Abstract
To study the feasibility of the classical image least significant bit (LSB) information hiding algorithm on quantum computer, a least significant qubit (LSQb) information hiding algorithm of quantum image is proposed. In this paper, we focus on a novel quantum representation for color digital images (NCQI). Firstly, by designing the three qubits comparator and unitary operators, the reasonability and feasibility of LSQb based on NCQI are presented. Then, the concrete LSQb information hiding algorithm is proposed, which can realize the aim of embedding the secret qubits into the least significant qubits of RGB channels of quantum cover image. Quantum circuit of the LSQb information hiding algorithm is also illustrated. Furthermore, the secrets extracting algorithm and circuit are illustrated through utilizing control-swap gates. The two merits of our algorithm are: (1) it is absolutely blind and (2) when extracting secret binary qubits, it does not need any quantum measurement operation or any other help from classical computer. Finally, simulation and comparative analysis show the performance of our algorithm.
Similar content being viewed by others
References
Benioff, P.: The computer as a physical system: a microscopic quantum mechanical Hamiltonian models of computers as represented by Turing machnies. J. Stat. Phys. 22(5), 563–591 (1980)
Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6/7), 467–488 (1982)
Mastriani, M.: Quantum image processing? arXiv: 1512.02942 [quan-ph] (2016)
Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. Proc. SPIE Conf. Quantum Inf. Comput. 5105, 137–147 (2003)
Venegas-Andraca, S.E., Ball, J.L., Burnett, K., Bose, S.: Processing images in entangled quantum systems. Quantum Inf. Process. 9, 1–11 (2010)
Latorre, J.I.: Image compression and entanglement. arXiv: quant-ph/0510031 (2005)
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 (2010)
Zhang, Y., Lu, K., Gao, Y.H., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12(9), 3103–3126 (2013)
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)
Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process 14(5), 1559–1571 (2015)
Sun, B., Le, P.Q., Iliyasu, A.M.: A multi-channel representation for images on quantum computers using the \(RGB\alpha \) color space. In: Intelligent Signal Processing, 2011 IEEE 7th International Symposium on. Floriana, Malta: IEEE. pp. 1–6 (2011)
Sang, J.Z., Wang, S., Li, Q.: A novel quantum representation for color digital images. Quantum Inf. Process, submitted (2016)
Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Fijany, A., Williams, C.: Quantum wavelet transform: fast algorithm and complete circuits. arXiv:quant-ph/9809004 (1998)
Klappenecker, A., Roetteler, M.: Discrete cosine transforms on quantum computers. In: IEEER8-EURASIP Symposium on Image and Signal Processing and Analysis (ISPA01), Pula, Croatia. pp. 464–468 (2001)
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)
Jiang, N., Wu, W.Y., Wang, L.: the quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223–1236 (2014)
Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert image scrambling. Int. J. Theor. Phys. 53(7), 2463–2484 (2014)
Wang, J., Jiang, N., Wang, L.: Quantum image translation. Quantum Inf. Process. 14(5), 1589–1604 (2014)
Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14(5), 1559–1571 (2014)
Sang, J.Z., Wang, S., Niu, X.M.: Quantum realization of the nearest-neighbor interpolation method for FRQI and NEQR. Quantum Inf. Process. 15, 37–64 (2016)
Jiang, N., Wu, W.Y., Wang, L., Zhao, N.: Quantum image pseudocolor coding based on the density-stratified method. Quantum Inf. Process. 13(5), 1735–1755 (2015)
Mastriani, M.: Quantum Boolean Image Denoising. Quantum Inf. Process. 14(5), 1647–1673 (2015)
Iliyasu, A.M., Phuc, Q.L., Dong, F., Hirota, K.: Watermarking and authentication of quantum images based on restricted geometric transformation. Inform. Sci. 186, 126–149 (2011)
Zhang, W.W., Gao, F., Liu, B., Jia, H.Y., Wen, Q., Chen, H.: A quantum watermark protocol. Int. J. Theor. Phys. 52(2), 504–513 (2013)
Zhang, W.W., Gao, F., Liu, B., Wen, Q., Chen, H.: A watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. 12(2), 792–803 (2012)
Song, X.H., Wang, S., Liu, S., El-Latif, 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.H., Wang, S., Liu, S., El-Latif, A.A., Niu, X.M.: Dynamic watermarking scheme for quantum images based on Hadamard transform. Multimedia Syst. 20(4), 379–388 (2014)
Miyake, S., Nakamae, K.: A quantum watermarking scheme using simple and small-scale quantum circuits. Quantum Inf. Process. (2016). doi:10.1007/s11128-016-1260-9
Jiang, N., Wang, L.: A novel strategy for quantum image steganography based on Moiré Pattern. Int. J. Theor. Phys. 54(3), 1021–1032 (2015)
Wang, S., Sang, J.Z., Song, X.H., Niu, X.M.: Least significant qubit (LSQb) information hiding algorithm for quantum image. Measurement 73, 352–359 (2015)
Jiang, N., Zhao, N., Wang, L.: LSB based quantum image steganography algorithm. Quantum Inf. Process. 55, 107–123 (2016)
Nielsom, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridfe University Press, Cambridge (2000)
Acknowledgments
This work is supported by the National Science Foundation of China (Grant Numbers: 61471141, 61301099, 61361166006), and Basic Research Project of Shenzhen, China (Grant Numbers: JCYJ20150513151706561). We deeply thanks the previous researchers’ work about NEQR. Thanks are due to many anonymous reviewers for their assistance with the discussion about the designed three qubits comparator and the quantum measurement.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Sang, J., Wang, S. & Li, Q. Least significant qubit algorithm for quantum images. Quantum Inf Process 15, 4441–4460 (2016). https://doi.org/10.1007/s11128-016-1411-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-016-1411-z