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Secure Communication Scheme Based on Projective Synchronization of Hyperchaotic Systems

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Cybersecurity

Part of the book series: Studies in Big Data ((SBD,volume 102))

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Abstract

This chapter develops a secure communication scheme based on the synchronization of two hyperchaotic systems, including key statistical, dynamical, and security analyses. First, the scheme is based on the projective synchronization between two hyperchaotic systems applied to image encryption. The encryption process comprises the generation and discretization of chaotic sequences, the transformation of the sequence elements into the image domain, and the modulo operation as encryption transformation. Second, the reliability and robustness of the proposed scheme are evaluated through the primary dynamical, statistical, and security analyses such as spectral and dynamical complexity, sensitivity, unpredictability, chaotic range, elements distribution, and randomness characteristics, key space definition, and resistance to distortion analysis, return map analysis, differential attack, decryption, and brute force attacks. Finally, the experimental results give evidence of the feasibility and robustness of the chaotic scheme. They show that using high-dimensional chaotic systems such as hyperchaotic systems combined with projective synchronization improves the confusion and diffusion properties, increases the key space, and limits the effectiveness of decryption, distortion, differential, generalized and adaptive synchronization, return map and brute force attacks.

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References

  1. Zhang, X., Wang, L., Wang, Y., Niu, Y., Li, Y.: An image encryption algorithm based on hyperchaotic system and variable-step josephus problem. Int. J. Opt. 2020 (2020)

    Google Scholar 

  2. Xu, Q., Sun, K., Cao, C., Zhu, C.: A fast image encryption algorithm based on compressive sensing and hyperchaotic map. Opt. Lasers Eng. 121, 203–214 (2019)

    Article  Google Scholar 

  3. Li, Z., Peng, C., Li, L., Zhu, X.: A novel plaintext-related image encryption scheme using hyper-chaotic system. Nonlinear Dyn. 94(2), 1319–1333 (2018)

    Article  Google Scholar 

  4. Ahmad, M., Doja, M.N., Beg, M.M.S.: Security analysis and enhancements of an image cryptosystem based on hyperchaotic system. J. King Saud Univ.-Comput. Inf. Sci. 33(1), 77–85 (2021)

    Google Scholar 

  5. Tsafack, N., Sankar, S., Abd-El-Atty, B., Kengne, J. Jithin,K., Belazi, A., Mehmood, I., Bashir, A.K., Song, O.-Y., Abd El-Latif, A.A.: A new chaotic map with dynamic analysis and encryption application in internet of health things. IEEE Access 8, 137731–137744 (2020)

    Google Scholar 

  6. Zhao, C.-F., Ren, H.-P.: Image encryption based on hyper-chaotic multi-attractors. Nonlinear Dyn. 100(1), 679–698 (2020)

    Article  Google Scholar 

  7. Chen, J., Wong, K., Cheng, L., Shuai, J.: A secure communication scheme based on the phase synchronization of chaotic systems. Chaos: Interdiscip. J. Nonlinear Sci. 13(2), 508–514 (2003)

    Google Scholar 

  8. Kocarev, L., Halle, K., Eckert, K., Chua, L.O., Parlitz, U.: Experimental demonstration of secure communications via chaotic synchronization. Int. J. Bifurc. Chaos 2(03), 709–713 (1992)

    Article  Google Scholar 

  9. Memon, Q.A.: Synchronized choas for network security. Comput. Commun. 26(6), 498–505 (2003)

    Article  Google Scholar 

  10. Wu, Z., Zhang, X., Zhong, X.: Generalized chaos synchronization circuit simulation and asymmetric image encryption. IEEE Access 7, 37989–38008 (2019)

    Article  Google Scholar 

  11. Parlitz, U., Chua, L.O., Kocarev, L., Halle, K., Shang, A.: Transmission of digital signals by chaotic synchronization. Int. J. Bifurc. Chaos 2(04), 973–977 (1992)

    Article  Google Scholar 

  12. Pellicer-Lostao, C., Lopez-Ruiz, R.: Notions of chaotic cryptography: sketch of a chaos based cryptosystem (2012). arXiv:1203.4134

  13. Alvarez, G., Li, S., Montoya, F., Pastor, G., Romera, M.: Breaking projective chaos synchronization secure communication using filtering and generalized synchronization. Chaos Solitons Fractals 24(3), 775–783 (2005)

    Article  Google Scholar 

  14. Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc. Chaos 16(08), 2129–2151 (2006)

    Article  MathSciNet  Google Scholar 

  15. Alvarez, G., Amigó, J.M., Arroyo, D., Li, S.: Lessons learnt from the cryptanalysis of chaos-based ciphers. In: Chaos-Based Cryptography, pp. 257–295. Springer (2011)

    Google Scholar 

  16. Bendoukha, S., Abdelmalek, S., Ouannas, A.: Secure communication systems based on the synchronization of chaotic systems. In: Mathematics Applied to Engineering, Modelling, and Social Issues, pp. 281–311. Springer (2019)

    Google Scholar 

  17. Özkaynak, F.: Brief review on application of nonlinear dynamics in image encryption. Nonlinear Dyn. 92(2), 305–313 (2018)

    Article  Google Scholar 

  18. Dachselt, F., Schwarz, W.: Chaos and cryptography. IEEE Trans. Circ. Syst. I: Fundam. Theory Appl. 48(12), 1498–1509 (2001)

    Google Scholar 

  19. Li, S., Alvarez, G., Li, Z., Halang, W.A.: Analog chaos-based secure communications and cryptanalysis: a brief survey (2007). arXiv:0710.5455

  20. Wu, Y., Noonan, J.P., Agaian, S., et al.: NPCR and UACI randomness tests for image encryption. Cyber J.: Multidiscip. J. Sci. Technol. J. Sel. Areas Telecommun. (JSAT) 1(2), 31–38 (2011)

    Google Scholar 

  21. Alvarez, G., Li, S.: Breaking network security based on synchronized chaos. Comput. Commun. 27(16), 1679–1681 (2004)

    Article  Google Scholar 

  22. Sambas, A., Vaidyanathan, S., Tlelo-Cuautle, E., Abd-El-Atty, B., Abd El-Latif, A.A., Guillén-Fernández, O., Hidayat, Y., Gundara, G., et al.: A 3-D multi-stable system with a peanut-shaped equilibrium curve: circuit design, FPGA realization, and an application to image encryption. IEEE Access 8, 137116–137132 (2020)

    Article  Google Scholar 

  23. Vaidyanathan, S., Sambas, A., Abd-El-Atty, B., Abd El-Latif, A.A., Tlelo-Cuautle, E., Guillén-Fernández, O., Mamat, M., Mohamed, M.A., Alçin, M., Tuna, M., et al.: A 5-D multi-stable hyperchaotic two-disk dynamo system with no equilibrium point: circuit design, fpga realization and applications to trngs and image encryption. IEEE Access (2021)

    Google Scholar 

  24. Mostafaee, J., Mobayen, S., Vaseghi, B., Vahedi, M., Fekih, A.: Complex dynamical behaviors of a novel exponential hyper-chaotic system and its application in fast synchronization and color image encryption. Sci. Prog. 104(1), 00368504211003388 (2021)

    Article  Google Scholar 

  25. Javan, A.A.K., Jafari, M., Shoeibi, A., Zare, A., Khodatars, M., Ghassemi, N., Alizadehsani, R., Gorriz, J.M.: Medical images encryption based on adaptive-robust multi-mode synchronization of chen hyper-chaotic systems. Sensors 21(11), 3925 (2021)

    Article  Google Scholar 

  26. Muthukumar, P., Balasubramaniam, P., Ratnavelu, K.: A novel cascade encryption algorithm for digital images based on anti-synchronized fractional order dynamical systems. Multimed. Tools Appl. 76(22), 23517–23538 (2017)

    Article  Google Scholar 

  27. Di, X., Li, J., Qi, H., Cong, L., Yang, H.: A semi-symmetric image encryption scheme based on the function projective synchronization of two hyperchaotic systems. PloS one 12(9), e0184586 (2017)

    Google Scholar 

  28. Zhang, F., Liu, J., Wang, Z., Jiang, C.: N-systems function projective combination synchronization–A review of real and complex continuous time chaos synchronization. IEEE Access 7, 179320–179338 (2019)

    Article  Google Scholar 

  29. Alvarez, G., Montoya, F., Romera, M., Pastor, G.: Breaking two secure communication systems based on chaotic masking. IEEE Trans. Circ. Syst. II: Express Briefs 51(10), 505–506 (2004)

    Google Scholar 

  30. Yang, T., Yang, L.-B., Yang, C.-M.: Breaking chaotic secure communication using a spectrogram. Phys. Lett. A 247(1–2), 105–111 (1998)

    Article  Google Scholar 

  31. Singh, S., Ahmad, M., Malik, D.: Breaking an image encryption scheme based on chaotic synchronization phenomenon. In: 2016 Ninth International Conference on Contemporary Computing (IC3), pp. 1–4. IEEE (2016)

    Google Scholar 

  32. Ahmad, M., Aijaz, A., Ansari, S., Siddiqui, M.M., Masood, S.: Cryptanalysis of image cryptosystem using synchronized 4D lorenz stenflo hyperchaotic systems. In: Information and Decision Sciences, pp. 367–376. Springer (2018)

    Google Scholar 

  33. Li, C., Lo, K.-T.: Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process. 91(4), 949–954 (2011)

    Article  Google Scholar 

  34. Li, C.: Cracking a hierarchical chaotic image encryption algorithm based on permutation. Signal Process. 118, 203–210 (2016)

    Article  Google Scholar 

  35. Li, C., Lin, D., Lü, J.: Cryptanalyzing an image-scrambling encryption algorithm of pixel bits. IEEE MultiMed. 24(3), 64–71 (2017)

    Article  Google Scholar 

  36. Wen, W., Zhang, Y., Su, M., Zhang, R., Chen, J.-X., Li, M.: Differential attack on a hyper-chaos-based image cryptosystem with a classic bi-modular architecture. Nonlinear Dyn. 87(1), 383–390 (2017)

    Article  Google Scholar 

  37. Fan, H., Li, M., Liu, D., Zhang, E.: Cryptanalysis of a colour image encryption using chaotic APFM nonlinear adaptive filter. Signal Process. 143, 28–41 (2018)

    Article  Google Scholar 

  38. Alanezi, A., Abd-El-Atty, B., Kolivand, H., El-Latif, A., Ahmed, A., El-Rahiem, A., Sankar, S., Khalifa, H.S., et al.: Securing digital images through simple permutation-substitution mechanism in cloud-based smart city environment. Secur. Commun. Netw. 2021 (2021)

    Google Scholar 

  39. Li, T., Zhang, D.: Hyperchaotic image encryption based on multiple bit permutation and diffusion. Entropy 23(5), 510 (2021)

    Article  MathSciNet  Google Scholar 

  40. Naim, M., Pacha, A.A., Serief, C.: A novel satellite image encryption algorithm based on hyperchaotic systems and josephus problem. Adv. Space Res. 67(7), 2077–2103 (2021)

    Article  Google Scholar 

  41. Yang, Y., Wang, L., Duan, S., Luo, L.: Dynamical analysis and image encryption application of a novel memristive hyperchaotic system. Opt. Laser Technol. 133, 106553 (2021)

    Google Scholar 

  42. Bouridah, M.S., Bouden, T., Yalçin, M.E.: Delayed outputs fractional-order hyperchaotic systems synchronization for images encryption. Multimed. Tools Appl. 80(10), 14723–14752 (2021)

    Article  Google Scholar 

  43. Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography (1996)

    Google Scholar 

  44. Aumasson, J.-P.: Serious Cryptography: a Practical Introduction to Modern Encryption. No Starch Press (2017)

    Google Scholar 

  45. electronics, M.: One time pad encryption the unbreakable encryption method (2016)

    Google Scholar 

  46. Li, C., Li, S., Asim, M., Nunez, J., Alvarez, G., Chen, G.: On the security defects of an image encryption scheme. Image Vis. Comput. 27(9), 1371–1381 (2009)

    Article  Google Scholar 

  47. Schmitz, R.: Use of chaotic dynamical systems in cryptography. J. Frank. Inst. 338(4), 429–441 (2001)

    Article  MathSciNet  Google Scholar 

  48. Arroyo, D., Diaz, J., Rodriguez, F.: Cryptanalysis of a one round chaos-based substitution permutation network. Signal Process. 93(5), 1358–1364 (2013)

    Article  Google Scholar 

  49. Li, S., Li, C., Chen, G., Bourbakis, N.G., Lo, K.-T.: A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process.: Image Commun. 23(3), 212–223 (2008)

    Google Scholar 

  50. Solak, E.: Cryptanalysis of chaotic ciphers. In: Chaos-Based Cryptography, pp. 227–256. Springer (2011)

    Google Scholar 

  51. Ott, E.: Chaos in Dynamical Systems. Cambridge University Press (2002)

    Google Scholar 

  52. Zhang H., Liu, D., Wang, Z.: Controlling Chaos: suppression, Synchronization and Chaotification. Springer Science & Business Media (2009)

    Google Scholar 

  53. Strogatz, S.H.: Nonlinear Dynamics and Chaos with Student Solutions Manual: with Applications to Physics, Biology, Chemistry, and Engineering. CRC Press (2018)

    Google Scholar 

  54. Cuomo, K.M., Oppenheim, A.V., Strogatz, S.H.: Synchronization of lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circ. Syst. II: Analog Dig. Signal Process. 40(10), 626–633 (1993)

    Google Scholar 

  55. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821 (1990)

    Article  MathSciNet  Google Scholar 

  56. Vaidyanathan, S., Pakiriswamy, S.: The design of active feedback controllers for the generalized projective synchronization of hyperchaotic Qi and hyperchaotic lorenz systems. In: Computer Information Systems—Analysis and Technologies, pp. 231–238. Springer (2011)

    Google Scholar 

  57. Wu, W., Chen, Z.: Hopf bifurcation and intermittent transition to hyperchaos in a novel strong four-dimensional hyperchaotic system. Nonlinear Dyn. 60(4), 615–630 (2010)

    Article  MathSciNet  Google Scholar 

  58. Gautschi, W.: Numerical integration of ordinary differential equations based on trigonometric polynomials. Numer. Math. 3(1), 381–397 (1961)

    Article  MathSciNet  Google Scholar 

  59. Pano-Azucena, A.D., Tlelo-Cuautle, E., Rodriguez-Gomez, G., de la Fraga, L.G.: FPGA-based implementation of chaotic oscillators by applying the numerical method based on trigonometric polynomials. AIP Adv. 8(7), 75217 (2018)

    Article  Google Scholar 

  60. Chai, X., Fu, X., Gan, Z., Lu, Y., Chen, Y.: A color image cryptosystem based on dynamic DNA encryption and chaos. Signal Process. 155, 44–62 (2019)

    Article  Google Scholar 

  61. Gan, Z.-H., Chai, X.-L., Han, D.-J., Chen, Y.-R.: A chaotic image encryption algorithm based on 3-D bit-plane permutation. Neural Comput. Appl. 31(11), 7111–7130 (2019)

    Article  Google Scholar 

  62. Tsafack, N., Iliyasu, A.M., De Dieu, N.J., Zeric, N.T., Kengne, J., Abd-El-Atty, B., Belazi, A., Abd EL-Latif, A.A.: A memristive rlc oscillator dynamics applied to image encryption. J. Inf. Secur. Appl. 61, 102944 (2021)

    Google Scholar 

  63. Biham, E., Shamir, A.: Differential Cryptanalysis of the Data Encryption Standard. Springer Science & Business Media (2012)

    Google Scholar 

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Acknowledgements

The first author is thankful to Consejo Nacional de Ciencia y Tecnología (CONACYT) for the scholarship 937653.

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Authors and Affiliations

  1. INAOE, Puebla, Mexico

    Freddy Alejandro Chaurra-Gutierrrez, Gustavo Rodriguez-Gomez, Claudia Feregrino-Uribe, Esteban Tlelo-Cuautle & Omar Guillen-Fernandez

Authors
  1. Freddy Alejandro Chaurra-Gutierrrez
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  2. Gustavo Rodriguez-Gomez
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  3. Claudia Feregrino-Uribe
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  4. Esteban Tlelo-Cuautle
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  5. Omar Guillen-Fernandez
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Corresponding author

Correspondence to Gustavo Rodriguez-Gomez .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shibin El Kom, Egypt

    Ahmed A. Abd El-Latif

  2. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Christos Volos

Appendix

Appendix

The appendix contains histogram and correlation analysis for different images from the USC-SIPI database (Figs. 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34 and 35).

Fig. 22
figure 22

Histogram values of the original message (Clock), and encrypted message. The corresponding histogram is shown below each figure

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Fig. 23
figure 23

Correlation figures of the original (Clock) and encrypted message. Figure a horizontal, vertical, and diagonal correlation for original message, and figure b the correlation for encrypted image

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Fig. 24
figure 24

Histogram values of the original message (BlockGray), and encrypted message. The corresponding histogram is shown below each figure

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Fig. 25
figure 25

Correlation figures of the original (BlockGray) and encrypted message. Figure a horizontal, vertical, and diagonal correlation for original message, and figure b the correlation for encrypted image

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Fig. 26
figure 26

Histogram values of the original message (CarToy), and encrypted message. The corresponding histogram is shown below each figure

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Fig. 27
figure 27

Correlation figures of the original (CarToy) and encrypted message. Figure a horizontal, vertical, and diagonal correlation for original message, and figure b the correlation for encrypted image

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Fig. 28
figure 28

Histogram values of the original message (Truck), and encrypted message. The corresponding histogram is shown below each figure

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Fig. 29
figure 29

Correlation figures of the original (Truck) and encrypted message. Figure a horizontal, vertical, and diagonal correlation for original message, and figure b the correlation for encrypted image

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Fig. 30
figure 30

Histogram values of the original message (Walter), and encrypted message. The corresponding histogram is shown below each figure

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Fig. 31
figure 31

Correlation figures of the original (Walter) and encrypted message. Figure a horizontal, vertical, and diagonal correlation for original message, and figure b the correlation for encrypted image

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Fig. 32
figure 32

Histogram values of the original message (chemical plant), and encrypted message. The corresponding histogram is shown below each figure

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Fig. 33
figure 33

Correlation figures of the original (chemical plant) and encrypted message. Figure a horizontal, vertical, and diagonal correlation for original message, and figure b the correlation for encrypted image

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Fig. 34
figure 34

Histogram values of the original message (cameraman), and encrypted message. The corresponding histogram is shown below each figure

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Fig. 35
figure 35

Correlation figures of the original (cameraman) and encrypted message. Figure a horizontal, vertical, and diagonal correlation for original message, and figure b the correlation for encrypted image

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Chaurra-Gutierrrez, F.A., Rodriguez-Gomez, G., Feregrino-Uribe, C., Tlelo-Cuautle, E., Guillen-Fernandez, O. (2022). Secure Communication Scheme Based on Projective Synchronization of Hyperchaotic Systems. In: Abd El-Latif, A.A., Volos, C. (eds) Cybersecurity. Studies in Big Data, vol 102. Springer, Cham. https://doi.org/10.1007/978-3-030-92166-8_6

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