Utilization of the Theories of Nonlinear Dynamics and Chaos in the Design of a New Cryptosystem

Main Challenge/Objective

  1. Analysis of the properties of various discrete chaotic systems to select/design an initial set of discrete systems that is appropriate for the design of new encryption algorithms. New generalized families of the discrete tent map and the discrete sine map were designed.
  2. Analysis of the properties of various continuous chaotic systems to select/design another initial set of continuous systems that is appropriate for the design of new encryption algorithms. New 1D and 2D multi-scroll chaotic attractors were designed.
  3. Design encryption algorithms which effectively utilize the chosen/designed chaotic systems.
  4. Implement the designed encryption algorithms.
  5. Evaluate the proposed algorithms by performing the security analysis tests, especially the statistical and sensitivity tests.
  6. Based on the evaluations performed in task 5, finalize the design/selection of the chaotic systems and adapt the details of the designed algorithms. The developed software package, CanCrypt, utilizes a representative set of the newly designed encryption systems.

Outcomes

Final product: Standalone software package which includes six different designs based on generalized discrete chaotic  maps, non-chaotic generators, fractals, Lorenz continuous chaotic system as well as different permutation techniques that utilize the chess horse move, the logistic map and the Arnold map. This software package has a simple Graphical User Interface (GUI) and gives different encryption choices for non-specialized users.

New theories: The new theoretical contributions include the design of generalized discrete chaotic maps, utilization of fractals in encryption, chess-based permutation technique, and simple designs (delay + multiplexer) for encryption systems.

  1. S.K. Abd-El-Hafiz, A.G. Radwan, S.H. AbdElHaleem and M.L. Barakat, “A fractal-based image encryption system,” IET Image Processing, vol. 8, no. 12, pp. 742-752, 2014.
  2. S.K. Abd-El-Hafiz, A.G. Radwan and S.H. AbdElHaleem, “Encryption applications of a generalized chaotic map,” Applied Mathematics & Information Sciences,
  3. S.H. AbdElHaleem, A.G. Radwan and S.K. Abd-El-Hafiz, “Utilizing LFSR and Feistel networks in image encryption,” Proceeding of the IEEE International Conference on Electronics, Circuits and Systems (ICECS 2013), Abu Dhabi, UAE, pp. 601-604, 2013.
  4. A.G. Radwan and S.K. Abd-El-Hafiz, “The generalized tent map in image encryption,” Proceeding of the IEEE International Conference on Electronics, Circuits and Systems (ICECS 2013), Abu Dhabi, UAE, pp. 653-656, December 2013.
  5. S.H. AbdElHaleem, A.G. Radwan and S.K. Abd-El-Hafiz, “Design of pseudo random keystream generator using fractals,” Proceeding of the IEEE International Conference on Electronics, Circuits and Systems (ICECS 2013), Abu Dhabi, UAE, pp. 877-880, 2013.
  6. S.H. AbdElHaleem, A.G. Radwan and S.K. Abd-El-Hafiz, “A chess-based chaotic block cipher,” Proceedings of the 12th IEEE International New Circuits and Systems Conference (NEWCAS 2014), Trois-Rivières, Canada, June 2014.
  7. A.G. Radwan, S.K. Abd-El-Hafiz and S.H. AbdElHaleem, “An image encryption system based on generalized discrete maps,” Proceeding of the IEEE International Conference on Electronics, Circuits and Systems (ICECS 2014), Marseille, France, pp. 283-286, 2014.
  8. A.G. Radwan and S.K. Abd-El-Hafiz, “The effect of multi-scrolls distribution on image encryption,” Proceeding of the IEEE International Conference on Electronics, Circuits and Systems (ICECS 2014), Marseille, France, pp. 435-438, December 2014.

Principal Investigator

Prof. Salwa Kamal Abdel Hafiz

Team Members

  • Prof. Salwa Kamal Abdel Hafiz (PI)
  • Prof. Ahmed Radwan (Co-PI)

Staff Number

2 Members

Start Date

2012

End Date

2015

Status

  • Completed

Categories

  • Innovation, Entrepreneurship and Competitiveness

AHMED RADWAN

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