Studying Special Operators for the Application of Evolutionary Algorithms in the Seek of Optimal Boolean Functions for Cryptography

The role of Boolean functions in modern cryptography has triggered the necessity of developing methods to construct them with adequate properties, such as balancedness and high non-linearity—making them more resistant to a variety of cryptanalytic attacks. Research into the construction of weight-wise perfectly balanced Boolean functions using Evolutionary Algorithms is scarce but encouraging (e.g., [1]). In this work, we first investigate the effect on an evolutionary algorithm’s performance when relying solely on the penalty function, as opposed to the solution repairment method. Second, we focus on the effect of problem-specific crossover operators (e.g., those used on [2]), and particularly proposing a novel one free of solution repairs to preserve balancedness. The results obtained suggest that an adequate penalty factor and the use of specifically designed evolutionary operators is sufficient to find Boolean functions with weight-wise perfect balancedness and high non-linearity, as desired.