The complexity of the connected graph access structure on seven participants

2017 ◽  
Vol 11 (1) ◽  
pp. 25-35
Author(s):  
Massoud Hadian Dehkordi ◽  
Ali Safi
Keyword(s):  
Lower Bound ◽  
Secret Sharing ◽  
Upper Bound ◽  
Connected Graph ◽  
Access Structure ◽  
Decomposition Techniques ◽  
Induced Subgraph ◽  
Access Structures ◽  
Graph Access

AbstractIn this paper, we study an important problem in secret sharing that determines the exact value or bound for the complexity. First, we use the induced subgraph complexity of the graph G with access structure Γ to obtain a lower bound on the complexity of the graph G. Then, applying decomposition techniques, we obtain an upper bound on the complexity of the graph G. We determine the exact values of the complexity for each of the ten graph access structures on seven participants. Also, we improve the value bound of the complexity for the six graph access structures with seven participants.

The Optimal Information Rates of the Graph Access Structures on Seven Participants

2013 ◽  
Vol 859 ◽  
pp. 596-601
Author(s):  
Zhi Hui Li ◽  
Yun Song ◽  
Yong Ming Li
Keyword(s):  
Secret Sharing ◽  
Information Rate ◽  
Secret Sharing Scheme ◽  
Access Structure ◽  
Open Problems ◽  
Information Rates ◽  
Access Structures ◽  
Sharing Scheme ◽  
Optimal Information ◽  
Graph Access

The information rate is an important metric of the performance of a secret-sharing scheme. In this paper, we deal with determining the exact values for the optimal information rates of the six graph access structures and improving the information rate of a graph access structure on seven participants, which remained as open problems in Song's and Wang's paper([1,2]). We prove that the optimal information rate for each of the six graph access structures is equal to 4/7

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.

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

2010 ◽  
Vol 24 (2) ◽  
pp. 617-638 ◽  
Author(s):  
Hung-Min Sun ◽  
Huaxiong Wang ◽  
Bying-He Ku ◽  
Josef Pieprzyk
Keyword(s):  
Polynomial Time ◽  
Secret Sharing ◽  
Secret Sharing Schemes ◽  
Access Structures ◽  
Graph Access

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.

scholarly journals Message randomization and strong security in quantum stabilizer-based secret sharing for classical secrets

2020 ◽  
Vol 88 (9) ◽  
pp. 1893-1907
Author(s):  
Ryutaroh Matsumoto
Keyword(s):  
Secret Sharing ◽  
Explicit Construction ◽  
Secret Sharing Schemes ◽  
Secret Sharing Scheme ◽  
Access Structure ◽  
Access Structures ◽  
Sharing Scheme ◽  
Randomized Encoding

Abstract We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert–Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple symbols in its classical secret are revealed to an intermediate set, and justify the necessity of incorporating strong security criterion of conventional secret sharing. Finally, we propose an explicit construction of strongly secure ramp secret sharing scheme by quantum stabilizers, which can support twice as large classical secrets as the McEliece–Sarwate strongly secure ramp secret sharing scheme of the same share size and the access structure.

ON THE DEALER'S RANDOMNESS REQUIRED IN PERFECT SECRET SHARING SCHEMES WITH ACCESS STRUCTURES OF CONSTANT RANK

2000 ◽  
Vol 11 (02) ◽  
pp. 263-281
Author(s):  
HUNG-MIN SUN
Keyword(s):  
Secret Sharing ◽  
Upper Bounds ◽  
Secret Sharing Schemes ◽  
Secret Sharing Scheme ◽  
Access Structure ◽  
Constant Rank ◽  
Computational Resource ◽  
Maximum Cardinality ◽  
Access Structures ◽  
Sharing Scheme

A secret sharing scheme is a method which allows a dealer to share a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret. The collection of subsets of participants that can reconstruct the secret in this way is called access structure. The rank of an access structure is the maximum cardinality of a minimal qualified subset. A secret sharing scheme is perfect if unqualified subsets of participants obtain no information regarding the secret. The dealer's randomness is the number of random bits required by the dealer to setup a secret sharing scheme. The efficiency of the dealer's randomness is the ratio between the amount of the dealer's randomness and the length of the secret. Because random bits are a natural computational resource, it is important to reduce the amount of randomness used by the dealer to setup a secret sharing scheme. In this paper, we propose some decomposition constructions for perfect secret sharing schemes with access structures of constant rank. Compared with the best previous results, our constructions have some improved upper bounds on the dealer's randomness and on the efficiency of the dealer's randomness.

A lower bound using Hamilton-type circuits and its applications

2003 ◽  
Vol 40 (4) ◽  
pp. 1121-1132 ◽  
Author(s):  
John T. Chen
Keyword(s):  
Time Series ◽  
Lower Bound ◽  
Statistical Inference ◽  
Dose Response ◽  
Upper Bound ◽  
Connected Graph ◽  
Probability Space ◽  
Response Curves ◽  
Dose Response Curves ◽  
Joint Probabilities

This paper presents a degree-two probability lower bound for the union of an arbitrary set of events in an arbitrary probability space. The bound is designed in terms of the first-degree Bonferroni summation and pairwise joint probabilities of events, which are represented as weights of edges in a Hamilton-type circuit in a connected graph. The proposed lower bound strengthens the Dawson–Sankoff lower bound in the same way that Hunter and Worsley's degree-two upper bound improves the degree-two Bonferroni-type optimal upper bound. It can be applied to statistical inference in time series and outlier diagnoses as well as the study of dose response curves.

Sign in / Sign up

Export Citation Format

Share Document