{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T04:29:27Z","timestamp":1768624167194,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T00:00:00Z","timestamp":1635120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41761080"],"award-info":[{"award-number":["41761080"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41930101"],"award-info":[{"award-number":["41930101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Industrial Support and Guidance Project of Universities in Gansu Province","award":["2019C-04"],"award-info":[{"award-number":["2019C-04"]}]},{"name":"Talent Innovation Venture Science and Technology Program of Lanzhou","award":["2016-RC-59"],"award-info":[{"award-number":["2016-RC-59"]}]},{"name":"Funded by LZJTU EP","award":["201806"],"award-info":[{"award-number":["201806"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Commutative encryption and watermarking (CEW) is an emerging method that combines encryption technology with digital watermarking technology. It has the dual capability of secure transmission and copyright protection. However, the existing CEW methods for vector maps have good robustness in resisting geometric attacks but poor resistance to vertex attacks (e.g., addition, deletion, etc.). To solve this problem, here we propose a novel invariant-based CEW algorithm for vector maps, which consists of permutation-based encryption scheme and coordinates-based watermarking scheme. In the encryption scheme, the encryption key is generated via the Gaussian distribution method combined with the SHA-512 hash method; then, the double random position permutation strategy is applied to the vector map encryption. In watermarking embedding scheme, the original watermark image is scrambled via logistic chaotic encryption before embedding, and the coordinates of all the vertices are normalized. Then, the scrambled watermark image is embedded into the normalized coordinates. Results show that: proposed method is more robust to conventional attacks (e.g., vertex addition and deletion, reordering and data format conversion) and geometric attacks (e.g., scaling and translation). In addition, compared with the existing CEW methods for vector maps, the proposed method has higher security and stronger robustness against vertex attacks.<\/jats:p>","DOI":"10.3390\/ijgi10110718","type":"journal-article","created":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T21:40:21Z","timestamp":1635198021000},"page":"718","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["A Novel Invariant Based Commutative Encryption and Watermarking Algorithm for Vector Maps"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6921-0776","authenticated-orcid":false,"given":"Yu","family":"Li","sequence":"first","affiliation":[{"name":"Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China"},{"name":"National Local Joint Engineering Research Center of Technologies and Application for National Geographic State Monitoring, Lanzhou 730070, China"},{"name":"Gansu Provincial Engineering Laboratory for National Geographic State Monitoring, Lanzhou 730070, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7904-7044","authenticated-orcid":false,"given":"Liming","family":"Zhang","sequence":"additional","affiliation":[{"name":"Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China"},{"name":"National Local Joint Engineering Research Center of Technologies and Application for National Geographic State Monitoring, Lanzhou 730070, China"},{"name":"Gansu Provincial Engineering Laboratory for National Geographic State Monitoring, Lanzhou 730070, China"}]},{"given":"Xiaolong","family":"Wang","sequence":"additional","affiliation":[{"name":"Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China"},{"name":"National Local Joint Engineering Research Center of Technologies and Application for National Geographic State Monitoring, Lanzhou 730070, China"},{"name":"Gansu Provincial Engineering Laboratory for National Geographic State Monitoring, Lanzhou 730070, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3016-9635","authenticated-orcid":false,"given":"Xingang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Geography and Ocean Science, Nanjing University, Nanjing 210008, China"}]},{"given":"Qihang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China"},{"name":"National Local Joint Engineering Research Center of Technologies and Application for National Geographic State Monitoring, Lanzhou 730070, China"},{"name":"Gansu Provincial Engineering Laboratory for National Geographic State Monitoring, Lanzhou 730070, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"30709","DOI":"10.1007\/s11042-020-08916-4","article-title":"A Robust Watermarking Algorithm for Vector Geographic Data Based on Qim and Matching Detection","volume":"79","author":"Yang","year":"2020","journal-title":"Multimed. 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