MMQW: Multi-Modal Quantum Watermarking Scheme

To address the problem that existing quantum image watermarking schemes have only a single watermarking mode with weak robustness, in this paper we propose a novel multi-modal quantum watermarking (MMQW) scheme using the generalized model of novel enhanced quantum representation. Our scheme provides four quantum watermarking modes (G_G, G_C, C_C, C_G), covering both types of grayscale and color images for the watermark and the carrier image. To enhance the robustness, we propose the Block Bit-plane Centrosymmetric Expansion (BBCE) method, which utilizes controlled quantum gates to extend the watermark, making our method resistant to noise and geometric attacks. Moreover, we propose a Brightness-based Watermarking Mechanism (BWM) for embedding and extraction. By uniform embedding, BWM not only minimizes the impact on the carrier image but also reduces the visual distortion of the extracted watermark. In the proposed MMQW, we implement three adaptive embedding strategies using controlled quantum gates, each of which is adaptively triggered according to the corresponding modalities. Detailed quantum circuits for quantum computing are provided. To evaluate imperceptibility and robustness of the MMQW, we conduct experiments using high-resolution images from the USC-SIPI dataset. The results show that PSNR of the watermarked image ranges from 36 dB to 56 dB, indicating the high visual quality. The PSNR of the extracted watermark is about 34 dB when the noise density is 0.05, while the PSNR is higher than 48 dB under common quantum rotation attacks, which indicate the high robustness against noise addition and geometric attacks. In addition, the proposed MMQW can resist to cropping attack with cropping percentage up to 55%. A comprehensive comparison with existing state-of-the-art works shows that our method has significant advantages.