由广义蝴蝶结构构造的4-一致BCT置换
信息论
2020-01-03 v1 math.IT
摘要
作为 Dillon 的 APN 置换的推广，蝴蝶结构及其推广自提出以来备受关注，因为它们在大小为 的域上生成具有已知最佳差分和非线性性质的置换。作为这些结果的补充，我们在本文中证明蝴蝶结构，更确切地说闭蝴蝶，也能生成具有最佳回飞棒一致性的置换，回飞棒一致性是一个与回飞棒式攻击相关的新的重要参数。这是文献中已知的第六个在此类域上具有已知最佳回飞棒一致性的无限置换族。
引用
@article{arxiv.2001.00464,
title = {$4$-uniform BCT permutations from generalized butterfly structure},
author = {Nian Li and Zhao Hu and Maosheng Xiong and Xiangyong Zeng},
journal= {arXiv preprint arXiv:2001.00464},
year = {2020}
}
备注
This paper was originally submitted on 5 December, 2019, and as we know later, is independent of arXiv:1912.02640 which appeared at the same time and obtained essentially the same results by using quite different methods. A substantial extension of this paper was recently obtained in arXiv:2001.00418