Decomposition construction for secret sharing schemes with graph access structures in polynomial time

Sun, Hung-Min, Wang, Huaxiong, Ku, Bying-He, & Pieprzyk, Josef (2010) Decomposition construction for secret sharing schemes with graph access structures in polynomial time. SIAM Journal on Discrete Mathematics, 24(2), pp. 617-638.

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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.

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ID Code: 69353
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: Secret sharing scheme, Graph access structure, Linear programming, Information rate
DOI: 10.1137/080733802
ISSN: 1095-7146
Divisions: Current > Schools > School of Electrical Engineering & Computer Science
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
Deposited On: 26 Mar 2014 22:28
Last Modified: 31 Mar 2014 01:44

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