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Multilevel Declassification Method for Geographic Vector Field Data: A Geometric Algebra Approach

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Abstract

There is increasing demand for multi-level declassification of geographic vector field data in the big data era. Different from traditional encryption, declassification does not aim at making the original data unavailable through perturbation and transformation. During declassification process, the general geospatial features are usually retained but the detailed information is hidden from the perspective of data security. Furthermore, when faced with different levels of confidentiality, different levels of declassification are needed. In this paper, A declassification and reversion method with multi-level schemes is realized under the geometric algebra (GA) framework. In our method, the geographic vector field data is uniformly expressed as a GA object. Then, the declassification methods are proposed for vector field data with the rotor operator and perturbation operator. The declassification methods can progressively hide the detailed information of the vector field by vector rotating and vector perturbating. To make our method more unified and adaptive, a GA declassification operator is also constructed to realize the declassification computing of geographic vector field data. Our method is evaluated quantitatively by comparing the numerical and structure characterization of the declassification results with the original data. Divergence and curl calculating results are also compared to evaluate the reanalysis ability of the declassification results. Experiments have shown that our method can perform effective multi-level controls and has good randomness and a high degree of freedom in numerical and structure characteristics of geophysical vector field data. The method can well capture the application needs of geographic vector field data in data disclosure, secure transmission, encapsulation storage, and other aspects.

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Data Availability

The 2D and 3D vector field data that support the findings of this study are available in figshare with the identifier https://doi.org/10.6084/m9.figshare.17762696.v3

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 41631177, 41976186, 42001320).

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Authors and Affiliations

  1. Key Laboratory of Virtual Geographic Environment, Nanjing Normal University, Ministry of Education, No.1 Wenyuan Road, Nanjing, 210023, Jiangsu, China

    Wen Luo, Yun Wang, Xueying Zhang, Dongshuang Li, Zhaoyuan Yu, Zhenjun Yan & Linwang Yuan

  2. State Key Laboratory Cultivation Base of Geographical Environment Evolution, Nanjing, 210023, Jiangsu, China

    Wen Luo, Yun Wang, Xueying Zhang, Dongshuang Li, Zhaoyuan Yu, Zhenjun Yan & Linwang Yuan

  3. Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing, 210023, Jiangsu, China

    Wen Luo, Yun Wang, Xueying Zhang, Dongshuang Li, Zhaoyuan Yu, Zhenjun Yan & Linwang Yuan

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  1. Wen Luo
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Correspondence to Linwang Yuan.

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This article is part of the ENGAGE 2020 Topical Collection on Geometric Algebra for Computing, Graphics and Engineering edited by Werner Benger, Dietmar Hildenbrand, Eckhard Hitzer, and George Papagiannakis.

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Luo, W., Wang, Y., Zhang, X. et al. Multilevel Declassification Method for Geographic Vector Field Data: A Geometric Algebra Approach. Adv. Appl. Clifford Algebras 32, 52 (2022). https://doi.org/10.1007/s00006-022-01229-9

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