Cryptosystem for Grid Data Based on Quantum Convolutional Neural Networks and Quantum Chaotic Map

Abstract

Motivated by the existing circuit model of quantum convolutional neural network, a new quantum convolutional neural network circuit model is devised, which is combined with quantum chaotic map to construct a symmetric cryptosystem. Quantum chaotic map produces key stream for encryption and decryption. The cryptosystem simulates the basic process of communication. Theoretical analysis manifests that the cryptosystem is effective. Additionally, simulation experiments based on MNIST data set show that the cryptosystem is secure. Furthermore, the proposed cryptosystem can be applied not only for image data, but for text data. Therefore, the grid data can be encrypted by utilizing the cryptosystem.

This is a preview of subscription content, access via your institution.

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

References

  1. 1.

    Zhou, N.R., Zhu, K.N., Zou, X.F.: Multi-party semi-quantum key distribution protocol with four-particle cluster states. Annalen Der Physik 531(8) (2019)

  2. 2.

    Fei, G., Qiaoyan, W., Fuchen, Z.: Teleportation attack on the QSDC protocol with a random basis and order. Chinese Physics B 17(9), 3189–3193 (2008)

    ADS  Article  Google Scholar 

  3. 3.

    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)

    ADS  MathSciNet  Article  Google Scholar 

  4. 4.

    Wang, J., Geng, Y., Han, L., Liu, J.: Quantum image encryption algorithm based on quantum key image. Int. J. Theor. Phys. 58(1), 308–322 (2019)

    Article  Google Scholar 

  5. 5.

    Miyake, S., Nakamae, K.: A quantum watermarking scheme using simple and small-scale quantum circuits. Quantum Inf. Process 15(5), 1849–1864 (2016)

    ADS  MathSciNet  Article  Google Scholar 

  6. 6.

    Cao, Y., Guerreschi, G.G., Aspuruguzik, A.: Quantum neuron: an elementary building block for machine learning on quantum computers. arxiv: Quantum Physics (2017)

  7. 7.

    Chatterjee, R., Yu, T.: Generalized coherent states, reproducing kernels, and quantum support vector machines. Quantum Information & Computation 17(15), 1292–1306 (2017)

    MathSciNet  Google Scholar 

  8. 8.

    Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85(2), 441–444 (2000)

    ADS  Article  Google Scholar 

  9. 9.

    Mao, C., Li, J., Zhu, J., Zhang, C., Wang, Q.: An improved proposal on the practical quantum key distribution with biased basis. Quantum Information Processing 16(10) (2017)

  10. 10.

    Lai, H., Luo, M.X., Zhan, C., Pieprzyk, J., Orgun, M.A.: An improved coding method of quantum key distribution protocols based on Fibonacci-valued OAM entangled states. Phys. Lett. A 381(35), 2922–2926 (2017)

    ADS  Article  Google Scholar 

  11. 11.

    Yan, X.Y., Zhou, N.R., Gong, L.H., Wang, Y.Q., Wen, X.J.: High-dimensional quantum key distribution based on qudits transmission with quantum Fourier transform. Quantum Information Processing 18(9) (2019)

  12. 12.

    Xu, Q.D., Chen, H.Y., Gong, L.H., Zhou, N.R.: Quantum private comparison protocol based on four-particle GHZ states. Int. J. Theor. Phys. 59(6), 1798–1806 (2020)

    MathSciNet  Article  Google Scholar 

  13. 13.

    Zhang, S., Chen, Z.K., Shi, R.H., Liang, F.Y.: A novel quantum identity authentication based on Bell states. Int. J. Theor. Phys. 59(1), 236–249 (2019)

    MathSciNet  Article  Google Scholar 

  14. 14.

    Xu, L.C., Chen, H.Y., Gong, L.H., Zhou, N.R.: Multi-party semi-quantum secure direct communication protocol with cluster states. Int. J. Theor. Phys. 59(7), 2175–2186 (2020)

    MathSciNet  Article  Google Scholar 

  15. 15.

    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)

    MathSciNet  Article  Google Scholar 

  16. 16.

    Hua, T.X., Chen, J.M., Pei, D.J., Zhang, W.Q., Zhou, N.R.: Quantum image encryption algorithm based on image correlation decomposition. International Journal of Theoretical Physics 54(2), 526–537 (2015)

    ADS  Article  Google Scholar 

  17. 17.

    Zhou, N.R., Hu, Y.Q., Gong, L.H., Li, G.Y.: Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations. Quantum Inf. Process 16(6), 1–23 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  18. 18.

    Wang, J., Geng, Y.C., Han, L., Liu, J.Q.: Quantum image encryption algorithm based on quantum key image. Int. J. Theor. Phys. 58(1), 308–322 (2019)

    Article  Google Scholar 

  19. 19.

    Li, H.S., Li, C.Y., Chen, X., Xia, H.Y.: Quantum image encryption based on phase-shift transform and quantum Haar wavelet packet transform. Modern Physics Letters A 34(26) (2019)

  20. 20.

    Wang, H.Q., Song, X.H., Chen, L.L., Xie, W.: A secret sharing scheme for quantum gray and color images based on encryption. Int. J. Theor. Phys. 58(5), 1626–1650 (2019)

    MathSciNet  Article  Google Scholar 

  21. 21.

    Qiu, J.F., Wu, Q.H., Ding, G.R., Xu, Y.H., Feng, S.: A survey of machine learning for big data processing. EURASIP Journal on Advances in Signal Processing. 2016, 67 (2016)

    Article  Google Scholar 

  22. 22.

    Rebentrost, P., Mohseni, M., Lloyd, S.: Quantum support vector machine for big data classification. Physical Review Letters 113(13) (2014)

  23. 23.

    Amin, M., Andriyash, E., Rolfe, J.T., Kulchytskyy, B., Melko, R.G.: Quantum boltzmann machine. Physical Review X 8(2) (2018)

  24. 24.

    Schuld, M., Killoran, N.: Quantum machine learning in feature Hilbert spaces. Physical Review Letters 122(4) (2019)

  25. 25.

    Lloyd, S., Garnerone, S., Zanardi, P.: Quantum algorithms for topological and geometric analysis of data. Nat. Commun. 7(1), 10138–10138 (2016)

    ADS  Article  Google Scholar 

  26. 26.

    Bishwas, A.K., Mani, A., Palade, V.: An all-pair quantum SVM approach for big data multiclass classification. Quantum Inf. Process 17(10), 282 (2018)

    ADS  MathSciNet  Article  Google Scholar 

  27. 27.

    Li, Y.Y., Xiao, J.J., Chen, Y.Q., Jao, L.C.: Evolving deep convolutional neural networks by quantum behaved particle swarm optimization with binary encoding for image classification. Neurocomputing 362, 156–165 (2019)

    Article  Google Scholar 

  28. 28.

    Youssry, A., Rafei, A., Elramly, S.: A quantum mechanics-based framework for image processing and its application to image segmentation. Quantum Inf. Process 14(10), 3613–3638 (2015)

    ADS  MathSciNet  Article  Google Scholar 

  29. 29.

    Dallairedemers, P., Killoran, N.: Quantum generative adversarial networks. Physical Review A 98(1) (2018)

  30. 30.

    Wang, Y.X., Wang, R.J., Li, D.F., Adu, D., Tian, K.B., Zhu, Y.X.: Improved handwritten digit recognition using quantum K-Nearest-Neighbor algorithm. Int. J. Theor. Phys. 58(7), 2331–2340 (2019)

    MathSciNet  Article  Google Scholar 

  31. 31.

    Wan, K.H., Dahlsten, O., Kristjánsson, H., Gardner, R., Kim, M.S.: Quantum generalisation of feedforward neural networks. NPJ Quantum Information 3, 36 (2017)

    ADS  Article  Google Scholar 

  32. 32.

    Shi, J., Chen, S., Lu, Y, Feng, Y., Shi, R., Yang, Y., Li, J.: An approach to cryptography based on continuous-variable quantum neural network. Sci. Rep. 10, 2107 (2020)

    ADS  Article  Google Scholar 

  33. 33.

    Gao, X., Duan, L.M.: Efficient representation of quantum many-body states with deep neural networks. Nat. Commun. 8, 2041–1723 (2017)

    ADS  Article  Google Scholar 

  34. 34.

    Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nat. Phys. 15(12), 1273–1278 (2019)

    Article  Google Scholar 

  35. 35.

    Henderson, M., Shakya, S., Pradhan, S., Cook, T.: Quanvolutional neural networks: powering image recognition with quantum circuits. arxiv: Quantum Physics (2019)

  36. 36.

    Pareek, N.K., Patidar, V., Sud, K.K.: Image encryption using chaotic logistic map. Image Vis. Comput. 24(9), 926–934 (2016)

    Article  Google Scholar 

  37. 37.

    Lu, X., Jiang, N., Hu, H., Ji, Z.: Quantum adder for superposition states. Int. J. Theor. Phys. 57(9), 2575–2584 (2018)

    MathSciNet  Article  Google Scholar 

  38. 38.

    Kotiyal, S., Thapliyal, H., Ranganathan, N.: Circuit for reversible quantum multiplier based on binary tree optimizing ancilla and garbage bits. In: 2014 27th International Conference on VLSI Design and 2014 13th International Conference on Embedded Systems, pp 545–550. IEEE (2014)

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant no. 61871205).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Li-Hua Gong.

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tan, RC., Liu, X., Tan, RG. et al. Cryptosystem for Grid Data Based on Quantum Convolutional Neural Networks and Quantum Chaotic Map. Int J Theor Phys (2021). https://doi.org/10.1007/s10773-021-04733-z

Download citation

Keywords

  • Cryptosystem
  • Quantum convolutional neural network
  • Quantum chaotic map