On the cycle structure of a class of Galois NFSRs: component sequences possessing identical periods

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2025-03-29 DOI:10.1007/s10623-025-01616-w

Xiao-juan Wang, Tian Tian, Wen-feng Qi

引用次数: 0

Abstract

Nonlinear feedback shift registers (NFSRs) are widely used in the design of stream ciphers and the cycle structure of an NFSR is a fundamental problem still open. In this paper, a new configuration of Galois NFSRs, called F-Ring NFSRs, is proposed. It is shown that an n-bit F-Ring NFSR generates n sequences with the same period simultaneously, that is, sequences from all bit registers have the same period. Recall that the ring-like cascade connection proposed by Zhao et al. (Des Codes Cryptogr 86:2775–2790, 2018) also has such period property. But it is abnormal that if every component shift register is nonsingular, then the ring-like cascade connection is singular. F-Ring NFSRs proposed in this paper could fix this weakness. Moreover, it is proved that when an n-stage m-sequence is input to the internal state of an F-Ring NFSR by xor, the periods of its internal state are multiples of \(2^n-1\). At last, two toy examples are given to illustrate the new configuration.

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一类伽罗瓦NFSRs的循环结构：具有相同周期的分量序列

非线性反馈移位寄存器（NFSRs）在流密码设计中得到了广泛的应用，而非线性反馈移位寄存器的周期结构是一个尚未解决的基本问题。本文提出了一种新的伽罗瓦NFSRs构型，称为f -环NFSRs。结果表明，一个n位的F-Ring NFSR同时产生n个具有相同周期的序列，即来自所有位寄存器的序列具有相同的周期。回想一下，Zhao等人（Des Codes Cryptogr 86:2775-2790, 2018）提出的环状级联连接也具有这样的周期性质。但如果每个分量移位寄存器都是非奇异的，那么环形级联连接就是奇异的，这是不正常的。本文提出的f环NFSRs可以弥补这一弱点。进一步证明了当n阶m序列以xor输入到f环NFSR的内部状态时，其内部状态周期为\(2^n-1\)的倍数。最后，给出了两个示例来说明新的结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.