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Digital Chaos Systems


Chaos is a nonlinear deterministic system that expresses random behavior. Chaos generators find applications in chaotic based digital communication systems, cryptography, and random number generation. In general chaos systems are implemented in analog scheme, which are sensitive to the operating conditions, process variations, and temperature. In addition, the initial conditions cannot be set precisely in analog generators. Analog circuit implementation typically requires a large on-chip area for the state capacitor realization. We Introduced a general technique for implementing differential equation based Chaos in a purely digitla fashion.. Various properties of the digital realization were studied, such as: effect of the numerical solution, the bus width, and the feedback delay. This Introduced technique was used for digitally generating random numbers and image encryption. The introduced systems were written in Verilog VHDL and realized on Xilinx Virtex 4 FPGA.

    
  
Sample oscilloscope output for an FPGA implementation of the generator

A parametric Verilog  implementation for a piecewise-based chaotic system. The digital implementation is very light are requires very small on-ship area, and very useful for digital PRNG and encryption systems. Download
(Feel free to use/modify these codes as you see fit. Any publications (codes, papers, technical reports,..) in which our codes (in their original or a modified format) have been used should  should cite the following references.)

Copyright (c) 2011, M. Affan Zidan, A. G. Radwan and K. N. Salama
King Abdullah University of Science and Technology
All rights reserved.


Refrences:
  1. A. S. Mansingka, M Barakat, M Zidan, A Radawan and K. N. Salama, Fibonacci-based Hardware Post-Processing for Non-Autonomous Signum Hyperchaotic System," International Conference on IT Convergence and Security (ICITCS), pp 1-4, 2013
  2. A. G. Radwan, A. S. Mansingka, M. Affan Zidan, and K. N. Salama, “On the Short-Term Predictability of Fully Digital Chaotic Oscillators forPseudo-Random Number Generation,” IEEE International Conference on Electronics, Circuits, and Systems (ICECS), Abu Dhabi, UAE, December,2013
  3. A. S. Mansingka, A. G. Radwan and K. N. SalamaSecure Ds-CDMA Spreading Codes Using Fully Digital Multidimensional Multiscroll Chaos,56th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), August 2013
  4.  M. barakat, A. Mansingka, A.G. Radwan and K. N. Salama,, Hardware Stream Cipher with Controllable Chaos Generator for Color Image Encryption, IET image processingVolume 8, Issue 1, p. 33 – 43, 2014. 
  5. A. S. Mansingka, M. L. Barakat, M. Affan Zidan, A. G. Radwan, K. N. Salama, Fully Digital Jerk-Based Chaotic Oscillators for High Throughput Pseudo Random Number Generators up to 8.77 Gbits/s Microelectronics journal, accepted June 2013
  6. M. barakat, A. Mansingka, A.G. Radwan and K. N. Salama," Generalized Hardware Post Processing Technique for Chaos-Based Pseudorandom Number Generators," ETRI, vol.35, no.3, pp.448-458, May 2013 
  7. M.A. Zidan, A.G. Radwan and K.N. Salama, "Controllable V-Shape Multi-Scroll Butterfly Attractor:System and Circuit Implementation," International Journal of Bifurcation and Chaos, 22, 1250143 (2012)
  8. A. S. Mansingka, A. G. Radwan and K. N. Salama, Fully Digital 1-D, 2-D and 3-D Multiscroll Chaos as Hardware Pseudo Random Number Generators55th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), August 2012
  9. A. S. Mansingka, A. G. Radwan and K. N. Salama, Fully Digital 1-D, 2-D and 3-D Multiscroll Chaos as Hardware Pseudo Random Number Generators, 55th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), August 2012 (submitted)
  10. Mohamd Barakat, Ahmed Radwan and Khaled Salama "Hardware Realization of Chaos Based Block Cipher for Image Encryption", IEEE international Conference on Microelectronics(ICM), 2011
  11. M. A. Zidan, A. G. Radwan and K. N. Salama, "The Effect of Numerical Techniques on Differential Equation Based Chaotic Generators", IEEE international Conference on Microelectronics (ICM), 2011
  12. A. S. Mansingka, A. G. Radwan and K. N. Salama,  "Design, Implementation and Analysis of Fully Digital 1-D Controllable Multiscroll Chaos" IEEE international Conference on Microelectronics (ICM), 2011
  13. M. Affan Zidan, A. G. Radwan and K. N. Salama, Random Number Generation Based on Digital Differential Chaos, 54th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), August 2011 A. S. Mansingka, A. G. Radwan, M. Affan Zidan and K. N. Salama, Analysis of Bus Width and Delay on a Fully Digital Signum Nonlinearity Chaotic Oscillator, 54th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), August  2011 
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