Secret Sharing Schemes for Dense Forbidden Graphs

Beimel, Amos; FarríS, Oriol; Peter, Naty

doi:10.1007/978-3-319-44618-9_27

Cited by 7 publications

(1 citation statement)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, in 2017, Liu, Vaikuntanathan, and Wee [36] proved that every forbidden graph access structure could be realized by a non-linear secret sharing scheme with the total share size n 1+o (1) . For the forbidden dense graph access structures having at least n 2 −n 1+β edges, where 0 ≤ β < 1 2 , Beimel, Farras, and Peter [7] constructed a linear secret sharing scheme with the total share size O(n 7/6+2β/3 ). Later, in 2020, Beimel, Farras, Mintz, and Peter [6] provided efficient constructions on the share size of linear secret sharing schemes for forbidden sparse and dense graph access structures based on the monotone span programs.…”

Section: Forbidden Graph Access Structuresmentioning

confidence: 99%

Linear Secret-Sharing Schemes for $k$-uniform access structures

Kim,

Kwon,

Lee

2021

Preprint

View full text Add to dashboard Cite

A k-uniform hypergraph H = (V, E) consists of a set V of vertices and a set E of hyperedges (k-hyperedges), which is a family of k-subsets of V . A forbidden k-homogeneous (or forbidden k-hypergraph) access structure A is represented by a k-uniform hypergraph H = (V, E) and has the following property: a set of vertices (participants) can reconstruct the secret value from their shares in the secret sharing scheme if they are connected by a k-hyperedge or their size is at least k + 1. A forbidden k-homogeneous access structure has been studied by many authors [1,2,10,45] under the terminology of k-uniform access structures. In this paper, we provide efficient constructions on the total share size of linear secret sharing schemes for sparse and dense k-uniform access structures for a constant k using the hypergraph decomposition technique and the monotone span programs.

show abstract