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流密码系统中常用的一种滚动密钥生成器由n个线性移位寄存器组成,这n个线性移位寄存器的输出序列用一个非线性函数组合后产生密钥流。因而控制非线性组合序列线性复杂度的问题是非常重要的。证明任意多最大长度GF(q)序列的乘积有最大线性复杂度如果它们的极小多项式有两两互素的次数。这个结果被扩展到乘积序列的任意线性组合。早期关于布尔形组合序列的结果被推广。
A popular rolling key generator in a stream cipher system consists of n linear shift registers. The output sequences of the n linear shift registers are combined to produce a keystream by a non-linear function. Therefore, it is very important to control the linear complexity of non-linear combination sequence. It is proved that the product of GF (q) sequences of any multiple maximum length has the greatest linear complexity if their minimal polynomials are mutually intertwined with each other. This result is extended to any linear combination of product sequences. Early results on Boolean combinatorial sequences were generalized.