A two-domain quantum color image watermarking scheme based on LSB algorithm

There are various challenges facing quantum watermarking, of which the most significant one is that unlike classical watermarking, there remain few achievements made to build a complete system. Allowing for this, a two-domain quantum color image watermarking scheme based on least significant bit (LSB) algorithm is proposed in this paper. For the purpose of image representation, the image of the carrier and that of the watermark are represented through the novel quantum representation of color digital images (NCQI) (Sang et al. in Quantum Inf Process 16:1-14, 2017), the size of which is 2nx2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2<^>{n} \times 2<^>{n}$$\end{document} and 2n-1x2n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2<^>{n-1} \times 2<^>{n-1}$$\end{document}, respectively. Firstly, the watermark image is scrambled by conducting operation on the color and position of the image. Through this simultaneous scrambling of color and position, the privacy of watermark images is better protected. Secondly, the scrambled watermark image is embedded into the spatial domain of the carrier image using the LSB algorithm. Additionally, the scrambled watermark image is embedded into the frequency domain of the carrier image through quantum Fourier transform and LSB algorithm, thus improving the capability to withstand illegal attacks. Lastly, both simulation experiment and comparative analysis are conducted to demonstrate the satisfactory visual quality of the proposed scheme and its strong robustness to the salt and pepper noises. These positive findings contributed to enriching the existing theory of color quantum image watermarking.