Quantum Watermarking Based on Neighbor Mean Interpolation and LSB Steganography Algorithms
This paper investigates a quantum watermarking scheme using image interpolation method. Based on the novel enhanced quantum representation of digital images (NEQR), a new scaling-up quantum carrier is generated via Neighbor Mean Interpolation (NMI) method first. Then, three binary watermark images are formed a conceptual quantum watermark image with 3-qubit grayscale based on NEQR, and it is embedded into the new generated quatnum carrier image pixel’s least significant bit (LSB). To achieve this aim, the Quantum Fourier Transform (QFT) is introduced first. Based on QFT operations, several QFT based quantum modules, i.e., quantum Adder, Subtractor and Divider are defined as well as some others commonly used quantum modules also reviewed. Following that, based on these quantum modules, the quantum circuit for image scaling-up is presented first, which can generate a new enlarged quantum carrier image. Then, based on the generated quantum carrier image, we further illustrate the integrated quantum circuit for how to embed quantum watermark images into quantum grayscale carrier images. Finally, the quantum circuit complexity is analyzed, which proves that we presented quantum watermarking scheme can be realized within polynomial time complexity, and the experiment results based on classical computer (i.e., non-quantum version) are simulated under the classical computer software MATLAB 2016a, which demonstrates that we investigated method has an acceptable visual effect and also easy to detect the attacks.
KeywordsQuantum watermarking Neighbor mean interpolation Least significant bit Circuit complexity
This work is supported by National Key R&D Plan under Grant No. 2018YFC1200200; the National Natural Science Foundation of China under Grant No.61463016 and No.61763014; Science and technology innovation action plan of Shanghai in 2017 under Grant No.17510740300.
- 4.Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science. 124–134 (1994)Google Scholar
- 5.Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing. 212–219 (1996)Google Scholar
- 7.Venegas-Andraca, S., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. In: Proceedings of SPIE Conference of Quantum Information and Computation. 5105(8), 134–147(2003)Google Scholar
- 8.Latorre, J.: Image Compression and Entanglement. arXiv:quant-ph/0510031 (2005)Google Scholar
- 19.Sang, J., Wang, S., Li, Q.: A novel quantum representation of color digital images. Quantum Inf. Process. 16(42), (2017)Google Scholar
- 28.Zhou, R.G., Hu, W.W., Luo, G.F., et al.: Quantum realization of the nearest neighbor value interpolation method for INEQR. Quantum Inf. Process. 17(166), (2018)Google Scholar
- 42.Tirkel A. Z., Rankin G. A., VanSchyndel R. M., et al.: Electronic watermark. Proceedings of Digital Image Computing: Techniques and Applications. pp. 666–672. Macquarie University (1993)Google Scholar
- 44.Draper T.G.: Addition on a Quantum Computer. quant-ph/0008033 (2000)Google Scholar
- 45.Ruiz-Perez, L., Garcia-Escartin, J.C.: Quantum arithmetic with the quantum Fourier transform. Quantum Inf. Process. 16(152), (2017)Google Scholar
- 46.Khosropour, A., Aghababa, H., Forouzandeh, B.: Quantum division circuit based on restoring division algorithm. Eighth International Conference on Information Technology: New Generations, IEEE. (2011)Google Scholar
- 47.Wang, D., Liu, Z.H., Zhu, W.N., Li, S.Z.: Design of quantum comparator based on extended general Toffoli gates with multiple targets. Comput. Sci. 39, 302–306 (2012)Google Scholar