Enhanced Three-Dimensional Double Random Phase Encryption: Overcoming Phase Information Loss in Zero-Amplitude Singularities for Simultaneous Two Primary Data

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper addresses an important limitation in three-dimensional double random phase encryption, namely the loss of phase information caused by zero-amplitude singularities, and proposes an enhanced encryption framework that aims to preserve phase characteristics while enabling simultaneous encryption of two primary data sets. The topic is relevant to the field of optical information security, and the proposed approach shows potential for improving robustness and reconstruction fidelity in three-dimensional encryption systems. The manuscript presents a technically interesting idea and includes experimental results that suggest improvements over conventional DRPE-based methods. However, several aspects of the methodology, mathematical formulation, experimental validation, and presentation require further clarification and strengthening before the contribution can be fully appreciated.

• The manuscript should provide a clearer mathematical derivation of the enhanced three-dimensional DRPE scheme, particularly explaining how phase information is preserved in regions affected by zero-amplitude singularities.

• The mechanism used to detect or handle zero-amplitude singularities should be described in detail, including how these regions are identified and treated during encryption and decryption.

• The process that enables simultaneous encryption of two primary data sets should be explained step-by-step, clarifying how the two inputs are multiplexed and later separated without introducing cross-interference.

• The authors should explicitly describe the structure and dimensionality of the random phase masks used in the proposed system and how they differ from those used in conventional 3D DRPE.

• More details are needed regarding the optical or computational implementation of the proposed framework, including whether the method is purely numerical or compatible with physical optical setups.

• The reconstruction procedure should be described more rigorously, with emphasis on how phase retrieval is stabilized in the presence of singularities.

• The experimental section would benefit from a more thorough description of the datasets used, including their size, resolution, and type of content.

• The authors should include quantitative performance metrics for both reconstructed amplitude and phase, and clearly explain how these metrics are computed.

• A direct comparison with standard 3D DRPE and other relevant encryption methods should be presented using the same experimental conditions.

• The manuscript should include an analysis of noise robustness, showing how the proposed method behaves under different noise levels in the encrypted data.

• The sensitivity of the system to key mismatch should be evaluated, demonstrating how small deviations in the random phase masks affect reconstruction quality.

• Computational complexity and memory requirements should be reported and compared with baseline methods.

• The security analysis should be expanded to discuss resistance to common attacks in optical encryption, including brute-force, known-plaintext, and chosen-plaintext scenarios.

• The manuscript would benefit from additional visual results illustrating encrypted patterns, decrypted outputs, and phase distributions for both primary data sets.

• The limitations of the proposed approach should be explicitly discussed, such as scalability to higher resolutions or multiple data channels beyond two inputs.

• The organization of the manuscript could be improved by separating theoretical formulation, algorithm description, and experimental evaluation into clearly defined sections.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a 3D optical encryption technique based on DRPE for the simultaneous encryption of two primary datasets. Specific comments are as follows:
1-The description of the contributions of this manuscript is not clear, especially the scientific description is insufficient. Please list the contributions or innovations of this article in the introduction section.
2-The introduction lacks some optimizing processing methods. The authors should provide some recent works, e.g. a dendrite net learning multi-objective artificial bee colony algorithm for UAV. It is better to introduce it in the introduction.
3-Section 4.3 provides a rather brief description of the reconstruction principle of the VCR, failing to explain the connection between "virtual pinhole array projection" and "pixel overlap averaging". As a result, readers find it difficult to understand the mechanism of noise suppression. Please add principles and Functions of Cohesion.
4-PLease explain the basis for choosing the bias value ε in Section 5.1.
5-Should we consider adding several mainstream methods for comparison? If not, please provide some explanations or clarifications in results.
6-Please introduce the implementation details of the experiment in Section 5.
7-Some typos: 'integal imaging', 'primaray data', etc.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript entitled "Enhanced Three-Dimensional Double Random Phase Encryption: Overcoming Phase Information Loss in Zero-Amplitude Singularities for Simultaneous Two Primary Data" continues and extends the research in the field of advanced three-dimensional optical encryption techniques based on double random phase encryption for the simultaneous encryption of two primary datasets. The research has been organized into advanced techniques, and the manuscript belongs to the thematic of the journal. However, significant writing errors prevent the presentation of the meanings of the topic. In any case, we believe that with appropriate and specific instructions, the article will be ready for publication.  Experimental results show that while the first dataset remains lossless, the lossy characteristics of the second dataset are significantly mitigated. For the better organization of the documentation text, we specifically suggest the following:

1) Congratulations on the abbreviations that are used in this manuscript at the end of the text; they are very much appreciated, but it would be much better if you removed them from the Abstract.

2) Regarding the issue of the introduction, there are serious objections to the way you introduce the reader to your topic. Initially, I would suggest that you limit yourself to the academic context of scientific publications. You should reconsider the functionality of the introduction and focus as content on an introductory text that will contain 1) the context of the problem, 2) the purpose, 3) the scientific questions, 4) the research questions, 5) the codified objective of the study, 6) the methodological approach, 7) the design tools and finally 8) the main findings and results and the contribution. All this with simple, concise, and focused sentences. Do nοt hesitate to think about these and expand on the introductory text if necessary.

3) Another very serious obstacle to understanding and approaching the content of the article is the use of references. Here, we must be very careful, as the time when "reference" as sources was difficult to find is over. Some references have been grouped, and even to a superlative degree. For example, “[1 -13], [18 - 27], etc. What is the point of having the references together? We do not use references at the same time without explaining exactly what we are referring to! References in an article function as tools for documenting evidence. References in an article function as tools for documenting evidence. Do not allow confusion to creep in by allowing the reader to “freely” interpret the use of your references. Rewrite and explain!!! Why is each reference used as the author anywhere in the article? What is the meaning of each reference? Explain why you use each reference in your documentation. Correct similar behavior everywhere in the work! Explain why you cite any reference! In addition, if you need a field study or state-of-the-art research, organize it, but not at the expense of introducing the reader to the topic of research.

4) At the end of the introduction, authors should accurately add the scientific questions of the article, which will be answered by the conclusions.

5) "Figure 1. Encryption process of double random phase encryption": explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded.

6)  "Figure 2. Decryption process of double random phase encryption": explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded.

7) "Figure 3. Examples of double random phase encryption. (a) primary data, (b) encrypted data, (c) decrypted data with correct key, and (d) decrypted data with incorrect key": explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded.

8) "3. Three-Dimensional Double Random Phase Encryption for Simultaneous Two Primary Data 3.1. Acquisition of 3D Information via SAII": as you did in chapter two, write a short introduction to justify the existence of the individual subchapters. Apply this guideline where there are individual subchapters in the manuscript.

9) Figure 4. Encryption process of DRPE for simultaneous two primary data: explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded.

10) Figure 5. Encryption examples of DRPE for simultaneous two primary data. (a) Primary data 1, (b) primary data 2, (c) encrypted data for (a) and (b), (d) primary data 1, (e) primary data 2, and (f)
encrypted data for (d) and (e): explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded. [Please be careful: (d) primaray?? data 1!].

11) Figure 6. Decryption process of DRPE for simultaneous two primary data: explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded.

12) Figure 7. Zero-amplitude singularity in (the!!!) decryption of conventional DRPE for simultaneous two primary data. (a) decrypted data 1 from encrypted data in Figure 5 (c), (b) decrypted data 2 from encrypted data in Figure 5 (c), (c) decrypted data 1 from encrypted data in Figure 5 (f), and (d) decrypted data 2 from encrypted data in Figure 5 (f): explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded. Additionally, make some modifications to this caption because four lines of text cannot be acceptable for a caption.

13) "4. Proposed Solution for Phase Information Loss (Biased Encoding) 4.1. Encryption Process of Our Method": as you did in chapter two, write a short introduction to justify the existence of the individual subchapters. Apply this guideline where there are individual subchapters in the manuscript.

14) "Figure 8. Proposed DRPE for simultaneous two primary data": excellent capture! Please explain everything in detail.

15) Figure 9. Examples by our method. (a) encrypted data for simultaneous two primary data with a constant bias of ε = 0.1, (b) primary data 1 for (a), (c) primary data 2 for (a), (d) encrypted data for simultaneous two primary data with a constant bias of ε = 0.1, (e) primary data 1 for (d), (f) primary data 2 for (d): explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded. Additionally, make some modifications to this caption because four lines of text cannot be acceptable for a caption.

16) "Figure 10. Elemental images for (a) LENA text and (b) Lena image.": explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text.

17) "Figure 11. Elemental images for (a) MANDRILL text and (b) Mandrill image.": explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text.

18) Figure 12. Decryption results by conventional DRPE for simultaneous two primary data without a constant bias ε. (a) encrypted data (b) primary data 1 from (a), (c) primary data 2 from (a), (d) encrypted data (e) primary data 1 from (d), and (f) primary data 2 from (d): explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded. Additionally, make some modifications to this caption because four lines of text cannot be acceptable for a caption.

19) Figure 13. Decryption results by (the!!) proposed DRPE for simultaneous two primary data with a constant bias of ε = 0.1. (a) encrypted data (b) primary data 1 from (a), (c) primary data 2 from (a), (d) encrypted data (e) primary data 1 from (d), and (f) primary data 2 from (d): explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded. Additionally, make some modifications to this caption because four lines of text cannot be acceptable for a caption.

20) Figure 14. 3D reconstruction results for decrypted LENA text and Lena image. (a) zr = 250 mm, (b) zr = 512 mm, (c) zr = 1000 mm, (d) zr = 500 mm, (e) zr = 1024 mm, and (f) zr = 1500 mm: explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded.

21) Figure 15. 3D reconstruction results for decrypted MANDRILL text and Mandrill image. (a) zr = 250 mm, (b) zr = 512 mm, (c) zr = 1000 mm, (d) zr = 500 mm (e) zr = 1024 mm, and (f) zr = 1500 mm: explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded.

 

22) Figure 16. Peak Sidelobe Ratio (PSR) results for LENA text, Lena image, MANDRILL text, and Mandrill image via different reconstruction depths: explain with which tool the figure was formatted, how the data was collected, and provide a descriptive description of what it contains. This should be done for each figure in the text. Figures and images are part of the documentation and should be fully decoded.

23) 6. Conclusions are not concluded! In the conclusions, in addition to the answers to the scientific and research questions, note the overall added value of the article, the difficulties in implementing parts of the research, and finally, suggestions for future research work.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I recommend this paper for publication in its current form.

Reviewer 2 Report

Comments and Suggestions for Authors

I suggest that this paper be accepted.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors of the manuscript "Enhanced Three-Dimensional Double Random Phase Encryption: Overcoming Phase Information Loss in Zero-Amplitude Singularities for Simultaneous Two Primary Data", formally implemented the proposed changes to their original text.

1) They have removed the abbreviations from the Abstract. 

2) In the introduction, they have presented the context of the problem, and they have described the purpose, the scientific and research questions, the codified objective of the study, the methodological approach, and the main contribution.

3) In the introduction, they have also revised several sentences for the scientific questions properly.

4) In the central part of the text, they corrected typical oversights in the captions and added explanatory notes.

5)  They add a new figure, and finally, 

6) They have revised their conclusion.

 

The article is conventionally ready for publication by the reviewer.