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Image Encryption Scheme Based on Non-autonomous Chaotic Systems

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Computation, Cryptography, and Network Security

Abstract

In this chapter, the great sensitivity of nonlinear systems, and especially of chaotic systems, on the initial conditions and on the variation of their parameters, was used to design a novel image encryption scheme. Until now, a great number of chaotic autonomous continuous systems or discrete dynamical systems, have been used in various image encryption processes, as a source of random numbers. However, in this work, a Chaotic Random Bit Generator (CRBG), which is based on a non-autonomous dynamical system, is used. For ridding from the system the influence of the external source and increasing the security of the proposed generator, the Poincar\(\acute{e}\) section for sampling the signal has been used. As a dynamical system, the very well-known Duffing–van der Pol system has been chosen, presenting very good statistical results. The aforementioned CRBG is the “heart” of the proposed image encryption scheme. Finally, the security analysis of the proposed encryption scheme, based on histogram analysis, correlation of two adjacent pixels, differential analysis and information entropy, demonstrate the robustness of the proposed chaotic encryption scheme against all kinds of statistical, cryptanalytic, and brute-force attacks.

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References

  1. Data Encryption Standard: NIST FIPS PUB 46-2. U.S. Department of Commerce (1993)

    Google Scholar 

  2. Lai, X., Massey, J.: A proposal for a new block encryption standard. In: Proceedings of Advances in Cryptology EUROCRYPT ’90, pp. 389–404. Springer, New York (1991)

    Google Scholar 

  3. Advanced Encryption Standard: NIST FIPS PUB 197. U.S. Department of Commerce (2001)

    Google Scholar 

  4. Chrysochos, E., Fotopoulos, V., Xenos, M., Skodras, A.N.: Hybrid watermarking based on chaos and histogram modification, signal, image and video processing. Signal Image Video Process. (2012). doi:10.1007/s11760-012-0307-3

    Google Scholar 

  5. Fotopoulos, V., Stavrinou, M.L., Skodras, A.N.: Medical image authentication and self-correction through an adaptive reversible watermarking technique. In: Proceedings of 8th IEEE International Conference on Bioinformatics and Bioengineering, vol. 1-2, pp. 910–914 (2008)

    Google Scholar 

  6. Rawat, S., Raman, B.: A blind watermarking algorithm based on fractional Fourier transform and visual cryptography. Signal Process. 92, 1480–1491 (2012)

    Article  Google Scholar 

  7. Yeung, M.M., Pankanti, S.: Verification watermarks on fingerprint recognition and retrieval. J. Electron. Imaging 9, 468–476 (2000)

    Article  Google Scholar 

  8. Chen, T.-H., Wu, C.-S.: Efficient multi-secret image sharing based on boolean operations. Signal Process. 91, 90–97 (2011)

    Article  MATH  Google Scholar 

  9. Liao, X., Lai, S., Zhou, Q.: A novel image encryption algorithm based on self-adaptive wave transmission. Signal Process. 90, 2714–2722 (2010)

    Article  MATH  Google Scholar 

  10. Wang, X., Teng, L., Qin, X.: A Novel colour image encryption algorithm based on chaos. Signal Process. 92, 1101–1108 (2012)

    Article  Google Scholar 

  11. Zhang, L., Liao, X., Wang X.: An image encryption approach based on chaotic maps. Chaos Solitons Fractals 24, 759–765 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Grebogi, C., Yorke, J.: The Impact of Chaos on Science and Society. United Nations University Press, Tokyo (1997)

    Google Scholar 

  13. Li, Z., Xu, D.: A secure communication scheme using projective chaos synchronization. Chaos Solitons Fractals 22, 477–481 (2004)

    Article  MATH  Google Scholar 

  14. Chen, J.Y., Wong, K.W., Cheng, L.M., Shuai, J.W.: A secure communication scheme based on the phase synchronization of chaotic systems. Chaos 13, 508–514 (2003)

    Article  Google Scholar 

  15. Baptista, M.S.: Cryptography with chaos. Phys. Lett. A 240, 50–54 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Habutsu, T., Nishio, Y., Sasase, I., Mori, S.: A secret key cryptosystem by iterating a chaotic map. In: Proceedings of Advances in Cryptology-CRYPTO ’91, pp. 127–140. Springer, New York (1991)

    Google Scholar 

  17. Yen, J.C., Guo, J.I.: A new key-based design for image encryption and decryption. In: Proceedings of IEEE Conference on Circuits and Systems, vol. 4, pp. 49–52 (2000)

    Google Scholar 

  18. Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos based cryptosystems. Int. J. Bifurcation Chaos 16, 2129–2151 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Poincare, J.H.: Sur le probleme des trois corps et les equations de la dynamique. Divergence des series de M. Lindstedt. Acta Math. 13, 1–270 (1890)

    MATH  Google Scholar 

  20. Lorenz, E.N.: Deterministic non-periodic flow. J. Atmos. Sci. 20, 130–141 (1963)

    Article  Google Scholar 

  21. Mandelbrot, B.: The Fractal Geometry of Nature. W.H. Freeman Company, New York (1977)

    Google Scholar 

  22. Laplace, P.S.: Trait\(\acute{e}\) du M\(\acute{e}\) canique C\(\acute{e}\) leste. Oeuvres Compl\(\acute{e}\) tes de Laplace. Gauthier-Villars, Paris (1825)

    Google Scholar 

  23. May, R.M., McLean, A.R.: Theoretical Ecology: Principles and Applications. Blackwell, Oxford (2007)

    Google Scholar 

  24. Kyrtsou, C., Vorlow, C.: Complex dynamics in macroeconomics: a novel approach. In: Diebolt, C., Kyrtsou, C. (eds.) New Trends in Macroeconomics, pp. 223–245. Springer, Berlin (2005). ISBN-13: 978-3-540-21448-9

    Google Scholar 

  25. Van der Pol, B., Van der Mark, J.: Frequency demultiplication. Nature 120, 363–364 (1927)

    Article  Google Scholar 

  26. Casperson, L.W.: Gas laser instabilities and their interpretation. In: Proceedings of the NATO Advanced Study Institute, pp. 83–98. Springer, Berlin (1988)

    Google Scholar 

  27. Field, R.J., Gy\(\ddot{o}\) rgyi, L.: Chaos in Chemistry and Biochemistry. World Scientific Publishing, Singapore (1993)

    Google Scholar 

  28. Baker, G.L.: Chaotic Dynamics: An Introduction. Cambridge University Press, Cambridge (1996)

    Book  MATH  Google Scholar 

  29. Moon, F.C.: Chaotic vibrations: An Introduction for Applied Scientists and Engineers. Wiley, New York (1987)

    MATH  Google Scholar 

  30. Hasselblatt, B., Katok, A.: A First Course in Dynamics: With a Panorama of Recent Developments. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  31. Ueda, Y., Akamatsu, N.: Chaotically transitional phenomena in the forced negative-resistance oscillator. IEEE Trans. Circuits Syst. CAS-28, 217–224 (1981)

    Article  MathSciNet  Google Scholar 

  32. Oishi, S., Inoue, H.: Pseudo-random number generators and chaos. Trans. Inst. Electr. Commun. Eng. Japan E 65, 534–541 (1982)

    Google Scholar 

  33. Bernstein, G.M., Lieberman, M.A.: Secure random number generation using chaotic circuits. IEEE Trans. Circuits Syst. 37(9), 1157–1164 (1990)

    Article  MathSciNet  Google Scholar 

  34. Kohda, T., Tsuneda, A. Statistics of chaotic binary sequences. IEEE Trans. Inf. Theory 43(1), 104–112 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  35. Tsuneda, A., Eguchi, K., Inoue. T.: Design of chaotic binary sequences with good statistical properties based on piecewise linear into maps. In: Proceedings of 7th International Conference on Microelectronics for Neural, Fuzzy and Bio-Inspired Systems, pp. 261–266 (1999)

    Google Scholar 

  36. Kolesov, V.V., Belyaev, R.V., Voronov, G.M.: Digital random-number generator based on the chaotic signal algorithm. J. Commun. Technol. Electron. 46, 1258–1263 (2001)

    Google Scholar 

  37. Stojanovski, T., Kocarev, L.: Chaos-based random number generators - part I: analysis. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48(3), 281–288 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  38. Stojanovski, T., Pihl, J., Kocarev, L.: Chaos-based random number generators - part II: practical realizations. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48(3), 382–385 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  39. Bernardini, R., Cortelazzo, G.: Tools for designing chaotic systems for secure random number generation. IEEE Trans. Circuits Syst. 48(5), 552–564 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  40. Gerosa, A., Bernardini, R., Pietri, S.: A fully integrated chaotic system for the generation of truly random numbers. IEEE Trans. Circuits Syst. I 49(7), 993–1000 (2001)

    Article  Google Scholar 

  41. Li, S., Mou, X., Cai, Y.: Pseudo-random bit generator based on coupled chaotic systems and its application in stream-ciphers cryptography. In: Progress in Cryptology - INDOCRYPT 2001. Lecture Notes in Computer Science, vol. 2247, pp. 316–329 (2001)

    Article  MathSciNet  Google Scholar 

  42. Li, K., Soh, Y.C., Li, Z.G. Chaotic cryptosystem with high sensitivity to parameter mismatch. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 50, 579–583 (2003)

    Article  MathSciNet  Google Scholar 

  43. Gentle, J.E.: Random Number Generation and Monte Carlo Method. Springer, New York (2003)

    Google Scholar 

  44. Kocarev, L.: Chaos-based cryptography: a brief overview. IEEE Circuits Syst. Mag. 1, 6–21 (2001)

    Article  Google Scholar 

  45. Fu, S.M., Chen, Z.Y., Zhou, Y.A.: Chaos based random number generators. Comput. Res. Dev. 41, 749–754 (2004)

    Google Scholar 

  46. Huaping, L., Wang, S., Gang, H.: Pseudo-random number generator based on coupled map lattices. Int. J. Mod. Phys. B 18, 2409–2414 (2004)

    Article  Google Scholar 

  47. Yalcin, M.E., Suykens, J.A.K., Vandewalle, J.: True random bit generation from a double-scroll attractor. IEEE Trans. Circuits Syst. I 51(7), 1395–1404 (2004)

    Article  MathSciNet  Google Scholar 

  48. Wei, J., Liao, X., Wong, K., Xiang, T.: A new chaotic cryptosystem. Chaos Solitons Fractals 30, 1143–1152 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  49. Volos, C.K., Kyprianidis, I.M., Stouboulos, I.N.: Experimental demonstration of a chaotic cryptographic scheme. WSEAS Trans. Circuits Syst. 5, 1654–1661 (2006)

    Google Scholar 

  50. Volos, C.K., Kyprianidis, I.M., Stouboulos, I.N.: Fingerprint images encryption process based on a chaotic true random bits generator. Int. J. Multimedia Intell. Secur. 1, 320–335 (2010)

    Article  Google Scholar 

  51. Volos, C.K., Kyprianidis, I.M., Stouboulos, I.N.: Image encryption process based on chaotic synchronization phenomena. Signal Process. 93, 1328–1340 (2013)

    Article  Google Scholar 

  52. Volos, C.K.: Chaotic random bit generator realized with a microcontroller. J. Comput. Model. 3(4), 115–136 (2013)

    Google Scholar 

  53. Kennedy, M.P., Rovatti, R., Setti, G.: Chaotic Electronics in Telecommunications. CRC Press, West Palm Beach, FL (2000)

    Google Scholar 

  54. Pareschi, F., Rovatti, R., Setti, G.: Simple and effective post-processing stage for random stream generated by a chaos-based RNG. In: Proceedings of 2006 International Symposium in Nonlinear Theory and its Applications, pp. 383–386 (2006)

    Google Scholar 

  55. Tang, K.W., Tang, W.: A low cost chaos-based random number generator realized in 8-bit precision environment. In: Proceedings of 2006 International Symposium in Nonlinear Theory and its Applications, pp. 395–398 (2006)

    Google Scholar 

  56. Von Neumann, J.: Various techniques used in connection with random digits. In: Forsythe, G.E. (eds.) Applied Mathematics Series, National Bureau of Standards, vol. 12, pp. 36–38 (1951)

    Google Scholar 

  57. NIST: Security Requirements for Cryptographic Modules. FIPS PUB 140-2. http://csrc.nist.gov/publications/fips/fips140-2/fips1402.pdf (2001)

  58. Marsaglia, G.: DIEHARD Statistical Tests. http://stst.fsu.edu/pub/diehard (1995)

  59. Gustafson, H., Dawson, H.E., Nielsen, L., Caelli, W.: A computer package for measuring the strength of encryption algorithms. J. Comput. Secur. 13, 687–697 (1994).

    Article  Google Scholar 

  60. Knuth, D.: The Art of Computer Programming: Semiemperical Algorithms. Addison Wesley, Reading (1998)

    Google Scholar 

  61. Fraser, A.M.: Information and entropy in strange attractors. IEEE Trans. Inf. Theory 35, 245–262 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  62. Volos, C.K., Kyprianidis, I.M., Strouboulos, I.N.: Fingerprint images encryption process based on a chaotic true random bits generator. Int. J. Multimedia Intell. Secur. 1, 320–335 (2010)

    Article  Google Scholar 

  63. Volos, C.K., Kyprianidis, I.M., Strouboulos, I.N.: Image encryption scheme based on coupled chaotic systems. J. Appl. Math. Bioinforma. 3, 123–149 (2013)

    Google Scholar 

  64. Chen, G.R., Mao, Y., Chui, C.: A symmetric image encryption scheme based on 3D chaotic cat map. Chaos Solitons Fractals 21, 749–761 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  65. Li, W.: On the relationship between complexity and entropy for Markov chains and regular languages. Complex Syst. 5, 381–399 (1991)

    MATH  Google Scholar 

  66. Chen, G.R., Mao, Y., Chui, C.: A symmetric image encryption scheme based on chaotic maps with finite precision representation. Chaos Solitons Fractals 32, 1518–1529 (2007)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Christos K. Volos, Ioannis M. Kyprianidis & Ioannis Stouboulos

  2. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam

    Viet-Thanh Pham

Authors
  1. Christos K. Volos
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  2. Ioannis M. Kyprianidis
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  3. Ioannis Stouboulos
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  4. Viet-Thanh Pham
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Corresponding author

Correspondence to Christos K. Volos .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Engineering, Hellenic Military Academy, Vari Attikis, Greece

    Nicholas J. Daras

  2. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Michael Th. Rassias

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Volos, C.K., Kyprianidis, I.M., Stouboulos, I., Pham, VT. (2015). Image Encryption Scheme Based on Non-autonomous Chaotic Systems. In: Daras, N., Rassias, M. (eds) Computation, Cryptography, and Network Security. Springer, Cham. https://doi.org/10.1007/978-3-319-18275-9_25

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