The expectation and variance of the joint linear complexity of random periodic multisequences
The expectation and variance of the joint linear complexity of random periodic multisequences
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DOI：
10.1016/j.jco.2005.07.001
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发表时间：
2005-12
期刊：
影响因子：
--
通讯作者：
Fang-Wei Fu;H. Niederreiter;Ming Su
中科院分区：
文献类型：
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作者：
Fang-Wei Fu;H. Niederreiter;Ming Su
序列的线性复杂性是流密码系统的重要安全指标之一。近年来，在向量化序列密码系统的研究中，人们研究了多序列的联合线性复杂度。利用多重序列的广义离散傅立叶变换，Meidl和Niederreiter明确地确定了随机N周期多重序列的联合线性复杂度的期望。本文研究了随机周期多序列的联合线性复杂度的期望和方差。给出了随机周期多序列联合线性复杂度期望的几个新的下界。这些新的下界改进了已知的随机周期多序列联合线性复杂度的下界。通过进一步发展Meidl和Niederreiter的方法，我们得到了随机N周期多序列联合线性复杂度的一般公式和一般上界。这些结果推广了Dai和Yang关于随机周期序列线性复杂度的方差的公式和上界。此外，我们还确定了具有一定周期的随机周期多序列的联合线性复杂度的方差。
The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, the joint linear complexity of multisequences has been investigated. By using the generalized discrete Fourier transform for multisequences, Meidl and Niederreiter determined the expectation of the joint linear complexity of random N-periodic multisequences explicitly. In this paper, we study the expectation and variance of the joint linear complexity of random periodic multisequences. Several new lower bounds on the expectation of the joint linear complexity of random periodic multisequences are given. These new lower bounds improve on the previously known lower bounds on the expectation of the joint linear complexity of random periodic multisequences. By further developing the method of Meidl and Niederreiter, we derive a general formula and a general upper bound for the variance of the joint linear complexity of random N-periodic multisequences. These results generalize the formula and upper bound of Dai and Yang for the variance of the linear complexity of random periodic sequences. Moreover, we determine the variance of the joint linear complexity of random periodic multisequences with certain periods.