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

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.