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.
Similar content being viewed by others
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).
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).
Wang, X., Zhao, J., Liu, H.: A new image encryption algorithm based on chaos [J]. Opt. Commun. 285 (5), 562–566 (2012).
Lian, S.: A block cipher based on chaotic neural networks [J]. Neurocomputing. 72 (4–6), 1296–1301 (2009).
Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps [J]. Int. J. Bifurcation Chaos. 8 (6), 1259–1284 (1998).
Guan, Z.H., Huang, F., Guan, W.: Chaos-based image encryption algorithm [J]. Phys. Lett. A. 346 (1), 153–157 (2005).
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).
Wang, X., Guo, K.: A new image alternate encryption algorithm based on chaotic map [J]. Nonlinear Dyn. 76 (4), 1943–1950 (2014).
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).
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).
Gao, T., Chen, Z.: A new image encryption algorithm based on hyper-chaos [J]. Phys. Lett. A. 372 (4), 394–400 (2008).
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).
Hermassi, H., Rhouma, R., Belghith, S.: Improvement of an image encryption algorithm based on hyper-chaos [J]. Telecommun. Syst. 52 (2), 539–549 (2013).
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).
Norouzi, B., Mirzakuchaki, S.: A fast color image encryption algorithm based on hyper-chaotic systems [J]. Nonlinear Dyn. 78 (2), 995–1015 (2014).
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).
Venegas-Andraca, S.E., Ball, J.L.: Processing images in entangled quantum systems [J]. Quantum Inf. Process. 9 (1), 1–11 (2010).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert image scrambling [J]. Int. J. Theor. Phys. 53 (7), 2463–2484 (2014).
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).
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).
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).
Yang, Y.G., Pan, Q.X., Sun, S.J., et al.: Novel image encryption based on quantum walks [J]. Sci. Rep. 5, 7784 (2015).
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).
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).
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).
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).
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).
Hennelly, B.M., Sheridan, J.T.: Image encryption and the fractional Fourier transform [C]. Image International Society for Optics and Photonics, Ireland (2003).
Lloyd, S.: Almost any quantum logic gate is universal [J]. Phys. Rev. Lett. 75 (2), 346–349 (1995).
Vedral, V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations [J]. Phys. Rev. A. 54 (1), 147–159 (1996).
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).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-016-2954-6