论文标题
$ 4 $ - 均匀的BCT置于广义蝴蝶结构的排列
$4$-uniform BCT permutations from generalized butterfly structure
论文作者
论文摘要
作为对Dillon APN置换的概括，蝴蝶结构和概括引起了人们的极大兴趣，因为它们在尺寸$ 2^{4K+2} $的字段上生成了最著名的微分和非线性属性的排列。与这些结果相辅相成，我们在本文中表明，蝴蝶结构，更确切地说，封闭的蝴蝶还产生了最佳的Boomerang均匀性的排列，这是与Boomerang式攻击有关的新的重要参数。这是文献中第六个已知的无限置换家族，其在此类领域中具有最著名的飞旋镖均匀性。
As a generalization of Dillon's APN permutation, butterfly structure and generalizations have been of great interest since they generate permutations with the best known differential and nonlinear properties over the field of size $2^{4k+2}$. Complementary to these results, we show in this paper that butterfly structure, more precisely the closed butterfly also yields permutations with the best boomerang uniformity, a new and important parameter related to boomerang-style attacks. This is the sixth known infinite family of permutations in the literature with the best known boomerang uniformity over such fields.
