论文标题
周期阵列的多维线性复杂性的分析和计算
Analysis and Computation of Multidimensional Linear Complexity of Periodic Arrays
论文作者
论文摘要
线性复杂性是用于信息安全性相关的应用程序中的数组的重要参数。在这项工作中，我们调查了两个和三维阵列的构造，并使用\ cite {arcagomoorruti，goohomoru，mohoru}中提出的定义和方法获得了有关定期阵列的多维线性复杂性的新结果。结果包括对线性复杂性的结合的概括，与多键的复杂性度量的比较以及对数组复杂性的计算，而阵列的复杂性与``展开方法''不起作用的周期相对较为主要的。制定了精确公式的猜想和某些阵列构造复杂性的渐近行为。我们还提出了用于构建多维阵列和计算其多维线性复杂性的开源软件。
Linear complexity is an important parameter for arrays that are used in applications related to information security. In this work we survey constructions of two and three dimensional arrays, and present new results on the multidimensional linear complexity of periodic arrays obtained using the definition and method proposed in \cite{ArCaGoMoOrRuTi,GoHoMoRu,MoHoRu}. The results include a generalization of a bound for the linear complexity, a comparison with the measure of complexity for multisequences, and computations of the complexity of arrays with periods that are not relatively prime for which the ``unfolding method'' does not work. Conjectures for exact formulas and the asymptotic behavior of the complexity of some array constructions are formulated. We also present open source software for constructing multidimensional arrays and for computing their multidimensional linear complexity.
