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Summary

The research presents a discrete Particle Swarm Optimization (PSO) algorithm which solves the problem of creating balanced Boolean functions that possess robust cryptographic characteristics. The authors use a permutation-based PSO which they modify to maintain Hamming weight while implementing a hill-climbing method to enhance both nonlinearity and correlation immunity. The PSO velocity parameters receive optimization through two meta-optimization approaches which include Local Unimodal Sampling (LUS) and Continuous Genetic Algorithms (CGA) and CGA produces better results than LUS. The proposed method achieves functions with equivalent or superior nonlinearity and correlation immunity and propagation criteria performance than current methods according to experimental tests of Boolean functions with 7 to 12 variables. The research contributes to the field through its combination of swarm intelligence with local search and meta-optimization which creates an optimized system for designing cryptographic Boolean functions that outperform previous optimization approaches.

Major issues

The experimental results show promising results yet the authors need to explain their selection of evaluation metrics and show how these metrics affect real-world cryptographic system operations. The research would gain from explicit examinations which explain the relationship between nonlinearity and its effects on correlation immunity and propagation criteria.

The evaluation process needs additional development to achieve better method comparison results. The comparison between methods requires complete information about their parameter settings and their stopping points and their computational resource usage.

The scalability of the proposed approach beyond n=12 variables is not discussed in depth. The research needs additional analysis of computational complexity and performance expectations for big problem sets to enhance its real-world value.

Minor issues

The algorithm description contains complex sections which need additional high-level explanations and pseudocode to enhance its readability.

The paper presents parameter selection and implementation methods in its final section but these details should appear earlier to improve the paper's organizational structure.

The text needs minimal additional editing to achieve better clarity because its experimental section and result section require improved organization.

Competing interests

The author declares that they have no competing interests.

Use of Artificial Intelligence (AI)

The author declares that they did not use generative AI to come up with new ideas for their review.