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Secured Quantum Image Communication Using New Two Dimensional Chaotic Map Based Encryption Methods

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Abstract

A chaos-based cryptosystem requires an extremely nonlinear chaotic map with many chaotic regions. Quantum computers efficiently provide speed and security in image communication. A new two-dimensional triangle function combined with a discrete chaotic map (2D-TFCDM) is proposed in this research. The generated map is tested on various grounds such as attractor plot, bifurcation diagram, sensitivity test, Lyapunov exponent, 0–1 Test, permutation entropy and National Institute of Standards and Technology (NIST) test suite. The proposed map combined with the Secure Hash Algorithm (SHA) is utilised in image cryptography applications. Furthermore, the encrypted image is communicated by the novel enhanced quantum representation (NEQR) method using the qasm_simulator of IBM quantum computer (Qiskit) to utilise the benefits of the laws of physics to secure data. The numerical analyses are done, and simulation results are compared with recent techniques that depict the effectiveness of the image encryption method in resisting various attacks.

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References

  1. Liu, Z., Xia, T.: Novel two dimensional fractional-order discrete chaotic map and its application to image encryption. Appl. Comput. Inform. 14(2), 177–185 (2018). https://doi.org/10.1016/j.aci.2017.07.002. ISSN 2210–8327

    Article  Google Scholar 

  2. Liang, Q., Zhu, C.: A new one-dimensional chaotic map for image encryption scheme based on random DNA codin. Opt. Laser Technol. 160, 09033 (2023). https://doi.org/10.1016/j.optlastec.2022.109033.3. ISSN 0030-4026

    Article  Google Scholar 

  3. Mansouri, A., Wang, X.: A novel one-dimensional chaotic map generator and its application in a new index representation-based image encryption scheme. Inf. Sci. 563, 91–110 (2021). https://doi.org/10.1016/j.ins.2021.02.022. ISSN 0020–0255

  4. Joan, S., Muthu, P.: Murali: A new chaotic map with large chaotic band for a secured image cryptosystem. Optik 242, 167300 (2021). https://doi.org/10.1016/j.ijleo.2021.167300. ISSN 0030–4026

    Article  ADS  Google Scholar 

  5. Cao, W., Cai, H., Hua, Z.: n-Dimensional Chaotic Map with application in secure communication. Chaos, Solitons & Fractals 163, 112519 (2022). https://doi.org/10.1016/j.chaos.2022.112519. ISSN 0960 – 0779

    Article  MathSciNet  Google Scholar 

  6. Wang, X., Liu, C., Jiang, D.: Visually meaningful image encryption scheme based on new-designed chaotic map and random scrambling diffusion strategy. Chaos, Solitons & Fractals 164, 112625 (2022). https://doi.org/10.1016/j.chaos.2022.112625. ISSN 0960 – 0779

    Article  MathSciNet  Google Scholar 

  7. Abdulaali, R.S., Jamal, R.K., Mousa, S.K.: Generating a new chaotic system using two chaotic Rossler-Chua coupling systems. Opt. Quant. Electron. 53, 667 (2021). https://doi.org/10.1007/s11082-021-03341-9

    Article  Google Scholar 

  8. Hui, Y., Liu, H., Fang, P.: A DNA image encryption based on a new hyperchaotic system. Multimed. Tools Appl. (2021). https://doi.org/10.1007/s11042-021-10526-7

    Article  Google Scholar 

  9. Ye, G., Wu, H., Liu, M., Yang, S.: Image encryption scheme based on blind signature and an improved Lorenz system. Expert Syst. Appl. 205, 117709 (2022). https://doi.org/10.1016/j.eswa.2022.117709. ISSN 0957–4174

    Article  Google Scholar 

  10. Xu, J., Li, P., Yang, F., Yan, H.: High intensity image encryption scheme based on quantum logistic chaotic map and complex hyperchaotic system. IEEE Access 7, 167904–167918 (2019). https://doi.org/10.1109/ACCESS.2019.2952140

    Article  Google Scholar 

  11. Li, Y., Li, C., Liu, S., et al.: A 2-D conditional symmetric hyperchaotic map with complete control. Nonlinear Dyn. 109, 1155–1165 (2022). https://doi.org/10.1007/s11071-022-07485-5

    Article  Google Scholar 

  12. Li, P., Min, L., Hu, Y., Zhao, G., Li, X.: Novel two dimensional discrete chaotic maps and simulations. 2012 IEEE 6th International Conference on Information and Automation for Sustainability, Beijing, pp. 159–162. (2012). https://doi.org/10.1109/ICIAFS.2012.6419897

  13. Liu, Z., Xia, T., Wang, J.: Image encryption technology based on fractional two-dimensional triangle function combination discrete chaotic map coupled with menezes-vanstone elliptic curve cryptosystem. Discrete Dyn. Nat. Soc. 2018, 4585083, 24 , (2018). https://doi.org/10.1155/2018/4585083

  14. Liu, Z., Xia, T., Wang, J.: Fractional two-dimensional discrete chaotic map and its applications to the information security with elliptic-curve public key cryptography. J. Vib. Control 24(20), 4797–4824 (2018). https://doi.org/10.1177/1077546317734712

    Article  MathSciNet  Google Scholar 

  15. Liu, Z.-Y., Xia, T.-C., Hu, Y.: Dynamic analysis of new two-dimensional fractional-order discrete chaotic map and its application in cryptosystem. Math. Meth. Appl. Sci. 46, 12319–12339 (2023). https://doi.org/10.1002/mma.8779

    Article  MathSciNet  Google Scholar 

  16. Mahalingam, H., Veeramalai, T., Menon, A.R., Amirtharajan, S.S.: Dual-domain image encryption in Unsecure Medium—A Secure Communication Perspective. Mathematics 11, 457 (2023). https://doi.org/10.3390/math11020457

    Article  Google Scholar 

  17. Natiq, H., Al-Saidi, N.M.G., Said, M.R.M., et al.: A new hyperchaotic map and its application for image encryption. Eur. Phys. J. Plus 133, 6 (2018). https://doi.org/10.1140/epjp/i2018-11834-2

    Article  ADS  Google Scholar 

  18. Wang, L., Cao, Y., Jahanshahi, H., Wang, Z., Mou, J.: Color image encryption algorithm based on double layer Josephus scramble and laser chaotic system. Optik 275, 70590 (2023). https://doi.org/10.1016/j.ijleo.2023.170590. ISSN 0030-4026

    Article  ADS  Google Scholar 

  19. Azam, N.A., Murtaza, G., Hayat, U.: A novel image encryption scheme based on elliptic curves and coupled map lattices. Optik 274, 170517 (2023). https://doi.org/10.1016/j.ijleo.2023.170517. ISSN 0030-4026

  20. Lai, Q., Hu, G., Erkan, U., Toktas, A.: High-efficiency medical image encryption method based on 2D logistic-gaussian hyperchaotic map. Appl. Math. Comput. 442, 127738 (2023). https://doi.org/10.1016/j.amc.2022.127738. ISSN 0030-4026

    Article  MathSciNet  Google Scholar 

  21. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. Proceeding of 35th Annual Symposium Foundations of Computer Science, IEEE Computer Soc. Press, Los Almitos, CA, pp. 124–134 (1994)

  22. Grover, L.: A fast quantum mechanical algorithm for database search. Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, pp. 212–219 (1996)

  23. Lisnichenko, M., Protasov, S.: Quantum image representation: A review. Quantum Mach. Intell. 5, 2 (2023). https://doi.org/10.1007/s42484-022-00089-7

    Article  Google Scholar 

  24. Li, C., Yang, X.: An image encryption algorithm based on discrete fractional wavelet transform and quantum chaos. Optik 260, 169042 (2022). https://doi.org/10.1016/j.ijleo.2022.169042. ISSN 0030-4026

    Article  ADS  Google Scholar 

  25. Le, P.Q., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Inf. Process. 10, 63–84 (2010)

    Article  MathSciNet  Google Scholar 

  26. Zhang, Y., Lu, K., Gao, Y., Wang, M.: NEQR: A novel enhanced quantum representation of digital images. Quantum Inf. Process 12, 2833–2860 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  27. Wang, J., Geng, Y.C., Han, L., et al.: Quantum image encryption algorithm based on quantum key image. Int. J. Theor. Phys. 58, 308–322 (2019). https://doi.org/10.1007/s10773-018-3932-y

    Article  Google Scholar 

  28. Gao, Y., Xie, H., Zhang, J., Zhang, H.: A novel quantum image encryption technique based on improved controlled alternated quantum walks and hyperchaotic system. Physica A 598, 127334 (2022). https://doi.org/10.1016/j.physa.2022.127334

    Article  MathSciNet  Google Scholar 

  29. Abd El-Latif, A.A., Abd-El-Atty, B., Talha, M.: Robust encryption of quantum medical images. IEEE Access 6, 1073–1081 (2018). https://doi.org/10.1109/ACCESS.2017.2777869

    Article  Google Scholar 

  30. Su, J., Guo, X., Liu, C., et al.: An improved novel quantum image representation and its experimental test on IBM quantum experience. Sci. Rep. 11, 13879 (2021). https://doi.org/10.1038/s41598-021-93471-7

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  31. Balamurugan, C., Singh, K., Ganesan, G., Rajarajan, M.: Post-quantum and Code-based cryptography—some prospective research directions. Cryptography 5, 38 (2021). https://doi.org/10.3390/cryptography5040038

    Article  Google Scholar 

  32. Suhail, S., Hussain, R., Khan, A., Hong, C.S.: On the role of hash-based signatures in quantum-safe internet of things: current solutions and future directions. IEEE Internet Things J. 8(1), 1–17 (2021). https://doi.org/10.1109/JIOT.2020.3013019

  33. Kumar, M.: Post-quantum cryptography Algorithm’s standardisation and performance analysis. Array 15, 100242 (2022). https://doi.org/10.1016/j.array.2022.100242. ISSN 2590–0056

    Article  MathSciNet  Google Scholar 

  34. https://ccia.ugr.es/cvg/dbimagenes/g256.php . Accessed on 22/01/2023.

  35. Wang, H.K., Xu, G.B., Jiang, D.H.: Quantum grayscale image encryption and secret sharing schemes based on Rubik’s Cube. Physica A Stat. Mech. Appl. 128482 (2023). https://doi.org/10.1016/j.physa.2023.128482

  36. Hao, W., Zhang, T., Chen, X., Zhou, X.: A hybrid NEQR image encryption cryptosystem using two-dimensional quantum walks and quantum coding. Signal Processing 205, 108890 (2023)

    Article  Google Scholar 

  37. Mfungo, D.E., Fu, X., Wang, X., Xian, Y.: Enhancing image encryption with the Kronecker Xor product, the Hill Cipher, and the Sigmoid Logistic Map. Appl. Sci. 13, 4034 (2023). https://doi.org/10.3390/app13064034

    Article  CAS  Google Scholar 

  38. Chen, C., Zhu, D., Wang, X., Zeng, L.: One-dimensional quadratic chaotic system and splicing model for image encryption. Electronics 12, 1325 (2023). https://doi.org/10.3390/electronics12061325

    Article  CAS  Google Scholar 

  39. Chen, X., Wang, Q., Fan, L., Yu, S.A.: Novel chaotic image encryption Scheme Armed with Global Dynamic Selection. Entropy 25, 476 (2023). https://doi.org/10.3390/e25030476

    Article  ADS  MathSciNet  PubMed  PubMed Central  Google Scholar 

  40. Chang, H., Wang, E., Liu, J.: Research on image encryption based on fractional seed Chaos Generator and Fractal Theory. Fractal Fract. 7, 221 (2023). https://doi.org/10.3390/fractalfract7030221

    Article  Google Scholar 

  41. Su, Y., Wang, X.: Quantum color image encryption based on controlled two-particle quantum walks. Multimed. Tools Appl. 82, 42679–42697 (2023). https://doi.org/10.1007/s11042-023-15189-0

    Article  Google Scholar 

  42. Mohamed, N.A.E.-S., El-Sayed, H., Youssif, A.: Mixed multi-chaos quantum image encryption scheme based on Quantum Cellular Automata (QCA). Fractal Fract. 7, 734 (2023). https://doi.org/10.3390/fractalfract7100734

    Article  Google Scholar 

  43. Wang, Y., Chen, L., Yu, K., Gao, Y., Ma, Y.: An image encryption scheme based on logistic quantum chaos. Entropy 24, 251 (2022). https://doi.org/10.3390/e24020251

    Article  ADS  MathSciNet  CAS  PubMed  PubMed Central  Google Scholar 

  44. Song, X., Chen, G., Abd El-Latif, A.A.: Quantum color image encryption scheme based on geometric transformation and intensity channel diffusion. Mathematics 10, 3038 (2022). https://doi.org/10.3390/math10173038

    Article  Google Scholar 

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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [Sakshi Patel], [Thanikaiselvan V] and [Amirtharajan Rengarajan]. The first draft of the manuscript was written by [Sakshi Patel] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to V. Thanikaiselvan.

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Patel, S., Thanikaiselvan, V. & Rearajan, A. Secured Quantum Image Communication Using New Two Dimensional Chaotic Map Based Encryption Methods. Int J Theor Phys 63, 49 (2024). https://doi.org/10.1007/s10773-024-05548-4

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