Chaos Meets Cryptography: Developing an S-Box Design with the Rössler Attractor

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper proposes a method to create chaotic S-boxes based on Rössler Attractor. And a large number of comparative experiments verify the effectiveness of the method. In the future, the proposed S-box generation method can be applied into encryption/decryption systems. 

(1) Up to now, there have been many kinds of chaotic systems. The Rossler chaos attractor is employed in this paper. Why chooses this attractor? What are its advantages over other attractors? 

(2) The strategy, many chaotic S-Box generation methods employed (for example in ref. [40]), is ignoring the repeated value when encountering repetition. However, the strategy provided by the article is to replace it with values not yet in the S-Box. Do different strategies affect the performance of S-BOX?  To answer this question, a set of comparative experiments with different strategies could be added. 

(3) The step 7 of the algorithm is to mix the prior S-box using the Rijndael S-box as a permutation box. It is better to provide the explanation of mixing. 

(4) It is recommended that the experimental results in Table 10 can be divided into two parts: chaotic S-box and other methods. You can describe how the chaos method compares to other methods. Also, the advantages and disadvantages of the proposed method can be described among all chaos-based methods.

Comments on the Quality of English Language

The manuscript needs careful editing and particular attention to English spelling, grammar and typing error. For example, in line 135, page 3, “Bestsides” would be “Besides”; in line163 and line 182, page 4, the symbol of multiplication is “´”, not letter “x”; in line 286, page 10, “he comparison” would be “the comparison”; in line 324, page 13, “Multiple” would be “multiple”; in the description of Figure 4, “others” would be “other”. 

Author Response

Comments 1: Up to now, there have been many kinds of chaotic systems. The Rossler chaos attractor is employed in this paper. Why chooses this attractor? What are its advantages over other attractors?

Response 1: Thank you for pointing this out. We agree with this comment, and for that reason in line 355, we add some advantages over other well-known methods.

Comments 2: The strategy, many chaotic S-Box generation methods employed (for example in ref. [40]), is ignoring the repeated value when encountering repetition. However, the strategy provided by the article is to replace it with values not yet in the S-Box. Do different strategies affect the performance of S-BOX? To answer this question, a set of comparative experiments with different strategies could be added.

Response 2: Agree. The decision to replace missing values rather than discard them was made to minimize execution time and optimize computational resources. This led to the addition of an execution time section at line 315. Additionally, as part of future work, is proposed to implement this algorithm on a mobile device for data transmission applications.

Comments 3: The step 7 of the algorithm is to mix the prior S-box using the Rijndael S-box as a permutation box. It is better to provide an explanation of mixing.

Response 3:  We strongly agree with this comment, and for that reason, in line 206, we add a subsection with the process used in the Rijndael S-box.

Comments 4: It is recommended that the experimental results in Table 10 can be divided into two parts: chaotic S-box and other methods. You can describe how the chaos method compares to other methods. Also, the advantages and disadvantages of the proposed method can be described among all chaos-based methods.

Response 4:  Thank you for pointing this out. We agree with this comment, so in line 349, we added a new table with other methods and a comparison with these. 

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript develops a fashion method to create chaotic s-boxes using the Rössler attractor as a chaotic process and the Rijndael S-box as a permutation box. The developed S-boxes are evaluated with bijectivity, NL, SAC, BIC, LAP, and DU. The authors clam that the analyses show that their method helps generate a high-resistance S-box to well-known attacks. The talked issue is interest, but there are several concerns.

1) What is the main question addressed by the research?

2) What does it add to the subject area compared with other published material?

3) Section 2 and Section 3 can be merged. In addition, Section 5 and Section 6 can be merged.

4) The proposed method is very simple. The novelty is very poor.

5) How this method can be implemented in hardware?

6) Why the authors select a=b=0.2 and c=0.7 in first step?

7) The analysis of the developed algorithm should be represented in detail.

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Comments 1: What is the main question addressed by the research?

Response 1: The main aim is to develop not only a new algorithm to create a strong S-box but also an efficient one in terms of computational time and memory usage.

Comments 2: What does it add to the subject area compared with other published material?

Response 2: Better metrics and a low execution time. The time values were added in line 316.

Comments 3: Section 2 and Section 3 can be merged. In addition, Section 5 and Section 6 can be merged.

Response 3: We strongly agree with this comment, and for that reason, we join the sections.

 

Comments 4: The proposed method is very simple. The novelty is very poor.

Response 4: Thank you for pointing this out. The method is designed to be simple because our primary goal is to develop a fast algorithm, and the report that the test was passed demonstrates the robustness of the proposed S-box.

Comments 5: Why the authors select a=b=0.2 and c=0.7 in first step?

Response 5: Thank you for pointing this out. Because of the complex and unpredictable behavior of the attractor with these values as initial conditions. In line 231 it is explained.

Comments 6: The analysis of the developed algorithm should be represented in detail.

Response 6: We agree with this comment; we added some information in lines 206, and 316, as well as incorporating insights about the importance of execution time into both the results and conclusions sections.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The Authors have revised the paper carefully according to my comments. Therefor, I think it can be published at present version.

Comments on the Quality of English Language

The Authors have revised the paper carefully according to my comments. Therefor, I think it can be published at present version.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors try to do my concerns. This paper can be accepted now.