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Quantum image encryption based on generalized Arnold transform and double random-phase encoding

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Abstract

A quantum realization of the generalized Arnold transform is designed. A novel quantum image encryption algorithm based on generalized Arnold transform and double random-phase encoding is proposed. The pixels are scrambled by the generalized Arnold transform, and the gray-level information of images is encoded by the double random-phase operations. The keys of the encryption algorithm include the independent parameters of coefficients matrix, iterative times and classical binary sequences, and thus, the key space is extremely large. Numerical simulations and theoretical analyses demonstrate that the proposed algorithm with good feasibility and effectiveness has lower computational complexity than its classical counterpart.

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References

  1. Zhang, Y., Xiao, D.: Cryptanalysis of S-box-only chaotic image ciphers against chosen plaintext attack. Nonlinear Dynam. 72(4), 751–756 (2013)

    Article  MathSciNet  Google Scholar 

  2. Refregier, P., Javidi, B.: Optical image encryption using input plane and Fourier plane random encoding. SPIE’s 1995 International Symposium on Optical Science, Engineering, and Instrumentation. International Society for Optics and Photonics, 62–68 (1995)

  3. Situ, G., Zhang, J.: Double random-phase encoding in the Fresnel domain. Opt. Lett. 29(14), 1584–1586 (2004)

    Article  ADS  Google Scholar 

  4. Unnikrishnan, G., Joseph, J., Singh, K.: Optical encryption by double-random phase encoding in the fractional Fourier domain. Opt. Lett. 25(12), 887–889 (2000)

    Article  ADS  Google Scholar 

  5. Zhou, X., Lai, D., Yuan, S., Li, D.H., Hu, J.P.: A method for hiding information utilizing double-random phase-encoding technique. Opt. Laser Technol. 39(7), 1360–1363 (2007)

    Article  ADS  Google Scholar 

  6. Tao, R., Xin, Y., Wang, Y.: Double image encryption based on random phase encoding in the fractional Fourier domain. Opt. Express 15(24), 16067–16079 (2007)

    Article  ADS  Google Scholar 

  7. Lu, P., Xu, Z., Lu, X., Liu, X.: Digital image information encryption based on compressive sensing and double random-phase encoding technique. Optik 124(16), 2514–2518 (2013)

    Article  MathSciNet  Google Scholar 

  8. Liu, Z., Li, S., Liu, W., Wang, Y., Liu, S.: Image encryption algorithm by using fractional Fourier transform and pixel scrambling operation based on double random phase encoding. Opt. Lasers Eng. 51(1), 8–14 (2013)

    Article  Google Scholar 

  9. Peng, X., Zhang, P., Wei, H., Yu, B.: Known-plaintext attack on optical encryption based on double random phase keys. Opt. Lett. 31(8), 1044–1046 (2006)

    Article  ADS  Google Scholar 

  10. Frauel, Y., Castro, A., Naughton, T.J., Javidi, B.: Resistance of the double random phase encryption against various attacks. Opt. Express 15(16), 10253–10265 (2007)

    Article  ADS  Google Scholar 

  11. Carnicer, A., Montes-Usategui, M., Arcos, S., Juvells, I.: Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys. Opt. Lett. 30(13), 1644–1646 (2005)

    Article  ADS  Google Scholar 

  12. Peng, X., Wei, H., Zhang, P.: Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain. Opt. Lett. 31(22), 3261–3263 (2006)

    Article  ADS  Google Scholar 

  13. Arnold, V.I., Avez, A.: Ergodic problems of classical mechanics. Benjamin, New York (1968)

    Google Scholar 

  14. Ye, R.S.: A novel image scrambling and watermarking scheme based on orbits of Arnold transform. Conference on Circuits, Communications and Systems, Pacific-Asia, 485–488 (2009)

  15. Ye, G., Wong, K.W.: An efficient chaotic image encryption algorithm based on a generalized Arnold map. Nonlinear Dynam. 69(4), 2079–2087 (2012)

    Article  MathSciNet  Google Scholar 

  16. Liu, Z., Gong, M., Dou, Y., Liu, F., Liu, S., Ashfaq Ahmad, M., Liu, S.: Double image encryption by using Arnold transform and discrete fractional angular transform. Opt. Lasers Eng. 50(2), 248–255 (2012)

    Article  Google Scholar 

  17. Chen, W., Quan, C., Tay, C.J.: Optical color image encryption based on Arnold transform and interference method. Opt. Commun. 282(18), 3680–3685 (2009)

    Article  ADS  Google Scholar 

  18. Chen, L., Zhao, D., Ge, F.: Image encryption based on singular value decomposition and Arnold transform in fractional domain. Opt. Commun. 291, 98–103 (2013)

    Article  ADS  Google Scholar 

  19. Liu, Z., Liu, S., Chen, H., Liu, T., Li, P., Xu, L., Dai, J.: Image encryption by using gyrator transform and Arnold transform. J. Electron. Imaging 20(1), 013020–013026 (2011)

    Article  ADS  Google Scholar 

  20. Guo, Q., Liu, Z., Liu, S.: Color image encryption by using Arnold and discrete fractional random transforms in IHS space. Opt. Lasers Eng. 48(12), 1174–1181 (2010)

    Article  Google Scholar 

  21. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

  22. Venegas-Andraca, S.E., Ball, J.L.: Processing images in entangled quantum systems. Quantum Inf. Process. 9(1), 1–11 (2010)

    Article  MathSciNet  Google Scholar 

  23. Le, P.Q., Dong, F.Y., 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  MATH  MathSciNet  Google Scholar 

  24. Sun, B., Le, P.Q., Iliyasu, A.M., Yan, F., Garcia, J.A., Dong, F., Hirota, K.: A multi-channel representation for images on quantum computers using the RGB\(\alpha \) color space. Intelligent Signal Processing (WISP), 2011 IEEE 7th International Symposium on Floriana, 160–165 (2011)

  25. Le, P.Q., Iliyasu, A.M., Garcia, J.A., Dong, F., Hirota, K.: Representing visual complexity of images using a 3D feature space based on structure, noise, and diversity. JACIII 16(5), 631–640 (2012)

    Google Scholar 

  26. Zhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12(9), 3101–3126 (2013)

    ADS  MathSciNet  Google Scholar 

  27. Yuan, S., Mao, X., Xue, Y., Chen, L., Xiong, Q., Compare, A.: SQR: a simple quantum representation of infrared images. Quantum Inf. Process. 13(6), 1353–1379 (2014)

  28. 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  MATH  MathSciNet  Google Scholar 

  29. Akhshani, A., Akhavan, A., Lim, S.C., Hassan, Z.: An image encryption scheme based on quantum logistic map. Commun. Nonlinear Sci. Numer. Simulat. 17(12), 4653–4661 (2012)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  30. 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 

  31. Zhang, W.W., Gao, F., Liu, B., Wen, Q.Y., Chen, H.: A watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. 12(2), 793–803 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  32. Zhou, N., Liu, Y., Zeng, G., Xiong, J., Zhu, F.: Novel qubit block encryption algorithm with hybrid keys. Physica A. 375(2), 693–698 (2007)

    Article  ADS  Google Scholar 

  33. Abd El-Latif, A.A., Li, L., Wang, N., Han, Q., Niu, X.: A new approach to chaotic image encryption based on quantum chaotic system, exploiting color spaces. Signal Process. 93(11), 2986–3000 (2013)

    Article  Google Scholar 

  34. Song, X., Wang, S., El-Latif, A.A.A., Niu, X.: Dynamic watermarking scheme for quantum images based on Hadamard transform. Multimedia Syst. 20(4), 379–388 (2014)

  35. Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert image scrambling. Int. J. Theor. Phys. 53(7), 2463–2484 (2014)

  36. Yang, Y.G., Xia, J., Jia, X., Zhang, H.: Novel image encryption/decryption based on quantum Fourier transform and double phase encoding. Quantum Inf. Process. 12(11), 3477–3493 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  37. Song, X.H., Wang, S., Abd El-Latif, A.A., Niu, X.M.: Quantum image encryption based on restricted geometric and color transformations. Quantum Inf. Process. 13(8), 1765–1787 (2014)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  38. Jiang, N., Wu, W.Y., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223–1236 (2014)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  39. Jiang, N., Wang, L.: Analysis and improvement of the quantum Arnold image scrambling. Quantum Inf. Process. 13(7), 1545–1551 (2014)

  40. Dyson, F.J., Falk, H.: Period of a discrete cat mapping. Am. Math. Mon. 99(7), 603–614 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  41. Vedral, V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations. Phys. Rev. A 54(1), 147–153 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  42. Chen, J.X., Zhu, Z.L., Fu, C., Yu, H.: A fast image encryption scheme with a novel pixel swapping-based confusion approach. Nonlinear Dynam. 77(4), 1191–1207 (2014)

    Article  Google Scholar 

  43. Ahmed, H., Kalash, H., Allah, O.: Implementation of rc5 block cipher algorithm for image cryptosystems. Int. J. Inf. Technol. 3(4), 245–250 (2007)

    Google Scholar 

  44. Enayatifar, R.: Image encryption via logistic map function and heap tree. Int. J. Phys. Sci. 6(2), 221–228 (2011)

    Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61462061 and 61262084), the Foundation for Young Scientists of Jiangxi Province (Jinggang Star) (Grant No. 20122BCB23002), the Research Foundation of the Education Department of Jiangxi Province (Grant Nos. GJJ14138 and GJJ13057) and the Open Project of Key Laboratory of Photoeletronics and Telecommunication of Jiangxi Province (Grant No. 2013003).

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Correspondence to Nan Run Zhou.

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Zhou, N.R., Hua, T.X., Gong, L.H. et al. Quantum image encryption based on generalized Arnold transform and double random-phase encoding. Quantum Inf Process 14, 1193–1213 (2015). https://doi.org/10.1007/s11128-015-0926-z

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  • DOI: https://doi.org/10.1007/s11128-015-0926-z

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