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Ideal Secret Sharing Schemes for Useful Multipartite Access Structures [chapter]

Oriol Farràs, Carles Padró
2011 Lecture Notes in Computer Science  
Namely, the construction of ideal linear secret sharing schemes for access structures that are natural generalizations of the threshold ones and have interesting properties for the applications.  ...  This paper is a survey of the main results and open problems in a line of work that was initiated shortly after secret sharing was introduced.  ...  Acknowledgments and Disclaimer The first author's work was partly funded by the Spanish Government through project CONSOLIDER INGENIO 2010 CSD2007-00004 "ARES", and by the Government of Catalonia through  ... 
doi:10.1007/978-3-642-20901-7_6 fatcat:ogbvgnqpnfcj5gn6s67o6eq6ca

Sharing one secret vs. sharing many secrets

Giovanni Di Crescenzo
2003 Theoretical Computer Science  
A multi-secret sharing scheme can be trivially realized by realizing a secret sharing scheme for each of the secrets.  ...  A multi-secret sharing scheme is the natural extension of a secret sharing scheme to the case in which many secrets need to be shared, each with respect to possibly di erent subsets of qualiÿed parties  ...  Further thanks go to Carlo Blundo and Alfredo De Santis for several interesting discussions on secret sharing schemes.  ... 
doi:10.1016/s0304-3975(02)00399-7 fatcat:ighg5gxuunas5do47dmbn5emty

Generalized Secret Sharing with Linear Hierarchical Secrets

Xi Chen, Yun Liu, Chin-Chen Chang, Cheng Guo
2014 International Journal of Network Security  
Generalized secret sharing is a method of constructing secret sharing from the perspective of access structure.  ...  The participants in the corresponding access structures can cooperate with each other to produce secrets in monotonous levels.  ...  Acknowledgments The authors gratefully acknowledge the anonymous reviewers for their valuable comments.  ... 
dblp:journals/ijnsec/ChenLCG14a fatcat:r2r3yy4qvzcgtgkktvxjmvlwii

A Generalized Information Theoretical Model for Quantum Secret Sharing

Chen-Ming Bai, Zhi-Hui Li, Ting-Ting Xu, Yong-Ming Li
2016 International Journal of Theoretical Physics  
In addition, we also analyse two kinds of important quantum access structures to illustrate the existence and rationality of the generalized quantum secret sharing schemes and consider the security of  ...  In our model, there are more quantum access structures which can be realized by our generalized quantum secret sharing schemes than those of the previous one.  ...  In Section 3, we show some properties for quantum access structures and analyze the model for quantum secret sharing schemes in Ref. [26] .  ... 
doi:10.1007/s10773-016-3121-9 fatcat:yrrfi5lulbbkrcvekzqsri2as4

Linear Secret-Sharing Schemes for Forbidden Graph Access Structures [chapter]

Amos Beimel, Oriol Farràs, Yuval Mintz, Naty Peter
2017 Lecture Notes in Computer Science  
with n vertices and at most n 1+β edges, for some 0 ≤ β < 1, we construct a linear secret-sharing scheme realizing its forbidden graph access structure in which the total size of the shares isÕ(n 1+β/2  ...  We study the complexity of realizing a forbidden graph access structure by linear secret-sharing schemes.  ...  Given a secret-sharing scheme for a graph access structure, we can construct a secret-sharing scheme for the forbidden graph access structure: We can independently share the secret using the scheme for  ... 
doi:10.1007/978-3-319-70503-3_13 fatcat:grz5upoppjgw5dovnm3zmv5n2a

Secret sharing schemes with detection of cheaters for a general access structure [chapter]

Sergio Cabello, Carles Padró, Germán Sáez
1999 Lecture Notes in Computer Science  
In a secret sharing scheme, some participants can lie about the value of their shares when reconstructing the secret in order to obtain some illicit benefits.  ...  Besides, those methods make it possible to construct robust and secure schemes for any access structure.  ...  The family of qualified subsets, Γ ⊂ 2 P , of a secret sharing scheme is called the access structure of the scheme.  ... 
doi:10.1007/3-540-48321-7_14 fatcat:vmhckta3nvae3mm6riilqhiaxu

Linear Secret-Sharing Schemes for k-uniform access structures [article]

Younjin Kim, Jihye Kwon, Hyang-Sook Lee
2021 arXiv   pre-print
In this paper, we provide efficient constructions on the total share size of linear secret sharing schemes for sparse and dense k-uniform access structures for a constant k using the hypergraph decomposition  ...  the secret value from their shares in the secret sharing scheme if they are connected by a k-hyperedge or their size is at least k+1.  ...  It means that bounds on the share size of secret sharing schemes for graph access structures imply the bounds on the share size of secret sharing schemes for forbidden graph access structures.  ... 
arXiv:2106.14833v1 fatcat:7mluxnlnjfbjfb4wzhx6c3j55a

Recursive constructions for perfect secret sharing schemes

Hung-Min Sun, Shiuh-Pyng Shieh
1999 Computers and Mathematics with Applications  
In this paper, we propose some recursive constructions for perfect secret sharing schemes with access structures of constant rank.  ...  The information rate of a secret sharing scheme is defined to be the ratio between the size of secret and the maximum size of the shares.  ...  We construct secret sharing schemes with uniform access structures of rank m by using the secret sharing schemes with uniform access structures of rank m-1.  ... 
doi:10.1016/s0898-1221(99)00049-8 fatcat:vfqrsv73o5ghna3twnjfzr6uue

Bounds on the information rate of quantum-secret-sharing schemes

Pradeep Sarvepalli
2011 Physical Review A. Atomic, Molecular, and Optical Physics  
An important metric of the performance of a quantum secret sharing scheme is its information rate.  ...  These results are the quantum analogues of the bounds for classical secret sharing schemes proved by Csirmaz.  ...  Purification of access structures is useful in that it gives an access structure that has a pure-state secret sharing scheme and the scheme for the original access structure can be obtained by discarding  ... 
doi:10.1103/physreva.83.042324 fatcat:3qtccyr2bzekhdeo7mzf7h2hni

Secret-Sharing Schemes: A Survey [chapter]

Amos Beimel
2011 Lecture Notes in Computer Science  
We will also present two results connecting secret-sharing schemes for a Hamiltonian access structure to the NP vs. coNP problem and to a major open problem in cryptography -constructing oblivious-transfer  ...  A secret-sharing scheme is a method by which a dealer distributes shares to parties such that only authorized subsets of parties can reconstruct the secret.  ...  Acknowledgment I would like to thank Benny Chor for introducing me to the field of secret-sharing schemes and guiding me in the early stages of my career.  ... 
doi:10.1007/978-3-642-20901-7_2 fatcat:qedpi6mj4rdvheumlv2vqznfxm

On Matroids and Nonideal Secret Sharing

Amos Beimel, Noam Livne
2008 IEEE Transactions on Information Theory  
It is shown that in any secret-sharing scheme realizing the access structure induced by the Vamos matroid with domain of the secrets of size k, the size of the domain of the shares is at least k + Ω( √  ...  The second result considers non-ideal secret-sharing schemes realizing access structures induced by matroids.  ...  An access structure is called ideal if there is an ideal secret-sharing scheme which realizes the access structure over some finite domain of secrets.  ... 
doi:10.1109/tit.2008.921708 fatcat:cinop7susffbphxbojfsjju6jm

On Matroids and Non-ideal Secret Sharing [chapter]

Amos Beimel, Noam Livne
2006 Lecture Notes in Computer Science  
It is shown that in any secret-sharing scheme realizing the access structure induced by the Vamos matroid with domain of the secrets of size k, the size of the domain of the shares is at least k + Ω( √  ...  The second result considers non-ideal secret-sharing schemes realizing access structures induced by matroids.  ...  An access structure is called ideal if there is an ideal secret-sharing scheme which realizes the access structure over some finite domain of secrets.  ... 
doi:10.1007/11681878_25 fatcat:bfvrdtcc3vbzndr5yemaqg2qbm

On secret sharing schemes, matroids and polymatroids

Jaume Martí-Farré, Carles Padró
2010 Journal of Mathematical Cryptology  
One of the main open problems in secret sharing is the characterization of the access structures of ideal secret sharing schemes.  ...  By combining those results with some techniques in secret sharing, we obtain new characterizations of matroid-related access structures.  ...  Acknowledgments The second author thanks Ronald Cramer, Bert Gerards, Robbert de Haan and Lex Schrijver for useful discussions, comments, and suggestions. Thanks to Lex Schrijver who pointed out  ... 
doi:10.1515/jmc.2010.004 fatcat:vh72wvzkmndt5c5bj3kxigjbcu

Weighted decomposition construction for perfect secret sharing schemes

Hung-Min Sun, Bor-Liang Chen
2002 Computers and Mathematics with Applications  
The purpose of this paper is to present a new decomposition technique, called the weighted decomposition construction, for perfect secret sharing schemes with general access structures.  ...  Based on the weighted decomposition construction, we improve the information rates in four cases out of the 18 cases of secret sharing schemes left unsolved for connected graphs on six vertices.  ...  SECRET SHARING SCHEMES FOR WEIGHTED ACCESS STRUCTURES In this section, we generalize secret sharing schemes for general access structures to secret sharing schemes for weighted access structures.  ... 
doi:10.1016/s0898-1221(01)00328-5 fatcat:tzi4ealj3ngqjclfvj3qpn2vru

A Linear Algebraic Approach to Metering Schemes

Carlo Blundo, Sebastià Martín, Barbara Masucci, CarlEs Padró
2004 Designs, Codes and Cryptography  
According to these bounds, the optimality of the metering schemes obtained by our method relies upon the optimality of the linear secret sharing schemes for the given access structure.  ...  Namely, given any access structure, we present a method to construct a metering scheme realizing it from any linear secret sharing scheme with the same access structure.  ...  The research of the rst and the third author is partially supported by C.N.R. under grant CN-RRG008BF3: \Pubblicit a Online: Nuove Misure per Nuovi Media. Auditing e Accounting Sicuro sul WEB".  ... 
doi:10.1023/b:desi.0000036249.86262.d5 fatcat:vzq3wi2vpbc2xogccekcpqdbbq
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