CAJ | 학술논문

非线性反馈移位寄存器(NFSR)是目前序列密码研究的热点问题之一。假定一个NFSR可以分解为更低级数NFSR的串联，该文讨论此分解是否唯一的问题。首先，对线性反馈移位寄存器(LFSR)而言，其串联分解等价于二元有限域F2上单变元多项式的分解，因而是唯一的。其次，针对给定NFSR可以分解为更低级数NFSR到LFSR串联的情形，该文给出了此 NFSR 具有这样分解的一个充分必要条件，并据此指出所有这样分解中级数最大的LFSR是唯一的。该文的最后构造了一类反例，此类反例表明对一般情形而言，NFSR的串联分解并不唯一。
비선성반궤이위기존기(NFSR)시목전서렬밀마연구적열점문제지일。가정일개NFSR가이분해위경저급수NFSR적천련，해문토론차분해시부유일적문제。수선，대선성반궤이위기존기(LFSR)이언，기천련분해등개우이원유한역F2상단변원다항식적분해，인이시유일적。기차，침대급정NFSR가이분해위경저급수NFSR도LFSR천련적정형，해문급출료차 NFSR 구유저양분해적일개충분필요조건，병거차지출소유저양분해중급수최대적LFSR시유일적。해문적최후구조료일류반례，차류반례표명대일반정형이언，NFSR적천련분해병불유일。
The Nonlinear Feedback Shift Register.(NFSR) is one of hot topics of stream cipher in recent studies. The uniqueness of a NFSR assuming to be decomposed into a cascade connection of smaller NFSRs is discussed in this paper. Firstly, the decomposition of Linear Feedback Shift Register.(LFSR) is equivalent to the decomposition of univariate polynomials over the finite field of two elements F2, thus it is unique. Secondly, for the case that a NFSR can be decomposed into a cascade connection of a NFSR into a LFSR, a necessary and sufficient condition is offered for a NFSR to have such a decomposition. Based on this condition, it is indicated that during all such decompositions, the largest LFSR is unique. However, the construction of counterexamples in a class shows that, for the general cases, the decomposition of a NFSR into a cascade connection of smaller NFSRs is not unique.