A scheme is proposed to watermark and recover unmarked greyscale images on quantum computers. The hitherto inaccessible data from a quantum image-watermark pair is extracted from their classical (conventional or non-quantum) versions using which two quantum sub-circuits are used to execute the two-tier transformations comprising of changes that: 1 embed a visible and translucent watermark logo in a predetermined sub-area of the quantum replica of the cover image 2 modify the remaining content of the cover image in a manner dictated by the watermark signal, so that the resulting distortions on the watermarked image are not easily discernible. Classical simulations of the image-watermark pairs and the various sub-circuits required to obtain the marked and unmarked images demonstrate the feasibility of the proposed scheme when the necessary quantum hardware are realised. The proposal advances available literature geared towards safeguarding quantum resources from unauthorised reproduction and confirmation of their proprietorship in cases of dispute thereby leading to commercial applications of quantum information.
A scheme is proposed to watermark and recover unmarked greyscale images on quantum computers. The hitherto inaccessible data from a quantum image-watermark pair is extracted from their classical (conventional or non-quantum) versions using which two quantum sub-circuits are used to execute the two-tier transformations comprising of changes that: 1 embed a visible and translucent watermark logo in a predetermined sub-area of the quantum replica of the cover image 2 modify the remaining content of the cover image in a manner dictated by the watermark signal, so that the resulting distortions on the watermarked image are not easily discernible. Classical simulations of the image-watermark pairs and the various sub-circuits required to obtain the marked and unmarked images demonstrate the feasibility of the proposed scheme when the necessary quantum hardware are realised. The proposal advances available literature geared towards safeguarding quantum resources from unauthorised reproduction and confirmation of their proprietorship in cases of dispute thereby leading to commercial applications of quantum information.
Exploiting the promise of security and efficiency that quantum computing offers, the basic foundations leading to commercial applications for quantum image processing are proposed. Two mathematical frameworks and algorithms to accomplish the watermarking of quantum images, authentication of ownership of already watermarked images and recovery of their unmarked versions on quantum computers are proposed. Encoding the images as 2n-sized normalised Flexible Representation of Quantum Images (FRQI) states, with n-qubits and 1-qubit dedicated to capturing the respective information about the colour and position of every pixel in the image respectively, the proposed algorithms utilise the flexibility inherent to the FRQI representation, in order to confine the transformations on an image to any predetermined chromatic or spatial (or a combination of both) content of the image as dictated by the watermark embedding, authentication or recovery circuits. Furthermore, by adopting an apt generalisation of the criteria required to realise physical quantum computing hardware, three standalone components that make up the framework to prepare, manipulate and recover the various contents required to represent and produce movies on quantum computers are also proposed. Each of the algorithms and the mathematical foundations for their execution were simulated using classical (i.e., conventional or non-quantum) computing resources, and their results were analysed alongside other longstanding classical computing equivalents. The work presented here, combined together with the extensions suggested, provide the basic foundations towards effectuating secure and efficient classical-like image and video processing applications on the quantum-computing framework.
Based on the NEQR representation of quantum grayscale images and binary images, the optimal LSBs-based quantum watermarking scheme is investigated in this paper, which embeds several binary images (watermark images) into a grayscale image (cover image). The size of the cover image and secret image are both assumed to be [Formula: see text]. Compared to quantum simple LSBs substitution method generating one stego-pixel, our presented quantum optimal LSBs-based method can generate three stego-pixel simultaneously first. Then one of them with lowest visual distortion is chosen as the final stego-pixel. To this end, first of all, the quantum circuits for a few basic quantum modules (i.e. Quantum Comparator, Parallel CNOT, Parallel Swap, ADDER MOD, Subtracter (SUB.ER) MOD and Absolute Value) are predefined. Following that, based on these simple modules, two composite quantum modules (i.e. the ADDER and SUB.ER MOD [Formula: see text] module and Choose final stego-pixel module) are further constructed. With the help of the basic and composite quantum modules, the integrated quantum circuit implementation of the optimal LSBs-based quantum watermark images embedding/extracting procedures are illustrated. Then, the experiment result are simulated under the classical computer software MATLAB 2014(b), which illustrates our presented optimal LSBs-based quantum watermarking methods are superior to the simple LSBs scheme in terms of PSNR and histogram graphs on the basis of visual effect, and the circuit’s complexity analysis also demonstrates our investigated scheme with a very low computational complexity. Finally, we analyze the security of quantum cryptography system, which verifies the quantum watermarking data can be securely transmitted to other legal normal users.
The development of new quantum watermarking is in full swing, and it is crucial to test the robustness of these proposed watermarking schemes. In this paper, different quantum circuits are introduced to realize geometric transformations on quantum images, which serve as a means of simulating geometric attacks on quantum watermark images. Receivers may get distorted images, and the extracted watermark images may also be disrupted. To recover the geometric order of the quantum watermark images, a strategy is proposed to identify the trajectory of qubit alterations. Quantum circuits can be designed accordingly to restore the original order of the watermark images, which receivers could use before the extraction process to mitigate the impact of geometric attacks. Experimental simulations demonstrate how attacks affect the quantum watermark images and the extracted watermark images. Additionally, it illustrates how quantum recovery circuits step by step act on images that have been geometrically attacked. An analysis of the complexity of geometric restoration circuits reveals that quantum circuits exhibit better performance compared to classical circuits.
Abstract Quantum watermarking is a technique to embed specific information, usually the owner’s identification, into quantum cover data such for copyright protection purposes. In this paper, a new scheme for quantum watermarking based on quantum wavelet transforms is proposed which includes scrambling, embedding and extracting procedures. The invisibility and robustness performances of the proposed watermarking method is confirmed by simulation technique. The invisibility of the scheme is examined by the peak-signal-to-noise ratio (PSNR) and the histogram calculation. Furthermore the robustness of the scheme is analyzed by the Bit Error Rate (BER) and the Correlation Two-Dimensional (Corr 2-D) calculation. The simulation results indicate that the proposed watermarking scheme indicate not only acceptable visual quality but also a good resistance against different types of attack.
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 computing represents a burgeoning computational paradigm that significantly advances the resolution of contemporary intricate problems across various domains, including cryptography, chemistry, and machine learning. Quantum circuits tailored to address specific problems have emerged as critical intellectual properties (IPs) for quantum computing companies, attributing to the escalating commercial value of quantum computing. Consequently, designing watermarking schemes for quantum circuits becomes imperative to thwart malicious entities from producing unauthorized circuit replicas and unlawfully disseminating them within the market. Unfortunately, the prevailing watermarking technique reliant on unitary matrix decomposition markedly inflates the number of 2-qubit gates and circuit depth, thereby compromising the fidelity of watermarked circuits when embedding detectable signatures into the corresponding unitary matrices. In this paper, we propose an innovative multi-stage watermarking scheme for quantum circuits, introducing additional constraints across various synthesis stages to validate the ownership of IPs. Compared to the state-of-the-art watermarking technique, our multi-stage watermarking approach demonstrates, on average, a reduction in the number of 2-qubit gates by 16% and circuit depth by 6%, alongside an increase in the fidelity of watermarked circuits by 8%, while achieving a 79.4% lower probabilistic proof of authorship.