参与者人数为9的一类连通超图存取结构的信息率

doi:10.6040/j.issn.1671-9352.2.2014.181

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (09): 74-82.doi: 10.6040/j.issn.1671-9352.2.2014.181

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The optimal information rate of a type of access structures based on connected hypergraphs on nine participants

ZHANG Na, LI Zhi-hui

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, Shaanxi, China

Received:2014-06-24 Revised:2014-08-27 Online:2014-09-20 Published:2014-09-30

Abstract

Abstract: Based on the relationship between access structures and connected hypergraph, 226 connected hypergraph access structures with 9 vertices, 3 ranks and 4 or 5 hyperedges were given. These structures are not mutually isomorphism, and their optimal information rates were estimated. First, it was proved that there exists ideal secret sharing scheme for a kind of hyperstar with 4 hyperedges and shown that the lower bounds of the optimal information rates of the connected hypergraph with n(5≤n≤11) vertices and 3 ranks are 2/3. Then using the theory of hypergraphs, the exact values for the optimal information rate of 16 access structures were computed. Final, the remaining 210 access structures were classified, and the bounds of the optimal information rates of these access structures were estimated.

Key words: ideal hypergraph, secret sharing schemes, hypergraph access structure, optimal information rate, hypergraph

CLC Number:

TP309

ZHANG Na, LI Zhi-hui. The optimal information rate of a type of access structures based on connected hypergraphs on nine participants[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(09): 74-82.

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