非线性反馈移位寄存器（NLFSR, Nonlinear feedback shift register）是相对于线性反馈移位暂存器而言的。它们的大体电路逻辑相似，仅仅在于NLFSR的反馈逻辑是由异或门和与门构成的，而LFSR中仅存在异或门。从代数表达式来看，异或门是加法（+），而与门是乘法（*）。由加法构成的反馈逻辑，其反馈表达式的最高项次数不会增长，而由乘法参与的反馈表达式项次数会增长、并可能超过定义多项式的最高项。

数学上的相关讨论可以参考：Janusz Szmidt: "The Search and Construction of Nonlinear Feedback Shift Registers", http://www.math.uni-magdeburg.de/~fq11/talks/Szmidt.pdf

A NLFSR (Non-Linear Feedback Shift Register) is a common component in modern stream ciphers, especially in RFID and smartcard applications. NLFSRs are known to be more resistant to cryptanalytic attacks than Linear Feedback Shift Registers (LFSRs). It is known how to generate a n-bit NLFSR of maximal length 2, generating a De Bruijn sequence, by extending a maximal-length LFSR with n stages; but the construction of other large NLFSRs with guaranteed long periods remains an open problem. Using bruteforce methods, a list of maximum-period n-bit NLFSRs for n < 25 has been made as well as for n=25 and n=27.