Related papers: Access Structures Determined by Uniform Polymatroi…
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…
In a secret sharing scheme, shares of a secret are distributed to participants in such a way that only certain predetermined sets of participants are qualified to reconstruct the secret. An access structure on a set of participants…
Bipartite secret sharing schemes have a bipartite access structure in which the set of participants is divided into two parts and all participants in the same part play an equivalent role. Such a bipartite scheme can be described by a…
Beimel, Tassa and Weinreb (2008) and Farras and Padro (2010) partially characterized access structures of ideal weighted threshold secret sharing schemes in terms of the operation of composition. They classified indecomposable ideal…
An ideal secret sharing scheme is a method of sharing a secret key in some key space among a finite set of participants in such a way that only the authorized subsets of participants can reconstruct the secret key from their shares which…
Secret sharing provides a means to distribute shares of a secret such that any authorized subset of shares, specified by an access structure, can be pooled together to recompute the secret. The standard secret sharing model requires public…
A $k$-uniform hypergraph is a hypergraph where each $k$-hyperedge has exactly $k$ vertices. A $k$-homogeneous access structure is represented by a $k$-uniform hypergraph $\mathcal{H}$, in which the participants correspond to the vertices of…
Secret sharing schemes are widely used now a days in various applications, which need more security, trust and reliability. In secret sharing scheme, the secret is divided among the participants and only authorized set of participants can…
The connection between secret sharing and matroid theory is well established. In this paper, we generalize the concepts of secret sharing and matroid ports to $q$-polymatroids. Specifically, we introduce the notion of an access structure on…
How to construct an ideal multi-secret sharing scheme for general access structures is difficult. In this paper, we solve an open problem proposed by Spiez et al.recently [Finite Fields and Their Application, 2011(17) 329-342], namely to…
In this paper, we give a new axioms system based on nonseparable flats with their ranks to define a matroid. We deduce a polynomial time algorithm for deciding if a given matroid (respectively, arbitrary structure) is an uniform matroid.…
The main aim of this paper is to construct a multi-secret sharing scheme for general access structure in a trusted dealer model using suitable hash function and Lagrange's interpolation method. Even though, the proposed scheme is a…
One of the methods used in order to protect a secret K is a secret sharing scheme. In this scheme the secret K is distributed among a finite set of participants P by a special participant called the dealer, in such a way that only…
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of…
In this paper we construct a subclass of the composite access structure introduced by Mart\'inez et al. based on schemes realizing the structure given by the set of codewords of minimal support of linear codes. This class enlarges the…
In this paper we define a kind of decomposition for a quantum access structure. We propose a conception of minimal maximal quantum access structure and obtain a sufficient and necessary condition for minimal maximal quantum access…
A phased matroid is a matroid with additional structure which plays the same role for complex vector arrangements that oriented matroids play for real vector arrangements. The realization space of an oriented (resp., phased) matroid is the…
A matroid is a machine capturing linearity of mathematical objects and producing combinatorial structures. Matroid structure arises everywhere since linearity is a ubiquitous concept. One natural way to obtain matroids is by considering…
This article studies two notions of generalized matroid representations motivated by algorithmic information theory and cryptographic secret sharing. The first (entropic representability) involves discrete random variables, while the second…
Multi-secret sharing is an extension of secret sharing technique where several secrets are shared between the participants, each according to a specified access structure. The secrets can be reconstructed according to the access structure…