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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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.