Nonlinear feedback shift registers (NFSR) are widely used in cryptography as the source of pseudo-random sequences used in ciphers. The nature of the feedback in a given NFSR affects its output sequence and its statistical quality. The complexity of the problem of restoring the initial state of an NFSR by partially known values of the output is one of the signs of a "good" NFSR. In this regard, we note that the presence of the output affine functions lowers the quality of an NFSR since the corresponding problem is reduced to the solution of a system of linear equations. This paper is concerned with the conditions providing the absence of nontrivial affine functions among NFSR output functions. The obtained theoretical results can be used to improve the effectiveness of experimental methods of finding NFSRs with no affine output functions.

非线性反馈移位寄存器 (NFSR) 在密码学中被广泛用作密码中使用的伪随机序列的来源。给定 NFSR 中反馈的性质会影响其输出序列及其统计质量。通过部分已知的输出值恢复 NFSR 初始状态的问题的复杂性是“好”NFSR 的标志之一。在这方面，我们注意到输出仿射函数的存在降低了 NFSR 的质量，因为相应的问题被简化为线性方程组的解。本文关注的是在 NFSR 输出函数中不存在非平凡仿射函数的条件。所获得的理论结果可用于提高寻找无仿射输出函数的 NFSR 的实验方法的有效性。