Metaheuristics in the Optimization of Cryptographic Boolean Functions.

Area of Science:

• Cryptography
• Computational Science
• Optimization Algorithms

Background:

• Generating Boolean Functions (BFs) with high nonlinearity is crucial for cryptographic applications.
• Algebraic constructions are the primary methods, but metaheuristics have shown potential.
• Existing metaheuristics struggle to match the performance of algebraic techniques for high-quality BFs.

Purpose of the Study:

• To propose a novel diversity-aware metaheuristic algorithm for generating high-nonlinearity Boolean Functions (BFs).
• To develop a cost function leveraging the Walsh Hadamard Transform (WHT) and a strategic replacement mechanism.
• To achieve BFs with quality comparable to algebraic methods, particularly for complex 10-variable functions.

Main Methods:

• Design of a diversity-aware metaheuristic incorporating a novel cost function.
• Utilization of information from the Walsh Hadamard Transform (WHT) within the cost function.
• Implementation of a replacement strategy promoting gradual exploration-exploitation balance and solution clustering.
• Balancing population-level entropy with intra-cluster entropy for effective optimization.

Main Results:

• The proposed memetic algorithm successfully generates 10-variable Boolean Functions (BFs) of quality comparable to algebraic methods.
• Experimental results demonstrate the high performance of the novel optimization mechanism.
• The algorithm achieves a balance between exploration and exploitation through population and cluster entropy management.

Conclusions:

• The novel diversity-aware metaheuristic offers a powerful alternative for generating high-quality Boolean Functions (BFs).
• This approach overcomes limitations of previous metaheuristic methods in this domain.
• The findings represent a significant step forward in optimizing Boolean Functions for cryptographic and other applications.