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.
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.
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.
Abstract This paper proposes a novel dual-mode quantum image watermarking scheme based on the Generalized model of Novel Enhanced Quantum Representation (GNEQR). The scheme supports both grayscale and color images and provides two embedding modes. A key innovation is the Interleaved Tri-Symmetric Structure (ITSS) mechanism. It combines quantum image scrambling using the Quantum Baker Map (QBM) and reconstruction techniques with quantum error correction (QEC), enhancing robustness against noise and geometric attacks such as cropping and rotation. Additionally, a Quantum Parity Detection (QPD) mechanism is employed to efficiently embed and extract the watermark, substantially improving the visual quality of watermarked images. Experimental results on the USC-SIPI dataset demonstrate that the scheme achieves high visual quality, with PSNR values above 44 dB for watermarked images. Under a salt-and-pepper noise attack with density 0.05, the extracted watermark maintains a PSNR of 42 dB, outperforming the existing schemes. The proposed method also fully resists common rotation attacks and allows effective watermark extraction even when the image is cropped by 55%, confirming its strong robustness against geometric attacks. Overall, this work advances secure and efficient quantum watermarking technologies and addresses key challenges in scalability, robustness, and computational complexity for quantum image processing.
This paper proposes a novel geometrically invariant quantum watermarking scheme using Quantum Error Correction (QEC) and Novel Enhanced Quantum Image Representation (NEQR). The Geometric Transformation-based Image Assembling (GTA) mechanism is proposed to reconstruct the quantum watermark image utilizing QEC principle. The proposed GTA mechanism involves Quantum Image Rotation (QIR) and Quantum Block Rotation (QBR), thus two corresponding quantum watermarking methods, GTA_QIR and GTA_QBR, are proposed and detailed quantum circuits with complexity O(n) are designed. Then the Quantum Majority Finder (QMF) is proposed for embedding the watermark uniformly. In the experiments, we employ dataset USC-SIPI to evaluate the visual quality and robustness of the proposed scheme. Comparisons with the recent quantum watermarking methods is conducted and the results show that our methods have a superior performance. When under attack of ’Salt and Pepper’ noise addition, the proposed GTA_QIR and GTA_QBR improve the average Peak Signal-to-Noise Ratio (PSNR) by 22.57% and 23.49% at a density of 0.05, while at a density of 0.1, the average improvement is 11.13% and 12.05% respectively. Moreover, to the best of our knowledge, this is one of the first quantum watermarking scheme which demonstrates resistance to geometric attacks.
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.
The Flexible Representation of Quantum Images (FRQI) is widely used for encoding images into normalized quantum states for secure processing. However, it suffers from high computational and qubit complexity, limiting its scalability. In addition, quantum comparator models, often employed for qubit comparison, remain vulnerable to geometric attacks such as scaling and rotation and require a slow embedding and extraction rate. To address these challenges, this paper proposes a novel quantum watermarking technique that integrates Quantum Image Representation (QIR) with the Novel Enhanced Quantum Representation (NEQR), offering improved efficiency, robustness, and security for quantum image processing (QIP). The proposed technique initiates watermark qubit (QB) generation by integrating pixel position bits (PPB) with an arithmetic average (AA)-based logic, implemented through a quantum circuit comprising reverse parallel adder (RPA), dividing-4 (D4) models, and controlled-NOT (CNOT) gates. For watermark embedding, the proposed circuit employs RPA, quantum equal (QE) models, CNOT gates, and Pauli-X gates, embedding the watermark via a least significant bit (LSB) strategy within the NEQR-encoded image. The extraction process mirrors the embedding architecture, utilizing reverse parallel subtractor (RPS), QE models, CNOT, and Pauli-X gates to ensure accurate watermark retrieval. Experimental results demonstrate high robustness by achieving the highest peak-signal-to-noise-ratio(PSNR) values of 59.97 decibels (dB) along with a structural similarity index matrix (SSIM) of 0.9999. The proposed framework is validated using IBM Qiskit-based quantum circuit simulation on classical computing hardware and is not intended to demonstrate fault-tolerant quantum hardware execution or provable quantum computational advantage. Rather, the work focuses on simulation-level reversible quantum-circuit modelling for secure image watermarking using NEQR-based image representation and quantum-compatible reversible logic structures. Furthermore, the proposed technique is subjected to a range of image processing attacks, quantum noise and decoherence to rigorously evaluate its resilience and performance. In addition, an AI-assisted attack classification module is incorporated to automatically identify the type of distortion applied to the attacked watermarked images. A lightweight Random Forest classifier is trained to classify different attack categories, including no attack, Gaussian noise, salt-and-pepper noise, median filtering, histogram equalization, JPEG compression, cropping, rotation, and text addition. The proposed AI-assisted module achieves an overall classification accuracy of 96.56%, demonstrating its effectiveness in automatic attack identification and further strengthening the applicability of the proposed quantum watermarking framework for secure image authentication. Resource analysis shows that the watermark generation circuit requires 354 QBs (including 320 for RPA, 10 for D4, and 24 for CNOT), while both embedding and extraction consume 400 QBs each. Theoretical evaluation and empirical validation confirm the technique’s effectiveness in preserving image integrity and confidentiality, establishing it as a viable approach for secure quantum image watermarking in real time applications.
This paper proposes a quantum watermarking scheme in spatial domain for quantum grayscale images, using the New Enhanced Quantum Image Representation (NEQR). The Quantum Majority Finder (QMF) is proposed and applied to determine the embedding rules of the watermark information. A Bit-plane Repositioning (BR) method is proposed to reconstruct the quantum watermark, in order to embed it uniformly into the quantum carrier image. The quantum circuits of the proposed scheme are designed. We simulate the proposed scheme on a classical computer using MATLAB and evaluate it with various metrics. The experimental results show that the proposed scheme can achieve good visual quality and robustness.