A robust and lossless commutative encryption and watermarking algorithm for vector geographic data

As an organic integration of encryption and watermarking technology, commutative encryption and watermarking (CEW) overcomes the limitation that a single security protection technology cannot provide full-process data protection. Existing CEW algorithms for vector geographic data, however, only take attack robustness into account, making them inappropriate for copyright protection of high-precision vector geographic data since the influence of embedding watermark on data accuracy. This study presents a CEW algorithm that utilizes geometric features and the initial vertex order of features to address this issue. The minimum bounding rectangle (MBR) is chosen as the geometric characteristic in this method to provide independent operating space for watermark and encryption. The encryption is completed by randomly shifting the coordinates of the features. At the same time, the watermark information is embedded by modifying the features' starting vertex order. The watermark can be extracted either from the plaintext or the ciphertext, as the order of the element's starting points remains unchanged regardless of the coordinates. Finally, the commutative, robustness, and lossless ness of the algorithm in this study are experimentally validated. As can be demonstrated by the results, the proposed algorithm is more robust, lossless, and secure than some state-of-the-art algorithms.