NDLI: Decomposition Construction for Secret Sharing Schemes with Graph Access Structures in Polynomial Time

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Wang, Huaxiong Ku, Bying-He Pieprzyk, Josef Sun, Hung-Min
Copyright Year	2010
Abstract	The purpose of this paper is to describe a new decomposition construction for perfect secret sharing schemes with graph access structures. The previous decomposition construction proposed by Stinson is a recursive method that uses small secret sharing schemes as building blocks in the construction of larger schemes. When the Stinson method is applied to the graph access structures, the number of such small schemes is typically exponential in the number of the participants, resulting in an exponential algorithm. Our method has the same flavor as the Stinson decomposition construction; however, the linear programming problem involved in the construction is formulated in such a way that the number of small schemes is polynomial in the size of the participants, which in turn gives rise to a polynomial time construction. We also show that if we apply the Stinson construction to the small schemes arising from our new construction, both have the same information rate.
Starting Page	617
Ending Page	638
Page Count	22
File Format	PDF
ISSN	08954801
DOI	10.1137/080733802
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	24
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-06-18
Access Restriction	Subscribed
Subject Keyword	secret sharing scheme Linear programming linear programming Directed graphs (digraphs), tournaments Entropy graph access structure Authentication and secret sharing information rate Cryptography
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Graph Decompositions and Secret Sharing Schemes (1995)

Graph Decompositions and Secret Sharing Schemes (2003)

The accessibility of an access structure

Decomposition Constructions for Secret Sharing Schemes (1998)

The optimal information rate of perfect secret sharing schemes

Secret sharing schemes for graph-based prohibited structures (1998).

An efficient construction of perfect secret sharing schemes for graph-based structures (1996)

Optimal Information Rates of Novel Graph Based Access Structures

The optimal information rate for graph access structures of nine participants

Decomposition Construction for Secret Sharing Schemes with Graph Access Structures in Polynomial Time

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