摘要： 周期序列的线性复杂度是衡量流密码系统安全性能的一个重要指标。事实表明周期序列中的若干位置上值的变化会影响改变后的周期序列的线性复杂度。基于此点该文提出了周期序列的线性复杂度k位置错误谱的概念以便于追踪错误位置对线性复杂度的影响。特别是对周期为2n的二元序列，发现了这类序列线性复杂度的1位置错误谱的周期并且给出了具有同样图像谱特征的序列数目。并把结果推广到了定义在Fp上周期为pn的序列上。

关键词: 流密码, 周期序列, 线性复杂度, k错线性复杂度, k位置错误谱

Abstract: The linear complexity of periodic sequences is an important security index of stream cipher systems. It is noticeable that the linear complexity of a periodic sequence will be influenced when the values in some positions change. According to this, this paper proposes the concept of the k positions error spectrum to trace this influence on the linear complexity. Especially for 2n -periodic binary sequences, the periods of the 1position error spectrum for this kind of sequences are discovered and the number of the sequences with the same characteristic of the spectrum is given. These results are generalized to pn-periodic sequences over Fp.

Key words: stream cipher, periodic sequence, linear complexity, k error linear complexity, k positions error spectrum

中图分类号: 

• TN918.1