地球信息科学学报 ›› 2022, Vol. 24 ›› Issue (6): 1120-1129.doi: 10.12082/dqxxkx.2022.210698
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:
WU Baiyan1,2,*(), DAI Qianyi1,2, PENG Yuwei3, WANG Wei4
Received:
2021-11-02
Revised:
2021-12-14
Online:
2022-06-25
Published:
2022-08-25
Contact:
*WU Baiyan wby@hnust.edu.cnSupported by:
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。
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
表1
量化步长 Q n与RMSE、最大误差的关系
| 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2
鲁棒性测试结果
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 | ![]() | ![]() | ![]() |
旋转30° | ![]() | ![]() | ![]() | |
缩放2.5倍 | ![]() | ![]() | ![]() | |
删除顶点 | 10% | ![]() | ![]() | ![]() |
50% | ![]() | ![]() | ![]() | |
90% | ![]() | ![]() | ![]() | |
修改顶点 | 10% | | ![]() | ![]() |
50% | ![]() | ![]() | ![]() | |
90% | ![]() | ![]() | ![]() | |
数据裁剪 | 10% | ![]() | ![]() | ![]() |
50% | ![]() | ![]() | ![]() | |
90% | ![]() | ![]() | ![]() |
[1] | 曹刘娟, 门朝光, 孙建国. 基于空间特征的二维矢量地图可逆水印算法原理[J]. 测绘学报, 2010, 39(4):422-427. |
[ Cao L J, Men C G, Sun J G. Space feature-based reversible watermarking theory for 2D-Vector maps[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(4):422-427. ] | |
[2] |
Wang N N. Reversible watermarking for 2D vector maps based on normalized vertices[J]. Multimed Tools and Applications, 2017, 76:20935-20953. DOI: 10.1007/s11042-016-3970-5
doi: 10.1007/s11042-016-3970-5 |
[3] |
Lin Z X, Peng F, Long M. A low-distortion reversible watermarking for 2D engineering graphics based on region nesting[J]. IEEE Transactions on Information Forensics and Security, 2018, 13(9):2372-2382. DOI: 10.1109/TIF S.2018.2819122
doi: 10.1109/TIF S.2018.2819122 |
[4] |
Peng F, Lin Z X, Zhang X, et al. A semi-fragile reversible watermarking for authenticating 2D engineering graphics based on improved region nesting[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2021, 31(1): 411-423. DOI: 10.1109/TCSVT.2020.2969464
doi: 10.1109/TCSVT.2020.2969464 |
[5] | 侯翔, 闵连权, 唐立文. 定位篡改实体组的矢量地图脆弱水印算法[J]. 武汉大学学报·信息科学版, 2020, 45(2):309-316. |
[ Hou X, Min L Q, Tang L W. Fragile watermarking algorithm for locating tampered entity groups in vector map data[J]. Geomatics and Information Science of Wuhan University, 2020, 45(2):309-316. ] DOI: 10.132 03/j.whugis20170404
doi: 10.132 03/j.whugis20170404 |
|
[6] | 杨成松, 朱长青, 陶大欣. 基于坐标映射的矢量地理数据全盲水印算法[J]. 中国图象图形学报, 2010, 15(4):684-688. |
[ Yang C S, Zhu C Q, Tao D X. A blind watermarking algorithm for vector geo-spatial data based on coordinate mapping[J]. Journal of Image and Graphics, 2010, 15(4):684-688. ] | |
[7] |
Yan H W, Li J, Wen H. A key points-based blind watermarking approach for vector geo-spatial data[J]. Computers, Environment and Urban Systems, 2011, 35(2011):485-492. DOI: 10.1016/j.compenvurbsys.2010.10.004
doi: 10.1016/j.compenvurbsys.2010.10.004 |
[8] |
Wang Y Y, Yang C S, Zhu C Q. A multiple watermarking algorithm for vector geographic data based on coordinate mapping and domain subdivision[J]. Multimedia Tools and Applications, 2017. DOI: 10.1007/s11042-017-5358-6
doi: 10.1007/s11042-017-5358-6 |
[9] |
Yan H W, Zhang L M, Yang W F. A normalization-based watermarking scheme for 2D vector map data[J]. Earth Science Informatics, 2017, 10(4):471-481. DOI: 10.1007/s12145-017-0310-x
doi: 10.1007/s12145-017-0310-x |
[10] | 许德合, 朱长青, 王奇胜. 利用QIM的DFT矢量空间数据盲水印模型[J]. 武汉大学学报·信息科学版, 2010, 35(9):1100-1103. |
[ Xu D H, Zhu C Q, Wang Q S. Blind watermarking model of vector spatial data based on DFT of QIM[J]. Geomatics and Information Science of Wuhan University, 2010, 35(9):1100-1103. ] DOI: 10.13203/j.whugis2010.09.014
doi: 10.13203/j.whugis2010.09.014 |
|
[11] | 张黎明, 闫浩文, 齐建勋,等. 基于DFT的可控误差矢量空间数据盲水印算法[J]. 武汉大学学报·信息科学版, 2015, 40(7):990-994. |
[ Zhang L M, Yan H W, Qi J X, et al. A blind watermarking algorithm for copyright protection of vector geospatial data under controllable errors based on DFT[J]. Geomatics and Information Science of Wuhan University, 2015, 40(7):990-994. ] DOI: 10.13203/j.whugis20130686
doi: 10.13203/j.whugis20130686 |
|
[12] | 杨成松, 朱长青. 基于常函数的抗几何变换的矢量地理数据水印算法[J]. 测绘学报, 2011, 40(2):256-262. |
[ Yang C S, Zhu C Q. Robust watermarking algorithm for geometrical transform for vector geospatial data based on invariant function[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(2):256-262. ] | |
[13] |
Wang C J, Peng Z Y, Peng Y W, et al. Watermarking geographical data on spatial topological relations[J]. Multimedia Tools and Applications, 2012, 57(1):67-89. DOI: 10.1007/s11042-010-0536-9
doi: 10.1007/s11042-010-0536-9 |
[14] | 张驰, 李安波, 闾国年,等. 以夹角调制的矢量地图可逆水印算法[J]. 地球信息科学学报, 2013, 15(2):180-186. |
[ Zhang C, Li A B, Lv G N, et al. A reversible watermarking algorithm for vector map based on angle modulating[J]. Journal of Geo-information Science, 2013, 15(2):180-186. ]
doi: 10.3724/SP.J.1047.2013.00180 |
|
[15] |
Lee S H, Huo X J, Kwon K R. Vector watermarking method for digital map protection using arc length distribution[J]. IEICE Transactions on Information and Systems, 2014, E97-D(1):34-42. DOI: 10.1587/transinf.E97.D.34
doi: 10.1587/transinf.E97.D.34 |
[16] |
Peng Z Y, Yue M L, Wu X, et al. Blind watermarking scheme for polylines in vector geo-spatial data[J]. Multimedia Tools and Applications, 2015, 74(24):11721-11739. DOI: 10.1007/s11042-014-2259-9
doi: 10.1007/s11042-014-2259-9 |
[17] | 佟德宇, 朱长青, 任娜. 小数据量矢量地理数据水印算法[J]. 测绘学报, 2018, 47(11):1518-1525. |
[ Tong D Y, Zhu C Q, Ren N. Watermarking algorithm applying to small amount of vector geographical data[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(11):1518-1525. ] | |
[18] |
Jang B J, Lee S H, Lee E J, et al. A crypto-marking method for secure vector map[J]. Multimedia Tools and Applications, 2017, 76:16011-16044. DOI: 10.1007/s11042-016-3893-1
doi: 10.1007/s11042-016-3893-1 |
[19] |
Peng F, Lin Z X, Zhang X, et al. Reversible data hiding in encrypted 2D vector graphics based on reversible mapping model for real numbers[J]. IEEE Transactions on Information Forensics and Security, 2019, 14(9):2400-2411. DOI: 10.1109/TIFS.2019.2899520
doi: 10.1109/TIFS.2019.2899520 |
[20] |
Peng F, Jiang W, Qi Y, et al. Separable robust reversible watermarking in encrypted 2D vector graphics[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2020, 30(8):2391-2405. DOI: 10.1109/TCSVT.2020.2986782
doi: 10.1109/TCSVT.2020.2986782 |
[21] | Paillier P. Public-Key cryptosystems based on composite degree residuosity classes[C]. In: Proc. of the Int'l Conf. on the Theory and Application of Cryptographic Techniques, Prague, 1999:233-238. |
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