Skip to main content
SpringerLink
Log in

Quantum Color Image Encryption Scheme Based on 3D Non-Equilateral Arnold Transform and 3D Logistic Chaotic Map

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In this paper, a quantum color image encryption scheme based on 3D non-equilateral Arnold transform and 3D logistic chaotic map is proposed for QRCI image representation model which requires less qubits. First, the original color image is stored as QRCI quantum image. Then, the position information and bit-plane order information of QRCI quantum image are scrambled simultaneously by quantum 3D non-equilateral Arnold transform to obtain the intermediate quantum image. Finally, three sequences generated from 3D logistic chaotic map are used to encrypt the color information of intermediate quantum image by XOR operations. The parameters of 3D non-equilateral Arnold transform and initial values of 3D logistic chaotic map are used as keys, which not only simplifies the keys transmission but also makes the cryptosystem own a large enough key space to resist brute-force attacks. In addition, the process and circuit to verify the validity of encryption system in quantum domain are also given. Simulation results and performance comparisons demonstrate that the proposed QRCI quantum color image encryption scheme outperforms the previous pertinent works in terms of security and computational complexity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Data Availability

The manuscript has no relevant data.

References

  1. Wang, X., Feng, L., Zhao, H.: Fast image encryption algorithm based on parallel computing system. Inform. Sci. 486, 340–358 (2019)

    Article  MATH  Google Scholar 

  2. Hua, Z., Zhou, Y., Huang, H.: Cosine-transform-based chaotic system for image encryption. Inform. Sci. 480, 403–419 (2019)

    Article  Google Scholar 

  3. Xu, L., Li, Z., Li, J., Hua, W.: A novel bit-level image encryption algorithm based on chaotic maps. Opt. Lasers Eng. 78, 17–25 (2016)

    Article  Google Scholar 

  4. Nielsen, M.A., Chuang, I.: Quantum computation and quantum information. Am. Assoc. Phys. Teach. (2002)

  5. Blais, A., Girvin, S.M., Oliver, W.D.: Quantum information processing and quantum optics with circuit quantum electrodynamics. Nat. Phys. 16(3), 247–256 (2020)

    Article  Google Scholar 

  6. Wang, Z., Xu, M., Zhang, Y.: Review of quantum image processing. Arch. Comput. Methods Eng.:1–25 (2021)

  7. Li, H.S., Li, C., Chen, X., Xia, H.: Quantum image encryption based on phase-shift transform and quantum haar wavelet packet transform. Mod Phys. Lett. A 34(26), 1950214 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Zhou, N.R., Huang, L.X., Gong, L.H., Zeng, Q.W.: Novel quantum image compression and encryption algorithm based on dqwt and 3d hyper-chaotic henon map. Quantum Inf. Process. 19(9), 1–21 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Wang, X., Su, Y., Luo, C., Nian, F., Teng, L.: Color image encryption algorithm based on hyperchaotic system and improved quantum revolving gate. Multimed. Tools Appl. 81(10), 13845–13865 (2022)

    Article  Google Scholar 

  10. Venegas-Andraca, S.E., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. In: Quantum Information and Computation, vol. 5105, pp. 137–147. SPIE (2003)

  11. Latorre, J.I.: Image compression and entanglement. arXiv:quant-ph/0510031 (2005)

  12. 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(1), 63–84 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang, Y., Lu, K., Gao, Y., Wang, M.: Neqr: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 2833–2860 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Sun, B., Iliyasu, A., Yan, F., Dong, F., Hirota, K.: An rgb multi-channel representation for images on quantum computers. J. Adv. Comput. Intell. Intell. Inform. 17(3) (2013)

  15. Yang, Y.G., Jia, X., Sun, S.J., Pan, Q.X.: Quantum cryptographic algorithm for color images using quantum fourier transform and double random-phase encoding. Inform. Sci. 277, 445–457 (2014)

    Article  Google Scholar 

  16. Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14(5), 1559–1571 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Khan, R.A.: An improved flexible representation of quantum images. Quantum Inf. Process. 18(7), 1–19 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  18. Sang, J., Wang, S., Li, Q.: A novel quantum representation of color digital images. Quantum Inf. Process. 16(2), 1–14 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Liu, K., Zhang, Y., Lu, K., Wang, X., Wang, X.: An optimized quantum representation for color digital images. Int. J. Theor. Phys. 57 (10), 2938–2948 (2018)

    Article  MATH  Google Scholar 

  20. Grigoryan, A.M., Agaian, S.S.: New look on quantum representation of images: fourier transform representation. Quantum Inf. Process. 19(5), 1–26 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  21. Chen, G.L., Song, X.H., Venegas-Andraca, S.E., El-Latif, A., Ahmed, A.: Qirhsi: novel quantum image representation based on hsi color space model. Quantum Inf. Process. 21(1), 1–31 (2022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Wang, L., Ran, Q., Ma, J., Yu, S., Tan, L.: Qrci: a new quantum representation model of color digital images. Opt. Commun. 438, 147–158 (2019)

    Article  ADS  Google Scholar 

  23. Zhou, R.G., Wu, Q., Zhang, M.Q., Shen, C.Y.: Quantum image encryption and decryption algorithms based on quantum image geometric transformations. Int. J. Theor. Phys. 52(6), 1802–1817 (2013)

    Article  MathSciNet  Google Scholar 

  24. Zhou, N.R., Hua, T.X., Gong, L.H., Pei, D.J., Liao, Q.H.: Quantum image encryption based on generalized arnold transform and double random-phase encoding. Quantum Inf. Process. 14(4), 1193–1213 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Yang, Y.G., Tian, J., Lei, H., Zhou, Y.H., Shi, W.M.: Novel quantum image encryption using one-dimensional quantum cellular automata. Inform. Sci. 345, 257–270 (2016)

    Article  Google Scholar 

  26. Tan, R.C., Lei, T., Zhao, Q.M., Gong, L.H., Zhou, Z.H.: Quantum color image encryption algorithm based on a hyper-chaotic system and quantum fourier transform. Int. J. Theor. Phys. 55(12), 5368–5384 (2016)

    Article  MATH  Google Scholar 

  27. Wang, H., Wang, J., Geng, Y.C., Song, Y., Liu, J.Q.: Quantum image encryption based on iterative framework of frequency-spatial domain transforms. Int. J. Theor. Phys. 56(10), 3029–3049 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  28. Li, X.Z., Chen, W.W., Wang, Y.Q.: Quantum image compression-encryption scheme based on quantum discrete cosine transform. Int. J. Theor. Phys. 57(9), 2904–2919 (2018)

    Article  MATH  Google Scholar 

  29. Ran, Q., Wang, L., Ma, J., Tan, L., Yu, S.: A quantum color image encryption scheme based on coupled hyper-chaotic lorenz system with three impulse injections. Quantum Inf. Process. 17(8), 1–30 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Abd-El-Atty, B., El-Latif, A., Ahmed, A., Venegas-Andraca, S.E.: An encryption protocol for neqr images based on one-particle quantum walks on a circle. Quantum Inf. Process. 18(9), 1–26 (2019)

    Article  MATH  Google Scholar 

  31. Musanna, F., Kumar, S.: Image encryption using quantum 3-d baker map and generalized gray code coupled with fractional chen’s chaotic system. Quantum Inf. Process. 19(8), 1–31 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  32. Liu, X., Xiao, D., Liu, C.: Three-level quantum image encryption based on arnold transform and logistic map. Quantum Inf. Process. 20(1), 1–22 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Song, X., Chen, G., Abd El-Latif, A.A.: Quantum color image encryption scheme based on geometric transformation and intensity channel diffusion. Mathematics 10(17), 3038 (2022)

    Article  Google Scholar 

  34. Li, Y.K., Feng, Q.S., Zhou, F., Li, Q.: 2-d arnold transformation and non-equilateral image scrambling transformation. Comput. Eng. Des. 30(13) (2009)

  35. Wu, C., Tian, X.: 3-dimensional non-equilateral arnold transformation and its application in image scrambling. J. Comput.-Aided Des. Comput. Graph. 22(10), 1831–1840 (2010)

    Google Scholar 

  36. Zhu, H.H., Chen, X.B., Yang, Y.X.: A multimode quantum image representation and its encryption scheme. Quantum Inf. Process. 20(9), 1–21 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  37. Khade, P.N., Narnaware, M.: 3d chaotic functions for image encryption. Int. J. Comput. Sc. Issues (IJCSI) 9(3), 323 (2012)

    Google Scholar 

  38. Zhou, R.G., Hu, W., Fan, P.: Quantum watermarking scheme through arnold scrambling and lsb steganography. Quantum Inf. Process. 16(9), 1–21 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Zhao, C., Yang, G.W., Li, X.Y.: Separability criterion for arbitrary multipartite pure state based on the rank of reduced density matrix. Int. J. Theor. Phys. 55(9), 3816–3826 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  40. Wang, L., Ran, Q., Ma, J.: Double quantum color images encryption scheme based on dqrci. Multimed. Tools Appl. 79(9), 6661–6687 (2020)

    Article  Google Scholar 

  41. Vedral, V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations. Phys. Rev. A 54(1), 147 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  42. Li, P., Zhao, Y.: A simple encryption algorithm for quantum color image. Int. J. Theor. Phys. 56(6), 1961–1982 (2017)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. School of Internet, Anhui University, Hefei, 230039, China

    Ling Wang

  2. National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin, 150001, China

    Qiwen Ran & Junrong Ding

Authors
  1. Ling Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiwen Ran
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junrong Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Ling Wang: Conceptualization, Methodology, Software. Qiwen Ran: Supervision, Validation. Junrong Ding: Formal analysis, Writing-Reviewing and Editing.

Corresponding author

Correspondence to Ling Wang.

Ethics declarations

Ethics approval and consent to participate

This declaration is not applicable.

Conflict of Interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, L., Ran, Q. & Ding, J. Quantum Color Image Encryption Scheme Based on 3D Non-Equilateral Arnold Transform and 3D Logistic Chaotic Map. Int J Theor Phys 62, 36 (2023). https://doi.org/10.1007/s10773-023-05295-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-023-05295-y

Keywords

Search

Navigation