Secret Sharing Schemes Based on Linear Codes Can Be Precisely Characterized by the Relative Generalized Hamming Weight

2012 ◽  
Vol E95.A (11) ◽  
pp. 2067-2075 ◽  
Author(s):  
Jun KURIHARA ◽  
Tomohiko UYEMATSU ◽  
Ryutaroh MATSUMOTO
Keyword(s):  
Secret Sharing ◽  
Linear Codes ◽  
Secret Sharing Schemes ◽  
Hamming Weight ◽  
Generalized Hamming Weight ◽  
Relative Generalized Hamming Weight

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.

Characterization of some minimal codes for secret sharing

2019 ◽  
Vol 12 (02) ◽  
pp. 1950026
Author(s):  
Sassia Makhlouf ◽  
Lemnouar Noui
Keyword(s):  
Secret Sharing ◽  
Linear Codes ◽  
Mds Codes ◽  
Secret Sharing Schemes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Dual Codes ◽  
Necessary And Sufficient ◽  
Minimal Codes

Recently, several authors used linear codes to construct secret sharing schemes. It is known that if each nonzero codeword of a code [Formula: see text] is minimal, then the dual code [Formula: see text] is suitable for secret sharing. To seek such codes Ashikhmin–Barg give a sufficient condition from weights; in [Formula: see text] code [Formula: see text], let [Formula: see text] and [Formula: see text] be the minimum and maximum nonzero weights, respectively. If [Formula: see text] then all nonzero codewords of [Formula: see text] are minimal. In this paper, a necessary and sufficient condition is given for self-dual codes and for MDS codes to verify the inequality (*). Special codes are examined and applied for secret sharing schemes.

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 Secret Sharing Schemes from Linear Codes over F2+vF2+v2F2

2021 ◽  
Vol 30 (5) ◽  
pp. 895-901
Author(s):  
WANG Yaru ◽  
LI Fulin ◽  
ZHU Shixin
Keyword(s):  
Secret Sharing ◽  
Linear Codes ◽  
Secret Sharing Schemes
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