As the foundation of information security, encryption technology employs encryption algorithms and keys to transform the vector map into an unrecognizable ciphertext state. Existing encryption algorithms for vector maps rely on symmetric encryption, which poses risks in key management and distribution. Secondly, most existing vector map encryption algorithms cannot encrypt point data. To address these issues, we designed a lossless asymmetric, encryption algorithm for vector maps based on the RSA public key system. Firstly, the integer part of the coordinate value in the vector map is dynamically selected to improve encryption efficiency, and RSA is used to perform asymmetric encryption on this part. Secondly, to achieve the encryption effect of one map and one ciphertext, the information from the vector map itself is used to generate the key for a two-dimensional chaotic system through the SHA-512 hash algorithm. Subsequently, a random sequence is generated through the iterative process of the chaotic system to scramble and reorganize the X and Y coordinates of the vector map. The experimental results demonstrate that the asymmetric encryption algorithm is applicable to all types of vector map data and can achieve lossless encryption and decryption. In addition, the algorithm can be applied to various types of geospatial data, such as 3D point clouds and oblique photography 3D models.