New Genetic Operators for Developing S-Boxes With Low Boomerang Uniformity
Man Ki Kang, Ming‐Sheng Wang
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 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.