New Genetic Operators for Developing S-Boxes With Low Boomerang Uniformity

Abstract

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-box es created by the Feistel structure have a poor property of boomerang uniformity. The genetic algorithm is introduced to improve the properties of the S-box es created by the Feistel structure. New genetic operators are designed for the genetic algorithm to improve its searchability. The new genetic algorithm generates some 8 $\times $ 8 bijective S-boxes with differential uniformity 6, nonlinearity 108, and boomerang uniformity 10, which has dramatically improved the properties of the S-boxes created by the Feistel structure. Furthermore, the new genetic algorithm also improves the properties of the S-box population created by the Feistel structure as a whole. We compare the S-boxes generated by the new genetic algorithm with those generated by the traditional one. 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, demonstrating the new genetic algorithm’s effectiveness and superiority in developing S-boxes.

Keywords

• Boomerang uniformity
• S-box
• genetic algorithm
• genetic operator