A lot of watermarking algorithms for vector geographic data are presented in the literature. Due to widely application of digital watermarking, more demands are required, such as multiple watermarking algorithm. However, vector geographic data attracted less research focus on multiple watermarking. Consequently, a multiple watermarking algorithm for vector geographic data is proposed. In particular, the vertices are mapped to the logic domains firstly based on the constructed function. Then every domain is subdivided into blocks according to dichotomy and the number of embedding watermarks. Then, every watermark is embedded in the corresponding block. During the watermark detection, the watermarks are detected without the original vector geographic data. Finally, the experiments are made to test the multiple watermark capacity and robustness against attacks, with an emphasis on cropping attacks. The experimental results show that the proposed algorithm has good robustness against common attacks, such as, data simplification, vertex addition, vertex deletion, feature deletion, and cropping attacks. Moreover, the algorithm provides high multiple watermark capacity.

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Vector geographic data play an important role in location information services. Digital watermarking has been widely used in protecting vector geographic data from being easily duplicated by digital forensics. Because the production and application of vector geographic data refer to many units and departments, the demand for multiple watermarking technology is increasing. However, multiple watermarking algorithm for vector geographic data draw less attention, and there are many urgent problems to be solved. Therefore, an efficient robust multiple watermark algorithm for vector geographic data is proposed in this paper. The coordinates in vector geographic data are first randomly divided into non-repetitive sets. The multiple watermarks are then embedded into the different sets. In watermark detection correlation, the Lindeberg theory is used to build a detection model and to confirm the detection threshold. Finally, experiments are made in order to demonstrate the detection algorithm, and to test its robustness against common attacks, especially against cropping attacks. The experimental results show that the proposed algorithm is robust against the deletion of vertices, addition of vertices, compression, and cropping attacks. Moreover, the proposed detection algorithm is compatible with single watermarking detection algorithms, and it has good performance in terms of detection efficiency. Therefore, multiple watermarking technology can effectively solve the above information security problems of vector geographic data.Currently, many scholars have been devoted to developing digital watermark technology, and they have proposed many algorithms [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. However, these algorithms focus on embedding only one watermark in the cover data, which then lacks multi-copyright protection. Multiple watermarking draws less attention than single watermarking, and it does not simply involve the embedding of different watermarks by using the single watermarking algorithm. The multiple watermarking algorithm commonly focuses on images and videos. There are three main methods for addressing the impact of multiple watermarks, as described in References [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The first is dividing the images into multiple blocks for multiple watermarks [17,18,27,29]. The second is embedding multiple watermarks into different frequency domains or channels [19][20][21][22][23]26,30]. The last is merging multiple watermarks into one [24,25,27]. Usually multiple methods are combined in one algorithm. In the above references, only a few previous works have been proposed for vector geographic data; for instance, References [24-29]. Sun et al. combined a child copyright watermark with another child watermark consisting of features selected by fuzzy clustering from the vector map. The new watermark was then embedded into the vector map [24]. Li et al. proposed a multiple watermark embedding solution through the generation of additional information with waterma...