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为使用线性反馈移位寄存器和非线性前馈运算的这一类二进制序列产生器介绍一种分析方法。这一类之所以重要是由于该产生器能产生很长的“不可予测”的序列。序列的周期由线性反馈连接决定,需要予测剩余的总周期的一部分由非线性前馈运算决定。用有限域上特征方程根的术语来阐述线性反馈移位寄存器,并证明了非线性运算给该表示法加入了另外的根。阐明产生器所需要根的个数是它复杂性的一个测度,也等于产生同样序列的最短线性反馈移位寄存器的长度(级数)。可将该分析过程用于任何任意组合的二进制移位寄存器产生器,也可将它用于具有所希望的特性复杂产生器的综合。虽然本文中的结论局限于二进制序列,但容易将该分析推广产生具有任何有限域上元素序列的类似设备。
An analytical method is presented for this type of binary sequence generator using linear feedback shift registers and nonlinear feedforward operations. This category is important because the generator produces long “unpredictable” sequences. The period of the sequence is determined by the linear feedback connection, and a portion of the remaining total period to be estimated is determined by the nonlinear feedforward operation. The linear feedback shift register is described in terms of the roots of the eigenvalue equations over finite fields and demonstrates that nonlinear operations add additional roots to the notation. The number of roots needed to clarify the generator is a measure of its complexity and is equal to the length (number of stages) of the shortest linear feedback shift register that produces the same sequence. This analysis can be used for any arbitrary combination of binary shift register generators, or it can be used for synthesis of complex generators with the desired characteristics. Although the conclusion in this article is limited to binary sequences, it is easy to generalize the analysis to produce similar devices with any finite element sequence on the horizon.