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Erschienen in: Quantum Information Processing 6/2017

01.06.2017

Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations

verfasst von: Nanrun Zhou, Yiqun Hu, Lihua Gong, Guangyong Li

Erschienen in: Quantum Information Processing | Ausgabe 6/2017

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Abstract

A new quantum image encryption scheme is suggested by using the iterative generalized Arnold transforms and the quantum image cycle shift operations. The times of the quantum image cycle shift operations are controlled by a hyper-chaotic sequence generated by a new 4D hyper-chaotic system. The image pixels are scrambled by the iterative generalized Arnold transform, and the values of the pixels are altered by the quantum image cycle shift operations. The four initial conditions of the new 4D hyper-chaotic system are exploited to control the two parameters, the iterative rounds of the generalized Arnold transform and the times of the quantum image cycle shift operations, respectively. Thus, the main keys of the proposed quantum image encryption scheme are the four initial conditions of the new 4D hyper-chaotic system and the key space is relatively large enough. Simulation results and theoretical analyses demonstrate that the proposed quantum image encryption scheme outperforms its classical counterparts apparently.

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Literatur
1.
2.
Zurück zum Zitat Guan, Z.H., Huang, F., Guan, W.: Chaos-based image encryption algorithm. Phys. Lett. A 346(1), 153–157 (2005)ADSCrossRefMATH Guan, Z.H., Huang, F., Guan, W.: Chaos-based image encryption algorithm. Phys. Lett. A 346(1), 153–157 (2005)ADSCrossRefMATH
3.
Zurück zum Zitat Gao, H., Zhang, Y., Liang, S., Li, D.: A new chaotic algorithm for image encryption. Chaos Solitons Fractals 29(2), 393–399 (2006)ADSCrossRefMATH Gao, H., Zhang, Y., Liang, S., Li, D.: A new chaotic algorithm for image encryption. Chaos Solitons Fractals 29(2), 393–399 (2006)ADSCrossRefMATH
4.
Zurück zum Zitat Wang, X., Guo, K.: A new image alternate encryption algorithm based on chaotic map. Nonlinear Dyn. 76(4), 1943–1950 (2014)CrossRefMATH Wang, X., Guo, K.: A new image alternate encryption algorithm based on chaotic map. Nonlinear Dyn. 76(4), 1943–1950 (2014)CrossRefMATH
5.
Zurück zum Zitat Ye, G., Wong, K.W.: An efficient chaotic image encryption algorithm based on a generalized Arnold map. Nonlinear Dyn. 69(4), 2079–2087 (2012)MathSciNetCrossRef Ye, G., Wong, K.W.: An efficient chaotic image encryption algorithm based on a generalized Arnold map. Nonlinear Dyn. 69(4), 2079–2087 (2012)MathSciNetCrossRef
6.
Zurück zum Zitat Chen, J.X., Zhu, Z.L., Fu, C., Yu, H.: Optical image encryption scheme using 3-D chaotic map based joint image scrambling and random encoding in gyrator domains. Opt. Commun. 341, 263–270 (2015)CrossRef Chen, J.X., Zhu, Z.L., Fu, C., Yu, H.: Optical image encryption scheme using 3-D chaotic map based joint image scrambling and random encoding in gyrator domains. Opt. Commun. 341, 263–270 (2015)CrossRef
7.
Zurück zum Zitat Peng, J., Zhang, D., Liao, X.: A digital image encryption algorithm based on hyper-chaotic cellular Neural network. Fundamenta Informaticae 90(3), 269–282 (2009)MathSciNet Peng, J., Zhang, D., Liao, X.: A digital image encryption algorithm based on hyper-chaotic cellular Neural network. Fundamenta Informaticae 90(3), 269–282 (2009)MathSciNet
8.
Zurück zum Zitat Hermassi, H., Rhouma, R., Belghith, S.: Improvement of an image encryption algorithm based on hyper-chaos. Telecommun. Syst. 52(2), 539–549 (2013) Hermassi, H., Rhouma, R., Belghith, S.: Improvement of an image encryption algorithm based on hyper-chaos. Telecommun. Syst. 52(2), 539–549 (2013)
9.
Zurück zum Zitat Zhu, H., Zhao, C., Zhang, X.: A novel image encryption-compression scheme using hyper-chaos and Chinese remainder theorem. Signal Process. Image Commun. 28(6), 670–680 (2013)CrossRef Zhu, H., Zhao, C., Zhang, X.: A novel image encryption-compression scheme using hyper-chaos and Chinese remainder theorem. Signal Process. Image Commun. 28(6), 670–680 (2013)CrossRef
10.
Zurück zum Zitat Tong, X.J., Liu, Y., Zhang, M., Xu, H., Wang, Z.: An image encryption scheme based on hyperchaotic rabinovich and exponential chaos map. Entropy 17(1), 181–196 (2015)ADSCrossRef Tong, X.J., Liu, Y., Zhang, M., Xu, H., Wang, Z.: An image encryption scheme based on hyperchaotic rabinovich and exponential chaos map. Entropy 17(1), 181–196 (2015)ADSCrossRef
11.
Zurück zum Zitat Norouzi, B., Mirzakuchaki, S.: A fast color image encryption algorithm based on hyper-chaotic systems. Nonlinear Dyn. 78(2), 995–1015 (2014)CrossRef Norouzi, B., Mirzakuchaki, S.: A fast color image encryption algorithm based on hyper-chaotic systems. Nonlinear Dyn. 78(2), 995–1015 (2014)CrossRef
12.
Zurück zum Zitat Gao, T., Gu, Q., Emmanuel, S.: A novel image authentication scheme based on hyper-chaotic cell neural network. Chaos Solitons Fractals 42(1), 548–553 (2009)ADSCrossRef Gao, T., Gu, Q., Emmanuel, S.: A novel image authentication scheme based on hyper-chaotic cell neural network. Chaos Solitons Fractals 42(1), 548–553 (2009)ADSCrossRef
13.
Zurück zum Zitat Zhang, Y., Wen, W., Su, M., Li, M.: Cryptanalyzing a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Optik 125(4), 1562–1564 (2014)ADSCrossRef Zhang, Y., Wen, W., Su, M., Li, M.: Cryptanalyzing a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Optik 125(4), 1562–1564 (2014)ADSCrossRef
14.
Zurück zum Zitat Özkaynak, F., Yavuz, S.: Analysis and improvement of a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Nonlinear Dyn. 78(2), 1311–1320 (2014)CrossRefMATH Özkaynak, F., Yavuz, S.: Analysis and improvement of a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Nonlinear Dyn. 78(2), 1311–1320 (2014)CrossRefMATH
15.
Zurück zum Zitat Zhou, N.R., Pan, S.M., Cheng, S., Zhou, Z.H.: Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing. Optics Laser Technol. 82, 121–133 (2016)ADSCrossRef Zhou, N.R., Pan, S.M., Cheng, S., Zhou, Z.H.: Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing. Optics Laser Technol. 82, 121–133 (2016)ADSCrossRef
16.
Zurück zum Zitat Zhou, L., Chen, Z., Wang, Z., Wang, J.: On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system. Chaos Solitons Fractals 91, 148–156 (2016)ADSMathSciNetCrossRef Zhou, L., Chen, Z., Wang, Z., Wang, J.: On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system. Chaos Solitons Fractals 91, 148–156 (2016)ADSMathSciNetCrossRef
17.
Zurück zum Zitat Venegas-Andraca, S.E., Ball, J.L.: Processing images in entangled quantum systems. Quantum Inf. Process. 9(1), 1–11 (2010)MathSciNetCrossRef Venegas-Andraca, S.E., Ball, J.L.: Processing images in entangled quantum systems. Quantum Inf. Process. 9(1), 1–11 (2010)MathSciNetCrossRef
18.
Zurück zum Zitat 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
19.
Zurück zum Zitat 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. In: Intelligent Signal Processing (WISP), 2011 IEEE 7th International Symposium on Floriana, pp. 62–67 (2011) 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. In: Intelligent Signal Processing (WISP), 2011 IEEE 7th International Symposium on Floriana, pp. 62–67 (2011)
20.
Zurück zum Zitat 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)CrossRef 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)CrossRef
21.
Zurück zum Zitat Zhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12(9), 3101–3126 (2013)ADSMathSciNetMATH Zhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12(9), 3101–3126 (2013)ADSMathSciNetMATH
22.
Zurück zum Zitat 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), 1–27 (2014)MathSciNetCrossRefMATH 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), 1–27 (2014)MathSciNetCrossRefMATH
23.
24.
Zurück zum Zitat Le, P.Q., Iliyasu, A.M., Dong, F.Y., Hirota, K.: Fast geometric transformations on quantum images. IAENG Int. J. Appl. Math. 40(3), 113–123 (2010)MathSciNetMATH Le, P.Q., Iliyasu, A.M., Dong, F.Y., Hirota, K.: Fast geometric transformations on quantum images. IAENG Int. J. Appl. Math. 40(3), 113–123 (2010)MathSciNetMATH
25.
Zurück zum Zitat Le, P.Q., Iliyasu, A.M., Dong, F.Y., Hirota, K.: Strategies for designing geometric transformations on quantum images. Theor. Comput. Sci. 412(15), 1406–1418 (2011)MathSciNetCrossRefMATH Le, P.Q., Iliyasu, A.M., Dong, F.Y., Hirota, K.: Strategies for designing geometric transformations on quantum images. Theor. Comput. Sci. 412(15), 1406–1418 (2011)MathSciNetCrossRefMATH
26.
Zurück zum Zitat Iliyasu, A.M., Le, P.Q., Dong, F.Y., Hirota, K.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186(1), 126–149 (2012)MathSciNetCrossRefMATH Iliyasu, A.M., Le, P.Q., Dong, F.Y., Hirota, K.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186(1), 126–149 (2012)MathSciNetCrossRefMATH
27.
Zurück zum Zitat 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)ADSMathSciNetCrossRefMATH 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)ADSMathSciNetCrossRefMATH
29.
Zurück zum Zitat Beach, G., Lomont, C., Cohen, C.: Quantum image processing. In: Proceedings of The 2003 IEEE Workshop on Applied Imagery Pattern Recognition, pp. 39–44 (2003) Beach, G., Lomont, C., Cohen, C.: Quantum image processing. In: Proceedings of The 2003 IEEE Workshop on Applied Imagery Pattern Recognition, pp. 39–44 (2003)
30.
Zurück zum Zitat Venegas-Andraca, S.E., Bose, S.: Quantum computation and image processing: new trends in artificial intelligence. In: Proceedings of the International Conference on Artificial Intelligence IJCAI-03, pp. 1563–1564 (2003) Venegas-Andraca, S.E., Bose, S.: Quantum computation and image processing: new trends in artificial intelligence. In: Proceedings of the International Conference on Artificial Intelligence IJCAI-03, pp. 1563–1564 (2003)
31.
Zurück zum Zitat Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. In: Proceedings of the SPIE Conference Quantum Information and Computation, pp. 137–147 (2003) Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. In: Proceedings of the SPIE Conference Quantum Information and Computation, pp. 137–147 (2003)
32.
Zurück zum Zitat 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)ADSMathSciNetCrossRefMATH 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)ADSMathSciNetCrossRefMATH
33.
Zurück zum Zitat 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)MathSciNetCrossRef 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)MathSciNetCrossRef
34.
Zurück zum Zitat 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)CrossRef 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)CrossRef
35.
Zurück zum Zitat Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert Image Scrambling. Int. J. Theor. Phys. 53(7), 2463–2484 (2014)CrossRefMATH Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert Image Scrambling. Int. J. Theor. Phys. 53(7), 2463–2484 (2014)CrossRefMATH
36.
Zurück zum Zitat 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)ADSMathSciNetCrossRefMATH 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)ADSMathSciNetCrossRefMATH
37.
Zurück zum Zitat Jiang, N., Wu, W.Y., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223–1236 (2014)ADSMathSciNetCrossRefMATH Jiang, N., Wu, W.Y., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223–1236 (2014)ADSMathSciNetCrossRefMATH
38.
Zurück zum Zitat Jiang, N., Wang, L.: Analysis and improvement of quantum Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(7), 1545–1551 (2014)ADSMathSciNetCrossRefMATH Jiang, N., Wang, L.: Analysis and improvement of quantum Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(7), 1545–1551 (2014)ADSMathSciNetCrossRefMATH
39.
Zurück zum Zitat Hua, T.X., Chen, J., Pei, D.J., Zhang, W.Q., Zhou, N.R.: Quantum image encryption algorithm based on image correlation decomposition. Int. J. Theor. Phys. 54(2), 526–537 (2014)CrossRefMATH Hua, T.X., Chen, J., Pei, D.J., Zhang, W.Q., Zhou, N.R.: Quantum image encryption algorithm based on image correlation decomposition. Int. J. Theor. Phys. 54(2), 526–537 (2014)CrossRefMATH
40.
Zurück zum Zitat 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)ADSMathSciNetCrossRefMATH 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)ADSMathSciNetCrossRefMATH
41.
Zurück zum Zitat Yang, Y.G., Pan, Q.X., Sun, S.J., Xu, P.: Novel image encryption based on quantum walks. Sci. Rep. 5, 7784 (2015)CrossRef Yang, Y.G., Pan, Q.X., Sun, S.J., Xu, P.: Novel image encryption based on quantum walks. Sci. Rep. 5, 7784 (2015)CrossRef
42.
Zurück zum Zitat Gong, L.H., He, X.T., Cheng, S., Hua, T.X., Zhou, N.R.: Quantum image encryption algorithm based on quantum image XOR operations. Int. J. Theor. Phys. 55(7):3234–3250 (2016) Gong, L.H., He, X.T., Cheng, S., Hua, T.X., Zhou, N.R.: Quantum image encryption algorithm based on quantum image XOR operations. Int. J. Theor. Phys. 55(7):3234–3250 (2016)
43.
Zurück zum Zitat Arnold, V.I., Avez, A.: Ergodic Problems of Classical Mechanics. Benjamin, New York (1968)MATH Arnold, V.I., Avez, A.: Ergodic Problems of Classical Mechanics. Benjamin, New York (1968)MATH
44.
Zurück zum Zitat Wang, X., Chen, F., Wang, T.: A new compound mode of confusion and diffusion for block encryption of image based on chaos. Commun. Nonlinear Sci. Numer. Simul. 15(9), 2479–2485 (2010)ADSMathSciNetCrossRefMATH Wang, X., Chen, F., Wang, T.: A new compound mode of confusion and diffusion for block encryption of image based on chaos. Commun. Nonlinear Sci. Numer. Simul. 15(9), 2479–2485 (2010)ADSMathSciNetCrossRefMATH
45.
Zurück zum Zitat Chen, J.X., Zhu, Z.L., Fu, C., Yu, H.: A fast image encryption scheme with a novel pixel swapping-based confusion approach. Nonlinear Dyn. 77(4), 1191–1207 (2014)CrossRef Chen, J.X., Zhu, Z.L., Fu, C., Yu, H.: A fast image encryption scheme with a novel pixel swapping-based confusion approach. Nonlinear Dyn. 77(4), 1191–1207 (2014)CrossRef
46.
Zurück zum Zitat Bhatnagar, G., Wu, Q.M.J., Raman, B.: Discrete fractional wavelet transform and its application to multiple encryption. Inf. Sci. 223, 297–316 (2013)MathSciNetCrossRefMATH Bhatnagar, G., Wu, Q.M.J., Raman, B.: Discrete fractional wavelet transform and its application to multiple encryption. Inf. Sci. 223, 297–316 (2013)MathSciNetCrossRefMATH
47.
Zurück zum Zitat Hennelly, B.M., Sheridan, J.T.: Image encryption and the fractional Fourier transform. In: International Society for Optics and Photonics, Ireland, pp. 126–137. (2003) Hennelly, B.M., Sheridan, J.T.: Image encryption and the fractional Fourier transform. In: International Society for Optics and Photonics, Ireland, pp. 126–137. (2003)
48.
Zurück zum Zitat Liu, Y., Wang, J., Fan, J., Gong, L.: Image encryption based on chaotic system and dynamic S-boxes composed of DNA sequences. Multimed. Tools Appl. 75, 4363–4382 (2016)CrossRef Liu, Y., Wang, J., Fan, J., Gong, L.: Image encryption based on chaotic system and dynamic S-boxes composed of DNA sequences. Multimed. Tools Appl. 75, 4363–4382 (2016)CrossRef
49.
Zurück zum Zitat Zhou, N.R., Yang, J.P., Tan, C.F., Zhou, Z.: Double-image encryption scheme combining DWT-based compressive sensing with discrete fractional random transform. Optics Commun. 354, 112–121 (2015)ADSCrossRef Zhou, N.R., Yang, J.P., Tan, C.F., Zhou, Z.: Double-image encryption scheme combining DWT-based compressive sensing with discrete fractional random transform. Optics Commun. 354, 112–121 (2015)ADSCrossRef
Metadaten
Titel
Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations
verfasst von
Nanrun Zhou
Yiqun Hu
Lihua Gong
Guangyong Li
Publikationsdatum
01.06.2017
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 6/2017
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-017-1612-0

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