{"title":"Design and practical implementation of a novel hyperchaotic system generator based on Apéry's constant","authors":"Omer Kocak , Uğur Erkan , Ismail Babaoglu","doi":"10.1016/j.vlsi.2025.102399","DOIUrl":null,"url":null,"abstract":"<div><div>Modern chaotic systems necessitate high levels of randomness and complexity, which can be achieved through adaptable seed functions. This paper proposes a new 2D Apéry chaotic system generator (2D-ACG) based on Apéry numbers to fulfill this need. The 2D-ACG generates various chaotic systems using classical seed functions. The effectiveness and the capabilities of 2D-ACG are demonstrated on three well-known example chaotic maps using pairs of seed functions such as Cos-Cos, Sin-Sin and Cos-Sin. The reliability of chaos metrics, such as the Lyapunov exponent (LE), sample entropy (SE), correlation dimension (CD), Kolmogorov entropy (KE), C0 test, and sensitivity, confirms the chaotic performance of these maps. This is further supported by a comparison with reported 2D chaotic systems. Furthermore, one of the maps derived from 2D-ACG has been implemented into an image encryption algorithm and has successfully passed the cryptanalysis tests. Additionally, the hardware implementation of 2D-ACG has been tested on a field programmable gate array (FPGA), thereby confirming its efficacy. The superior results obtained indicate that the proposed 2D-ACG, with its enhanced diversity and complex structure derived from the Apéry's constant, exhibits higher-performance chaotic characteristics.</div></div>","PeriodicalId":54973,"journal":{"name":"Integration-The Vlsi Journal","volume":"103 ","pages":"Article 102399"},"PeriodicalIF":2.2000,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Integration-The Vlsi Journal","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167926025000562","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, HARDWARE & ARCHITECTURE","Score":null,"Total":0}
引用次数: 0
Abstract
Modern chaotic systems necessitate high levels of randomness and complexity, which can be achieved through adaptable seed functions. This paper proposes a new 2D Apéry chaotic system generator (2D-ACG) based on Apéry numbers to fulfill this need. The 2D-ACG generates various chaotic systems using classical seed functions. The effectiveness and the capabilities of 2D-ACG are demonstrated on three well-known example chaotic maps using pairs of seed functions such as Cos-Cos, Sin-Sin and Cos-Sin. The reliability of chaos metrics, such as the Lyapunov exponent (LE), sample entropy (SE), correlation dimension (CD), Kolmogorov entropy (KE), C0 test, and sensitivity, confirms the chaotic performance of these maps. This is further supported by a comparison with reported 2D chaotic systems. Furthermore, one of the maps derived from 2D-ACG has been implemented into an image encryption algorithm and has successfully passed the cryptanalysis tests. Additionally, the hardware implementation of 2D-ACG has been tested on a field programmable gate array (FPGA), thereby confirming its efficacy. The superior results obtained indicate that the proposed 2D-ACG, with its enhanced diversity and complex structure derived from the Apéry's constant, exhibits higher-performance chaotic characteristics.
期刊介绍:
Integration''s aim is to cover every aspect of the VLSI area, with an emphasis on cross-fertilization between various fields of science, and the design, verification, test and applications of integrated circuits and systems, as well as closely related topics in process and device technologies. Individual issues will feature peer-reviewed tutorials and articles as well as reviews of recent publications. The intended coverage of the journal can be assessed by examining the following (non-exclusive) list of topics:
Specification methods and languages; Analog/Digital Integrated Circuits and Systems; VLSI architectures; Algorithms, methods and tools for modeling, simulation, synthesis and verification of integrated circuits and systems of any complexity; Embedded systems; High-level synthesis for VLSI systems; Logic synthesis and finite automata; Testing, design-for-test and test generation algorithms; Physical design; Formal verification; Algorithms implemented in VLSI systems; Systems engineering; Heterogeneous systems.