Paper 2025/2144
On Equivalence of the Butterfly Structure
, Hong Kong University of Science and Technology, Hetao Institute of Mathematics and Interdisciplinary SciencesAbstract
The butterfly structures were introduced by Perrin et al. as a generalization of the Dillon's APN permutation operated in 6 bits. It was proved by several authors independently that such butterflies are differentially 4-uniform and have best known nonlinearity among functions over $\mathbb{F}_{2^{2k}}$. In [LLHQ21, LHXZ22] authors provided sufficient coefficient conditions such that the closed butterfly is a permutation and they further prove that such functions have boomerang uniformity 4 and are linear equivalent to Gold functions. In this paper, we adopt techniques from [DZ23] and [GK] to classify closed butterfly structures satisfying more general conditions in terms of EA-equivalence and CCZ-equivalence.
Metadata
- Available format(s)
-
PDF
- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- Keywords
- Butterfly structurebiprojective functionslinear equivalenceEA-equivalenceCCZ-equivalence
- Contact author(s)
- chenzhanxi @ himis-sz cn
- History
- 2026-01-30: revised
- 2025-11-24: received
- See all versions
- Short URL
- https://ia.cr/2025/2144
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2025/2144,
author = {Chin Hei Chan},
title = {On Equivalence of the Butterfly Structure},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/2144},
year = {2025},
url = {https://eprint.iacr.org/2025/2144}
}
