###### Abstract  
Multiple digital watermarking is an important and challenging task in geographic information science and data security. Vector geographic data are a basic data format for digital geographic data storage, and the security protection of these data involves copyright protection and tracking. As part of the solution, existing digital watermarking algorithms have made contributions to vector geographic data protection. However, when vector geographic data flow through multiple units, they need to be marked to ensure that the original data are not destroyed during data processing. Existing single or multiple data watermarking algorithms often fail in the presence of data processing because the new watermarks overlay the old ones. Consequently, a multiple digital watermarking algorithm based on multiple QIM (quantization index modulation) is proposed. First, based on traditional quantization index modulation (QIM), a multiple QIM is proposed. Unlike traditional QIM, in multiple QIM, the process of quantization is executed multiple times depending on the number of watermarks. Then, the vertices are quantized into different quantization intervals according to the multiple QIM. Finally, multiple watermarks are embedded into different quantization intervals to reduce the interference among multiple watermarks, and the original watermarks are not needed in the process of watermark detection. We then conducted experiments to test the multiple watermark method's robustness and capacity, with an emphasis on datasets with a lower data volume. The experimental results show that the proposed algorithm achieves good performance in terms of its robustness against common issues, such as vertices addition, data simplification, data cropping, and feature deletion; this holds true for both normal and small amounts of data. Additionally, it has a high multiple watermark capacity. multiple watermarking; QIM; vector geographic data +
Footnote †: journal: Applied Sciences  
1
Footnote †: journal: Applied Sciences  
1 State Key Laboratory of Geo-Information Engineering, Xi'an 710054, China; [EMAIL_ADDRESS]  
2 College of Intelligent Science and Control Engineering, Jinling Institute of Technology, Nanjing 211169, China; [EMAIL_ADDRESS]  
3 Institute of Field Engineering, Army Engineering University of PLA, Nanjing 210007, China  
*Correspondence: [EMAIL_ADDRESS]; Tel. : +86-13951748164  
**Citation:** [PERSON]; [PERSON]; [PERSON] Multiple Watermarking Algorithms for Vector Geographic Data Based on Multiple Quantization Index Modulation. _Appl. Sci._**2023**, 13, 12390. [[https://doi.org/10.3390/appl32212390](https://doi.org/10.3390/appl32212390)]([https://doi.org/10.3390/appl32212390](https://doi.org/10.3390/appl32212390))
to be solved in the field of information security. The application prospects of digital watermarking technology in securing vector geographic data are highly significant. Numerous scholars have extensively investigated digital watermarking technology for vector geographic data, yielding a plethora of valuable research findings [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. The current research on digital watermarking technology for vector geographic data primarily focuses on robust and fragile watermarking techniques, which are predominantly employed to address issues related to data copyright protection, single-user usage tracking, and content authentication. With the continuous advancement of data management and distribution technology, the transmission of vector geographic data has become increasingly convenient. During the transmission process, vector geographic data may undergo multiple transformations and be accessed by various entities. The security protection of vector geographic data based on digital watermarking technology entails novel challenges. For example, different distributors are allowed to embed multiple different watermarks in the same cover data, either in heterogeneous time and space or not.