论文标题
在低嘉利群岛排列的回旋镖均匀性上
On the Boomerang Uniformity of Permutations of Low Carlitz Rank
论文作者
论文摘要
在许多块密码的S-box设计中，找到具有低差分和回旋镖均匀性的置换多项式。例如，AES选择逆函数作为其S-box，其差异为4-均匀和Boomerang 6-均匀。同样，已经对许多非二次排列进行了大量研究，这些置换是通过从逆函数中修改某些点来获得的。在本文中，我们提供了一种新颖的方法，表明对逆功能的大量现有修改实际上与低carlitz等级的排列相同，除非Carlitz等级很大，否则这些修改不能为APN（几乎是完美的非线性）。使用Carlitz形式排列的良好属性，我们介绍了Carlitz等级3的完整排列列表，具有Boomerang均匀性六，并且还提供了Carlitz等级3的差异均匀性的完整分类。我们还提供了伴侣等价的副本，所有carlitz carlitz级别的均匀性均为Boomang 3具有Boomang unboolang unboorang unboorang unibory carlite carlity。
Finding permutation polynomials with low differential and boomerang uniformityis an important topic in S-box designs of many block ciphers. For example, AES chooses the inverse function as its S-box, which is differentially 4-uniform and boomerang 6-uniform. Also there has been considerable research on many non-quadratic permutations which are obtained by modifying certain set of points from the inverse function. In this paper, we give a novel approach that shows that plenty of existing modifications of the inverse function are in fact affine equivalent to permutations of low Carlitz rank and those modifications cannot be APN (almost perfect nonlinear) unless the Carlitz rank is very large. Using nice properties of the permutations of Carlitz form, we present the complete list of permutations of Carlitz rank 3 having the boomerang uniformity six, and also give the complete classification of the differential uniformity of permutations of Carlitz rank 3. We also provide, up to affine equivalence, all the involutory permutations of Carlitz rank 3 having the boomerang uniformity six.
