基于同态加密系统的图像鲁棒可逆水印算法

同态加密技术可用于保护数据隐私并允许对密文数据进行算术操作，在云计算安全上有着很好的应用前景.针对云计算中的隐私保护和数据安全等问题，本文提出了一种基于同态加密系统的图像鲁棒可逆水印算法，主要思想为：1）对原始图像进行分块和利用Paillier加密系统进行加密得到密文图像；2）在加密域中，通过模乘法逆元MMI （Modular Multiple Inverse）方法和查询相应的密文映射表得到每个密文分块的统计量，然后利用同态特性对统计量进行直方图平移来嵌入水印信息；3）在接收方，可从含水印的密文图像的统计量直方图中完整提取水印，并可通过对统计量进行与嵌入过程相反的直方图平移操作来恢复原始密文图像；4）含水印的密文图像在直接解密后可从其统计量直方图中完整提取水印信息和恢复原始图像；5）解密后的含水印图像在受到一定程度的攻击后（如JPEG/JPEG2000压缩和叠加高斯噪声等），水印仍能正确提取.该算法实现了在不对原始图像进行预处理的情况下可直接在加密后的密文图像中嵌入水印，并可分别在加密域或明文域提取水印和恢复原始密文图像或原始明文图像，而且嵌入的水印对常见的图像处理操作具有一定的鲁棒性.实验仿真结果验证了本文算法的有效性.

Robust and Reversible Image Watermarking Algorithm in Homomorphic Encrypted Domain

Homomorphic encryption technique can be used for protection of data privacy and some algebraic operations can be implemented on the ciphertext data. This is very userful in the field of cloud computing security, such as analyzing and processing the encrypted data in cloud without exposing the content of data. For privacy protection and data security problems in cloud computing, this paper proposes a robust and reversible image watermarking algorithm in homomorphic encrypted domain, including five aspects:1)The original image is divided into a number of non-overlapping blocks and each pixel in a block is encrypted with Paillier cryptosystemto obtain the encrypted image; 2)The statistical values of the encrypted blocks can be retrieved in encrypted domain by employing modular multiplicative inverse(MMI) method and looking for a mapping table. After that, watermark information can be reversibly embedded into encrypted image by shifting the histogram of the statistical values with the homomorphic property of Paillier cryptosystem; 3)On the receiver side, the marked histogram of the watermarked and encrypted image can be obtained for extraction of the watermark from the marked histogram. The encrypted image can be restored by inverse operations of histogram shifting in the embedding phase; 4)The marked histogram can be obtained from the directly decrypted image. This is followed by the watermark extraction and restoration of original image; 5)The watermark can still be extracted correctly under some attacks (such as JPEG/JPEG2000 compression and additive gussian noise) to some extent on the watermarked and decrypted image. The proposed method have achieved to embed information bits directly into the encrypted image without preprocessing operations on the original image, and can extract the watermark and restore the encrypted image in encrypted domain or the original image in plaintext domain after decryption. Besides, the watermark is robust to those common image processing operations. The experimental results have shown the validity of the proposed scheme.