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Designs, Codes and Cryptography

, Volume 87, Issue 12, pp 2913–2940 | Cite as

Efficient explicit constructions of compartmented secret sharing schemes

  • Qi ChenEmail author
  • Chunming Tang
  • Zhiqiang Lin
Article
  • 81 Downloads

Abstract

Multipartite secret sharing schemes have been an important object of study in the area of secret sharing schemes. Two interesting families of multipartite access structures are hierarchical access structures and compartmented access structures. This work deals with efficient and explicit constructions of ideal compartmented secret sharing schemes, while most of the known constructions are either inefficient or randomized. We construct ideal linear secret sharing schemes for three types of compartmented access structures, such as compartmented access structures with upper bounds, compartmented access structures with lower bounds, and compartmented access structures with upper and lower bounds. There exist some methods to construct ideal linear schemes realizing these compartmented access structures in the literature, but those methods are inefficient in general because non-singularity of many matrices has to be determined to check the correctness of the scheme. Our constructions do not need to do these computations. Our methods to construct ideal linear schemes realizing these access structures combine polymatroid-based techniques with Gabidulin codes. Gabidulin codes play a fundamental role in the constructions, and their properties imply that our methods are efficient.

Keywords

Secret sharing schemes Multipartite access structures Compartmented access structures Matroids Polymatroids Gabidulin codes 

Mathematics Subject Classification

94A62 94B05 

Notes

Acknowledgements

The authors are very grateful to the reviewers and Dr. Yue Zhou for their detailed comments and suggestions that much improved the presentation and quality of this paper. Special thanks to the reviewer who suggests to use polymatroid–based techniques and gives many guidance to improve the presentation of our main result by using polymatroid-based techniques.

Funding

This research was supported in part by the Foundation of National Natural Science of China (Nos. 61772147, 61702124), Guangdong Province Natural Science Foundation of major basic research and Cultivation project (No. 2015A030308016) and Project of Ordinary University Innovation Team Construction of Guangdong Province (No. 2015KCXTD014).

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Authors and Affiliations

  1. 1.Advanced Institute of Engineering Science for Intelligent ManufacturingGuangzhou UniversityGuangzhouChina
  2. 2.College of Mathematics and Information ScienceGuangzhou UniversityGuangzhouChina
  3. 3.Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education InstitutesGuangzhou UniversityGuangzhouChina

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