Discrete Dynamical Systems And Chaotic Machines
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Discrete Dynamical Systems and Chaotic Machines
For computer scientists, especially those in the security field, the use of chaos has been limited to the computation of a small collection of famous but unsuitable maps that offer no explanation of why chaos is relevant in the considered contexts. Discrete Dynamical Systems and Chaotic Machines: Theory and Applications shows how to make finite machines, such as computers, neural networks, and wireless sensor networks, work chaotically as defined in a rigorous mathematical framework. Taking into account that these machines must interact in the real world, the authors share their research results on the behaviors of discrete dynamical systems and their use in computer science. Covering both theoretical and practical aspects, the book presents: Key mathematical and physical ideas in chaos theory Computer science fundamentals, clearly establishing that chaos properties can be satisfied by finite state machines Concrete applications of chaotic machines in computer security, including pseudorandom number generators, hash functions, digital watermarking, and steganography Concrete applications of chaotic machines in wireless sensor networks, including secure data aggregation and video surveillance Until the authors’ recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues. This self-contained book illustrates how chaos theory enables the study of computer security problems, such as steganalysis, that otherwise could not be tackled. It also explains how the theory reinforces existing cryptographically secure tools and schemes.
Discrete Dynamical Systems and Chaotic Machines
Until the authors' recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues. This self-contained book shows how to make finite machines, such as computers, neural networks, and wireless sensor networks, work chaotically as defined in a rigorous mathematical framework. Taking into account that these machines must interact in the real world, the authors share their research results on the behaviors of discrete dynamical systems and their use in computer science.
Design of Digital Chaotic Systems Updated by Random Iterations
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 chaos on the domain of finite precision. The book presents Lyapunov exponents, as well as implementations to show the potential application of digital chaotic systems in the real world; the authors also discuss the basic advantages and practical benefits of this approach. The authors explore the solutions to dynamic degradation (including short cycle length, decayed distribution and low linear complexity) by proposing novel modelling methods and hardware designs for two different one-dimensional chaotic systems, which satisfy Devaney’s definition of chaos. They then extend it to a higher-dimensional digital-domain chaotic system, which has been used in image-encryption technology. This ensures readers do not encounter large differences between actual and theoretical chaotic orbits through small errors. Digital Chaotic Systems serves as an up-to-date reference on an important research topic for researchers and students in control science and engineering, computing, mathematics and other related fields of study.