Designing a Secure Mechanism for Image Transferring System Based on Uncertain Fractional Order Chaotic Systems and NLFPID Sliding Mode Controller
Round 1
Reviewer 1 Report
The work should be improved, in theorem 1 you demonstrate that master slave system is stable for the proposed control law, nevertheless U_00 defined in (25) go to infinite, and you propose a modification, for which the stability demonstration does not correspond. Furthermore in section 6 you present numerical simulations using the control law (26), not the one modified.
In section 6 is not defined \delta\epsilon
In section 7 you do not justify why the cyphered information need to be masked, since the information encrypted is unreadable and could be transmitted by an insecure channel. Furthermore in the paper is not described the masking process and in which stage the proofs are made, since the encryption algorithm should already fulfil the test.
line 119 with respect to "x"
line 123 Then "x=0"
line 125 "incremental"
line 132
line 138
line 142 "are" as follows:
in line 174 you define l1 norm and in line 206 use the same symbol to define first norm
line 237 and??
line 315 ???(?)will be
Author Response
Comments of Reviewer #1
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The authors would like to cordially appreciate the respectable reviewer for his/her deep concentration and appropriate comments. In the following, we separately answer each comment of the reviewer.
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Comment 1: The work should be improved, in theorem 1 you demonstrate that master slave system is stable for the proposed control law, nevertheless U_00 defined in (25) go to infinite, and you propose a modification, for which the stability demonstration does not correspond. Furthermore in section 6 you present numerical simulations using the control law (26), not the one modified.
Answer: Thanks to the respected reviewer, The description is as follows:
The Eq. (26) was corrected.
In such a way that modified by in Eq. (46) causes to be modified in Eq. (26).
At the beginning of the synchronization when the of s is large, the modified in Eq. (46) is basically the same as the introduced in Eq. (25). After s tends to zero, the derivative of the Lyapunov function is negative, so the Lyapunov function is decreasing and tends to zero. Therefore, all variables of the system will be bounded and the problem of instability will not occur.
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Comment 2: In section 6 is not defined \delta\epsilon
Answer: Delta is defined in section 6 and its value is introduced as . The value of was added to the article.
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Comment 3: In section 7 you do not justify why the cyphered information need to be masked, since the information encrypted is unreadable and could be transmitted by an insecure channel. Furthermore in the paper is not described the masking process and in which stage the proofs are made, since the encryption algorithm should already fulfil the test.
Answer: The main goal of this article is the synchronization of chaotic systems with unknown time delay and disturbance with unknown limit and uncertainty. So that its sliding surface is based on NLFOPID which is provided in these systems. The topic of secure communication is presented as an application of the proposed mechanism. If the encryption is of higher quality (correlation, NPCR, PSNR, and information entropy criteria) are improved, the overall quality of the method is also improved. In this cryptography article reference 27 is used. In addition, the proposed method has the ability to change its encryption method.
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Comment 4: Comments on the Quality of English Language
line 119 with respect to "x"
Answer: Was corrected.
line 123 Then "x=0"
Answer: Was corrected.
line 125 "incremental"
Answer: Was corrected.
line 132
Answer: Was corrected.
line 138
Answer: Was corrected.
line 142 "are" as follows:
Answer: Was corrected.
in line 174 you define l1 norm and in line 206 use the same symbol to define first norm
Answer: Was corrected.
line 237 and??
Answer: Was corrected.
line 315 ???(?)will be
Answer: Was corrected.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Content corrections:
- Chaotic masking is known to be less secure; this is why Masking/Demasking algorithms must be tested
- Self-citation [25], must not be used, especially to sustain classic theoretical aspects, such as Riemann-Liouville fractional integral.
- Reference [69] specifying the encryption method does not exist
Editing corrections:
- Section 2 is not identified
- Space between section can be reduced
- The text in ithe graph representations must be more visible
Author Response
Comments of Reviewer #2
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The authors would like to cordially appreciate the respectable reviewer for his/her deep concentration and appropriate comments. In the following, we separately answer each comment of the reviewer.
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Comment 1: Chaotic masking is known to be less secure; this is why Masking/Demasking algorithms must be tested.
Answer: Thanks to the respected reviewer, The description is as follows:
The main goal of this article is the synchronization of chaotic systems with unknown time delay and disturbance with unknown limit and uncertainty. So that its sliding surface is based on NLFOPID which is provided in these systems. The topic of secure communication is presented as an application of the proposed mechanism. If the encryption is of higher quality (correlation, NPCR, PSNR, and information entropy criteria) are improved, the overall quality of the method is also improved. In this cryptography article reference 27 is used. In addition, the proposed method has the ability to change its encryption method. In addition, the proposed mechanism has the ability to change its encryption method. Considering that chaotic masking alone does not provide good encryption indices, in the proposed algorithm presented in Figure 9, encryption and decryption are added to the mechanism to improve the encryption indices. In addition, the encryption method can be updated.
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Comment 2: Self-citation [25], must not be used, especially to sustain classic theoretical aspects, such as Riemann-Liouville fractional integral.
Answer: Was corrected.
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Comment 3: Reference [69] specifying the encryption method does not exist.
Answer: Was corrected.
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Comment 4 Editing corrections:
- Section 2 is not identified
Answer: The title of section 2 was modified. Also, the numbering for all sections was rewritten.
- Space between section can be reduced
Answer: Was corrected.
- The text in ithe graph representations must be more visible
Answer: The quality of images has improved.
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Author Response File: Author Response.docx
Reviewer 3 Report
The manuscript examined an adaptive sliding mode control approach for robust synchronization of a class of fractional order chaotic systems with uncertainty, external disturbance, and unknown parameters, such as unknown time delay.
The topics appears interesting, but the paper needs more care in writing and presentation (quality of figures appears to be very low).
Some questions and suggestions follow.
To avoid repetitions, I would suggest to change ``The Lyapunov method is used to determine the update laws. The Lyapunov method is used to prove the stability of the proposed mechanism and guarantee the convergence of the synchronization errors to zero'' with `The Lyapunov method is used to determine the update laws, prove the stability of the proposed mechanism and guarantee the convergence of the synchronization errors to zero''.
I also would suggest to modify the way this sentence starts: ``Also, about 300 years ago, fractional calculations...'' It is misleading to use ``also'' to relate chaos and fractional calculus.
In is not very clear to me in which sense ``It is evident that modeling using fractional order systems can have more accuracy than modeling with integer order systems.'' Where is the claimed evidence?
The sentence ``In fact, two chaotic systems synchronization can be characterized as a condition in which two or more chaotic systems alter their responses or some of their features as a result of coupling or forcing.'' is not very clear to me.
In line 57 ``adaptive sliding terminal mode controller (ATSMC)'', based on the acronym should be 'adaptive terminal sliding mode controller'. Please, check.
Is it correct ``time-varying time delay''? Please, check.
In line 65 ``nonlinear fractional PID sliding surface (NLFOPID)'', based on the acronym should be 'nonlinear fractional order PID'. Therefore sliding surface should be after the acronym. Please, check.
I would suggest to change ``Finally, in the final section, conclusions and recommendations are offered.'' with ``Finally, in the last section, conclusions and recommendations are proposed.''
In line 82, the tiny text ``SOS method'' what stands for?
The section ``Preliminary Definitions of Fractional Order Differentiation:'' is a mere sequence of definitions and lemmas. Both the reader with solid expertise on the subject and the novice reader would find the section unhelpful. Please reorganize the section from scratch. Also pay attention to the numbering of section titles and equations. Also, the use of bold type should not be casual.
There a list of known and celebrated equations in lines 146-147. Why? That's not clear to me.
Unfortunately, I do not understand why Definition 1-2, Assumption 2-1 and Assumption 2-2 have those names. Furthermore, Section 3, as the previous one, appears as a list of concepts, without any specific description. Table 1, also, is puzzling. It seems a nomenclature section in the wrong place.
Function as sgn should not be written italicized.
In line 371 there is a wrong cross-referencing to Figure (1) instead to Figure (2). Instead, Figure (1) ``Sigma function behavior diagram'' seems not referenced at all.
The Sect. 6 seems to follow Sect. 4, while no part of the text seem reported as Sect. 5. Please, check.
Labels and texts in figures (mainly, but not limited to) 8 to 11 are really too small.
Please, pay attention to cross references. For instance Figures (4) and (20) are apparently not cited in the text.
Some sentences are not very clear. Repetitions should be avoided whenever possible.
Author Response
Comments of Reviewer #3
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The authors would like to cordially appreciate the respectable reviewer for his/her deep concentration and appropriate comments. In the following, we separately answer each comment of the reviewer.
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The manuscript examined an adaptive sliding mode control approach for robust synchronization of a class of fractional order chaotic systems with uncertainty, external disturbance, and unknown parameters, such as unknown time delay.
The topics appear interesting, but the paper needs more care in writing and presentation (quality of figures appears to be very low).
Some questions and suggestions follow.
Comment 1: To avoid repetitions, I would suggest to change ``The Lyapunov method is used to determine the update laws. The Lyapunov method is used to prove the stability of the proposed mechanism and guarantee the convergence of the synchronization errors to zero'' with `The Lyapunov method is used to determine the update laws, prove the stability of the proposed mechanism and guarantee the convergence of the synchronization errors to zero''.
Answer: While thanking the esteemed referee for her (his) accuracy, the previous text in the abstract section was removed and the reference sentence was replaced.
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Comment 2: I also would suggest to modify the way this sentence starts: ``Also, about 300 years ago, fractional calculations...'' It is misleading to use ``also'' to relate chaos and fractional calculus.
Answer: Was corrected.
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Comment 3: In is not very clear to me in which sense ``It is evident that modeling using fractional order systems can have more accuracy than modeling with integer order systems.'' Where is the claimed evidence?
Answer: Fractional order systems have more capacity to model a variety of physical systems. In fact, integer order systems are a special case of fractional order systems. These items are mentioned in the references:
DOI : 10.3390/e21090876
DOI : 10.1109/SMC.2019.8914631
DOI : 10.1155/2020/7643812
DOI : 10.1016/j.cnsns.2010.06.030
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Comment 4: The sentence ``In fact, two chaotic systems synchronization can be characterized as a condition in which two or more chaotic systems alter their responses or some of their features as a result of coupling or forcing.'' is not very clear to me.
Answer: It was modified as follows:
In fact, synchronization of two chaotic systems can be described as a situation in which two or more chaotic systems coordinate their responses by the controller.
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Comment 5: In line 57 ``adaptive sliding terminal mode controller (ATSMC)'', based on the acronym should be 'adaptive terminal sliding mode controller'. Please, check.
Answer: Was corrected.
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Comment 6: In line 65 ``nonlinear fractional PID sliding surface (NLFOPID)'', based on the acronym should be 'nonlinear fractional order PID'. Therefore sliding surface should be after the acronym. Please, check.
Answer: Was corrected.
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Comment 7: I would suggest to change ``Finally, in the final section, conclusions and recommendations are offered.'' with ``Finally, in the last section, conclusions and recommendations are proposed.''
Answer: Was corrected.
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Comment 8: In line 82, the tiny text ``SOS method'' what stands for?
Answer: Was corrected.
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Comment 9: The section ``Preliminary Definitions of Fractional Order Differentiation:'' is a mere sequence of definitions and lemmas. Both the reader with solid expertise on the subject and the novice reader would find the section unhelpful. Please reorganize the section from scratch. Also pay attention to the numbering of section titles and equations. Also, the use of bold type should not be casual.
Answer: The organization of the above was done again. In this regard, the title of section 2 was modified. Also, the numbering for all sections was rewritten.
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Comment 10: There a list of known and celebrated equations in lines 146-147. Why? That's not clear to me.
Answer: In lines 146-147, equations (13) and (14) are the dynamics of base and follower systems which are described canonically.
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Comment 11: those names. Furthermore, Section 3, as the previous one, appears as a list of concepts, without any specific description. Table 1, also, is puzzling. It seems a nomenclature section in the wrong place.
Answer: In section 2, the basic concepts of fractional order derivative are introduced and in section 3, equations describing the system are presented. Considering the large number of parameters defined in this article, especially in these two sections, a table describing the parameters used in this article has been presented in order to better understand the equations.
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Comment 12: Function as sgn should not be written italicized.
Answer: In order to maintain integrity in the presentation of equations, italic font has been used according to the template file.
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Comment 13: In line 371 there is a wrong cross-referencing to instead to Figure (2). Instead, Figure (1) ``Sigma function behavior diagram'' seems not referenced at all.
Answer: Was corrected.
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Comment 14: The Sect. 6 seems to follow Sect. 4, while no part of the text seem reported as Sect. 5. Please, check.
Answer: The organization of the above was done again. In this regard, the number of section 5 was corrected.
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Comment 15: Labels and texts in figures (mainly, but not limited to) 8 to 11 are really too small.
Answer: Image quality improved.
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Comment 16: Please, pay attention to cross references. For instance Figures (4) and (20) are apparently not cited in the text.
Answer: Descriptions for all images were added as follows:
Figure (4) shows the synchronization of master and slave system. It is clear that after applying the control signal based on the proposed mechanism, the slave system follows the master system well.
Figures (10), (12), (14), (16), (18) and (20) show the original, recovered, and recovered images for black-and-white, color, or medical modes.
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Comment 17: Comments on the Quality of English Language.
Some sentences are not very clear. Repetitions should be avoided whenever possible.
Answer: Was corrected.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The paper is interesting and well written
Reviewer 3 Report
The revised version of the paper contains many improvements. The Author replied to my comments in a correct and satisfactory way. I have no further questions, comments, or suggestions. In my opinion, the paper is worthy of publication as is.
