矢量地图同态加密域鲁棒水印算法

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。本文针对云端地图水印系统，首次提出一种基于同态加密系统的矢量地图鲁棒水印方法。主要思想为：(1)将地图坐标基于坐标变换转换为相对坐标。然后，基于量化步长，将相对坐标量化成整数坐标。最后，对整数量化坐标基于同态加密系统进行加密，形成密文地图；(2)云端水印系统基于加密系统的同态特性，在密文地图中嵌入水印；(3)在接收端，数据用户解密含水印密文地图，并进行坐标逆变换，得到含水印明文地图。针对水印的不可见性及鲁棒性，本文做了一系列相关仿真实验。实验结果表明，本文提出的加密域水印算法具有很好的水印不可见性及鲁棒性，尤其对RST几何攻击具有很好的鲁棒性。

Robust Vector Map 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 useful in the field of cloud computing security, such as analyzing and processing the encrypted data in cloud without exposing the content of data. Based on this feature, aiming at the map watermarking system in cloud, this paper first proposes a robust vector map watermarking algorithm in homomorphic encrypted domain. The main ideas are as follows: (1) Firstly, the original map coordinates are transformed into relative coordinates. Secondly, the relative coordinates are quantized into integer coordinates based on a predefined quantization step. Lastly, the integer quantization coordinates are encrypted by using the homomorphic encryption system, obtaining the ciphertext map; (2) The map watermarking system in cloud directly embeds the watermark into the ciphertext map based on the homomorphism of the encryption system; (3) In the receiver side, the data user decrypts the watermarked ciphertext map, and performs inverse coordinate transformations to the decrypted map, obtaining the final watermarked plaintext map. A series of simulation experiments are done to evaluate the invisibility and robustness of the watermark. The experimental results show that the watermarking algorithm in the homomorphic encrypted domain proposed in this paper has good invisibility and robustness. Especially, it is robust to RST geometric attacks.