Boosting the Diversity of a Similarity-Aware Genetic Algorithm Using a Siamese Network for Optimized S-Box Generation

Area of Science:

• Cryptography
• Optimization Algorithms
• Machine Learning

Background:

• Designing cryptographically robust substitution-boxes (S-boxes) is an NP-hard problem.
• Genetic Algorithms (GAs) are commonly used but suffer from premature convergence and lack of diversity.
• Limited a priori knowledge in traditional GAs hinders performance in S-box optimization.

Purpose of the Study:

• To propose a similarity-aware crossover strategy integrated with a Siamese learning framework for improved S-box optimization.
• To enhance parental diversity within the GA to ensure propagation of diverse traits.
• To achieve faster convergence and generate S-boxes with superior cryptographic properties.

Main Methods:

• A Siamese learning framework is integrated with a genetic algorithm.
• A similarity-aware crossover strategy is introduced, employing 'regressive' crossover when parents are too similar.
• The model is evaluated using contrastive loss, KL divergence loss, and a hybrid loss function.

Main Results:

• The proposed similarity-aware GA effectively optimizes S-boxes, demonstrating improved diversity and faster convergence.
• The strategy ensures propagation of parental diversity, leading to superior offspring.
• Generated S-boxes exhibit strong cryptographic properties, validated through rigorous testing.

Conclusions:

• The similarity-aware GA with Siamese learning offers a significant advancement in S-box design.
• This approach addresses the limitations of traditional GAs by incorporating local parental information.
• The method successfully generates high-quality S-boxes with enhanced cryptographic robustness.