A novel lossless commutative encryption and watermarking algorithm for vector geographic dataset

Combining the advantages of cryptography and digital watermarking, commutative encryption and watermarking (CEW) addresses the limitations of traditional information security technologies by simultaneously ensuring security and confirming copyright ownership. Existing CEW algorithms for vector geographic data cannot simultaneously meet the requirements of lossless and applicability to all types of vector geographic data. This investigation proposes a lossless CEW algorithm for all types vector geographic data. In the encryption scheme, all coordinate points are stored in a one-dimensional set for permutation encryption. This procedure is applicable to all types of vector geographic data. Then, the original coordinates are replaced with the encrypted coordinates according to the original spatial structure. Since encryption preserves the size of coordinate values, they can be gridded after normalization to ensure compatibility between encryption and watermarking. Subsequently, a characteristic matrix is generated by conducting singular value decomposition on the coordinate values within the grid. Finally, the XOR operation is executed between the encrypted watermark information and this matrix to complete the construction of the zero watermark. Experiments demonstrate that the encryption scheme can yield favorable encryption outcomes with just one scrambling, and the efficiency is greatly improved. The watermarking scheme is robust against most attacks on vector geographic data.