论文标题
查找AGW标准排列的组成逆
Finding compositional inverses of permutations from the AGW criterion
论文作者
论文摘要
置换多项式及其组成逆在密码学，编码理论和组合设计中具有广泛的应用。以先前的几个结果发现了不同形式的置换多项式的组成逆，我们提出了一种找到由AGW标准构建的置换多项式媒介的一般方法。结果，我们减少了在有限的场上找到这种排列多项式的组成倒数的问题，即在较小的集合上找到两者的倒数。我们通过解释最近的几个已知结果，以及通过在不同类型中提供更多类别的置换多项式来证明我们的方法。此外，我们给出了这些置换多项式的新标准。还为所有不参考标准提供了明确的结构。
Permutation polynomials and their compositional inverses have wide applications in cryptography, coding theory, and combinatorial designs. Motivated by several previous results on finding compositional inverses of permutation polynomials of different forms, we propose a general method for finding these inverses of permutation polynomials constructed by the AGW criterion. As a result, we have reduced the problem of finding the compositional inverse of such a permutation polynomial over a finite field to that of finding the inverse of a bijection over a smaller set. We demonstrate our method by interpreting several recent known results, as well as by providing new explicit results on more classes of permutation polynomials in different types. In addition, we give new criteria for these permutation polynomials being involutions. Explicit constructions are also provided for all involutory criteria.
