The second-order zero differential uniformity of the swapped inverse functions over finite fields
<|reference_start|>The second-order zero differential uniformity of the swapped inverse functions over finite fields: The Feistel Boomerang Connectivity Table (FBCT) was proposed as the feistel counterpart of the Boomerang Connectivity Table. The entries of the FBCT are actually related to the second-order zero differential spectrum. Recently, several results on the second-order zero differential uniformity of some functions were introduced. However, almost all of them were focused on power functions, and there are only few results on non-power functions. In this paper, we investigate the second-order zero differential uniformity of the swapped inverse functions, which are functions obtained from swapping two points in the inverse function. We also present the second-order zero differential spectrum of the swapped inverse functions for certain cases. In particular, this paper is the first result to characterize classes of non-power functions with the second-order zero differential uniformity equal to 4, in even characteristic.<|reference_end|>
@article{jeong2024the,
    title={The second-order zero differential uniformity of the swapped inverse
  functions over finite fields},
    author={Jaeseong Jeong, Namhun Koo, Soonhak Kwon},
    journal={arXiv preprint arXiv:2405.16784},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.16784},
    primaryClass={cs.IT cs.CR math.IT}
}