Design of digital chaotic systems updated by random iterations. (2018)

• Record Type: Book
• Further Information: Note: Qianxue Wang, Simin Yu, Christophe Guyeux.
• Authors: Wang, Qianxue; Yu, Simin; Guyeux, Christophe
• 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource (xiii, 110 pages), illustrations (some color)
• Subjects: 003/.857; Engineering; Chaotic behavior in systems -- Mathematics; Iterative methods (Mathematics); TECHNOLOGY & ENGINEERING -- Operations Research; Chaotic behavior in systems -- Mathematics; Iterative methods (Mathematics); Technology & Engineering -- Mechanical; Science -- System Theory; Dynamics & vibration; Cybernetics & systems theory; Systems engineering; Vibration; Systems theory; Technology & Engineering -- Electronics -- Circuits -- General; Circuits & components; Electronic books
• Languages: English
• ISBNs: 9783319735498; 3319735497
• Related ISBNs: 9783319735481; 3319735489
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed February 28, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.