二元周期多维序列的联合复杂度分析

The Research of Joint Linear Complexity of Binary Periodic Multi-Sequences

线性复杂度是度量密钥流序列安全性的重要指标。倒序序列和对偶序列是两类特殊序列。本文在二元周期倒序单序列的对偶序列已有研究结果的基础上,进一步讨论了二元周期倒序广义对偶多维序列的联合线性复杂度的性质,并明确给出二元周期倒序广义对偶多维序列与原多维序列之间的联合线性复杂度的关系式。针对二元周期倒序广义对偶多维序列的联合重量复杂度也进行了相关讨论。这些结果促进了密钥流多维序列的联合线性复杂度研究的进一步发展,具有一定的应用价值。

Linear complexity is the key index of safety of stream ciphers.Periodic inverted sequences and bit-wise negative sequences are two special kinds of sequences.Basing on the conclusion of binary periodic inverted generalized bit-wise negative sequences,this paper discusses the minimum generate polynomials of binary periodic inverted generalized bit-wise negative multi-sequences.The relation between binary periodic inverted generalized bit-wise negative multi-sequences and original periodic multi-sequences is pointed out and some discussion of the joint weight complexity about them is also presented.The results presented can develop the analysis of the joint complexity of periodic mult i-sequences of stream ciphers.