The transformation algorithm for Nonlinear Feedback Shift Registers (NLFSRs) converts NLFSRs between Fibonacci and Galois configurations. Up to now, three types of Galois NLFSRs namely Type-I, Type-II and Type-III Galois NLFSRs have been discovered to be equivalent to Fibonacci NLFSRs in existing works. However, either no transformation algorithm has been proposed or the proposed algorithm has very high complexity for these Galois NLFSRs. More importantly, the common issue is that the output sequence is assumed to be generated by the first stage of the NLFSR. The sequences generated by other stages are not considered. In this paper, we develop a compensation method to address all these issues. Based on this unified method, we propose Fibonacci-to-Galois and Galois-to-Fibonacci transformation algorithms for the three types of Galois NLFSRs. Moreover, we discover a new type of Galois NLFSRs (Type-IV) that can be transformed to Fibonacci NLFSRs and propose transformation algorithms based on the same compensation method. No matter what the output function is, the output sequences are the same before and after being transformed by any of the proposed transformation algorithms.

非线性反馈移位寄存器 (NLFSR) 的转换算法在斐波那契和伽罗瓦配置之间转换 NLFSR。到目前为止，已经发现三种类型的Galois NLFSR，即Type-I、Type-II和Type-III Galois NLFSRs在现有工作中与Fibonacci NLFSRs等效。然而，对于这些 Galois NLFSR，要么没有提出转换算法，要么提出的算法具有非常高的复杂性。更重要的是，常见的问题是假设输出序列是由 NLFSR 的第一阶段生成的。不考虑其他阶段生成的序列。在本文中，我们开发了一种补偿方法来解决所有这些问题。基于这种统一的方法，我们针对三种类型的 Galois NLFSR 提出了 Fibonacci-to-Galois 和 Galois-to-Fibonacci 变换算法。此外，我们发现了一种新型的 Galois NLFSR（Type-IV），它可以转换为 Fibonacci NLFSR，并提出了基于相同补偿方法的转换算法。无论输出函数是什么，输出序列在被任何提出的转换算法转换之前和之后都是相同的。