Reversible data hiding in encrypted images based on EMD and PSIS

• Propose two ( k, n )-threshold RDHEI schemes fusing EMD and PSIS, solving poor fault-tolerance and separability in existing schemes. • Eliminate location map overhead via EMD, boosting embedding payload and simplifying the framework. • Achieve high performance, with embedding rate up to 2 bpp, PSNR > 53 dB, SSIM > 0.99 (EMD-RDHP scheme) and lossless recovery (Modified EMD-RDHP scheme). • Avoid complex computations while ensuring security, fitting secure cloud storage and multi-party collaboration. With the development of cloud computing and related technologies, Reversible Data Hiding in Encrypted Image (RDHEI) has emerged as a privacy-preserving technique that enables embedding additional data into cover image while ensuring its confidentiality. However, most existing RDHEI schemes rely on a single encrypted image, lacking fault-tolerance for both image reconstruction and data extraction. Additionally, many schemes suffer from high computational complexity and the separability of image reconstruction and data extraction. To address these limitations, in this paper, we propose two novel ( k, n )-threshold RDHEI schemes by combining Exploiting Modification Direction (EMD) and polynomial-based secret image sharing (PSIS) techniques, achieving fault-tolerance for both image and embedded data, while improving embedding capacity and supporting lossless recovery. The first scheme, EMD-based Reversible Data Hiding with Polynomial (EMD-RDHP) scheme, employs PSIS to share the secret image and embeds secret data during the sharing process using EMD. This approach achieves high embedding capacity and high-quality image reconstruction (PSNR > 53 dB, SSIM > 0.99). However, it introduces slight distortion, failing to losslessly recover the secret image. To address this limitation, we further propose a Modified EMD-RDHP scheme, which records pixel modification operation in the polynomial coefficients, enabling lossless reconstruction of the secret image. Both proposed schemes support independent data extraction and image reconstruction, ensuring their separability. Experimental results demonstrate that the proposed schemes outperform existing methods in terms of fault-tolerance, embedding capacity, and computational efficiency.