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Design of digital chaotic systems updated by random iterations

Author: Qianxue Wang; Simin Yu; Christophe Guyeux
Publisher: Cham, Switzerland : Springer, 2018.
Series: SpringerBriefs in applied sciences and technology., Nonlinear circuits
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This brief studies the general problem of constructing digital chaotic systems in devices with finite precision from low-dimensional to high-dimensional settings, and establishes a general framework for composing them. The contributors demonstrate that the associated state networks of digital chaotic systems are strongly connected. They then further prove that digital chaotic systems satisfy Devaney's definition of  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(OCoLC)1013944143
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Qianxue Wang; Simin Yu; Christophe Guyeux
ISBN: 9783319735498 3319735497
OCLC Number: 1025340339
Description: 1 online resource (xiii, 110 pages) : illustrations (some color).
Contents: Intro; Preface; References; Acknowledgements; Contents; Abbreviations; 1 An Introduction to Digital Chaotic Systems Updated by Random Iterations; 1.1 General Presentation; 1.2 Mathematical Definitions of Chaos; 1.2.1 Approaches Similar to Devaney; 1.2.2 Li --
Yorke Approach; 1.2.3 Topological Entropy Approach; 1.2.4 Lyapunov Exponent; 1.3 TestU01; 1.4 Plan of This Book; References; 2 Integer Domain Chaotic Systems (IDCS); 2.1 Description of IDCS; 2.1.1 Real Domain Chaotic Systems (RDCS); 2.1.2 IDCS; 2.2 Proof of Chaos for IDCS; 2.2.1 Dense Periodic Points; 2.2.2 Transitive Property. 2.2.3 Further Investigations of the Chaotic Behavior of IDCS2.2.4 Relationship Between Iterative Input and Output; 2.3 Network Analysis of the State Space of IDCS; 2.3.1 The Corresponding State Transition Diagram and Its Connectivity Analysis for IDCS with N = 3; 2.3.2 The Corresponding State Transition Diagram and Its Connectivity Analysis for IDCS with N = 4; 2.4 Circuit Implementation of IDCS; References; 3 Chaotic Bitwise Dynamical Systems (CBDS); 3.1 Improvements of Chaotic Bitwise Dynamical Systems (CBDS); 3.2 Proof of Chaos for CBDS; 3.2.1 Dense Periodic Points. 3.2.2 Transitive Property3.3 Uniformity; 3.4 TestU01 Statistical Test Results; 3.5 FPGA-Based Realization of CBDS; References; 4 One-Dimensional Digital Chaotic Systems (ODDCS); 4.1 The Structure of One-Dimensional Digital Chaotic Systems; 4.1.1 The Conventional Iterative Update Mechanism; 4.1.2 The Iterative Update Mechanism Controlled by Random Sequences; 4.2 The Connection Between a Chaotic System and Its Strongly Connected Network; 4.2.1 Transitive Property of ODDCS; 4.2.2 Dense Periodic Points of ODDCS; 4.2.3 Chaotic System and Its Strongly Connected Network. 4.3 Lyapunov Exponents of a Class of ODDCS4.3.1 General Expression of Equivalent Decimal for GF; 4.3.2 Mathematical Expression for G(y)y; 4.3.3 Estimating the Lyapunov Exponents; Reference; 5 Higher-Dimensional Digital Chaotic Systems (HDDCS); 5.1 Design of HDDCS; 5.1.1 Higher-Dimensional Integer Domain Chaotic Systems (HDDCS); 5.1.2 Description of HDDCS; 5.1.3 Comparative Study of RDCS, IDCS, CBDS, and HDDCS; 5.1.4 Network Analysis of the State Space of HDDCS; 5.2 Chaotic Performance of HDDCS; 5.2.1 Dense Periodic Points of HDDCS; 5.2.2 Transitive Property of HDDCS. 5.3 Lyapunov Exponents of a Class of HDDCS5.3.1 General Expression of Equivalent Decimal for GF; 5.3.2 Mathematical Expression for gi(y1,y2,Â#x83;, ym)yj; 5.3.3 Estimating the Lyapunov Exponents; 5.4 FPGA-Based Real-Time Application of 3D-DCS; 5.4.1 Design of 3D-DCS in FPGA; 5.4.2 Design of the FPGA-Based Hardware System for Image Encryption and Decryption; 5.4.3 FPGA-Based Implementation Result for Image Encryption and Decryption; References; 6 Investigating the Statistical Improvements of Various Chaotic Iterations-Based PRNGs; 6.1 Various Algorithms for Pseudorandom Number Generation.
Series Title: SpringerBriefs in applied sciences and technology., Nonlinear circuits
Responsibility: Qianxue Wang, Simin Yu, Christophe Guyeux.

Abstract:

This brief studies the general problem of constructing digital chaotic systems in devices with finite precision from low-dimensional to high-dimensional settings, and establishes a general framework  Read more...

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