中文摘要：

同态加密技术在加密信息、对信息进行隐私保护的同时,还允许密文数据进行相应的算术运算（如云端可直接对同态加密后的企业经营数据进行统计分析）,已成为云计算领域的研究热点之一.然而,由于云存在多种安全威胁,加密后信息的安全保护和完整性认证问题仍然突出.另外,信息在加密后丢失了很多特性,密文检索成为了云计算需要攻克的关键技术.为了实现对加密图像的有效管理及其安全保护,提出了一种基于同态加密系统的图像可逆信息隐藏算法.该算法首先在加密前根据密钥选择目标像素,并利用差分扩展DE（difference expansion）的方法将目标像素的各比特数据嵌入到其他像素中.然后,利用Paillier同态加密系统对图像进行加密得到密文图像.在加密域中,利用待嵌入信息组成伪像素,加密后替换目标像素,完成额外信息的嵌入.当拥有相应的密钥时,接收方可以分别在密文图像或明文图像中提取出已嵌入的信息.当图像解密后,通过提取出自嵌入目标像素的各比特数据来恢复原始图像.仿真实验结果表明,该算法能够在数据量保持不变的前提下完成同态加密域中额外信息的嵌入,信息嵌入快速高效,并可分别从加密域和明文域中提取出嵌入的信息.

英文摘要：

Homomorphic encryption, which protects privacy effectively and allows algebraic operations directly in the ciphertext, has been a active topic in the study of cloud computing. Due to security threats in cloud computing, the security protection and integrity authentication of encrypted data remain critical problems. The challenge lies in how to retrieve the encrypted data. To achieve more effective management and security protection of encrypted images on-line, this paper proposes a reversible data hiding scheme for ciphertext based on the public key cryptosystems with homomorphic and probabilistic properties. In the proposed scheme, partial pixels are selected as target pixels by a secret key and all bits of the target pixels are embedded into the other pixels with difference expansion（DE） to vacate room before encryption. As a bonus, secret data can be embedded directly in homomorphic encrypted domain by altering the target pixels with the fake pixels which are comprised of secret data. With the legal key, the receiver can extract the embedded data from the encrypted image and the directly decrypted image. Furthermore, user can accurately recover the original image after decryption and data extraction. Finally, experimental results show that extra data can be embedded more efficiently in homomorphic encrypted domain while keeping the quantity of data unchanged. Besides, the embedded data can be extracted in both ciphertext and plaintext.