The access structure of some secret-sharing schemes

1996 ◽  
pp. 67-78 ◽  
Author(s):  
Ari Renvall ◽  
Cunsheng Ding
Keyword(s):  
Secret Sharing ◽  
Secret Sharing Schemes ◽  
Access Structure

Secret Sharing Schemes from Linear Codes overFp + vFp

2016 ◽  
Vol 27 (05) ◽  
pp. 595-605 ◽  
Author(s):  
Xianfang Wang ◽  
Jian Gao ◽  
Fang-Wei Fu
Keyword(s):  
Secret Sharing ◽  
Linear Code ◽  
Linear Codes ◽  
Difficult Problem ◽  
Secret Sharing Schemes ◽  
Secret Sharing Scheme ◽  
Access Structure ◽  
Chain Ring ◽  
Sharing Scheme

In principle, every linear code can be used to construct a secret sharing scheme. However, determining the access structure of the scheme is a very difficult problem. In this paper, we study MacDonald codes over the finite non-chain ring [Formula: see text], where p is a prime and [Formula: see text]. We provide a method to construct a class of two-weight linear codes over the ring. Then, we determine the access structure of secret sharing schemes based on these codes.

scholarly journals Secret sharing and duality

2020 ◽  
Vol 15 (1) ◽  
pp. 157-173
Author(s):  
Laszlo Csirmaz
Keyword(s):  
Secret Sharing ◽  
Open Problem ◽  
Building Block ◽  
Linear Codes ◽  
Partial Answer ◽  
Secret Sharing Schemes ◽  
Access Structure ◽  
Optimal Complexity ◽  
Linear Scheme ◽  
Important Building Block

AbstractSecret sharing is an important building block in cryptography. All explicit secret sharing schemes which are known to have optimal complexity are multi-linear, thus are closely related to linear codes. The dual of such a linear scheme, in the sense of duality of linear codes, gives another scheme for the dual access structure. These schemes have the same complexity, namely the largest share size relative to the secret size is the same. It is a long-standing open problem whether this fact is true in general: the complexity of any access structure is the same as the complexity of its dual. We give a partial answer to this question. An almost perfect scheme allows negligible errors, both in the recovery and in the independence. There exists an almost perfect ideal scheme on 174 participants whose complexity is strictly smaller than that of its dual.

scholarly journals Multi Secret Image Sharing Scheme of General Access Structure with Meaningful Shares

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1582
Author(s):  
Hongliang Cai ◽  
Dan Tang
Keyword(s):  
Secret Sharing ◽  
Secret Sharing Schemes ◽  
Access Structure ◽  
Secret Image Sharing ◽  
Secret Image ◽  
Image Sharing ◽  
Sharing Scheme ◽  
General Access Structure ◽  
Multi Secret Sharing ◽  
Secret Image Sharing Scheme

A Multi Secret Image sharing scheme can share several secret images among certain participators securely. Boolean-based secret sharing schemes are one kind of secret sharing method with light-weighted computation compared to the previous complex algebraic-based methods, which can realize the sharing of multi secret images. However, the existing Boolean-based multi secret sharing schemes are mostly restricted to the particular case of (2, n) and (n, n), only few Boolean-based multi secret sharing schemes study the general access structure, and the shares are mostly meaningless. In this paper, a new Boolean-based multi secret sharing scheme with the general access structure is proposed. All the shares are meaningful, which can avoid attracting the attention of adversaries, and the secret images can be recovered in a lossless manner. The feasibility of the scheme is proven, the performance is validated by the experiments on the gray images, and the analysis of the comparison with other methods is also given out.

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