FPGA based hardware and device-independent implementation of chaotic generators

Abstract In this paper we will describe the use of Matlab/Simulink without third party toolboxes as a single integrated environment to study and generate the HDL description of chaotic systems for rapid prototyping purposes. We will provide a review of different approaches to implement chaos generators in both analog and digital forms with a focus on digital one. We will present a rapid prototyping method of digital chaos generators on FPGAs that is of great use for a seamless study, simulation and implementation of those systems in one environment. This will ease the design phase of the chaotic systems and will provide more flexibility for their study. Multiple chaos generators, such as Lorenz, Rossler, Chua, Linz-Sprott, and Sprott types have been designed using this method to showcase its effectiveness. In addition, for a better investigation of the chaotic dynamics, this work makes use of an implementation scheme that permits the visualization of the 3D chaotic attractor on the oscilloscope. The main focus of this paper is to provide a common implementation framework of chaos generators to target various applications, mainly cryptographic one. Newcomers to the field will easily dive in and active researchers will be able to speak the same language and build upon one anothers works more efficiently by adopting the presented guidelines.

[1]  Carlos Sánchez-López,et al.  Integrated circuit generating 3- and 5-scroll attractors , 2012 .

[2]  Esteban Tlelo-Cuautle,et al.  Simulation of Piecewise-Linear One-Dimensional Chaotic Maps by Verilog-A , 2015 .

[3]  E. Tlelo-Cuautle,et al.  Generating a 50-scroll chaotic attractor at 66 MHz by using FPGAs , 2016 .

[4]  Manuel Delgado-Restituto,et al.  CMOS design of chaotic oscillators using state variables: a monolithic Chua's circuit , 1993 .

[5]  Esteban Tlelo-Cuautle,et al.  A survey on the integrated design of chaotic oscillators , 2013, Appl. Math. Comput..

[6]  César Cruz-Hernández,et al.  Chaotic Communication System Using Chua's oscillators Realized with Ccii+s , 2009, Int. J. Bifurc. Chaos.

[7]  Michal Fečkan,et al.  Bifurcation and Chaos in Discontinuous and Continuous Systems , 2011 .

[8]  Esteban Tlelo-Cuautle,et al.  Optimizing the maximum Lyapunov exponent and phase space portraits in multi-scroll chaotic oscillators , 2014 .

[9]  Pawel Dabal,et al.  A chaos-based pseudo-random bit generator implemented in FPGA device , 2011, 14th IEEE International Symposium on Design and Diagnostics of Electronic Circuits and Systems.

[10]  C. Varsakelis,et al.  On the susceptibility of numerical methods to computational chaos and superstability , 2016, Commun. Nonlinear Sci. Numer. Simul..

[11]  Chun-Hung Liou,et al.  High Frequency Implementation of Sprott's Chaotic Oscillators Using Current-Feedback Op Amps , 2007, 2007 International Symposium on Signals, Circuits and Systems.

[12]  J. Butcher Numerical methods for ordinary differential equations , 2003 .

[13]  Julien Clinton Sprott,et al.  Algebraically Simple Chaotic Flows , 2000 .

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

[15]  Xu Jianping,et al.  Multi-scroll hyperchaotic system based on colpitts model and its circuit implementation , 2010 .

[16]  Ana Dalia Pano-Azucena,et al.  Arduino-based chaotic secure communication system using multi-directional multi-scroll chaotic oscillators , 2016, Nonlinear Dynamics.

[17]  M. Glesner,et al.  Advantages of the Linz-Sprott weak nonlinearity on the FPGA implementation of chaotic systems: a comparative analysis , 2005, International Symposium on Signals, Circuits and Systems, 2005. ISSCS 2005..

[18]  Luis Gerardo de la Fraga,et al.  Engineering Applications of FPGAs , 2016 .

[19]  Zhineng Li,et al.  Research on new implementation method of chaotic model based on FPGA , 2007, 2007 7th International Conference on ASIC.

[20]  L. De Micco,et al.  Analysis of the digital implementation of a chaotic deterministic-stochastic attractor , 2012, 2012 Argentine School of Micro-Nanoelectronics, Technology and Applications (EAMTA).

[21]  Nguyen Xuan Quyen,et al.  A Chaos-Based Secure Direct-Sequence/Spread-Spectrum Communication System , 2013 .

[22]  Jesus M. Munoz-Pacheco,et al.  Frequency limitations in generating multi-scroll chaotic attractors using CFOAs , 2014 .

[23]  Abdelkrim Boukabou,et al.  Predictive control and synchronization of chaotic and hyperchaotic systems based on a T-S fuzzy model , 2014, Math. Comput. Simul..

[24]  E. Tlelo-Cuautle,et al.  FPGA realization of a chaotic communication system applied to image processing , 2015 .

[25]  José-Cruz Nuñez Pérez,et al.  FPGA realization of multi-scroll chaotic oscillators , 2015, Commun. Nonlinear Sci. Numer. Simul..

[26]  Esteban Tlelo-Cuautle,et al.  Design and Applications of Continuous-Time Chaos Generators , 2011 .

[27]  H. Castro,et al.  Rapid prototyping of chaotic generators using LabView-FPGA , 2012, 2012 IEEE 4th Colombian Workshop on Circuits and Systems (CWCAS).

[28]  Esteban Tlelo-Cuautle,et al.  VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators , 2016, PloS one.

[29]  Mohammed Affan Zidan,et al.  The effect of numerical techniques on differential equation based chaotic generators , 2011, ICM 2011 Proceeding.

[30]  Ángel Rodríguez-Vázquez,et al.  A switched‐capacitor skew‐tent map implementation for random number generation , 2017, Int. J. Circuit Theory Appl..

[31]  Lucas Illing Digital Communication using Chaos and Nonlinear Dynamics , 2006 .

[32]  A. Boukabou,et al.  Stabilizing Unstable Periodic Orbits of the Multi-Scroll Chua's Attractor , 2007 .

[33]  Ashraf A. Zaher,et al.  On the design of chaos-based secure communication systems , 2011 .

[34]  Song Zhang,et al.  Design Method for Duffing System Based on DSP Builder , 2012, 2012 International Conference on Systems and Informatics (ICSAI2012).

[35]  Nguyen Xuan Quyen On the performance of low-rate wireless correlation-delay-shift-keying system , 2017 .

[36]  P. Arena,et al.  Weak Chaos Control for Action-Oriented Perception: Real Time Implementation via FPGA , 2006, The First IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics, 2006. BioRob 2006..

[37]  A. Bouridane,et al.  Implementation and evaluation of a new unified hyperchaos-based PRNG , 2014, 2014 26th International Conference on Microelectronics (ICM).

[38]  Mostafa Y. Makkey Implementation of real time chaotic generator models (continuous and discrete) using digital hardware , 2003, 10th IEEE International Conference on Electronics, Circuits and Systems, 2003. ICECS 2003. Proceedings of the 2003.

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

[40]  Jan Danckaert,et al.  Simple Two-Transistor Single-Supply Resistor–Capacitor Chaotic Oscillator , 2015, IEEE Transactions on Circuits and Systems II: Express Briefs.

[41]  Ángel Rodríguez-Vázquez,et al.  Integrated chaos generators , 2002 .

[42]  Karthikeyan Rajagopal,et al.  FPGA implementation of novel fractional-order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization , 2017 .

[43]  A. Boukabou,et al.  Chaotic cryptography using external key , 2011, International Workshop on Systems, Signal Processing and their Applications, WOSSPA.

[44]  Julyan H. E. Cartwright,et al.  THE DYNAMICS OF RUNGE–KUTTA METHODS , 1992 .

[45]  Julien Clinton Sprott,et al.  Elementary chaotic flow , 1999 .

[46]  Mohammed Affan Zidan,et al.  Random number generation based on digital differential chaos , 2011, 2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS).

[47]  O. Rössler An equation for continuous chaos , 1976 .

[48]  I. Kovacic,et al.  The Duffing Equation: Nonlinear Oscillators and their Behaviour , 2011 .

[49]  Hilda A. Larrondo,et al.  FPGA implementation of a chaotic oscillator using RK4 method , 2011, 2011 VII Southern Conference on Programmable Logic (SPL).