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Quantum watermarking scheme based on a novel geometric transformation and Fibonacci scrambling

Jilong Cui, Wenyang Li, Yang Qiu, Zongzhe Wei, Tao Li

Published Feb 21, 2025• 4 citations
Publisher

Abstract

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.

DOI
10.1364/oe.551603

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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.
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.
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.
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.
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.
In order to improve the security of watermark image, a scheme of quantum watermarking algorithm which is based on chaotic affine scrambling is proposed and it includes scrambling, embedding and extracting procedures. In the embedding process, the position and the color of the watermark image are scrambled by chaotic affine and the size of the scrambled watermark image is extended from [Formula: see text] to [Formula: see text]. Meanwhile, the color value of the pixel is changed from 24-bits to 3-[Formula: see text](1-bit per channel) bits. The extended watermark image is embedded into the carrier image through a two-bit embedding strategy, and the extraction process is the inverse one of the embedding process. The simulation results show that the proposed scheme is superior to the comparison scheme in terms of visual quality, peak signal-to-noise ratio (PSNR).
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.