文档介绍：第24卷 第6期 ,
2022年6月 es. 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
收稿日期：2021-11-02；修回日期：2021-12-14.
基金项目：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）。[ Foundation items: Innovative Research Groups of the Natural Science Foundation of Hunan
Province, ; Na