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Erschienen in: Quantum Information Processing 7/2021

01.07.2021

Quantum multi-image compression-encryption scheme based on quantum discrete cosine transform and 4D hyper-chaotic Henon map

verfasst von: Jing-Yi Dai, Yan Ma, Nan-Run Zhou

Erschienen in: Quantum Information Processing | Ausgabe 7/2021

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Abstract

A new quantum multi-image compression and encryption algorithm combining quantum discrete cosine transform with 4D hyper-chaotic Henon map is proposed. The four original images are firstly transformed by quantum discrete cosine transform, and then the obtained frequency coefficient matrices are compressed with the measurement matrices to construct four compressed images. Subsequently, four compressed images are selected to reconstruct a new quantum image. Under the control of four initial values and two parameters, a quantum key image is constructed by a 1D chaotic sequence originated from the 4D hyper-chaotic Henon map, and XORed with the reconstructed quantum image. Ultimately, to enhance the security of the algorithm, the cycle shift operations controlled by the logistic map are employed to scramble the pixels of the produced quantum image to acquire the encryption image. Numerical simulations confirm the reliability and the security of the designed quantum multi-image compression and encryption algorithm.

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Literatur
1.
Zurück zum Zitat Deepak, V.K., Rajakumaran, C., Kavitha, R.: Chaos based encryption of quantum images. Multimed. Tools Appl. 79(5), 23849–23860 (2020)CrossRef Deepak, V.K., Rajakumaran, C., Kavitha, R.: Chaos based encryption of quantum images. Multimed. Tools Appl. 79(5), 23849–23860 (2020)CrossRef
2.
3.
Zurück zum Zitat Li, H.S., Zhu, Q., Zhou, R.G., Song, L., Yang, X.J.: Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state. Quantum Inf. Process. 13(4), 991–1011 (2014)ADSMathSciNetMATHCrossRef Li, H.S., Zhu, Q., Zhou, R.G., Song, L., Yang, X.J.: Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state. Quantum Inf. Process. 13(4), 991–1011 (2014)ADSMathSciNetMATHCrossRef
4.
Zurück zum Zitat Venegas-Andraca, S.E., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. Proc. SPIE Int. Soc. Opt. Eng. 5105, 1085–1090 (2003) Venegas-Andraca, S.E., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. Proc. SPIE Int. Soc. Opt. Eng. 5105, 1085–1090 (2003)
5.
Zurück zum Zitat Le, P.Q., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Inf. Process. 10(1), 63–84 (2011)MathSciNetMATHCrossRef Le, P.Q., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Inf. Process. 10(1), 63–84 (2011)MathSciNetMATHCrossRef
6.
Zurück zum Zitat Zhang, Y., Lu, K., Gao, Y.H., Wang, M.: NEQR: A novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 2833–2860 (2013)ADSMathSciNetMATHCrossRef Zhang, Y., Lu, K., Gao, Y.H., Wang, M.: NEQR: A novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 2833–2860 (2013)ADSMathSciNetMATHCrossRef
7.
Zurück zum Zitat Jiang, N., Wang, J., Mu, Y.: Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio. Quantum Inf. Process. 14(11), 4001–4026 (2015)ADSMathSciNetMATHCrossRef Jiang, N., Wang, J., Mu, Y.: Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio. Quantum Inf. Process. 14(11), 4001–4026 (2015)ADSMathSciNetMATHCrossRef
8.
Zurück zum Zitat Song, X.H., Wang, S., El-Latif, A., Niu, X.M.: Quantum image encryption based on restricted geometric and color transformations. Quantum Inf. Process. 13(8), 1765–1787 (2014)ADSMathSciNetMATHCrossRef Song, X.H., Wang, S., El-Latif, A., Niu, X.M.: Quantum image encryption based on restricted geometric and color transformations. Quantum Inf. Process. 13(8), 1765–1787 (2014)ADSMathSciNetMATHCrossRef
9.
Zurück zum Zitat Abd-El-Atty, B., El-Latif, A., Venegas-Andraca, S.E.: An encryption protocol for NEQR images based on one-particle quantum walks on a circle. Quantum Inf. Process. 18(9), 272 (2019)ADSCrossRef Abd-El-Atty, B., El-Latif, A., Venegas-Andraca, S.E.: An encryption protocol for NEQR images based on one-particle quantum walks on a circle. Quantum Inf. Process. 18(9), 272 (2019)ADSCrossRef
10.
Zurück zum Zitat Liu, X.B., Xiao, D., Liu, C.: Quantum image encryption algorithm based on bit-plane permutation and sine logistic map. Quantum Inf. Process. 19(8), 1570–1573 (2020)MathSciNetCrossRef Liu, X.B., Xiao, D., Liu, C.: Quantum image encryption algorithm based on bit-plane permutation and sine logistic map. Quantum Inf. Process. 19(8), 1570–1573 (2020)MathSciNetCrossRef
11.
Zurück zum Zitat Khan, M., Rasheed, A.: Permutation-based special linear transforms with application in quantum image encryption algorithm. Quantum Inf. Process. 18(10), 298 (2019)ADSCrossRef Khan, M., Rasheed, A.: Permutation-based special linear transforms with application in quantum image encryption algorithm. Quantum Inf. Process. 18(10), 298 (2019)ADSCrossRef
12.
Zurück zum Zitat Jiang, N., Dong, X., Hu, H., Ji, Z.X., Zhang, W.Y.: Quantum image encryption based on Henon mapping. Int. J. Theor. Phys. 58(3), 979–991 (2019)MathSciNetMATHCrossRef Jiang, N., Dong, X., Hu, H., Ji, Z.X., Zhang, W.Y.: Quantum image encryption based on Henon mapping. Int. J. Theor. Phys. 58(3), 979–991 (2019)MathSciNetMATHCrossRef
13.
Zurück zum Zitat Tan, R.C., Lei, T., Zhao, Q.M., Gong, L.H., Zhou, Z.H.: Quantum color image encryption algorithm based on a hyper-chaotic system and quantum Fourier transform. Int. J. Theor. Phys. 55(12), 5368–5384 (2016)MATHCrossRef Tan, R.C., Lei, T., Zhao, Q.M., Gong, L.H., Zhou, Z.H.: Quantum color image encryption algorithm based on a hyper-chaotic system and quantum Fourier transform. Int. J. Theor. Phys. 55(12), 5368–5384 (2016)MATHCrossRef
14.
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)ADSMathSciNetMATHCrossRef 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)ADSMathSciNetMATHCrossRef
15.
Zurück zum Zitat 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. Mod. Phys. Lett. A 34(26), 1950214 (2019)ADSMathSciNetMATHCrossRef 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. Mod. Phys. Lett. A 34(26), 1950214 (2019)ADSMathSciNetMATHCrossRef
16.
Zurück zum Zitat Hu, W.W., Zhou, R.G., Luo, J., Jiang, S.X., Luo, G.F.: Quantum image encryption algorithm based on Arnold scrambling and wavelet transforms. Quantum Inf. Process. 19(3), 82 (2020)ADSMathSciNetCrossRef Hu, W.W., Zhou, R.G., Luo, J., Jiang, S.X., Luo, G.F.: Quantum image encryption algorithm based on Arnold scrambling and wavelet transforms. Quantum Inf. Process. 19(3), 82 (2020)ADSMathSciNetCrossRef
17.
Zurück zum Zitat Ko, H.J., Huang, C.T., Horng, G., Wang, S.J.: Robust and blind image watermarking in DCT domain using inter-block coefficient correlation. Inform. Sciences 517, 128–147 (2020)CrossRef Ko, H.J., Huang, C.T., Horng, G., Wang, S.J.: Robust and blind image watermarking in DCT domain using inter-block coefficient correlation. Inform. Sciences 517, 128–147 (2020)CrossRef
18.
Zurück zum Zitat Pan, S.M., Wen, R.H., Zhou, Z.H., Zhou, N.R.: Optical multi-image encryption scheme based on discrete cosine transform and nonlinear fractional Mellin transform. Multimed. Tools Appl. 76(2), 2933–2953 (2017)CrossRef Pan, S.M., Wen, R.H., Zhou, Z.H., Zhou, N.R.: Optical multi-image encryption scheme based on discrete cosine transform and nonlinear fractional Mellin transform. Multimed. Tools Appl. 76(2), 2933–2953 (2017)CrossRef
19.
Zurück zum Zitat Klappenecker, A., Rotteler, M.: Discrete cosine transforms on quantum computers. Quantum Phys. 2(11), 464–468 (2001) Klappenecker, A., Rotteler, M.: Discrete cosine transforms on quantum computers. Quantum Phys. 2(11), 464–468 (2001)
20.
Zurück zum Zitat Li, X.Z., Chen, W.W., Wang, Y.Q.: Quantum image compression-encryption scheme based on quantum discrete cosine transform. Int. J. Theor. Phys. 57(9), 2904–2919 (2018)MATHCrossRef Li, X.Z., Chen, W.W., Wang, Y.Q.: Quantum image compression-encryption scheme based on quantum discrete cosine transform. Int. J. Theor. Phys. 57(9), 2904–2919 (2018)MATHCrossRef
21.
Zurück zum Zitat Chen, K.H., Yan, F., Abdullah, M.I., Zhao, J.P.: Dual quantum audio watermarking schemes based on quantum discrete cosine transform. Int. J. Theor. Phys. 58, 502–521 (2019)MATHCrossRef Chen, K.H., Yan, F., Abdullah, M.I., Zhao, J.P.: Dual quantum audio watermarking schemes based on quantum discrete cosine transform. Int. J. Theor. Phys. 58, 502–521 (2019)MATHCrossRef
22.
Zurück zum Zitat Jiang, N., Wen, Y.W., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223–1236 (2014)ADSMathSciNetMATHCrossRef Jiang, N., Wen, Y.W., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223–1236 (2014)ADSMathSciNetMATHCrossRef
23.
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)ADSMathSciNetMATHCrossRef 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)ADSMathSciNetMATHCrossRef
24.
Zurück zum Zitat 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), 164 (2017)ADSMathSciNetMATHCrossRef 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), 164 (2017)ADSMathSciNetMATHCrossRef
25.
Zurück zum Zitat Hou, C.G., Liu, X.B., Feng, S.Y.: Quantum image scrambling algorithm based on discrete Baker map. Mod. Phys. Lett. A 35(17), 2050145 (2020)ADSMathSciNetMATHCrossRef Hou, C.G., Liu, X.B., Feng, S.Y.: Quantum image scrambling algorithm based on discrete Baker map. Mod. Phys. Lett. A 35(17), 2050145 (2020)ADSMathSciNetMATHCrossRef
26.
Zurück zum Zitat Zhou, N.R., Huang, L.X., Gong, L.H., Zeng, Q.W.: Novel quantum image compression and encryption algorithm based on DQWT and 3D hyper-chaotic Henon map. Quantum Inf. Process. 19(9), 284 (2020)ADSMathSciNetCrossRef Zhou, N.R., Huang, L.X., Gong, L.H., Zeng, Q.W.: Novel quantum image compression and encryption algorithm based on DQWT and 3D hyper-chaotic Henon map. Quantum Inf. Process. 19(9), 284 (2020)ADSMathSciNetCrossRef
27.
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)MathSciNetMATHCrossRef 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)MathSciNetMATHCrossRef
28.
Zurück zum Zitat Liang, H.R., Tao, X.Y., Zhou, N.R.: Quantum image encryption based on generalized affine transform and logistic map. Quantum Inf. Process. 15(7), 2701–2724 (2016)ADSMathSciNetMATHCrossRef Liang, H.R., Tao, X.Y., Zhou, N.R.: Quantum image encryption based on generalized affine transform and logistic map. Quantum Inf. Process. 15(7), 2701–2724 (2016)ADSMathSciNetMATHCrossRef
29.
Zurück zum Zitat Ran, Q.W., Wang, L., Ma, J., Tan, L.Y., Yu, S.Y.: A quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections. Quantum Inf. Process. 17(8), 188 (2018)ADSMathSciNetMATHCrossRef Ran, Q.W., Wang, L., Ma, J., Tan, L.Y., Yu, S.Y.: A quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections. Quantum Inf. Process. 17(8), 188 (2018)ADSMathSciNetMATHCrossRef
30.
Zurück zum Zitat Zhou, N.R., Chen, W.W., Yan, X.Y., Wang, Y.Q.: Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system. Quantum Inf. Process. 17(6), 137 (2018)ADSMathSciNetMATHCrossRef Zhou, N.R., Chen, W.W., Yan, X.Y., Wang, Y.Q.: Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system. Quantum Inf. Process. 17(6), 137 (2018)ADSMathSciNetMATHCrossRef
31.
Zurück zum Zitat Musanna, F., Kumar, S.: Image encryption using quantum 3-D Baker map and generalized gray code coupled with fractional Chen’s chaotic system. Quantum Inf. Process. 19(8), 220 (2020)ADSMathSciNetCrossRef Musanna, F., Kumar, S.: Image encryption using quantum 3-D Baker map and generalized gray code coupled with fractional Chen’s chaotic system. Quantum Inf. Process. 19(8), 220 (2020)ADSMathSciNetCrossRef
32.
Zurück zum Zitat Pang, C.Y., Zhou, R.G., Hu, B.Q., Hu, W.W., El-Rafei, A.: Signal and image compression using quantum discrete cosine transform. Inf. Sci. 473, 121–141 (2019)MathSciNetMATHCrossRef Pang, C.Y., Zhou, R.G., Hu, B.Q., Hu, W.W., El-Rafei, A.: Signal and image compression using quantum discrete cosine transform. Inf. Sci. 473, 121–141 (2019)MathSciNetMATHCrossRef
33.
Zurück zum Zitat Jiang, N., Lu, X.W., Hu, H., Dang, Y.J., Cai, Y.Q.: A novel quantum image compression method based on JPEG. Int. J. Theor. Phys. 57(3), 611–636 (2018)MathSciNetMATHCrossRef Jiang, N., Lu, X.W., Hu, H., Dang, Y.J., Cai, Y.Q.: A novel quantum image compression method based on JPEG. Int. J. Theor. Phys. 57(3), 611–636 (2018)MathSciNetMATHCrossRef
34.
Zurück zum Zitat Rössler, O.E., Klein, M., Baier, G., Parisi, J., Hudson, J.L.: Sierpin´ski sponge in a simple generic diffeomorphism. Comput. Phys. 4(5), 494–498 (1990)ADSCrossRef Rössler, O.E., Klein, M., Baier, G., Parisi, J., Hudson, J.L.: Sierpin´ski sponge in a simple generic diffeomorphism. Comput. Phys. 4(5), 494–498 (1990)ADSCrossRef
35.
Zurück zum Zitat Vedral, V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations. Physics Review A 54(1), 147 (1996)ADSMathSciNetCrossRef Vedral, V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations. Physics Review A 54(1), 147 (1996)ADSMathSciNetCrossRef
36.
Zurück zum Zitat Lu, X.W., Jiang, N., Hu, H., Dang, Y.J., Cai, Y.Q.: Quantum adder for superposition states. Int. J. Theor. Phys. 57(9), 2575–2584 (2018)MathSciNetMATHCrossRef Lu, X.W., Jiang, N., Hu, H., Dang, Y.J., Cai, Y.Q.: Quantum adder for superposition states. Int. J. Theor. Phys. 57(9), 2575–2584 (2018)MathSciNetMATHCrossRef
37.
Zurück zum Zitat Li, H.S., Fan, P., Xia, H., Long, G.L.: Efficient quantum arithmetic operation circuits for quantum image processing. Sci. China Phys. Mech. Astron. 63(8), 280311 (2020)ADSCrossRef Li, H.S., Fan, P., Xia, H., Long, G.L.: Efficient quantum arithmetic operation circuits for quantum image processing. Sci. China Phys. Mech. Astron. 63(8), 280311 (2020)ADSCrossRef
38.
Zurück zum Zitat 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)MATHCrossRef 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)MATHCrossRef
39.
Zurück zum Zitat Mohimani, H., Babaie-Zadeh, M., Jutten, C.: A Fast Approach for overcomplete sparse decomposition based on smoothed l-0 norm. IEEE Trans. Signal Process. 57(1), 289–301 (2009)ADSMathSciNetMATHCrossRef Mohimani, H., Babaie-Zadeh, M., Jutten, C.: A Fast Approach for overcomplete sparse decomposition based on smoothed l-0 norm. IEEE Trans. Signal Process. 57(1), 289–301 (2009)ADSMathSciNetMATHCrossRef
40.
Zurück zum Zitat Luo, Y.L., Lin, J., Liu, J.X., Wei, D.Q., Cao, L.C., Zhou, R.L., Cao, Yi., Ding, X.M.: A robust image encryption algorithm based on Chua’s circuit and compressive sensing. Signal Process. 161, 227–247 (2019)CrossRef Luo, Y.L., Lin, J., Liu, J.X., Wei, D.Q., Cao, L.C., Zhou, R.L., Cao, Yi., Ding, X.M.: A robust image encryption algorithm based on Chua’s circuit and compressive sensing. Signal Process. 161, 227–247 (2019)CrossRef
41.
Zurück zum Zitat Zhou, N.R., Yan, X.Y., Liang, H.R., Tao, X.Y., Gong, L.H.: Multi-image encryption scheme based on quantum 3D Arnold transform and scaled Zhongtang chaotic system. Quantum Inf. Process. 17(12), 338 (2018)ADSMATHCrossRef Zhou, N.R., Yan, X.Y., Liang, H.R., Tao, X.Y., Gong, L.H.: Multi-image encryption scheme based on quantum 3D Arnold transform and scaled Zhongtang chaotic system. Quantum Inf. Process. 17(12), 338 (2018)ADSMATHCrossRef
42.
Zurück zum Zitat Hu, Y.Q., Xie, X.W., Liu, X.B., Zhou, N.R.: Quantum multi-image encryption based on iteration Arnold transform with parameters and image correlation decomposition. Int. J. Theor. Phys. 56(7), 2192–2205 (2017)MathSciNetMATHCrossRef Hu, Y.Q., Xie, X.W., Liu, X.B., Zhou, N.R.: Quantum multi-image encryption based on iteration Arnold transform with parameters and image correlation decomposition. Int. J. Theor. Phys. 56(7), 2192–2205 (2017)MathSciNetMATHCrossRef
43.
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
44.
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)MathSciNetMATHCrossRef Bhatnagar, G., Wu, Q.M.J., Raman, B.: Discrete fractional wavelet transform and its application to multiple encryption. Inf. Sci. 223, 297–316 (2013)MathSciNetMATHCrossRef
45.
Zurück zum Zitat Ralph, T.C., Resch, K.J., Gilchrist, A.: Efficient Toffoli gates using qubits. Phys. Rev. A 75(2), 441–445 (2008) Ralph, T.C., Resch, K.J., Gilchrist, A.: Efficient Toffoli gates using qubits. Phys. Rev. A 75(2), 441–445 (2008)
Metadaten
Titel
Quantum multi-image compression-encryption scheme based on quantum discrete cosine transform and 4D hyper-chaotic Henon map
verfasst von
Jing-Yi Dai
Yan Ma
Nan-Run Zhou
Publikationsdatum
01.07.2021
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 7/2021
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-021-03187-w

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