基于Paillier的同态加密域可逆信息隐藏  

Reversible data hiding in homomorphic encrypted domain based on Paillier

作　　者：张敏情[1] 周能 刘蒙蒙 王涵 柯彦[1] ZHANG Min-qing;ZHOU Neng;LIU Meng-meng;WANG Han;KE Yan(Key Laboratory of Network and Information Security under Chinese People Armed Police Force(PAP),College of Cryptography Engineering,Engineering University of PAP,Xi'an 710086,Shaanxi,China)

机构地区：[1]武警工程大学密码工程学院,网络与信息安全武警部队重点实验室,陕西西安710086

出　　处：《山东大学学报（理学版）》2020年第3期1-8,18,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61379152,61872384)。

摘　　要：利用Paillier密码体制的同态和概率特性,提出了一种基于Paillier的同态加密域可逆信息隐藏。首先对原始图像分块,图像所有者随机选择的像素组中有一个参考像素和8个目标像素,将参考像素的最低有效位和目标像素的所有比特通过可逆信息隐藏的方法自嵌入到图像的其他部分中,参考像素的最低有效位在加密前置0避免嵌入数据时溢出,加密的参考像素替代像素组中围绕它的目标像素,从而构造出镜像中心密文。在一组镜像中心密文中,数据嵌入者通过同态加法在目标像素的最低有效位嵌入额外信息,而参考像素保持不变。接收者可直接在目标像素和对应的参考像素之间进行模乘法逆元提取额外信息,或者在直接解密后通过明文减法提取额外信息并能无损还原原始图像。实验结果表明:在保证直接解密图像质量的前提下算法平均嵌入率为0.18 bpp (bit per pixel)。Based on the homomorphism and probability characteristics of Paillier cryptosystem, a reversible data hiding in homomorphic encrypted domain based on Paillier is proposed. First, the original image is divided into blocks. The pixel groups randomly selected by the image owner have one reference pixel and eight target pixels. Least significant bits(LSBs) of reference pixel and all bits of target pixel are self-embedded into other parts of the image by a method of RDH. In order to avoid overflow when embedding data, LSBs of the reference pixel are reset to zero before encryption. The encrypted reference pixel replaces the target pixels surrounding it, thereby constructing mirror central ciphertext. In a set of mirroring central ciphertext, the data hider embeds data in the LSBs of the target pixels by homomorphic addition, while the reference pixel remains unchanged. The receiver can directly extract the extra information by modular multiplication inverse between the target pixels and the corresponding reference pixel or directly extract the secret information by plaintext subtraction and can restore the original image without loss. The experimental results show that the average embedding rate of the algorithm is 0.18 bpp(bit per pixel) under the premise of ensuring the quality of the directly decrypted image.

关 键 词：可逆信息隐藏 同态加密域 Paillier 镜像中心密文 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]