Matroid Characterization and Ideal Secret Sharing for Complete t-Partite k-Uniform Hypergraph Access Structures

12 pages•Published: August 6, 2026

Chunming Tang, Zheng Chen, Haonan Fu and Hongwei Zhu

Abstract

Secret sharing schemes are an important class of cryptographic protocols, and linear codes are one of the main tools for constructing such schemes. This paper presents a matroid characterization and the construction of an ideal secret sharing scheme for complete t-partite k-uniform hypergraph access structures. First, we present a representable connected matroid and prove that the complete t-partite k-uniform hypergraph access structure is exactly the port of this matroid. Then, based on the theory of Brickell and Davenport on matroids and ideal access structures, and using linear codes as a tool, we give an ideal secret sharing scheme that realizes this access structure. This scheme unifies Shamir's threshold scheme and the complete t-partite graph scheme of Brickell et al. as special cases.

Keyphrases: complete t partite k uniform hypergraph, linear codes, representable matroid, secret sharing

In: Tung-Tso Tsai, Huy Kang Kim, Yujue Wang and Akira Yamada (editors). Proceedings of The 21st Asia Joint Conference on Information Security, vol 111, pages 135-146.

Links:	https://easychair.org/publications/paper/g5PG
	https://doi.org/10.29007/9vpl

BibTeX entry

@inproceedings{AsiaJCIS2026:Matroid_Characterization_Ideal_Secret,
  author    = {Chunming Tang and Zheng Chen and Haonan Fu and Hongwei Zhu},
  title     = {Matroid Characterization and Ideal Secret Sharing for Complete t-Partite k-Uniform Hypergraph Access Structures},
  booktitle = {Proceedings of The 21st Asia Joint Conference on Information Security},
  editor    = {Tung-Tso Tsai and Huy Kang Kim and Yujue Wang and Akira Yamada},
  series    = {EPiC Series in Computing},
  volume    = {111},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/g5PG},
  doi       = {10.29007/9vpl},
  pages     = {135-146},
  year      = {2026}}

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