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New Journal of Physics

Quantum color image watermarking scheme based on quantum error correction coding *

Yumin Dong, Dingkang Mou, Hengrui Liu, Tingting Zhu

Published Nov 1, 2023• 13 citations
Publisher

Abstract

Abstract Quantum image processing, which merges classical image processing techniques with quantum computing, provides exceptional storage capacity and unparalleled parallel computing power. In this study, we present a quantum color image watermarking scheme that employs quantum error correction codes to address issues such as pixel loss and image distortion during watermark embedding and extraction. By utilizing the least significant bit method to embed the color values of the watermark image into those of the carrier image, we improve the scheme’s robustness. We also address the error correction capabilities of channel coding for phase-flip errors and follow the majority principle, resulting in more accurate extraction of the watermark image’s color and enhancing the watermarking scheme’s reliability and integrity. Our experimental simulations demonstrate that the proposed watermarking scheme boasts high security, strong robustness, and excellent concealment.

DOI
10.1088/1367-2630/ad08ca

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Abstract Quantum image processing, which merges classical image processing techniques with quantum computing, provides exceptional storage capacity and unparalleled parallel computing power. In this study, we present a quantum color image watermarking scheme that employs quantum error correction codes to address issues such as pixel loss and image distortion during watermark embedding and extraction. By utilizing the least significant bit method to embed the color values of the watermark image into those of the carrier image, we improve the scheme’s robustness. We also address the error correction capabilities of channel coding for phase-flip errors and follow the majority principle, resulting in more accurate extraction of the watermark image’s color and enhancing the watermarking scheme’s reliability and integrity. Our experimental simulations demonstrate that the proposed watermarking scheme boasts high security, strong robustness, and excellent concealment.
Quantum watermarking uses quantum images as carriers to achieve secure transmission of secret information. In this paper, a quantum color image watermarking protocol based on LSB (Least Significant Bit, LSB) is proposed. Firstly, the protocol divides an image into several 2×2 non-overlapping blocks. Next, watermarking image calculates the absolute differences with R channels of carrier image, and embeds it into the minimum difference position. Then, taking watermarking image clockwise is embedded into the carrier image counterclockwise. Embedding all blocks generates a 2n×2n2^{n}\times2^{n}2n×2n watermarked image finally. The extraction is the reverse process of embedding. This protocol also gives quantum circuit diagrams for embedding and extraction. Simulation results show that the protocol has a high embedding capacity up to 8 bits/pixel, PSNR (Peak Signal-to-Noise Ratio, PSNR) over 40 dB, SSIM (Structural Similarity Index Metric, SSIM) around 0.98, and the complexity lower than o(22n2)o(2^{2n2})o(22n2).
In this paper, a quantum color image watermarking scheme is proposed through twice-scrambling of Arnold transformations and steganography of least significant bit (LSB). Both carrier image and watermark images are represented by the novel quantum representation of color digital images model (NCQI). The image sizes for carrier and watermark are assumed to be [Formula: see text] and [Formula: see text], respectively. At first, the watermark is scrambled into a disordered form through image preprocessing technique of exchanging the image pixel position and altering the color information based on Arnold transforms, simultaneously. Then, the scrambled watermark with [Formula: see text] image size and 24-qubit grayscale is further expanded to an image with size [Formula: see text] and 6-qubit grayscale using the nearest-neighbor interpolation method. Finally, the scrambled and expanded watermark is embedded into the carrier by steganography of LSB scheme, and a key image with [Formula: see text] size and 3-qubit information is generated at the meantime, which only can use the key image to retrieve the original watermark. The extraction of watermark is the reverse process of embedding, which is achieved by applying a sequence of operations in the reverse order. Simulation-based experimental results involving different carrier and watermark images (i.e. conventional or non-quantum) are simulated based on the classical computer’s MATLAB 2014b software, which illustrates that the present method has a good performance in terms of three items: visual quality, robustness and steganography capacity.
The development of future technology allows the transfer of information transmission in quantum form to be more widely used. However, research related to data security is still in progress and is limited so that it can provide greater potential for data theft with quantum technology. One of them is the theft of visual information data (image). Thus, we need a data security system that can protect image information in quantum computing. Quantum image watermarking is a data security technique by inserting a watermark that aims to protect property rights for multimedia products, such as images. This study proposes a quantum image watermarking scheme based on (Least Significant Bits) LSB for copyright protection for color images. In the embedding process, the watermark image is inserted into the cover image using the LSB method, then transformed into a quantum state. In the receiver, the quantum value detection is carried out on the watermarked image to extract back the watermark that has been inserted. From simulation result, the quantum watermarking system obtains high imperceptibility, the watermark robustness to Pauli-X and Pauli-Controlled-NOT (CNOT) noise and high watermark payload.
Quantum image watermarking technology is influenced by embedding algorithm, which permanently distorts the embedded quantum carrier image.To protect and authenticate quantum images without damaging the carrier images, this study proposed a quantum image reversible watermarking algorithm combining the most significant qubit (MSQb) and the least significant qubit (LSQb).First, a binary watermark image, a grayscale carrier image, and an empty key image were represented using the novel enhanced quantum representation of digital images.Second, the encrypted qubit of the binary watermark image was matched with the MSQb of the carrier image.If they were equal, then the high qubit of the quantum key image was flipped.Otherwise, the encrypted qubit of the binary watermark image was matched with the XOR value of the lowest two qubits of the carrier image.The LSQb of the carrier image was modified according to the matching result.Finally, the quantum watermarked image was obtained.Simulation experiments and theoretical analysis verified the feasibility and watermark performance of the scheme.Results demonstrate that the scheme achieves correct extraction of quantum image watermark and lossless restoration of original image.The visual quality PSNR of the carrier image embedded with watermark through the scheme is improved by approximately 4% compared with that through the traditional LSQb method.The study provides a reference for studying and implementing reversible image watermarking technology in the era of quantum computer, which can be applied to harsh copyright protection and authentication of the visual quality of the original carrier image.
Quantum watermarking can be used for image ownership protection. This paper proposes a quantum watermarking scheme based on Novel Enhanced Quantum Representation (NEQR), DNA encoding, and quantum error correction (QEC). First, XOR operations are performed between the watermark image and a DNA key sequence. Then, performing DNA addition between the resulting image and DNA key image, the encrypted watermark image is obtained. Using the quantum parity determination (QPD) method, the encrypted quantum watermark image is embedded into the least significant bit (LSB) of the carrier image. The quantum circuits for the scheme are also provided. In order to evaluate the effect of the scheme, the watermarking scheme is simulated using MATLAB. The simulation results show that the embedded watermark has good visual quality, and the PSNR of watermarked image is about 51 dB. When ‘salt and pepper’ noise with a density of 0.10 is added to the watermarked image, the PSNR for extracted watermark is 20.38 dB. When the cropping proportion is 50%, the PSNR for extracted watermark is 22.08 dB. These results indicate that the proposed watermarking scheme has strong robustness against noise and cropping attacks. The extraction of watermark is also simulated for cases where the DNA key sequence or key image is damaged. If there is a small amount of damage to DNA key sequence or key image, the watermark cannot be extracted effectively. The watermark encryption further increases the difficulty of unauthorized watermark extraction. Applying DNA encoding to quantum watermarking research also offers significant novelty.
In quantum image steganography, embedding capacity and security are two important issues. This paper presents a novel quantum steganography scheme using color images as cover images. First, the secret information is divided into 3-bit segments, and then each 3-bit segment is embedded into the LSB of one color pixel in the cover image according to its own value and using Gray code mapping rules. Extraction is the inverse of embedding. We designed the quantum circuits that implement the embedding and extracting process. The simulation results on a classical computer show that the proposed scheme outperforms several other existing schemes in terms of embedding capacity and security.