A note on complete polynomials over finite fields and their applications in cryptography
A note on complete polynomials over finite fields and their applications in cryptography
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DOI：
10.1016/j.ffa.2013.10.008
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Muratovic-Ribic;E. Pasalic
中科院分区：
文献类型：
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作者：
A. Muratovic-Ribic;E. Pasalic
这项工作提供了有限域上完整映射的递归构造。这些置换多项式的特征是 f (x) ∈ F q [x] 及其相关映射 f (x)+ x 都是置换，它们在密码学中的弯曲负函数构造中具有重要的应用，这实际上导致了这些函数的一些新类别。此外，我们还提供了奇数特征的有限域上的映射的递归构造，具有一个有趣的属性，即 f (x) 和 f (x+ c)+ f (x) 都是每个 c∈ F q 的排列。处理多变量和单变量表示，并给出一些关于不动点和这些排列的循环结构的结果。最后，我们利用我们的主要结果在有限域上构造所谓的负弯曲函数和弯曲函数。
A recursive construction of complete mappings over finite fields is provided in this work. These permutation polynomials, characterized by the property that both f (x)∈ F q [x] and its associated mapping f (x)+ x are permutations, have an important application in cryptography in the construction of bent–negabent functions which actually leads to some new classes of these functions. Furthermore, we also provide a recursive construction of mappings over finite fields of odd characteristic, having an interesting property that both f (x) and f (x+ c)+ f (x) are permutations for every c∈ F q. Both the multivariate and univariate representations are treated and some results concerning fixed points and the cycle structure of these permutations are given. Finally, we utilize our main result for the construction of so-called negabent functions and bent functions over finite fields.