Purpose: This work aims to apply Quantum Hilbert Scrambling to enhance the security and integrity of image watermarking without affecting visual quality degradation. Further conception of the surveyed methods could result in a very good solution to conventional methods of watermarking in solving some problems of digital image security and integrity with new concepts of quantum computing. Methods: The paper reviews Quantum Hilbert Scrambling, whose computational complexity is . The process involves encoding the image into a quantum state, permuting qubits by the Hilbert curve, and embedding a watermark using quantum gates. Result: The quantitative performance evaluation metrics, like Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index (SSIM), have shown high Peak Signal to Noise Ratio (PSNR) values from 56.13 dB to 57.87 dB and Structural Similarity Index (SSIM) from 0.9985 to 0.9990, correspondingly. This justifies the fact that the quality degradation is very slight and the fine details of the structure are well maintained. Novelty: The proposed method uniquely integrates quantum computing with traditional watermarking steps for a secure and effective approach in digital watermarking. Further development should focus on improving the quantum circuit regarding computation efficiency, extending the applicability of the method to a wide range of images, and various situations in watermarking, and finding hybrid approaches by combining quantum and classical approaches towards better performance and scalability.
Purpose: This work aims to apply Quantum Hilbert Scrambling to enhance the security and integrity of image watermarking without affecting visual quality degradation. Further conception of the surveyed methods could result in a very good solution to conventional methods of watermarking in solving some problems of digital image security and integrity with new concepts of quantum computing. Methods: The paper reviews Quantum Hilbert Scrambling, whose computational complexity is . The process involves encoding the image into a quantum state, permuting qubits by the Hilbert curve, and embedding a watermark using quantum gates. Result: The quantitative performance evaluation metrics, like Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index (SSIM), have shown high Peak Signal to Noise Ratio (PSNR) values from 56.13 dB to 57.87 dB and Structural Similarity Index (SSIM) from 0.9985 to 0.9990, correspondingly. This justifies the fact that the quality degradation is very slight and the fine details of the structure are well maintained. Novelty: The proposed method uniquely integrates quantum computing with traditional watermarking steps for a secure and effective approach in digital watermarking. Further development should focus on improving the quantum circuit regarding computation efficiency, extending the applicability of the method to a wide range of images, and various situations in watermarking, and finding hybrid approaches by combining quantum and classical approaches towards better performance and scalability.
Information and Communication Technology (ICT) has significantly developed nowadays, making things easier for users. However, alongside the ease of communication, several concerns arise, particularly regarding data authenticity. Security, which affects the authenticity of data, is a major concern. Quantum watermarking offers a much better solution for this problem in the next generation of technology, as it provides superior security compared to classical watermarking. In this paper, we propose a quantum watermarking method using Taylor sequence modification and rotation gates for watermark embedding. Before the embedding process, we convert the images into the quantum domain using the Flexible Representation of Quantum Images (FRQI). We then calculate the phase representation of the host and watermark pixels. Using a Taylor sequence, we modify the watermarked phase and calculate the difference between the host and watermarked phases. Several rotation gates are used to modify the host phase on the quantum circuit. At the end of the embedding process, we reconstruct the watermarked quantum images into a classical images. The experimental results demonstrated watermarking imperceptibility, represented by Peak Signal to Noise Ratio-H (PSNR-H) and watermark robustness, represented by Peak Signal to Noise Ratio-W (PSNR-W). The PSNR-H values ranged between 10–80 dB, while the PSNR-W values reached up to 20 dB. This proposed method has a unique outcome even when the PSNR-H value is infinite, the watermark can still be detected and is subjectively visible to the human eye.
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.
The paper presents a novel hybrid quantum water-marking method designed to enhance the security and robustness of digital media protection. The proposed scheme integrates a two-step encryption process, achieving high security while pre-serving quality. Key features include classical LSB substitution, quantum chaos matrix, and an improved quantum representation, offering superior resistance to attacks. By combining spatial and transform domain encryption, the method overcomes vulner-abilities in singular value decomposition, enhancing robustness and peak signal-to-noise ratio (PSNR). Compared to the latest developments-such as sinusoidal-tent map, multi-scale pattern-based quantum text watermarking (MPQTW), maximum pixel difference, tri-way pixel, and NEQR with Quantum Majority Finder (QMF)-the proposed approach shows an average PSNR improvement of approximately 20 % and a significant reduction in Bit Error Rate (BER) by 15.41 %. Additionally, the method demonstrates strong resistance to various attack types with a correlation two-dimensional (Corr 2D) value near 1, such as 0.994 against salt and pepper noise attacks. These results highlight a significant advancement in quantum watermarking technology, balancing improved perceptual quality, security, and robustness.
Quantum watermarking technology embeds invisible watermark images into carrier images to mark ownership, which has broad application prospects. In the paper, with using the novel enhanced quantum representation (NEQR) of the image, a quantum watermarking scheme based on a novel space geometric transformation and Fibonacci scrambling is proposed. Combined with the Quantum Majority Finder (QMF) method, the watermark information is embedded into various positions of the carrier image. The Fibonacci scrambling disperses the pixel information of the watermark image into the entire image range, and the space geometric transformation rearranges the individual watermark pixel information. These methods improve the robustness and security of watermarked images against noise and cropping attacks and ensure the watermark's visual invisibility. Applying simulation experiments, these quantum processes are implemented on a classical computer. The visual quality quantified by Peak Signal-to-Noise Ratio (PSNR) and robustness of the proposed method are analyzed. Our watermarking scheme has good visual quality, and the PSNR of the watermarked image is approximately 45. Compared to existing methods, our scheme exhibits robustness to resist noise and cropping attacks. Especially in large-scale cropping, the proposed scheme has excellent advantage. Experiment results verify the effectiveness and superiority of the proposed scheme and provide new ideas and methods for developing quantum watermarking technology.
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.
Quantum information technologies are reshaping communication systems, but reliable integration of classical data, particularly images, into quantum frameworks remains a challenge. Circuit-based quantum image encoding methods are susceptible to noise-induced degradation, which undermines reproducibility and reliability. Here, we investigate the impact of quantum noise channels across the encoding and measurement stages within a hybrid quantum-classical distributed system. We also introduce noise into selected gate operations and measurements to demonstrate its distinct effects on the quantum circuit. To quantify the results, we compute the mean squared error (MSE), the structural similarity index measure (SSIM), and the peak signal-to-noise ratio (PSNR), and benchmark the results across various settings of the noise parameter. Finally, we present experimental results highlighting how image complexity affects encoding robustness using the Linnaeus and MNIST datasets. We anticipate that the presented results will contribute to the development of dependable quantum-classical orchestration strategies for resilient image processing.