矢量地图同态加密域鲁棒水印算法

doi:10.12082/dqxxkx.2022.210698

地球信息科学学报 ›› 2022, Vol. 24 ›› Issue (6): 1120-1129.doi: 10.12082/dqxxkx.2022.210698

• 地球信息科学理论与方法 • 上一篇下一篇

矢量地图同态加密域鲁棒水印算法

吴柏燕¹^,²^,^*(), 戴千一¹^,², 彭煜玮³, 王伟⁴

1.湖南科技大学地理空间信息技术国家地方联合工程实验室,湘潭 411201
2.湖南科技大学测绘遥感信息工程湖重点实验室,湘潭 411201
3.武汉大学计算机学院,武汉 430072
4. 武汉大学测绘遥感信息工程国家重点实验室,武汉 430079

收稿日期:2021-11-02 修回日期:2021-12-14 出版日期:2022-06-25 发布日期:2022-08-25
作者简介:吴柏燕（1980— ）,女,湖南衡阳人,博士,副教授,主要从事地理空间信息安全研究。E-mail: wby@hnust.edu.cn
基金资助:
湖南省自然科学基金创新研究群体项目(2020JJ1003);国家自然科学基金项目(41201389);湖南省教育厅资助科研项目(20C0770)

Robust Vector Map Watermarking Algorithm in Homomorphic Encrypted Domain

WU Baiyan¹^,²^,^*(), DAI Qianyi¹^,², PENG Yuwei³, WANG Wei⁴

1. National-Local Joint Engineering Laboratory of Geo-Spatial Information Technology, Hunan University of Science and Technology, Xiangtan 411201, China
2. Hunan Provincial Key Laboratory of Geo-information Engineering in Surveying, Mapping and Remote Sensing, Hunan University of Science and Technology, Xiangtan 411201, China
3. School of Computer Science, Wuhan University, Wuhan 430072, China
4. State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China

Received:2021-11-02 Revised:2021-12-14 Online:2022-06-25 Published:2022-08-25
Contact: *WU Baiyan wby@hnust.edu.cn
Supported by:
Innovative Research Groups of the Natural Science Foundation of Hunan Province(2020JJ1003);National Natural Science Foundation of China(41201389);Scientific Research Fund of Hunan Provincial Education Department(20C0770)

摘要/Abstract

摘要：

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。

关键词: 矢量地图, 同态加密, 矢量地图水印, 加密域水印, 鲁棒水印, 版权保护, 地理空间数据安全, 云计算

Abstract:

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.

Key words: vector map, homomorphic encryption, vector map watermarking, watermarking in encrypted domain, robust watermarking, copyright protection, geospatial data security, cloud computing

吴柏燕, 戴千一, 彭煜玮, 王伟. 矢量地图同态加密域鲁棒水印算法[J]. 地球信息科学学报, 2022, 24(6): 1120-1129.DOI:10.12082/dqxxkx.2022.210698

WU Baiyan, DAI Qianyi, PENG Yuwei, WANG Wei. Robust Vector Map Watermarking Algorithm in Homomorphic Encrypted Domain[J]. Journal of Geo-information Science, 2022, 24(6): 1120-1129.DOI:10.12082/dqxxkx.2022.210698

图/表 6

图1

图2

表1

量化步长 Q n与RMSE、最大误差的关系

$Q n$	RMSE	MaxError	NC
0.000001	9.730 243E-7	2.809 785E-6	1.0
0.000005	4.558 026E-6	1.403 611E-5	1.0
0.00001	9.543 711E-6	2.804 673E-5	1.0
0.00005	4.759 338E-5	1.405 176E-4	1.0
0.0001	9.480 721E-5	2.814 349E-4	1.0
0.0005	4.747 438E-4	1.406 901E-3	1.0
0.001	9.496 267E-4	2.821 113E-3	1.0
0.005	4.741 121E-3	1.410 342E-2	1.0
0.01	9.543 460E-3	2.819 083E-2	1.0
0.05	4.738 265E-2	1.407 552E-1	1.0

表1

图3

表2

表3

参考文献 21

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攻击类型	攻击强度	算法1	算法2	本文算法
几何攻击	平移10 m	1.0	1.0	1.0
	旋转30°	>0.443848	0.564087	1.0
	缩放2.5倍	0.449463	1.0	1.0
删除顶点	10%	1.0	1.0	1.0
	50%	0.999756	0.999878	1.0
	90%	0.966309	0.968506	0.981934
修改顶点	10%	1.0	1.0	1.0
	50%	0.758301	0.997192	0.822998
	90%	0.000488	0.742188	0.001343
数据裁剪	10%	1.0	1.0	1.0
	50%	1.0	0.999878	1.0
	90%	0.967163	0.966553	0.962158

复合攻击方式	几何攻击后删除50%顶点	删除50%顶点后修改90%顶点坐标	修改90%顶点坐标后裁剪50%数据	删除50%顶点后裁剪50%数据
提取水印
NC	1.0	0.001465	0.001343	0.972045

矢量地图同态加密域鲁棒水印算法

Robust Vector Map Watermarking Algorithm in Homomorphic Encrypted Domain

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