Discrete Wheel-Switching Chaotic System and Applications

This paper introduces a discrete wheel-switching chaotic system (DWSCS). Changing the controlling sequence of the wheel switch allows DWSCS to generate a large number of new chaotic sequences from a set of existing chaotic maps (seed maps). Simulations and analysis demonstrate the DWSCS's characteristics and chaotic behaviors. An FPGA design of DWSCS shows its effectiveness in hardware implementation. We also propose a pseudo-random number generator using DWSCS whose excellent performance has been shown in experiments and comparisons.

[1]  Anne Canteaut.  Berlekamp-Massey Algorithm , 2011, Encyclopedia of Cryptography and Security.

[2]  Walter C. Labys,et al.  Detecting Positive Feedback in Multivariate Time Series: The Case of Metal Prices and US Inflation , 2007 .

[3]  Sos S. Agaian,et al.  (n, k, p)-Gray code for image systems , 2013, IEEE Transactions on Cybernetics.

[4]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[5]  Chun-Mei Yang,et al.  Cryptanalyzing chaotic secure communications using return maps , 1998 .

[6]  Martin Hasler,et al.  Low-Density Codes Based on Chaotic Systems for Simple Encoding , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  José Carlos Pizolato,et al.  Chaotic Communication Based on the Particle-in-a-Box Electronic Circuit , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Zengqiang Chen,et al.  A new image encryption algorithm based on hyper-chaos , 2008 .

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

[10]  H. Leung,et al.  Identification of linear systems driven by chaotic signals using nonlinear prediction , 2002 .

[11]  Igor E. Shparlinski,et al.  On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators , 2003, IEEE Trans. Inf. Theory.

[12]  G. Álvarez,et al.  Cryptanalysis of an ergodic chaotic cipher , 2003 .

[13]  K. Alan Shore,et al.  An Extended Kalman Filtering Approach to Nonlinear Time-Delay Systems: Application to Chaotic Secure Communications , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

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

[16]  Guanrong Chen,et al.  Controlling a unified chaotic system to hyperchaotic , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[17]  S. Agaian,et al.  A wheel-switch chaotic system for image encryption , 2011, Proceedings 2011 International Conference on System Science and Engineering.

[18]  Xun Yi,et al.  Hash function based on chaotic tent maps , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[19]  Yicong Zhou,et al.  A new 1D chaotic system for image encryption , 2014, Signal Process..

[20]  Guanrong Chen,et al.  Identifying chaotic systems using Wiener and Hammerstein cascade models , 2001 .

[21]  Yuri Maistrenko,et al.  An introduction to the synchronization of chaotic systems: coupled skew tent maps , 1997 .

[22]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[23]  Jacques M. Bahi,et al.  A Novel Pseudo-random Number Generator Based on Discrete Chaotic Iterations , 2009, 2009 First International Conference on Evolving Internet.

[24]  K. Murali,et al.  Chaos based spread spectrum image steganography , 2004, IEEE Transactions on Consumer Electronics.

[25]  Kwok-Wo Wong,et al.  A Modified Chaos-Based Joint Compression and Encryption Scheme , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[26]  Ling Cong,et al.  A general efficient method for chaotic signal estimation , 1999 .

[27]  Yicong Zhou,et al.  Image encryption using binary bitplane , 2014, Signal Process..

[28]  Xinghuo Yu,et al.  Design and Implementation of Grid Multiwing Butterfly Chaotic Attractors From a Piecewise Lorenz System , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  D. Lathrop.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 2015 .

[30]  Guanrong Chen,et al.  Performance of SIMO FM-DCSK UWB System Based on Chaotic Pulse Cluster Signals , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[31]  Adrian Skrobek.  Cryptanalysis of chaotic stream cipher , 2007 .

[32]  Cong Ling,et al.  A general efficient method for chaotic signal estimation , 1999, IEEE Trans. Signal Process..

[33]  B. Kendall.  Nonlinear Dynamics and Chaos , 2001 .

[34]  Haralabos C. Papadopoulos,et al.  Maximum-likelihood estimation of a class of chaotic signals , 1995, IEEE Trans. Inf. Theory.

[35]  Antonio Loría,et al.  Adaptive Unknown-Input Observers-Based Synchronization of Chaotic Systems for Telecommunication , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[36]  Riccardo Rovatti,et al.  Implementation and Testing of High-Speed CMOS True Random Number Generators Based on Chaotic Systems , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[37]  Sos S. Agaian,et al.  A symmetric image cipher using wave perturbations , 2014, Signal Process..

[38]  Jacques M. Bahi,et al.  Randomness Quality of CI Chaotic Generators: Applications to Internet Security , 2010, 2010 2nd International Conference on Evolving Internet.

[39]  Antonio Loría,et al.  Adaptive Tracking Control of Chaotic Systems With Applications to Synchronization , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[40]  S. Finch.  Lyapunov Exponents , 2007 .

[41]  Xuanqin Mou,et al.  Pseudo-random Bit Generator Based on Couple Chaotic Systems and Its Applications in Stream-Cipher Cryptography , 2001, INDOCRYPT.

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

[43]  Alan V. Oppenheim,et al.  Quasi-Orthogonal Wideband Radar Waveforms Based on Chaotic Systems , 2010, IEEE Transactions on Aerospace and Electronic Systems.

[44]  Xiaogang Wu,et al.  Parameter estimation only from the symbolic sequences generated by chaos system , 2004 .

[45]  Kwok-Wo Wong,et al.  Simultaneous Arithmetic Coding and Encryption Using Chaotic Maps , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[46]  Z. Q. Chen,et al.  Chaotic Characteristics Analysis and Circuit Implementation for a Fractional-Order System , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[47]  Ying Chen,et al.  Identifying chaotic systems via a Wiener-type cascade model , 1997 .