A Novel Image Tamper Detection and Self-Recovery Algorithm Based on Watermarking and Chaotic System

Round 1

Reviewer 1 Report

The article presents image self-recovery scheme based on watermarking technique algorithm.

The subject of the article is current and interesting. However, the article as a whole is hardly understood. This is due to, among others, the following points:

1) a lot of editorial errors regarding whitespace

2) The Introduction is too short and would require a more detailed description of the problem along with the related work description

3) formula 1: logistic map does not generate random strings as it was written in line 66. In turn in line 69 it is said that chaos occurs for a parameter in the range (3.6; 4), which is not true. In this range we have the so-called periodic windows. It is worth that the authors familiarize themselves with, among others:

+ On the inadequacy of the logistic map for cryptographic applications. David Arroyo, Gonzalo Alvarez, Veronica Fernandez; https://arxiv.org/pdf/0805.4355.pdf

+ Generalized logistic map and its application in chaos based cryptography. Marcin Lawnik, 2017 J. Phys .: Conf. Ser. 936 012017

4) line 79: in the case of many chaotic mappings (e.g. logistic map given by formula (1)), the key space is not large enough - see above listed articles.

5) What exactly does Fig. 1 mean? How was part (b) obtained?

6) formula 4: are the summation limits good?

7) what do the operations in formulas 10-13 mean?

8) not all Figures have been cited in the text, e.g. 6 and 8

9) the bibliography is definitely too short

10) English needs improvement

Considering the above remarks, I propose that the Authors look again at the article, including language correction.

Author Response

Dear reviewer, please see the word document for details.

Author Response File: Author Response.docx

Reviewer 2 Report

(1) Please check that the Figure 2 fully describes the method your thought for your watermarking design.

(2) There must be sufficient explanation and examples of the generation of L' and L''.
- You should also explain l_0', .... and l_0''.

(3) Since there are two charts in Figure 5, they should be divided into (a) and (b) and explained.

(4) The reason for using LCC in Equation-4 should be explained fully.

(5) You should make and explain an example of "watermark generation procedure" to help readers understand.

(6) Write an example for the "watermark embedding procedure" and explain it fully.

(7) The process of tamper detection and restoration of "tampered watermaked image" should be described as an example.

(8) In Figure 10, the "level-2 restoration procedure" is a description of the process that was not previously seen in the "watermark embedding procedure". Usually watermark concealment and reconstruction are symmetrical, but the process of this painting does not seem to be. What is the reason?

(9) "collage" is a noun. However, it is used as a verb in verse 4.2.1.
     -"we collage ..."

Author Response

Dear reviewer, please see the word document for details.

Author Response File: Author Response.docx

Reviewer 3 Report

The paper proposes a mechanism for image tampering detection and recovery based on digital watermarking and chaotic dynamics. The are some issues that need to be solved:

1. Even the ideas encapsulated in the proposed algorithm seem reasonable, they are not backed by mathematical evidence. Some examples: a) in lines  79-80 it is written “Because the double pseudo-random circular chain is generated by a chaotic system, the key space is large enough” but no proof is presented; b) figure 1 doesn’t prove “The security of the pseudo-random cyclic chain” (this idea is also claimed in lines 81-83 but without a formal mathematical proof); c) line 156: it is written that “The smooth function gets better image quality” again with no proof.

2. Line 69: The logistic map is not chaotic for all values lambda between 3.6 and 4 as presented in the paper. In this interval there are some isolated ranges for lambda that show non-chaotic behavior (sometimes called “islands of stability”). See for example lambda=1+sqrt(8) (approximately 3.82843). As a direct consequence, the interval for lambda needs to be decreased.

3. Line 66 or line 69: there is a need to include a reference for the logistic map.

4. The term “Double Pseudo-random Circular Chain” must be defined. In my view, this term is strange by putting together “random” sequences with “circular chain”.

5. Line 70-71: the sentence “A double…” is strange or badly-shaped;

6. English needs polishing. There are many grammar mistakes, typos or badly shaped sentences. Some examples: a) lines 9-10: the sentence “the recovery …” is confusing and badly-shaped; b) line 20: “gotten” must be replaced by “acquired” or “obtained”; c) line 20: instead of “image editing software” it is written “image edited software”; d) line 20: it is written in a single word “becomestronger”;  e) line 26: it is written in a single word “informationhas”; f) line 42 and line 41 contain the same information; g) line 48: instead of “used to recover information” it is written “used to recovery information”; and many more.

7. Lines 21, 22, 26: what the authors mean by “reality” of an image?

8. Lines 48-49: the sentence “The method achieves good recovery information” is strange; What the authors mean by "good recovery information"?

9. Lines 57-59: The sentence is strange especially the use of “more”;

10. Lines 77: what the authors mean by “ensuring that the mapping sequences of the two chains are irrelevant.”?

11. Line 113: It is written “However, the mechanism of remapping is too simple”. In my view, it is not a matter of simple/complex but effective/ ineffective.

12. In the first line of page 5 it is written “Figure 5 is the difference of Arnold Transform and the double pseudo-random chain. “ which is confusing. Moreover no details about Arnold map that was considered were given (e.g. the values of its parameters).

13. Line 156-159: how this paragraph is linked with eq. (13) and (14)? It seems there is a contradiction between them.

14. In many places in the manuscript, the authors speak about “Section A”, but there is no such section in the manuscript.

15. The steps from paragraph 3.4 must be carefully explained. For example why do we have to compare ew11 with ~ ew10 (see line 166)?

16. The proposed method needs to be compared with one or two state-of-the-art methods.

Author Response

Dear reviewer, please see the word document for details.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Thank you to the authors for the answers to the review. The article has been significantly improved. The authors have eliminated most of the language and editorial errors. In addition, some of my substantive comments have been taken into account. However, the comment still requires:

1) line 68: logistic mapping instead of logical mapping, this error also appears further in the text

2) line 70: the expression that for each value of x_0 in [0,1] we get a chaotic orbit for the lambda parameter in the range [3,99,4] is very risky and ignoring obvious cases like x_0 = 0 or x_0 = 1 not true. I propose that the authors still recast this fragment of the article, bearing in mind that logistic map generates chaotic solutions for lambda values ​​in the range [3.57; 4] excluding the so-called periodic windows, which form a dense set.

3) Figure 1: in line 82, the authors write, that part b is formed after permuting pixels with the use of logistic map - how exactly does this procedure of pixel conversion look like?

4) equation 4: what does the "overline" in the first factor of the sum mean?

5) formulas 10,11,12: what do the operations in these formulas mean? E.g. what is ~ in the case of 11.

6) minor editorial errors still appear, e.g. in equation 13 and 14

Author Response

Thank you for your valuable comments, I have made changes, please see the attachment for details.

Author Response File: Author Response.docx

Reviewer 2 Report

The author has made great efforts to improve the quality of the paper through the revision process of the paper.
Therefore, this paper is suitable for publication.

Author Response

Thanks for reviewing my paper and giving valuable review comments. Best wishes to you!

Reviewer 3 Report

The authors have successfully solved the issues I raised and have substantially improved their manuscript. However, English still needs some polishing.

Author Response

Thank you for reviewing my paper and giving valuable review comments. I have reviewed the paper again and modified the grammar errors. Please see the latest revised paper for details.