Commutative Encryption and Watermarking Algorithm Based on Feature Invariants for Secure Vector Map

The existing commutative encryption and watermarking (CEW) methods based on feature invariants can achieve both the robustness of the watermarking algorithm and the security of the encryption algorithm. However, they are only applicable to the raster data such as images, videos, etc. In particular, the organization structure and storage structure of vector map have not been considered in these methods. Therefore, they cannot be used for vector map. This paper derives two feature invariants to solve this problem, which are the sum of inner angles and the storage direction of two adjacent objects according to the inherent characteristics of vector map. Based on these two feature invariants, a new CEW method is proposed in this paper, which includes the feature invariants based watermarking algorithm and the perceptual stream cipher based encryption algorithm on coordinates. Since the coordinate values used in encryption and the feature invariants used in watermarking are independent of each other, the commutativity is achieved for the proposed CEW method. The experiments are given to verify that the proposed CEW method can achieve the commutativity between encryption and watermarking without deteriorating accuracy of data. Besides, it has been verified that the proposed method is more robust to rotate, scaling, translation, and projection transformation compared with the existing CEW methods and has high security. The proposed algorithm has good scalability of encryption, and arbitrary encryption methods based on encrypting the coordinate values can be applied without affecting the extracted feature invariants.