Quantum Hilbert Image Scrambling

International Journal of Theoretical Physics

Volumn 53, Issue 7, 2014, Pages 2463-2484

  Jiang, Nan ^a   Wang, Luo ^a   Wu, Wen Ya ^a  

^a BEIJING UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Hilbert image scrambling; Quantum circuit; Quantum computation; Quantum watermarking

Indexed keywords

EID: 84956798975     PISSN: 00207748     EISSN: 15729575     Source Type: Journal    
DOI: 10.1007/s10773-014-2046-4     Document Type: Article

References (33)

1. Vedral, V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations. Phys. Rev. A 54(1), 147–153 (1996)
2. Feynman, R.: Quantum mechanical computers. Found. Phys. 16(6), 507–531 (1986)
3. Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
4. Williams, C.: Explorations in quantum computing. In: Texts in Computer Science (2011)
5. Caraiman, S., Manta, V.: Image processing using quantum computing. In: International Conference on 16th System Theory, Control and Computing (ICSTCC), pp 1–6 (2012)
6. Beach, G., Lomont, C., Cohen, C.: Quantum image processing (QuIP). In: 32nd Applied Imagery Pattern Recognition Workshop, pp 39–44 (2003)
7. Venegas-Andraca, S.E., Ball, J.L.: Processing images in entangled quantum system. J. Quantum. Inf. Process. 9(1), 1–11 (2010)
8. Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. In: Proceedings of the SPIE Conference on Quantum Information and Computation, pp 137–147 (2003)
9. Latorre, J.I.: Image Compression and Entanglement. (2005). arXiv:quantph/0510031
10. 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)
11. Zhang, Y., Lu, K., Gao, Y.-H., Wang, M.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(12), 2833–2860 (2013)
12. Fijany, A., Williams, C.: Quantum Wavelet Transform: Fast Algorithm and Complete Circuits (1998). arXiv:quant-ph/9809004
13. Klappenecker, A., Roetteler, M.: Discrete cosine transforms on quantum computers. In: IEEER8-EURASIP Symposium on Image and Signal Processing and Analysis (ISPA01), pp. 464–468. Pula (2001)
14. Tseng, C., Hwang, T.: Quantum circuit design of 8 × 8 discrete cosine transforms using its fast computation flow graph. In: IEEE International Symposium on Circuits and Systems, pp 828–831 (2005)
15. Lomont, C.: Quantum Convolution and Quantum Correlation Algorithms are Physically Impossible (2003). arXiv:quant-ph/0309070
16. Zhang, W.-W., Gao, F., Liu, B., et al.: A watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. 12(4), 793–803 (2013)
17. Weiwei, Z., Fei, G., Bing, L., et al.: A quantum watermark protocol. Int. J. Theor. Phys. 52, 504–513 (2013)
18. Iliyasu, A. M., Le, P. Q., Dong, F., Hirota, K.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186, 126–149 (2012)
19. Hu, M.-Y., Tian, X.-L., Xia, S.-W., et al.: Image scrambling based on 3-D Hilbert curve. In: 3rd International Congress on Image and Signal Processing, vol. 1, pp. 147–149 (2010)
20. Guo, J.-M., Yang, Y., Wang, N.: Chaos-based gray image watermarking algorithm. In: International Conference on Uncertainty Reasoning and Knowledge Engineering, vol.1, pp. 158–160 (2011)
21. Lien, B.K.: Robust data hiding by Hilbert curve decomposition. In: IEEE Intelligent Information Hiding and Multimedia Signal Processing, pp 937–940 (2009)
22. Sun Y.-Y., Kong R.-Q., Wang X.-Y.: An image encryption algorithm utilizing Mandelbrot set. In: International Workshop on Chaos-Fractal Theory and Its Applications, pp 170–173 (2010)
23. Moreno, J., Otazu, X.: Image compression algorithm based on Hilbert scanning of embedded quadtrees: an introduction of the hi-set coder. In: IEEE International Conference on Multimedia and Expo, pp 1–6 (2011)
24. Lin, X.-H., Cai, L.-D.: Scrambling research of digital image based on Hilbert curve. Chinese J. Stereology Image Anal. 9(4), 224–227 (2004)
25. Shang, Z., Ren, H., Zhang, J.: A block location scrambling algorithm of digital image based on Arnold transformation. In: 9th International Conference for Young Computer Scientists, pp 2942–2947 (2008)
26. Zou, W.-G., Huang, J.-Y., Zhou C.-Y.: Digital image scrambling technology based on two dimension Fibonacci transformation and its periodicity. In: 3rd International Symposium on Information Science and Engineering, pp 415–418 (2010)
27. Wen M.-G., Huang S.-C., Han C.-C.: An information hiding scheme using magic squares. In: IEEE International Conference on Broadband, Wireless Computing, Communication and Applications, pp 556–560 (2010)
28. Wang, S., Xu, X.-S.: A new algorithm of Hilbert scanning matrix and its MATLAB program. J. Image Graph. 11(1), 119–122 (2006)
29. Le, P. Q., Iliyasu, A. M., Dong, F. Y., Hirota, K.: Fast geometric transformation on quantum images. IAENG Int. J. Appl. Math. 40(3), 113–123 (2010)
30. Jiang, N., Wu, W.-Y., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. accepted.
31. Peano, G.: Sur une courbe, qui remplit toute une aire plane. Math. Ann. 36(1), 157–160 (1890)
32. Hilbert, D.: Ueber die stetige Abbildung einer Linie auf ein Flächenstück. Math. Ann. 38(3), 459–460 (1891)
33. Kamata, S., Eason, R.O., Bandou, Y.: A new algorithm for N-dimensional Hilbert scanning. IEEE Trans. Image Process. 8(7), 964–973 (1999)