journal article·2018-11-02Open access

A Chaotic System with Infinite Equilibria and Its S-Box Constructing Application

Xiong Wang, Akif Akgul, Unal Cavusoglu, Viet-Thanh Pham, Duy Vo Hoang, Xuan Quynh Nguyen

Applied Sciences· Volume 8· Issue 11

Abstract

Systems with many equilibrium points have attracted considerable interest recently. A chaotic system with a line equilibrium has been studied in this work. The system has infinite equilibria and exhibits coexisting chaotic attractors. The system with an infinite number of equilibria has been realized by an electronic circuit, which confirms the feasibility of the system. Based on such a system, we have developed a new S-Box generation algorithm. With the developed algorithm, two new S-Boxes are produced. Performance tests of S-Boxes are performed. The tests have shown that proposed S-Boxes have good performance results.
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Research context

OpenAlex topics: Chaos control and synchronization · Chaos-based Image/Signal Encryption · Mathematical Dynamics and Fractals

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China

Department of Electrical and Electronics Engineering, Faculty of Technology, Sakarya University of Applied Sciences, 54187 Serdivan, Turkey

Department of Computer Engineering, Faculty of Computer and Information Sciences, Sakarya University, 54187 Serdivan, Turkey

Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

National Council for Science and Technology Policy, Hanoi, Vietnam

Funding

National Natural Science Foundation of China · Shenzhen Overseas High Level Talent Peacock Project Fund · Sakarya University Scientific Research Projects Unit

References (62)

Show source-provided references
1. Deterministic nonperiodic flow10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 ↗
2. An equation for continuous chaos10.1016/0375-9601(76)90101-8 ↗
3. Strogatz, S. (1994). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Perseus Books.10.1063/1.4823332 ↗
4. Chen, G., and Yu, X. (2003). Chaos Control: Theory and Applications, Springer.10.1007/b79666 ↗
5. Sprott, J.C. (2010). Elegant Chaos Algebraically Simple Chaotic Flows, World Scientific.10.1142/9789812838827 ↗
6. Some simple chaotic flows10.1103/PhysRevE.50.R647 ↗
7. Yet another chaotic attractor10.1142/S0218127499001024 ↗
8. A new chaotic attractor coined10.1142/S0218127402004620 ↗
9. A unified Lorenz-type system and its canonical form10.1142/S0218127406016501 ↗
10. Chaotic attractors of the conjugate Lorenz-type system10.1142/S0218127407019792 ↗
11. Analysis and circuitry realization of a novel three-dimensional chaotic system10.1016/j.cnsns.2012.08.036 ↗
12. A new 3D chaotic system: Dynamical analysis, electronic circuit design, active control synchronization and chaotic masking communication application10.1016/j.ijleo.2016.01.069 ↗
13. A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors10.1016/j.physleta.2009.07.088 ↗
14. Constructing a chaotic system with any number of equilibria10.1007/s11071-012-0669-7 ↗
15. Simple chaotic flows with a line equilibrium10.1016/j.chaos.2013.08.018 ↗
16. New class of chaotic systems with circular equilibrium
17. Simple chaotic flow with circle and square equilibrium10.1142/S0218127416501376 ↗
18. Dynamical behavior, chaos control and synchronization of a memristor-based ADVP circuit10.1016/j.cnsns.2012.06.011 ↗
19. Discrete chaotic systems with one-line equilibria and their application to image encryption10.1142/S0218127417500468 ↗
20. A method for designing dynamical S-boxes based on discretized chaotic map10.1016/S0960-0779(04)00454-0 ↗
21. A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems10.1007/s11071-012-0621-x ↗
22. Chaos-based color image block encryption scheme using S-box10.1016/j.aeue.2014.02.002 ↗
23. Secure image encryption algorithm design using a novel chaos based S-Box10.1016/j.chaos.2016.12.018 ↗
24. A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm10.1007/s11071-012-0573-1 ↗
25. A novel method for designing S-boxes based on chaotic maps10.1016/j.chaos.2004.04.023 ↗
26. A method for designing strong S-Boxes based on chaotic Lorenz system10.1016/j.physleta.2010.07.019 ↗
27. A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system10.1007/s11071-016-3099-0 ↗
28. Designing chaotic S-boxes based on time-delay chaotic system10.1007/s11071-013-0987-4 ↗
29. Katz, J., and Lindell, Y. (2014). Introduction to Modern Cryptography, CRC Press. [2nd ed.].10.1201/b17668 ↗
30. Ferguson, N., Schneier, B., and Kohno, T. (2011). Cryptography Engineering: Design Principles and Practical Applications, Wiley. [1st ed.].
31. Stallings, W. (2016). Cryptography and Network Security: Principles and Practice, Pearson. [7th ed.].
32. Schneier, B. (2017). Applied Cryptography: Protocols, Algorithms, and Source Code in C, Wiley. [20th ed.].
33. Efficient and secure chaotic S-Box for wireless sensor network10.1002/sec.728 ↗
34. An efficient chaotic image encryption scheme10.1007/s00521-014-1800-0 ↗
35. A color image watermarking scheme based on affine transformation and S4 permutation10.1007/s00521-014-1691-0 ↗
36. A copyright protection using watermarking scheme based on nonlinear permutation and its quality metrics10.1007/s00521-014-1747-1 ↗
37. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (2007). Numerical Recipes: The Art of Scientific Computing, Cambridge University Press. [3rd ed.].
38. Determining Lyapunov exponents from a time series10.1016/0167-2789(85)90011-9 ↗
39. Extreme multistability in a chemical model system10.1103/PhysRevE.83.056206 ↗
40. Control of multistability10.1016/j.physrep.2014.02.007 ↗
41. Extreme multistability: Attractors manipulation and robustness10.1063/1.4921351 ↗
42. Multistability and bifurcation in a delayed neural network10.1016/j.neucom.2016.05.064 ↗
43. Analysis of a new three-dimensional system with multiple chaotic attractors10.1007/s11071-013-1069-3 ↗
44. Dynamical analysis of a simple autonomous jerk system with multiple attractors10.1007/s11071-015-2364-y ↗
45. Coexistence of multiple attractors and crisis route to chaos in a novel chaotic jerk circuit10.1142/S0218127416500814 ↗
46. Fortuna, L., Frasca, M., and Xibilia, M.G. (2009). Chua’s Circuit Implementation: Yesterday, Today and Tomorrow, World Scientific.10.1142/9789812839251 ↗
47. Chaos, coexisting attractors, and circuit design of the generalized Sprott C system with only two stable equilibria
48. Theory and practice of chaotic cryptography10.1016/j.physleta.2007.02.021 ↗
49. Chaos and cryptography: Block encryption ciphers based on chaotic maps10.1109/81.904880 ↗
50. A new chaos-based fast image encryption algorithm10.1016/j.asoc.2009.12.011 ↗
51. Image encryption using 2D Logistic-adjusted-Sine map10.1016/j.ins.2016.01.017 ↗
52. A novel lossless color image encryption scheme using 2D DWT and 6D hyperchaotic system10.1016/j.ins.2016.02.041 ↗
53. Secure chaotic system with application to chaotic ciphers10.1016/j.ins.2012.09.037 ↗
54. Improvement of the security of zigbee by a new chaotic algorithm10.1109/JSYST.2013.2246011 ↗
55. A novel chaos-based encryption algorithm over TCP data packet for secure communication10.1002/sec.1414 ↗
56. A specification for Rijndael, the AES algorithm
57. An efficient technique for the construction of substitution box with chaotic partial differential equation10.1007/s11071-013-0904-x ↗
58. The structured design of cryptographically good S-boxes10.1007/BF00203967 ↗
59. Webster, A., and Tavares, S.E. (1985). On the design of S-boxes. Conference on the Theory and Application of Cryptographic Techniques, Springer.
60. Differential cryptanalysis of DES-like cryptosystems
61. Matsui, M. (1993). Linear cryptanalysis method for DES cipher. Workshop on the Theory and Application of of Cryptographic Techniques, Springer.10.1007/3-540-48285-7_33 ↗
62. Brickell, E.F., Denning, D.E., Kent, S.T., Maher, D.P., and Tuchman, W. (1995). SKIPJACK review: Interim report. Building in Big Brother, Springer.