Nonlinear feedback shift registers (NFSRs) are widely used as building blocks in the design of stream ciphers. Let NFSR(f) be an NFSR with the characteristic function f and let G(f) be the set of output sequences of NFSR(f). For a given NFSR(f), if there exists an affine Boolean function l such that G(l) ⊆ G(f), then G(l) is called an affine sub-family of NFSR(f). In this paper, by skillfully combining previous ideas, the authors give a new upper bound on the order of affine sub-families of NFSR(f). Compared with the four known bounds, the bound is better than three of them, and in some cases is also better than the rest one.

中文翻译：

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NFSR的仿射亚家族的一个新的上界

非线性反馈移位寄存器（NFSR）被广泛用作流密码设计的基础。令NFSR（f）为具有特征函数f的NFSR，令G（f）为NFSR（f）的输出序列的集合。对于给定的NFSR（˚F），如果存在的仿射布尔函数升使得ģ（升）⊆ ģ（˚F），则G ^（升）被称为NFSR（的仿射子系列˚F）。在本文中，通过巧妙地结合先前的观点，作者为NFSR的仿射亚族的顺序提供了新的上限（f）。与四个已知边界相比，该边界要比其中三个更好，并且在某些情况下也要比其余三个更好。