Related papers: Access structure in graphs in high dimension and a…
In a recent work, Markham and Sanders have proposed a framework to study quantum secret sharing (QSS) schemes using graph states. This framework unified three classes of QSS protocols, namely, sharing classical secrets over private and…
We consider secret sharing schemes with a classical secret and quantum shares. One example of such schemes was recently reported whose access structure cannot be realized by any secret sharing schemes with classical shares. In this paper,…
We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties…
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…
We introduce a new family of quantum secret sharing protocols with limited quantum resources which extends the protocols proposed by Markham and Sanders and by Broadbent, Chouha, and Tapp. Parametrized by a graph G and a subset of its…
The entangled graph states have emerged as an elegant and powerful quantum resource, indeed almost all multiparty protocols can be written in terms of graph states including measurement based quantum computation (MBQC), error correction and…
We study a simple graph-based classical secret sharing scheme: every player's share consists of a random key together with the encryption of the secret with the keys of his neighbours. A characterisation of the authorised and forbidden sets…
We investigate quantum secret sharing schemes constructed from $[[n,k,\delta]]_D$ non-binary stabilizer quantum error correcting codes with carrier qudits of prime dimension $D$. We provide a systematic way of determining the access…
Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult.…
The multiple assignment scheme is to assign one or more shares to single participant so that any kind of access structure can be realized by classical secret sharing schemes. We propose its quantum version including ramp secret sharing…
Distributed quantum communication and quantum computing offer many new opportunities for quantum information processing. Here networks based on highly nonlocal quantum resources with complex entanglement structures have been proposed for…
We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by…
We show a simple example of a secret sharing scheme encoding classical secret to quantum shares that can realize an access structure impossible by classical information processing with limitation on the size of each share. The example is…
Secret sharing is a multi-party cryptographic primitive that can be applied to a network of partially distrustful parties for encrypting data that is both sensitive (it must remain secure) and important (it must not be lost or destroyed).…
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…
We propose a decision procedure for analysing security of quantum cryptographic protocols, combining a classical algebraic rewrite system for knowledge with an operational semantics for quantum distributed computing. As a test case, we use…
We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called…
We show a construction of a quantum ramp secret sharing scheme from a nested pair of linear codes. Necessary and sufficient conditions for qualified sets and forbidden sets are given in terms of combinatorial properties of nested linear…
This paper investigates the construction of efficient quantum secret sharing schemes for quantum access structures based on hypergraphs with three hyperedges. We prove that hypercycles with three hyperedges are quantum access structures if…
In this paper, we investigate a novel $(2,2)$-threshold scheme and then generalize this to a $(n,n)$-threshold scheme for quantum secret sharing (QSS) which makes use of the fundamentals of Analytic Geometry. The dealer aptly selects GHZ…