Robust reversible watermarking in encrypted images (RRWEI) faces an inherent challenge in simultaneously achieving robustness, reversibility, and content privacy under severely constrained embedding capacity. Existing RRWEI schemes often exhibit limited robustness against noise, lossy compression, and cropping attacks due to insufficient redundancy in the encrypted domain. To address this challenge, this paper proposes a novel RRWEI framework that couples dual most significant bit-plane (dual-MSBs) embedding with spatial redundancy and error-correcting coding. By compressing prediction-error bit-planes, sufficient embedding space and auxiliary information for lossless reconstruction are reserved. The dual-MSBs are further reorganized using a spiral embedding strategy to distribute multiple redundant watermark copies across spatially dispersed regions, enhancing robustness against both noise and spatial loss.Experimental results on standard test images demonstrate that the proposed method consistently outperforms under evaluated settings robustness against Gaussian noise, JPEG compression, and diverse cropping attacks, while maintaining perfect reversibility and high embedding capacity. Compared with state-of-the-art RRWEI schemes, the proposed framework achieves substantially lower bit-error rates and more stable performance under a wide range of attack scenarios.

翻译：加密图像中的鲁棒可逆水印（RRWEI）面临一个固有挑战：在严重受限的嵌入容量下同时实现鲁棒性、可逆性和内容隐私。现有的RRWEI方案由于加密域中冗余不足，通常在抵抗噪声、有损压缩和裁剪攻击方面表现出有限的鲁棒性。为应对这一挑战，本文提出了一种新颖的RRWEI框架，该框架将双最高有效位平面嵌入与空间冗余及纠错编码相结合。通过压缩预测误差位平面，为无损重建预留了充足的嵌入空间和辅助信息。采用螺旋嵌入策略对双最高有效位进行重组，将多个冗余水印副本分布在空间分散的区域，从而增强了对噪声和空间丢失的鲁棒性。在标准测试图像上的实验结果表明，所提方法在评估设置下始终表现出更优的鲁棒性，能有效抵抗高斯噪声、JPEG压缩及多种裁剪攻击，同时保持完美的可逆性和高嵌入容量。与最先进的RRWEI方案相比，所提框架在广泛的攻击场景下实现了显著更低的误码率和更稳定的性能。