Decomposition of permutations in a finite field
Decomposition of permutations in a finite field
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有限域中排列的分解
DOI：
10.1007/s12095-018-0317-2
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
V. Rijmen
中科院分区：
文献类型：
--
作者：
S. Nikova;V. Nikov;V. Rijmen
我们描述了一种方法来分解任何功率置换，作为一个序列的功率置换的低代数次数。作为结果，我们得到的GF（2n）的小n从3到16，以及APN功能，当n = 5的反演分解。更准确地说，我们发现分解成quadraticpower排列为任何nnot 4的倍数和分解成nmultiple 4的quadraticpower排列。最后，利用Carlitz定理证明了当3 ≤n≤ 16时，任意n位置换可分解为二次置换和三次置换。
We describe a method to decompose any power permutation, as a sequence of power permutations of lower algebraic degree. As a result we obtain decompositions of the inversion in GF(2n) for smallnfrom 3 up to 16, as well as for the APN functions, whenn= 5. More precisely, we find decompositions intoquadraticpower permutations for anynnot multiple of 4 and decompositions intocubicpower permutations fornmultiple of 4. Finally, we use the Theorem of Carlitz to prove that for 3 ≤n≤ 16 anyn-bit permutation can be decomposed in quadratic and cubic permutations.