modified 2-D logistic map has been developed for encryption. The following is its definition [25].

                             (4)

                           (5)

Comment:

3) The equations still look terrible. In addition, authors should note the use of math mode for math symbols appearing in the text. Moreover, in the formulas, attention should be paid to the spelling of the function, i.e. not log but log.

Response 3: Using the equation editor, all equations were reviewed and rewritten. 

Comment:

4) Part 4 (Simulation Results and Discussions) lacks details (e.g., parameter values) for the obtained signal examples.

Response: Section 4 was reviewed, and we ensured that all of the necessary values for our experiments were specified. See, for example, lines 321, 353-354, and Tables 4 and 5. It is worth noting that we have no other parameter settings to discuss.

Comment:

5) In Conclusions, the authors still describe something that does not exist in the earlier sections ("Then, it employs the 2-D chaotic map to produce permutations.").

Response 5: We thank the reviewer for this remark. We addressed the comment by adding description of Backer chaotic map as shown in response to comment 1: in page 7 lines 286-294

The Baker map is the third tool used in the suggested cryptosystems. It is a two-dimensional chaotic map that shifts each square matrix element [24]. The purpose of using these maps is to nonlinearly randomize the square matrix's components in a framework that is sensitive to the starting conditions. Cryptosystems must be highly sensitive to initial conditions in order to achieve confusion and diffusion. The chaotic Baker map has two main characteristics that can be summarized as follows:

1. Its output is highly random, unpredictable, and correlated little with the input.
2. It is highly dependent on the input parameters, starting values, and early conditions.

Baker maps are classified into two types: generalized Baker maps and discretized Baker maps. The discretized map is better suited to data blocks. It employs a mapping technique to transfer elements from one location to another [24]. Given k selected integers, u₁, u₂,……, and u_k,  the discretized map is represented as a square matrix B where each element B(r,s) is mapped according to the following Equation 2:

  (2)

 Where 0 ≤ s ≤ Z, Z_i ≤ r ≤ Z_i + u_i, Z_i = u₁ + …… + u_i and each integer u_i divides Z [24].

Author Response File: Author Response.docx

Round 3

Reviewer 5 Report

Thanks to the authors for their answers. However, not all comments were properly addressed:

1) The methods are still not properly described. Each of the presented procedures, apart from a textual description, should be given in an algorithm form, for example, in the form of pseudocode. For example - in section 3.3 the authors mention that the cryptosystem consists of three stages - Fusion, Substitution, and Chaotic Permutation - where is the exact description of these procedures? What is the key of this cryptosystem? What is the keyspace? etc. Where is the decryption algorithm?

2) In the fourth point of the answer, the authors claim that all the necessary parameters have been described in the text. What are the parameter and initial condition values of the logistic mapping?

3) What exactly is the Baker's map used for? Authors in previous versions mentioned this map by name. Now comes a paragraph that describes this dynamical system. However, in no procedure is this mapping explicitly used! The same applies to the logistic map, which is also not directly related to any procedure!

Author Response

Authors Response for reviewer 5 Comments

We thank the editor and the reviewers for their time and effort in evaluating the manuscript. We greatly appreciate all of the insightful comments and ideas which helped us improve the manuscript's quality. We have carefully considered the comments and made every effort to address each one.

Below we provide the point-by-point responses. All modifications in the manuscript were highlighted .

Comment:

• The methods are still not properly described. Each of the presented procedures, apart from a textual description, should be given in an algorithm form, for example, in the form of pseudocode. For example - in section 3.3 the authors mention that the cryptosystem consists of three stages - Fusion, Substitution, and Chaotic Permutation - where is the exact description of these procedures. What is the key of this cryptosystem? What is the keyspace? etc. Where is the decryption algorithm?

Response 1: for sake of clarity, we added the following updates to further explain the whole process. Please refer to page 7 lines 270-322.

As we previously mentioned, Fusion, Substitution, and Chaotic Permutation are the three layers of encryption that make up the proposed cryptosystem as shown in figure 3.

   Layer 1 fusion:  The fusion is carried out using the two previously described techniques, namely the Random Projection Based on 1D DWT and the Salting Based on 1-DWT.

Layer 2 the substitution: We use the discrete cosine transform DCT transform or the DST discrete sine transform to substitute the fused values from layer 1 with frequency components.

Layer3 permutation: The third tool in the suggested cryptosystems for permuting the coefficients from layer 2 to obscure the output of the second layer is the chaotic Baker map. The horizontal and vertical stretching and folding of the coefficients provide the foundation of the Baker map. The positions of each coefficient in the output of the second layer are changed by repeating this process. More specifically, the chaotic Baker map is a two-dimensional map that shifts each square matrix element [24]. These maps are used to nonlinearly randomize the elements of the square matrix in a framework that is sensitive to the initial conditions. To achieve confusion and diffusion, cryptosystems must be extremely sensitive to the starting conditions. The two key properties of the chaotic Baker map are as follows:

1. Its output is highly random, unpredictable, and correlated little with the input.
2. It is highly dependent on the input parameters, starting values, and early conditions.

Let B ( … ), denote the discretized map, where the vector, [ … ] represents the secret key, . Defining N as the number of data items in one row, the secret key is chosen such that each integer  divides N, and  + … +  = N.

   (2 )

 Let  =  + … + . The data item at the indices (q, z), is moved to the indices:

 where  ≤ q <  + , and 0 ≤ z < N.

The chaotic permutation is performed in the following steps:

1. An N × N square matrix is divided into k rectangles of width and number of elements N.
2. The elements in each rectangle are rearranged to a row in the permuted rectangle. Rectangles are taken from left to right beginning with upper rectangles then lower ones.
3. Inside each rectangle, the scan begins from the bottom left corner towards upper elements.

Figure 4 below shows a popular example that explains how permutation is performed for a chaotic map of a (8 × 8) square image (i.e. N = 8). The secret key,  = [n1, n2, n3] = [2, 4, 2].

What is the key of this cryptosystem?

    As previously stated, we added key information to the chaotic baker technique.                                               = [n1, n2, n3] = [2, 4, 2]. But fusion and substitution are keyless

Where is the decryption algorithm?

We did not provide a description of the decryption algorithm because we believed it was easily deducible from the encryption algorithm as they operate in inverse ways. To address the comment, we added the following description and figure. 

The Decryption Algorithm

The inverse of the encryption process is used in the decryption algorithm. As shown in Figure 5, the encrypted signal is transformed using DCT or DST, and the resulting coefficients are passed through a pipeline that begins with chaotic decryption followed by an inverse discrete cosine transform or inverse discrete sine transform, then DWT. After this stage, inverse fusion is performed, where like in salting we subtract the speech coefficients from the audio coefficients (in case of a random projection we apply division), then an inverse DWT is applied, and finally a conversion operation is performed to obtain the decrypted signal.

 Comment:

• In the fourth point of the answer, the authors claim that all the necessary parameters have been described in the text. What are the parameter and initial condition values of the logistic mapping?

Response 2: We appreciate the author's comment. Indeed, the previous position's description of the logistic map was misleading. We would like to highlight that, as stated in the abstract, the logistic map was used for comparison purposes. To avoid confusion, we reorganized the manuscript. We moved the logistic map from section 3 to section 4 as a technique for comparison. Please see lines 337-348 on page 9. In addition, we specified the parameter settings.

We also considered logistic map encryption, which is used in many comparable publications, for comparison purposes. The logistic map is one of the traditional chaotic maps that can be used to generate keys for an encryption scheme [25]. The 1D logistic map is defined as follows:

                                      (3)

Where h is a constant with values ranging from 0 to 4, and  has a value range of 0 to 1. The value of h determines how the logistic map behaves. As the repetitions become entirely chaotic, h is chosen for encryption purposes to be 3.57. Due to the 1-D logistic map's limitations, a modified 2-D logistic map has been developed for encryption. It is defined as follows [25].

                              (4)

                           (5)

Comment:

3. What exactly is the Baker's map used for? Authors in previous versions mentioned this map by name. Now comes a paragraph that describes this dynamical system. However, in no procedure is this mapping explicitly used! The same applies to the logistic map, which is also not directly related to any procedure!

Response 3 : Baker's map is used for encryption as the third layer of three layers cryptosystem, as explained in the previous version. We simply made a reference to this method in the first version. Then, in response to the reviewer's comment, we added a detailed description because it is an important part of the entire process. We believe that the new updates make it clearer how it is used and how it fits into the overall process. For the logistic map, we addressed this point as explained in the previous comment.

Author Response File: Author Response.pdf