Genetic Approach to Improve Cryptographic Properties of Balanced Boolean Functions Using Bent Functions

Round 1

Reviewer 1 Report

A genetic algorithm used to improve the cryptographic properties of some boolean functions by using Bent functions is presented.

The results are interesting but the new ideas could be better put in evidence. The results could be better presented and interpreted from a cryptographic point of view. Also a comparison with similar solutions would be necessary to show the improvements obtained from a cryptographic point of view.

It seems that there are no major english usage problems.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

This paper presents a genetic algorithm approach to improve cryptographic properties of balanced Boolean functions.

The authors should take into consideration the following issues:

-        Page 3: define triplets (x, y, z) presented in Table 1.

-        Page 7, Table 3: you should use the international notations for minutes and seconds (i.e. min. and sec.) instead of notations ‘ and “.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

1. The place of "Table 1. Comparison of our results with those in the literature" should be in section Results, not in section 1. Introduction.

 More discussion of the presented in Table 1 results is needed.

 2. "Figure 1. Genetic algorithm structure" does not describe the presented GA mainly in the part "Resetting". If (lines 168-170) "More specifically, if those values are the same for a generation, then one of them is kept and the other 39 individuals are generated by forming a new population of size 1000 randomly and then applying the selection operation to them." according to the flowchart, if stop** criteria is not met, the new population of size 1000 goes to the crossover step. The selection of 40 parent individuals is not foreseen in the flowchart in Fig. 1.

 3. GAs are stochastic technique and the results are usually presented as average obtained results based on 20-30 GA runs, the best obtained and the worst obtained. Presented in Table 1 results are the best obtained or ?

4. There are no comments about the algorithm performance - some statistical results - standard deviation, distribution of the results, etc.

 5. How GA parameters are selected - initial population of 1000, selection of 100, parent population of 40?

 6. "The mutation is applied to the offspring obtained from the crossover in order to ensure diversity." I think that a mutation rate (pm) of 0.0001 (n = 12) or 3.052E-5 (n = 16) cannot ensure any diversity. For n>12 the values are so small (n = 24, pm = 1.192E-7), so there is no any mutation.

 7. The references are too old. There are not enough recent publications from the last 5 years.

 

In summary, the paper needs some revision. There are some issues that need to be addressed:

1. The correctness of the GA flowchart presented.

2. The selection of the values of the main parameters of the GA.

3. Evaluation of algorithm performance.

4. More discussion of the presented results.

 

5. Update references with recent ones.

 

 Minor editing of English language required

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have answered at my observations and I think the paper can be accepted from my point of view.

There are no major english errors.

Reviewer 3 Report

The authors have edited the manuscript according to the my remarks and comments. The manuscript may be accepted for publication.