An Introduction to Digital Chaotic Systems Updated by Random Iterations

The objective of this first chapter is to introduce the so-called digital chaotic systems updated by random iterations and to present the latest developments in this field of research. Basic notations and terminologies are also provided for the sake of completeness.

[1]  Binder,et al.  Simulating chaotic behavior with finite-state machines. , 1986, Physical review. A, General physics.

[2]  Jinhu Lu,et al.  Towards A Theoretical Framework for Analysis and Intervention of Random Drift on General Networks , 2015, IEEE Transactions on Automatic Control.

[3]  Elaine B. Barker,et al.  A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2000 .

[4]  Frank Y. Shih,et al.  Digital Watermarking and Steganography: Fundamentals and Techniques , 2007 .

[5]  Sergej Celikovský,et al.  Message Embedded Chaotic Masking Synchronization Scheme Based on the Generalized Lorenz System and Its Security Analysis , 2016, Int. J. Bifurc. Chaos.

[6]  Z. Galias,et al.  The Dangers of Rounding Errors for Simulations and Analysis of Nonlinear Circuits and Systems?and How to Avoid Them , 2013, IEEE Circuits and Systems Magazine.

[7]  Lih-Yuan Deng,et al.  Period Extension and Randomness Enhancement Using High-Throughput Reseeding-Mixing PRNG , 2012, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[8]  Sundarapandian Vaidyanathan,et al.  Dynamic Analysis, Adaptive Feedback Control and Synchronization of An Eight-Term 3-D Novel Chaotic System with Three Quadratic Nonlinearities , 2016, Advances in Chaos Theory and Intelligent Control.

[9]  L. Chua,et al.  On chaos of digital filters in the real world , 1991 .

[10]  Pierre L'Ecuyer,et al.  TestU01: A C library for empirical testing of random number generators , 2006, TOMS.

[11]  Jacques M. Bahi,et al.  Suitability of chaotic iterations schemes using XORshift for security applications , 2014, J. Netw. Comput. Appl..

[12]  J. Banks,et al.  On Devaney's definition of chaos , 1992 .

[13]  W. Schwarz,et al.  Chaos and cryptography , 2001 .

[14]  Xiaole Fang,et al.  Theoretical Design and Circuit Implementation of Integer Domain Chaotic Systems , 2014, Int. J. Bifurc. Chaos.

[15]  R. Devaney An Introduction to Chaotic Dynamical Systems , 1990 .

[16]  T. Kohda,et al.  Statistics of chaotic binary sequences , 1997, IEEE Trans. Inf. Theory.

[17]  Guanrong Chen,et al.  A Systematic Methodology for Constructing Hyperchaotic Systems With Multiple Positive Lyapunov Exponents and Circuit Implementation , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Sundarapandian Vaidyanathan,et al.  A Chaotic System With Equilibria Located on the Rounded Square Loop and Its Circuit Implementation , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

[19]  J. Cernák Digital generators of chaos , 1996 .

[20]  M. Blank Pathologies generated by round-off in dynamical systems , 1994 .

[21]  Jianfeng Ma,et al.  Robust extended chaotic maps-based three-factor authentication scheme preserving biometric template privacy , 2016 .

[22]  Bharathwaj Muthuswamy A Route to Chaos Using FPGAs : Volume I: Experimental Observations , 2015 .

[23]  Naixue Xiong,et al.  Analysis and Design of Digital Chaotic Systems With Desirable Performance via Feedback Control , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[24]  Guanrong Chen,et al.  Designing Hyperchaotic Systems With Any Desired Number of Positive Lyapunov Exponents via A Simple Model , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  Jun Lin,et al.  A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map , 2017, Int. J. Bifurc. Chaos.

[26]  Roy,et al.  Communication with chaotic lasers , 1998, Science.

[27]  Guanrong Chen,et al.  Chaotifying continuous-Time nonlinear Autonomous Systems , 2012, Int. J. Bifurc. Chaos.

[28]  Laurent Larger,et al.  Chaos-based communications at high bit rates using commercial fibre-optic links , 2005, Nature.

[29]  Gonzalo Álvarez,et al.  Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems , 2003, Int. J. Bifurc. Chaos.

[30]  Ali Hajimiri,et al.  A general theory of phase noise in electrical oscillators , 1998 .

[31]  C. Beck,et al.  Effects of phase space discretization on the long-time behavior of dynamical systems , 1987 .

[32]  Chengqing Li,et al.  Cryptanalyzing image encryption using chaotic logistic map , 2013, Nonlinear Dynamics.

[33]  X. Mou,et al.  On the security of a chaotic encryption scheme: problems with computerized chaos in finite computing precision , 2003 .

[34]  Guanrong Chen,et al.  Making a dynamical system chaotic: feedback control of Lyapunov exponents for discrete-time dynamical systems , 1997 .

[35]  Jacques M. Bahi,et al.  Class of Trustworthy Pseudo-Random Number Generators , 2011, ArXiv.

[36]  S. Li,et al.  Cryptographic requirements for chaotic secure communications , 2003, nlin/0311039.

[37]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[38]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[39]  L. Chua,et al.  The double scroll family , 1986 .

[40]  W. F. Wolff,et al.  Transients and asymptotics in granular phase space , 1986 .

[41]  Yicong Zhou,et al.  Discrete Wheel-Switching Chaotic System and Applications , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[42]  Nithin Nagaraj,et al.  Increasing average period lengths by switching of robust chaos maps in finite precision , 2008, 0811.1823.

[43]  Jinhu Lu,et al.  Bridging the Gap Between Transmission Noise and Sampled Data for Robust Consensus of Multi-Agent Systems , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[44]  H. Schuster Deterministic chaos: An introduction , 1984 .

[45]  Jacques M. Bahi,et al.  Hash Functions Using Chaotic Iterations , 2017, ArXiv.

[46]  Guanrong Chen,et al.  Design and ARM-Embedded Implementation of a Chaotic Map-Based Real-Time Secure Video Communication System , 2015, IEEE Transactions on Circuits and Systems for Video Technology.

[47]  Luis Gerardo de la Fraga,et al.  Engineering Applications of FPGAs: Chaotic Systems, Artificial Neural Networks, Random Number Generators, and Secure Communication Systems , 2016 .

[48]  David A. Johns,et al.  Variable-structure compensation of delta-sigma modulators: stability and performance , 2002 .

[49]  Xiao-jian Tian,et al.  Pseudo-random sequence generator based on the generalized Henon map , 2008 .

[50]  Jacques M. Bahi,et al.  Evaluating Quality of Chaotic Pseudo-Random Generators: Application to Information Hiding , 2011, ArXiv.

[51]  C. Chui,et al.  A symmetric image encryption scheme based on 3D chaotic cat maps , 2004 .

[52]  Chengqing Li,et al.  Cracking a hierarchical chaotic image encryption algorithm based on permutation , 2015, Signal Process..

[53]  Sang Tao,et al.  Perturbance-based algorithm to expand cycle length of chaotic key stream , 1998 .

[54]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[55]  In-Kwon Lee,et al.  Chaotic image encryption using pseudo-random masks and pixel mapping , 2016, Signal Process..

[56]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[57]  Guanrong Chen,et al.  On the Dynamical Degradation of Digital Piecewise Linear Chaotic Maps , 2005, Int. J. Bifurc. Chaos.

[58]  Bharathwaj Muthuswamy,et al.  A Route to Chaos Using FPGAs , 2015 .

[59]  Naixue Xiong,et al.  A general hybrid model for chaos robust synchronization and degradation reduction , 2015, Inf. Sci..

[60]  Liu Kexin,et al.  Finite-time adaptive consensus of a class of multi-agent systems , 2016 .