论文标题
线性排列及其组成倒置在$ \ mathbb {f} _ {q^n} $上
Linear Permutations and their Compositional Inverses over $\mathbb{F}_{q^n}$
论文作者
论文摘要
置换多项式的使用与它们的组成倒置有关，作为加密系统实施的一个不错的选择。因此，对这些系数属于有限领域的这些多项式的构造的需求。作为置换多项式的一种特殊情况，高度需要相关性，因为其组成逆为本身。在这项工作中，我们提出了一种有效的方法，即如何在$ \ mathbb {f} _ {q^n} $上构建几个线性置换多项式，以及它们使用$ \ displayStyle的分解来进行构成倒置{ \ right \ rangle}}} $基于其原始iDempotents。结果，提出了立即构造的互动构造。
The use of permutation polynomials has appeared, along to their compositional inverses, as a good choice in the implementation of cryptographic systems. Hence, there has been a demand for constructions of these polynomials which coefficients belong to a finite field. As a particular case of permutation polynomial, involution is highly desired since its compositional inverse is itself. In this work, we present an effective way of how to construct several linear permutation polynomials over $\mathbb{F}_{q^n}$ as well as their compositional inverses using a decomposition of $\displaystyle{\frac{\mathbb{F}_q[x]}{\left\langle x^n -1 \right\rangle}}$ based on its primitive idempotents. As a consequence, an immediate construction of involutions is presented.
