New results on multipartite access structures

2006 ◽  
Vol 153 (4) ◽  
pp. 153 ◽  
Author(s):  
J. Herranz ◽  
G. Saez
Keyword(s):  
Access Structures ◽  
Multipartite Access Structures

scholarly journals An Efficient Compartmented Secret Sharing Scheme Based on Linear Homogeneous Recurrence Relations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Guoai Xu ◽  
Jiangtao Yuan ◽  
Guosheng Xu ◽  
Zhongkai Dang
Keyword(s):  
Secret Sharing ◽  
Recovery Phase ◽  
Threshold Scheme ◽  
Secret Sharing Schemes ◽  
Access Structure ◽  
Recurrence Sequence ◽  
Access Structures ◽  
Sharing Scheme ◽  
Global Threshold ◽  
Multipartite Access Structures

Multipartite secret sharing schemes are those that have multipartite access structures. The set of the participants in those schemes is divided into several parts, and all the participants in the same part play the equivalent role. One type of such access structure is the compartmented access structure, and the other is the hierarchical access structure. We propose an efficient compartmented multisecret sharing scheme based on the linear homogeneous recurrence (LHR) relations. In the construction phase, the shared secrets are hidden in some terms of the linear homogeneous recurrence sequence. In the recovery phase, the shared secrets are obtained by solving those terms in which the shared secrets are hidden. When the global threshold is t , our scheme can reduce the computational complexity of the compartmented secret sharing schemes from the exponential time to polynomial time. The security of the proposed scheme is based on Shamir’s threshold scheme, i.e., our scheme is perfect and ideal. Moreover, it is efficient to share the multisecret and to change the shared secrets in the proposed scheme.

Further ideal multipartite access structures from integer polymatroids

2015 ◽  
Vol 58 (7) ◽  
pp. 1-13 ◽  
Author(s):  
YuJue Wang ◽  
QianHong Wu ◽  
Duncan S. Wong ◽  
Bo Qin ◽  
Yi Mu ◽  
...  
Keyword(s):  
Access Structures ◽  
Multipartite Access Structures ◽  
Integer Polymatroids

scholarly journals Secret Sharing Schemes on Sparse Homogeneous Access Structures with Rank Three

10.37236/1825 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Jaume Martí-Farré ◽  
Carles Padró
Keyword(s):  
Secret Sharing ◽  
Access Structure ◽  
Open Problems ◽  
Access Structures ◽  
The Family ◽  
Ideal Access Structures ◽  
Optimal Information ◽  
Made In ◽  
The Ideal

One of the main open problems in secret sharing is the characterization of the ideal access structures. This problem has been studied for several families of access structures with similar results. Namely, in all these families, the ideal access structures coincide with the vector space ones and, besides, the optimal information rate of a non-ideal access structure is at most $2/3$. An access structure is said to be $r$-homogeneous if there are exactly $r$ participants in every minimal qualified subset. A first approach to the characterization of the ideal $3$-homogeneous access structures is made in this paper. We show that the results in the previously studied families can not be directly generalized to this one. Nevertheless, we prove that the equivalences above apply to the family of the sparse $3$-homogeneous access structures, that is, those in which any subset of four participants contains at most two minimal qualified subsets. Besides, we give a complete description of the ideal sparse $3$-homogeneous access structures.

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