LAUSR

The boomerang uniformity measures the resistance of block ciphers to boomerang attacks and has become an essential criterion of the substitution box (S-box). However, the S-boxes created by the Feistel structure have a poor property of boomerang uniformity. The genetic algorithm is introduced to improve the properties of the S-boxes created by the Feistel structure. New genetic operators are designed for genetic algorithm to improve its searchability. The new genetic algorithm searches for the bijective S-boxes with low differential uniformity, high nonlinearity, and low boomerang uniformity. The experimental results show that the new genetic algorithm dramatically improves the properties of the S-boxes created by the Feistel structure and obtains some 8 × 8 S-boxes with excellent performance. We compare the S-boxes generated by the new genetic algorithm with those generated by the traditional genetic algorithm. The comparison results show that the S-boxes generated by the new genetic algorithm have better properties than the S-boxes generated by the traditional genetic algorithm, which demonstrates the effectiveness and superiority of the new genetic algorithm in generating S-boxes.