{"title":"原始线性反馈移位寄存器中整数序列的混沌性质","authors":"Hyojeong Choi;Gangsan Kim;Hong-Yeop Song;Hongjun Noh","doi":"10.1109/TCSII.2025.3585913","DOIUrl":null,"url":null,"abstract":"In this brief, we investigate the chaotic characteristics of the integer sequences generated by primitive linear feedback shift registers (LFSRs) by interpreting the internal states as integers. We prove that the discrete Lyapunov exponent (dLE) of the permutations induced by these sequences from an L-stage primitive LFSR approches to the range between <inline-formula> <tex-math>$\\ln (\\sqrt {3})$ </tex-math></inline-formula> and <inline-formula> <tex-math>$\\ln (2)$ </tex-math></inline-formula> as L increases indefinitely and hence the dynamic systems satisfy the definition of discrete chaos. Furthermore, the 0–1 test of the sequences yields statistics close to 1, supporting the conclusion that these sequences exhibit chaotic dynamics under both theoretical and empirical evaluations.","PeriodicalId":13101,"journal":{"name":"IEEE Transactions on Circuits and Systems II: Express Briefs","volume":"72 9","pages":"1268-1272"},"PeriodicalIF":4.9000,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Chaotic Nature of Integer Sequences From Primitive Linear Feedback Shift Registers\",\"authors\":\"Hyojeong Choi;Gangsan Kim;Hong-Yeop Song;Hongjun Noh\",\"doi\":\"10.1109/TCSII.2025.3585913\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this brief, we investigate the chaotic characteristics of the integer sequences generated by primitive linear feedback shift registers (LFSRs) by interpreting the internal states as integers. We prove that the discrete Lyapunov exponent (dLE) of the permutations induced by these sequences from an L-stage primitive LFSR approches to the range between <inline-formula> <tex-math>$\\\\ln (\\\\sqrt {3})$ </tex-math></inline-formula> and <inline-formula> <tex-math>$\\\\ln (2)$ </tex-math></inline-formula> as L increases indefinitely and hence the dynamic systems satisfy the definition of discrete chaos. Furthermore, the 0–1 test of the sequences yields statistics close to 1, supporting the conclusion that these sequences exhibit chaotic dynamics under both theoretical and empirical evaluations.\",\"PeriodicalId\":13101,\"journal\":{\"name\":\"IEEE Transactions on Circuits and Systems II: Express Briefs\",\"volume\":\"72 9\",\"pages\":\"1268-1272\"},\"PeriodicalIF\":4.9000,\"publicationDate\":\"2025-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Transactions on Circuits and Systems II: Express Briefs\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/11071980/\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Circuits and Systems II: Express Briefs","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/11071980/","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Chaotic Nature of Integer Sequences From Primitive Linear Feedback Shift Registers
In this brief, we investigate the chaotic characteristics of the integer sequences generated by primitive linear feedback shift registers (LFSRs) by interpreting the internal states as integers. We prove that the discrete Lyapunov exponent (dLE) of the permutations induced by these sequences from an L-stage primitive LFSR approches to the range between $\ln (\sqrt {3})$ and $\ln (2)$ as L increases indefinitely and hence the dynamic systems satisfy the definition of discrete chaos. Furthermore, the 0–1 test of the sequences yields statistics close to 1, supporting the conclusion that these sequences exhibit chaotic dynamics under both theoretical and empirical evaluations.
期刊介绍:
TCAS II publishes brief papers in the field specified by the theory, analysis, design, and practical implementations of circuits, and the application of circuit techniques to systems and to signal processing. Included is the whole spectrum from basic scientific theory to industrial applications. The field of interest covered includes:
Circuits: Analog, Digital and Mixed Signal Circuits and Systems
Nonlinear Circuits and Systems, Integrated Sensors, MEMS and Systems on Chip, Nanoscale Circuits and Systems, Optoelectronic
Circuits and Systems, Power Electronics and Systems
Software for Analog-and-Logic Circuits and Systems
Control aspects of Circuits and Systems.