基于广义蝶形结构的$4$ -一致BCT置换
$4$-uniform BCT permutations from generalized butterfly structure
摘要：
作为Dillon的APN置换的推广，蝶形结构和推广已经引起了极大的兴趣，因为它们产生在大小为$2^{4k+2}$的域上具有最佳已知微分和非线性性质的置换。作为对这些结果的补充，我们在本文中表明，蝴蝶结构，更准确地说，封闭的蝴蝶也产生最好的回飞棒均匀性，一个新的和重要的参数相关的回飞棒式攻击的排列。这是第六个已知的无限家庭的排列在文献中最有名的回旋镖均匀性等领域。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
