Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/118046
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- Title
- Decomposition construction for secret sharing schemes with graph access structures in polynomial time
- Related
- SIAM journal on discrete mathematics, Vol. 24, No. 2 (2011), p.617-638
- DOI
- 10.1137/080733802
- Publisher
- Society for Industrial and Applied Mathematics
- Date
- 2011
- FoR/RFCD Code(s)
-
080200 Computation Theory and Mathematics
010100 Pure Mathematics
- Author/Creator
- Sun, Hung-Min
- Author/Creator
- Wang, Huaxiong
- Author/Creator
- Ku, Bying-He
- Author/Creator
- Pieprzyk, Josef
- Description
- 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.
- Description
- 22 page(s)
- Subject Keyword
- 080200 Computation Theory and Mathematics
- Subject Keyword
- 010100 Pure Mathematics
- Subject Keyword
- secret sharing scheme
- Subject Keyword
- graph access structure
- Subject Keyword
- linear programming
- Subject Keyword
- information rate
- Resource Type
- journal article
- Organisation
- Macquarie University. Dept. of Computing
- Identifier
- http://hdl.handle.net/1959.14/118046
- Identifier
- ISSN:1095-7146
- Identifier
- mq-rm-2010004005
- Language
- eng
- Rights
- Copyright SIAM Publications. Article archived for private and non-commercial use with the permission of the author and according to publisher conditions. For further information see http://www.siam.org/
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