构造给定k错线性复杂度谱的2~n周期序列

k错线性复杂度是度量序列密码安全性的重要指标之一。基于方体理论和Games-Chan算法的逆向推导提出构造方法,构造了具有给定k错线性复杂度谱的2n周期序列。首先使用标准方体分解算法对k错线性复杂度具有第一下降点k=2、第二下降点k′=6、第三下降点k″=10的2n周期序列进行分类,再讨论每一类序列下降点线性复杂度参数之间的关系,最后给出每种参数关系下序列的计数公式以及构造过程。事实上,所使用的方法可以用于构造具有更多下降点的2n周期序列。

Construction of 2n periodic periodic binary sequences with given k error linear complexity spectrum

The k error linear complexity is an important stability index of pseudorandom sequences. Based on the cube theory and the reverse process of the Games Chan algorithm, we propose an constructive approach for constructing 2n periodic binary sequences with given k error linear complexity spectrum. We use the standard cube decomposition algorithm to classify 2n periodic binary sequences with the k error linear complexity of them with the first descent point k=2, the second descent point k′=6 and the third descent point k″=10. We then discuss the relationship between linear complexity parameters in each category. Finally, we derive the counting formula and construction process on the number of the periodic sequences for each case. In fact, we can construct 2n periodic binary sequence with more descent points of k error linear complexity by the methods.