On the constructions of n-cycle permutations
On the constructions of n-cycle permutations
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关于n循环排列的构造
DOI：
10.1016/j.ffa.2021.101847
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发表时间：
2021
影响因子：
1
通讯作者：
Shixin Zhu
中科院分区：
文献类型：
--
作者：
Yuting Chen;Liqi Wang;Shixin Zhu
任何置换多项式都是n圈置换。当n是一个特定的小正整数时，可以得到有效的置换，如对合、三圈置换和四圈置换。这些置换在密码学和编码理论中有重要的应用。受AGW准则的启发，我们提出了n圈置换的准则，其主要形式为xrh（xs）.然后，我们提出了统一的构造方法，包括递归的方式和分圆的方式，这种形式的n-圈置换。我们通过构造三类高指数的显式三圈置换和两类低指数的n圈置换来证明我们的方法，其中许多在置换性质和循环性质的水平上都是新的。
Any permutation polynomial is an n-cycle permutation. When n is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These permutations have important applications in cryptography and coding theory. Inspired by the AGW Criterion, we propose criteria for n-cycle permutations, which mainly are of the form x r h (x s). We then propose unified constructing methods including recursive ways and a cyclotomic way for n-cycle permutations of such form. We demonstrate our approaches by constructing three classes of explicit triple-cycle permutations with high index and two classes of n-cycle permutations with low index, many of which are new both at levels of permutation property and cycle property.