Robust Reversible Watermarking in Encrypted Images Based on Dual-MSBs Spiral Embedding

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.