On secret sharing schemes, matroids and polymatroids
نویسندگان
چکیده
منابع مشابه
On Secret Sharing Schemes, Matroids and Polymatroids
The complexity of a secret sharing scheme is defined as the ratio between the maximum length of the shares and the length of the secret. The optimization of this parameter for general access structures is an important and very difficult open problem in secret sharing. We explore in this paper the connections of this open problem with matroids and polymatroids. Matroid ports were introduced by L...
متن کاملMatroids and Quantum Secret Sharing Schemes
A secret sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such...
متن کاملNonperfect Secret Sharing Schemes and Matroids
This paper shows that nonperfect secret sharing schemes (NSS) have matroid structures and presents a direct link between the secret sharing matroids and entropy for both perfect and nonperfect schemes. We deene natural classes of NSS and derive a lower bound of jVij for those classes. \Ideal" nonperfect schemes are deened based on this lower bound. We prove that every such ideal secret sharing ...
متن کاملOn Representable Matroids and Ideal Secret Sharing
In secret sharing, the exact characterization of ideal access structures is a longstanding open problem. Brickell and Davenport (J. of Cryptology, 1991) proved that ideal access structures are induced by matroids. Subsequently, ideal access structures and access structures induced by matroids have attracted a lot of attention. Due to the difficulty of finding general results, the characterizati...
متن کاملOn Secret Sharing Schemes
The concept of secret sharing has been introduced independently by Shamir and Blakley, as a tool to protect a secret from getting exposed or from being lost. It allows a so-called dealer to share a secret among the members of a set P , which are usually called players or participants, in such a way that only certain specified subsets of players are able to reconstruct the secret while smaller s...
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ژورنال
عنوان ژورنال: Journal of Mathematical Cryptology
سال: 2010
ISSN: 1862-2976,1862-2984
DOI: 10.1515/jmc.2010.004