Vector geographic data commutative encryption and watermarking algorithm based on prediction differences

Commutative encryption and watermarking (CEW) is a seamless integration of encryption and watermarking technologies, overcoming the limitations of single security protection methods that may fail to provide comprehensive data protection. It is a research hotspot in the field of geographic information security. However, constructing or selecting stable features for vector point data to apply CEW algorithms remains a challenging problem. To address this, this paper utilizes space-filling curves to organize discrete points into line or polygon types and proposes a CEW algorithm for vector data based on prediction differences. Specifically, feature points are used to fit curves, providing independent operational spaces for watermarking and encryption. The segmented fitted curves are arbitrarily flipped to achieve perceptual encryption, while watermarks are embedded in the differences between the fitted curves and the actual data. Experimental results demonstrate that the proposed algorithm effectively addresses the issue of existing algorithms being unsuitable for point data. In simulated real-world scenarios, the extracted watermark information achieved NC values above 0.75, indicating strong robustness. Under conditions using existing lossless algorithms, the watermark capacity of the proposed method is thousands of times higher than that of existing algorithms, and it exhibits excellent encryption security, providing a new perspective for further research on lossless CEW. •The proposed algorithm solves the problem that cannot be applied to datasets.•Combination of reversible watermarking and encryption balances data accuracy and security.•This algorithm implements selective encryption, decryption and lossless recovery.•The algorithm is suitable for Geoinformation data with similar structure.