基于多项式秘密共享的图像密文域可逆信息隐藏

针对密文域可逆信息隐藏在多用户场景下算法嵌入率低、载体图像容灾性能较弱等问题，该文提出一种基于多项式秘密共享的图像密文域可逆信息隐藏方案。通过将图像分割成多幅影子图像并存储在不同的用户端，可以增强图像的容灾性，为了实现额外信息在图像重构前后提取的可分离性，该方案包括两种嵌入算法:算法1在图像分割的过程中，将额外信息嵌入多项式的冗余系数中得到含有额外信息的影子图像，该算法支持在图像重构之后提取额外信息；算法2针对图像分割后的任一影子图像，利用秘密共享的加法同态特性实施嵌入，该算法支持直接从影子图像中提取额外信息。实验在不同门限方案和影子图像压缩率的条件下进行测试，当压缩率为50%时，(3, 4)门限方案的嵌入率达4.18 bpp(bit per pixel)，(3, 5)门限方案的嵌入率达3.78 bpp。结果表明，两种嵌入算法分别支持从影子图像与重构图像中提取额外信息，实现了方案的可分离性；与现有方案相比，所提算法嵌入率较高、计算复杂度较低，具有较强的实用性。

Reversible Data Hiding in Encrypted Images Based on Polynomial Secret Sharing

In order to solve the problems of low embedding rate of reversible data hiding in encrypted domain with multi-users and weak disaster tolerance of cover image, a reversible data hiding in encrypted images based on polynomial secret sharing scheme is proposed. The cover image is divided into multiple shadow images and stored to multiple users, so that the image disaster tolerance can be enhanced. Separability is achieved by combining two embedding algorithms, where Algorithm 1 embeds additional data into the redundancy coefficients of the polynomial during the process of image sharing to generate shadow images containing additional data, which can extract data after image reconstruction; Algorithm 2, for any shadow image, embeds additional data by using the additive homomorphism of secret sharing, which supports extracting additional data directly from the shadow image. Experiments are performed in different threshold and shadow image compression rates. When the compression rate is 50%, the embedding rate reaches 4.18 bit per pixel (bpp) for the (3, 4) threshold scheme and 3.78 bpp for the (3, 5) threshold scheme. The results show that the algorithms support extracting additional data from the shadow images and the reconstructed images respectively, which achieves the separability of the scheme. The proposed scheme has a higher embedding rate and lower computational complexity than the existing schemes, and is more practical.