Abstract
A new quantum gray-scale image watermarking scheme by using simple and small-scale quantum circuits is proposed. The NEQR representation for quantum images is used. The image sizes for carrier and watermark are assumed to be \(2n \times 2n\) and \(n \times n\), respectively. At first, a classical watermark with \(n \times n\) image size and 8 bits gray scale is expanded to an image with \(2n \times 2n\) image size and 2 bits gray scale. Then the expanded image is scrambled to be a meaningless image by the SWAP gates that controlled by the keys only known to the operator. The scrambled image is embedded into the carrier image by the CNOT gates (XOR operation). The watermark is extracted from the watermarked image by applying operations in the reverse order. Simulation-based experimental results show that our proposed scheme is excellent in terms of three items, visual quality, robustness performance under noises, and computational complexity.
Similar content being viewed by others
References
Gea-Banacloche, J.: Hiding messages in quantum data. J. Math. Phys. 43(9), 4531–4536 (2002)
Martin, K.: Secure communication without encryption? IEEE Secur. Priv. 5(2), 68–71 (2007)
Mogos, G.: A quantum way to data hiding. Int. J. Multimed. Ubiquitous Eng. 4(2), 13–20 (2009)
Iliyasu, A.M., Le, P.Q., Dong, F., Hirota, K.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186(1), 126–149 (2012)
Iliyasu, A.M., Le, Q.P., HIROTA, K., et al.: Restricted geometric transformation and their applications for quantum image watermarking and authentication. In: Asian Conference on Quantum Information Science 2010 (AQIS2010), pp. 96–97 (2010)
Shaw, B.A., Brun, T.A.: Quantum steganography with noisy quantum channels. Phys. Rev. A 83(2), 022310-1–022310-8 (2011)
Williams, C.P.: Explorations in Quantum Computing, 2nd edn. Springer, London (2011)
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)
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)
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)
Song, X.H., Wang, S., Liu, S., El-Latif, A.A.A., Niu, X.M.: A dynamic watermarking scheme for quantum images using quantum wavelet transform. Quantum Inf. Process. 12(12), 3689–3706 (2013)
Song, X., Wang, S., El-Latif, A.A.A., Niu, X.: Dynamic watermarking scheme for quantum images based on Hadamard transform. Multimed. Syst. 20(4), 379–388 (2014)
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. 12(8), 2765–2769 (2013)
Yang, Y.G., Xu, P., Tian, J., Zhang, H.: Analysis and improvement of the dynamic watermarking scheme for quantum images using quantum wavelet transform. Quantum Inf. Process. 13(9), 1931–1936 (2014)
Yang, Y.G., Wang, Y., Zhao, Q.Q.: Letter to the Editor regarding Dynamic watermarking scheme for quantum images based on Hadamard transform by Song et al. Multimed. Syst. 20(4), 379–388 (2014)
Jiang, N., Wang, L.: A novel strategy for quantum image steganography based on Moiré pattern. Int. J. Theor. Phys. 54, 1021–1032 (2015)
Gottesman, D.: Stabilizer Codes and Quantum Error Correction. Ph.D. Thesis, California, Institute of Technology, Pasadena, California (1997). arXiv:quant-ph/9705052
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Miyake, S., Nakamae, K. A quantum watermarking scheme using simple and small-scale quantum circuits. Quantum Inf Process 15, 1849–1864 (2016). https://doi.org/10.1007/s11128-016-1260-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-016-1260-9