A Deterministic Chaos-Model-Based Gaussian Noise Generator

Round 1

Reviewer 1 Report

This paper analyzed that sum of chaotic signals will produce Gaussian distribution. The main theroetical basis is center limit theorem. Many experiment verify the theory analysis. It is noverty and applicable in image encryption in future. The only drawback is lack of theoretical proof. I suggest that this paper can be publised in this journal.

Comments for author File: Comments.pdf

Author Response

Thank you for the positive feedback about the article.

Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper, the authors propose an approach to generate Gaussian-distributed chaotic signals by processing the output of chaotic systems. Skewness, kurtosis, and entropy power are employed to quantify the degree of Gaussian distribution approximation. Additionally, the authors investigate the minimum number of independent chaotic signals required to produce a Gaussian-distributed combined signal. The paper is interesting and holds significant practical value. However, there are some comments:

(1) The paper's significance is not sufficiently emphasized in the abstract and introduction. The authors should explicitly highlight the unique contributions of their work.

(2) The article focuses on 40 continuous chaotic systems, but consideration should be given to the case of discrete chaotic systems.

(3) The paper uses skewness (k1), kurtosis (k2), entropy power of PDF (k3), envelop (k4), and phase (k5) as metrics to measure the proximity to a Gaussian distribution. Further clarification is needed regarding the setting of threshold values. Should k1, k2, k3, k4, and k5 all simultaneously meet the thresholds?

(4) The incorporation of additional statistical testing tools would enhance the paper's credibility in assessing the degree of conformity to a Gaussian distribution.

(5) The paper mentions that parameters and initial values of chaotic systems significantly impact signal distribution. A more detailed analysis, including the presentation of quality metrics graphs similar to Fig. 3 and Fig. 4, would enhance understanding.

Author Response

Thank you for all your comments. We carefully considered and took into account all of them. Our detailed response you can find below. We are very thankful such as the comments and their correction made our paper better.

Author Response File: Author Response.pdf

Reviewer 3 Report

The article titled "Deterministic chaos models-based Gaussian noise generator" introduces concept of deterministic chaos and its potential in creating Gaussian-distributed chaotic signals, and emphasizes the importance of such signals in various applications. This study is certainly interesting and is worthy to be considered for publication in this journal. I think, it is acceptable for publication after some revisions:

1.     Could the authors elaborate on how the deterministic nature of chaotic systems can be leveraged to enhance security in communication systems beyond the generation of Gaussian noise, and highlight the novelty of their work.?

2.     In Section 2.2, why was white Gaussian noise chosen as the reference signal, and could other distributions serve a similar purpose in different contexts?

3.     How do the authors ensure that the signals from different chaotic systems are indeed independent, as required by the Central Limit Theorem?

4.     Suggestion: Including a discussion on the potential scalability of the experimental setups to include more chaotic systems could provide valuable insights into practical applications. It might be useful to discuss any limitations of the current study and how they might be addressed.

5.     A detailed information about the experimental parameters and setup will be helpful, especially in cases where specific choices significantly impact the outcomes.

6.     What are the theoretical or practical limitations to the number of chaotic signals that can be summed to achieve a Gaussian distribution?

The language can be made more better.

Author Response

Thank you for all your comments. We carefully considered and took into account all of them. Our detailed response you can find below. We are very thankful such as the comments and their correction made our paper better.

Author Response File: Author Response.pdf