Nonlinear feedback shift registers (NFSRs) are widely used in stream cipher design as building blocks. The cascade connection of NFSRs, known as an important architecture, has been adopted in Grain family of stream ciphers. In this paper, a new sufficient condition under which an NFSR cannot be decomposed into the cascade connection of two smaller NFSRs is presented, which is easy to be verified from the algebraic normal form (ANF) of the characteristic function. In fact, our results are also applicable to nonsingular Boolean functions, which actually improve a previous research of Rhodes [6] where the characteristic functions of NFSRs cannot be contained.

非线性反馈移位寄存器（NFSR）被广泛用作流密码设计的基础。谷物流密码家族已采用了称为重要架构的NFSR级联连接。本文提出了一个新的充分条件，在该条件下不能将NFSR分解为两个较小的NFSR的级联，这很容易从特征函数的代数范式（ANF）进行验证。实际上，我们的结果也适用于非奇异布尔函数，这实际上改善了Rhodes [6]以前的研究，其中无法包含NFSR的特征函数。