Access Structure in Graphs in High Dimension and Application to Secret Sharing
نویسندگان
چکیده
We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension q, as well as explicit decoding operations for quantum secret sharing based on graph state protocols. We give a lower bound on k for the existence of a ((k, n))q scheme and prove, using probabilistic methods, that there exists α such that a random multigraph has an accessing parameter k ≤ αn with high probability. 1998 ACM Subject Classification F.1.1 Models of Computation
منابع مشابه
Secret Sharing Based On Cartesian product Of Graphs
The purpose of this paper is to study the information ratio of perfect secret sharing of product of some special families of graphs. We seek to prove that the information ratio of prism graphs $Y_{n}$ are equal to $frac{7}{4}$ for any $ngeq 5$, and we will gave a partial answer to a question of Csirmaz cite{CL}. We will also study the information ratio of two other families $C_{m}times C_{n}$ a...
متن کاملOn the design and security of a lattice-based threshold secret sharing scheme
In this paper, we introduce a method of threshold secret sharing scheme (TSSS) in which secret reconstruction is based on Babai's nearest plane algorithm. In order to supply secure public channels for transmitting shares to parties, we need to ensure that there are no quantum threats to these channels. A solution to this problem can be utilization of lattice-based cryptosystems for these channe...
متن کاملA Fast Publicly Verifiable Secret Sharing Scheme using Non-homogeneous Linear Recursions
A non-interactive (t,n)-publicly veriable secret sharing scheme (non-interactive (t,n)-PVSS scheme) is a (t,n)-secret sharing scheme in which anyone, not only the participants of the scheme, can verify the correctness of the produced shares without interacting with the dealer and participants. The (t,n)-PVSS schemes have found a lot of applications in cryptography because they are suitable for<...
متن کاملA New Bound on the Average Information Ratio of Perfect Secret-Sharing Schemes for Access Structures Based On Bipartite Graphs of Larger Girth
In a perfect secret-sharing scheme, a dealer distributes a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of the participants in any unqualified subset is statistically independent of the secret. The access structure of the scheme refers to the collection of all qualified subsets. In a graph-based access st...
متن کاملOn the Information Rate of Secret Sharing Schemes
We derive new limitations on the information rate and the average information rate of secret sharing schemes for access structure represented by graphs. We give the rst proof of the existence of access structures with optimal information rate and optimal average information rate less that 1=2 + , where is an arbitrary positive constant. We also consider the problem of testing if one of these ac...
متن کامل