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Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations

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An Erratum to this article was published on 18 August 2016

Abstract

A novel encryption algorithm for quantum images based on quantum image XOR operations is designed. The quantum image XOR operations are designed by using the hyper-chaotic sequences generated with the Chen’s hyper-chaotic system to control the control-NOT operation, which is used to encode gray-level information. The initial conditions of the Chen’s hyper-chaotic system are the keys, which guarantee the security of the proposed quantum image encryption algorithm. Numerical simulations and theoretical analyses demonstrate that the proposed quantum image encryption algorithm has larger key space, higher key sensitivity, stronger resistance of statistical analysis and lower computational complexity than its classical counterparts.

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References

  • Liu, Y.J., Zheng, Y.Q.: Adaptive robust fuzzy control for a class of uncertain chaotic systems [J]. Nonlinear Dyn. 57 (3), 431–439 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  • Han Q., Liu C.X., Sun L., et al: A fractional order hyper-chaotic system derived from a Liu system and its circuit realization [J]. Chinese Phy. B. 22 (2), 020502 (2013).

    Article  ADS  Google Scholar 

  • Wang, X., Zhao, J., Liu, H.: A new image encryption algorithm based on chaos [J]. Opt. Commun. 285 (5), 562–566 (2012).

    Article  ADS  Google Scholar 

  • Lian, S.: A block cipher based on chaotic neural networks [J]. Neurocomputing. 72 (4–6), 1296–1301 (2009).

    Article  Google Scholar 

  • Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps [J]. Int. J. Bifurcation Chaos. 8 (6), 1259–1284 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  • Guan, Z.H., Huang, F., Guan, W.: Chaos-based image encryption algorithm [J]. Phys. Lett. A. 346 (1), 153–157 (2005).

    Article  ADS  MATH  Google Scholar 

  • Gao, H.J., Zhang, Y., Liang, S., et al.: A new chaotic algorithm for image encryption [J]. Chaos, Solitons Fractals. 29 (2), 393–399 (2006).

    Article  ADS  MATH  Google Scholar 

  • Wang, X., Guo, K.: A new image alternate encryption algorithm based on chaotic map [J]. Nonlinear Dyn. 76 (4), 1943–1950 (2014).

    Article  Google Scholar 

  • Chen, C.H., Sheu, L.J., Chen, H.K., et al.: A new hyper-chaotic system and its synchronization [J]. Nonlinear Anal. Real World Appl. 10 (4), 2088–2096 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  • Gao, T., Chen, Z., Gu, Q., et al.: A new hyper-chaos generated from generalized Lorenz system via nonlinear feedback [J]. Chaos, Solitons Fractals. 35 (2), 390–397 (2008).

    Article  ADS  Google Scholar 

  • Gao, T., Chen, Z.: A new image encryption algorithm based on hyper-chaos [J]. Phys. Lett. A. 372 (4), 394–400 (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Wei, X., Guo, L., Zhang, Q., et al.: A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system [J]. Syst. Softw. 85 (2), 290–299 (2012).

    Article  Google Scholar 

  • Hermassi, H., Rhouma, R., Belghith, S.: Improvement of an image encryption algorithm based on hyper-chaos [J]. Telecommun. Syst. 52 (2), 539–549 (2013).

    Google Scholar 

  • Zhu, H., Zhao, C., Zhang, X.: A novel image encryption-compression scheme using hyper-chaos and Chinese remainder theorem [J]. Signal Process. Image Commun. 28 (6), 670–680 (2013).

    Article  Google Scholar 

  • Norouzi, B., Mirzakuchaki, S.: A fast color image encryption algorithm based on hyper-chaotic systems [J]. Nonlinear Dyn. 78 (2), 995–1015 (2014).

    Article  Google Scholar 

  • Beach, G., Lomont, C., Cohen, C.: Quantum image processing (quip) [C]. IEEE 32nd Applied imagery pattern recognition workshop, Proceedings, 39–44 (2003).

  • Nielson, M.A., Chuang, I.L.: Quantum computation and quantum information [M]. Cambridge University Press, Cambridge (2000).

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Le, P.Q., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations [J]. Quantum Inf. Process. 10 (1), 63–84 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  • Sun, B., Le, P.Q., Iliyasu, A.M., et al.: A multi-channel representation for images on quantum computers using the RGB color space [C]. IEEE 7th international symposium on intelligent signal processing (WISP), 1–6 (2011).

  • Le, P.Q., Iliyasu, A.M., Garcia, J.A., et al.: Representing visual complexity of images using a 3D feature space based on structure, noise, and diversity [J]. J. Adv. Comp. Intell. Intell. Infor. 16 (5), 631–640 (2012).

    Google Scholar 

  • Zhang, Y., Lu, K., Gao, Y., et al.: A novel quantum representation for log-polar images [J]. Quantum Inf. Process. 12 (9), 3103–3126 (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Yuan, S., Mao, X., Xue, Y., et al.: SQR: a simple quantum representation of infrared images [J]. Quantum Inf. Process. 13 (6), 1353–1379 (2014).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Zhang, Y., Lu, K., Gao, Y., et al.: NEQR: a novel enhanced quantum representation of digital images [J]. Quantum Inf. Process. 12 (8), 2833–2860 (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Akhshani, A., Akhavan, A., Lim, S.C., et al.: An image encryption scheme based on quantum logistic map [J]. Commun. Nonlinear Sci. Numer. Simul. 17 (12), 4653–4661 (2012).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Abd El-Latif, A.A., Li, L., Wang, N., et al.: A new approach to chaotic image encryption based on quantum chaotic system, exploiting color spaces [J]. Signal Process. 93 (11), 2986–3000 (2013).

    Article  Google Scholar 

  • Zhou, R.G., Wu, Q., Zhang, M.Q., et al.: Quantum image encryption and decryption algorithms based on quantum image geometric transformations [J]. Int. J. Theor. Phys. 52 (6), 1802–1817 (2013).

    Article  MathSciNet  Google Scholar 

  • Zhang, W.W., Gao, F., Liu, B., et al.: A watermark strategy for quantum images based on quantum Fourier transform [J]. Quantum Inf. Process. 12 (2), 793–803 (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Song, X., Wang, S., Abd El-Latif, A.A., et al.: Dynamic watermarking scheme for quantum images based on Hadamard transform [J]. Multimed. Syst. 20 (4), 379–388 (2014).

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Song, X.H., Wang, S., Abd El-Latif, A.A., et al.: Quantum image encryption based on restricted geometric and color transformations [J]. Quantum Inf. Process. 13 (8), 1765–1787 (2014).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Wang, S., Song, X.H., Niu, X.M.: A novel encryption algorithm for quantum images based on quantum wavelet transform and diffusion [M]. Intelligent Data Analysis and Its Applications, Volume II. Springer International Publishing. 298, 243–250 (2014).

    Google Scholar 

  • Cao, G.H., Zhou, J., Zhang, Y.Z., et al.: Quantum chaotic image encryption with one time running key [J]. Int. J. Secur. Appl. 8 (4), 77–88 (2014).

    Google Scholar 

  • Yang, Y.G., Pan, Q.X., Sun, S.J., et al.: Novel image encryption based on quantum walks [J]. Sci. Rep. 5, 7784 (2015).

    Article  ADS  Google Scholar 

  • Zhou, N.R., Hua, T.X., Gong, L.H., et al.: Quantum image encryption based on generalized Arnold transform and double random-phase encoding [J]. Quantum Inf. Process. 14 (4), 1193–1213 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Hua, T.X., Chen, J.M., Pei D.J., et al.: Quantum image encryption algorithm based on image correlation decomposition [J]. Int. J. Theor. Phys. 54 (2), 526–537 (2015).

    Article  MATH  Google Scholar 

  • Wang, X., Chen, F., Wang, T.: A new compound mode of confusion and diffusion for block encryption of image based on chaos [J]. Commun. Nonlinear Sci. Numer. Simul. 15 (9), 2479–2485 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Chen, J.X., Zhu, Z.L., Fu, C., et al.: A fast image encryption scheme with a novel pixel swapping-based confusion approach [J]. Nonlinear Dyn. 77 (4), 1191–1207 (2014).

    Article  Google Scholar 

  • Bhatnagar, G., Wu, Q.M.J., Raman, B.: Discrete fractional wavelet transform and its application to multiple encryption [J]. Inform. Sci. 223, 297–316 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  • Hennelly, B.M., Sheridan, J.T.: Image encryption and the fractional Fourier transform [C]. Image International Society for Optics and Photonics, Ireland (2003).

    Google Scholar 

  • Lloyd, S.: Almost any quantum logic gate is universal [J]. Phys. Rev. Lett. 75 (2), 346–349 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  • Vedral, V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations [J]. Phys. Rev. A. 54 (1), 147–159 (1996).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61462061, 61262084 and 61561033), the Foundation for Young Scientists of Jiangxi Province (Jinggang Star) (Grant No. 20122BCB23002), the Natural Science Foundation of Jiangxi Province, China (grant no. 20151BAB207002), and the Research Foundation of the Education Department of Jiangxi Province (Grant No. GJJ14138).

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Correspondence to Nan-Run Zhou.

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Gong, LH., He, XT., Cheng, S. et al. Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations. Int J Theor Phys 55, 3234–3250 (2016). https://doi.org/10.1007/s10773-016-2954-6

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  • DOI: https://doi.org/10.1007/s10773-016-2954-6

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