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Published in: Quantum Information Processing 11/2013

01-11-2013

Novel image encryption/decryption based on quantum Fourier transform and double phase encoding

Authors: Yu-Guang Yang, Juan Xia, Xin Jia, Hua Zhang

Published in: Quantum Information Processing | Issue 11/2013

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Abstract

A novel gray-level image encryption/decryption scheme is proposed, which is based on quantum Fourier transform and double random-phase encoding technique. The biggest contribution of our work lies in that it is the first time that the double random-phase encoding technique is generalized to quantum scenarios. As the encryption keys, two phase coding operations are applied in the quantum image spatial domain and the Fourier transform domain respectively. Only applying the correct keys, the original image can be retrieved successfully. Because all operations in quantum computation must be invertible, decryption is the inverse of the encryption process. A detailed theoretical analysis is given to clarify its robustness, computational complexity and advantages over its classical counterparts. It paves the way for introducing more optical information processing techniques into quantum scenarios.

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Literature
1.
go back to reference Bourbakis, N., Alexopoulos, C.: Picture data encryption using SCAN pattern. Pattern Recognit. 25(6), 567–581 (1992)CrossRef Bourbakis, N., Alexopoulos, C.: Picture data encryption using SCAN pattern. Pattern Recognit. 25(6), 567–581 (1992)CrossRef
2.
go back to reference Refregier, R., Javidi, B.: Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20(7), 767–769 (1995)CrossRefADS Refregier, R., Javidi, B.: Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20(7), 767–769 (1995)CrossRefADS
3.
go back to reference Liu, Z., Guo, Q., Xu, L., Ahmad, M.A., Liu, S.: Double image encryption by using iterative random binary encoding in gyrator domains. Opt. Exp. 18(11), 12033–12043 (2010) Liu, Z., Guo, Q., Xu, L., Ahmad, M.A., Liu, S.: Double image encryption by using iterative random binary encoding in gyrator domains. Opt. Exp. 18(11), 12033–12043 (2010)
4.
go back to reference Chang, C.C., Hwang, M.S., Chen, T.S.: A new encryption algorithm for image cryptosystems. J. Syst. Softw. 58(7), 83–91 (2001)CrossRef Chang, C.C., Hwang, M.S., Chen, T.S.: A new encryption algorithm for image cryptosystems. J. Syst. Softw. 58(7), 83–91 (2001)CrossRef
5.
go back to reference Chang, H.K.L., Liu, J.L.: A linear quad tree compression scheme for image encryption. Signal Process. 10(4), 279–290 (1997) Chang, H.K.L., Liu, J.L.: A linear quad tree compression scheme for image encryption. Signal Process. 10(4), 279–290 (1997)
6.
go back to reference Cheng, H., Li, X.B.: Partial encryption of compressed image and videos. IEEE Trans. Signal Process. 48(8), 2439–2451 (2000)CrossRefADS Cheng, H., Li, X.B.: Partial encryption of compressed image and videos. IEEE Trans. Signal Process. 48(8), 2439–2451 (2000)CrossRefADS
7.
go back to reference Zhang, G., Liu, Q.: A novel image encryption method based on total shuffling scheme. Opt. Commun. 284(12), 2775–2780 (2011)CrossRefADS Zhang, G., Liu, Q.: A novel image encryption method based on total shuffling scheme. Opt. Commun. 284(12), 2775–2780 (2011)CrossRefADS
8.
go back to reference Scharinger, J.: Fast encryption of image data using chaotic Kolmogorov flow. J. Electron. Eng. 7(2), 318–325 (1998) Scharinger, J.: Fast encryption of image data using chaotic Kolmogorov flow. J. Electron. Eng. 7(2), 318–325 (1998)
9.
go back to reference Wang, B., Sun, C.-C., Su, W.-C.: Shift-tolerance property of an optical double-random phase-encoding encryption system. Appl. Opt. 39(26), 4788–4793 (2000)CrossRefADS Wang, B., Sun, C.-C., Su, W.-C.: Shift-tolerance property of an optical double-random phase-encoding encryption system. Appl. Opt. 39(26), 4788–4793 (2000)CrossRefADS
10.
go back to reference Bahram, J., Arnaud, S., Guanshen, Z., et al.: Fault tolerance properties of a double phase encoding encryption technique. Opt. Eng. 36(4), 992–998 (1997)CrossRef Bahram, J., Arnaud, S., Guanshen, Z., et al.: Fault tolerance properties of a double phase encoding encryption technique. Opt. Eng. 36(4), 992–998 (1997)CrossRef
11.
go back to reference Frauel, Y., Castro, A., Naughton, T., et al.: Resistance of the double random phase encryption against various attacks. Opt. Exp. 15(16), 10253–10265 (2007)CrossRefADS Frauel, Y., Castro, A., Naughton, T., et al.: Resistance of the double random phase encryption against various attacks. Opt. Exp. 15(16), 10253–10265 (2007)CrossRefADS
12.
go back to reference Peng, X., Zhang, P., Wei, H., et al.: Known-plaintext attack on optical encryption scheme based on double random phase keys. Opt. Lett. 31(8), 1044–1046 (2006)CrossRefADS Peng, X., Zhang, P., Wei, H., et al.: Known-plaintext attack on optical encryption scheme based on double random phase keys. Opt. Lett. 31(8), 1044–1046 (2006)CrossRefADS
13.
go back to reference Carnicer, A., Montes-Usategui, M., Arcos, S., et al.: Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys. Opt. Lett. 30(13), 1644–1646 (2005)CrossRefADS Carnicer, A., Montes-Usategui, M., Arcos, S., et al.: Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys. Opt. Lett. 30(13), 1644–1646 (2005)CrossRefADS
14.
go back to reference 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)CrossRefADS 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)CrossRefADS
15.
go back to reference Shor, P.W.: In Proceedings of 35th Annual Symposium on the Foundations of Computer Science, Santa Fe, New Mex-ico, p. 124 (1994) Shor, P.W.: In Proceedings of 35th Annual Symposium on the Foundations of Computer Science, Santa Fe, New Mex-ico, p. 124 (1994)
16.
go back to reference Grover, L.K.: In Proceedings of 28th Annual ACM Symposium on Theory of Computing, New York, p. 212 (1996) Grover, L.K.: In Proceedings of 28th Annual ACM Symposium on Theory of Computing, New York, p. 212 (1996)
17.
go back to reference Bennett, C.H., Brassard, G.: In Proceedings of IEEE International Conference on Computers, Systems and Signal, Bangalore, India, p.175 (1984) Bennett, C.H., Brassard, G.: In Proceedings of IEEE International Conference on Computers, Systems and Signal, Bangalore, India, p.175 (1984)
18.
go back to reference Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)CrossRefADS Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)CrossRefADS
19.
go back to reference 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
20.
go back to reference 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)
21.
go back to reference Latorre, J.I.: Image compression and entanglement, arXiv:quant-ph/0510031(2005) Latorre, J.I.: Image compression and entanglement, arXiv:quant-ph/0510031(2005)
22.
go back to reference 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
23.
go back to reference Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, New York (2000)MATH Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, New York (2000)MATH
24.
go back to reference Klappenecker, A., Rotteler, M.: Discrete cosine transforms on quantum computers. In: Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis, pp. 464–468 (2001) Klappenecker, A., Rotteler, M.: Discrete cosine transforms on quantum computers. In: Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis, pp. 464–468 (2001)
25.
go back to reference Tseng, C.C., Hwang, T.M.: Quantum circuit design of \(8\times 8\) discrete cosine transforms using its fast computation on graph. In: Proceedings of ISCAS 2005, pp. 828–831 (2005) Tseng, C.C., Hwang, T.M.: Quantum circuit design of \(8\times 8\) discrete cosine transforms using its fast computation on graph. In: Proceedings of ISCAS 2005, pp. 828–831 (2005)
26.
go back to reference Fijany, A., Williams, C.P.: Quantum wavelet transform: fast algorithm and complete circuits, URL: arXiv:quantph/9809004 (1998) Fijany, A., Williams, C.P.: Quantum wavelet transform: fast algorithm and complete circuits, URL: arXiv:quantph/9809004 (1998)
27.
go back to reference Labunets, V., Labunets-Rundblad, E., Egiazarian, K., Astola, J.: Fast classical and quantum fractional Walsh transforms. In: Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis, pp. 558–563 (2001) Labunets, V., Labunets-Rundblad, E., Egiazarian, K., Astola, J.: Fast classical and quantum fractional Walsh transforms. In: Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis, pp. 558–563 (2001)
28.
go back to reference Tseng, C.C., Hwang, T.M.: Quantum circuit design of \(8\times 8\) discrete Hartley transform. ISCAS III, 397–400 (2004) Tseng, C.C., Hwang, T.M.: Quantum circuit design of \(8\times 8\) discrete Hartley transform. ISCAS III, 397–400 (2004)
29.
go back to reference Tseng, C.C., Hwang, T.M.: Quantum circuit design of discrete Hartley transform using recursive decomposition formula. ISCAS 1–6, 824–827 (2005) Tseng, C.C., Hwang, T.M.: Quantum circuit design of discrete Hartley transform using recursive decomposition formula. ISCAS 1–6, 824–827 (2005)
30.
go back to reference Lomont, C.: Quantum convolution and quantum correlation algorithms are physically impossible, arXiv:quantph/0309070 (2003) Lomont, C.: Quantum convolution and quantum correlation algorithms are physically impossible, arXiv:quantph/0309070 (2003)
31.
go back to reference Iliyasu, A.M., et al.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186(1), 126–149 (2012)MathSciNetCrossRefMATH Iliyasu, A.M., et al.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186(1), 126–149 (2012)MathSciNetCrossRefMATH
32.
go back to reference 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)MathSciNetCrossRefADSMATH 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)MathSciNetCrossRefADSMATH
33.
go back to reference 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 (2012)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 (2012)MathSciNetCrossRef
34.
go back to reference Yang, Y.G., Jia, X., Xu, P., Tian, J.: Analysis and improvement of the watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. doi:10.1007/s11128-013-0561-5 (2013) Yang, Y.G., Jia, X., Xu, P., Tian, J.: Analysis and improvement of the watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. doi:10.​1007/​s11128-013-0561-5 (2013)
35.
go back to reference Gaitan, F.: Quantum Error Correction and Fault Tolerant Quantum Computing. CRC Press, Taylor and Francis Group, UK (2008)CrossRefMATH Gaitan, F.: Quantum Error Correction and Fault Tolerant Quantum Computing. CRC Press, Taylor and Francis Group, UK (2008)CrossRefMATH
36.
go back to reference Yan, F., Le, P.Q., Iliyasu, A.M., Sun, B., Garcia, J.A., Dong, F., Hirota, K.: Assessing the similarity of quantum images based on probability measurements. In 2012 IEEE World Congress on Computational Intelligence, Brisbane, 10–15 June 2012, pp. 1–6 (2012) Yan, F., Le, P.Q., Iliyasu, A.M., Sun, B., Garcia, J.A., Dong, F., Hirota, K.: Assessing the similarity of quantum images based on probability measurements. In 2012 IEEE World Congress on Computational Intelligence, Brisbane, 10–15 June 2012, pp. 1–6 (2012)
37.
go back to reference Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurcat. Chaos 16(8), 2129–2151 (2006)MathSciNetCrossRefMATH Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurcat. Chaos 16(8), 2129–2151 (2006)MathSciNetCrossRefMATH
Metadata
Title
Novel image encryption/decryption based on quantum Fourier transform and double phase encoding
Authors
Yu-Guang Yang
Juan Xia
Xin Jia
Hua Zhang
Publication date
01-11-2013
Publisher
Springer US
Published in
Quantum Information Processing / Issue 11/2013
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-013-0612-y

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