Related papers: Secret sharing on the $d$-dimensional cube
Perfect secret sharing scheme is a method of distribute a secret information $s$ among participants such that only predefined coalitions, called qualified subsets of the participants can recover the secret, whereas any other coalitions, the…
The information rate for an access structure is the reciprocal of the load of the optimal secret sharing scheme for this structure. We determine this value for all trees: it is 1/(2-1/c), where c is the size of the largest core of the tree.…
We investigate graph based secret sharing schemes and its information ratio, also called complexity, measuring the maximal amount of information the vertices has to store. It was conjectured that in large girth graphs, where the interaction…
For a secret sharing scheme, two parameters $d_{min}$ and $d_{cheat}$ are defined in [12] and [13]. These two parameters measure the error-correcting capability and the secret-recovering capability of the secret sharing scheme against…
A model for information spreading in a population of $N$ mobile agents is extended to $d$-dimensional regular lattices. This model, already studied on two-dimensional lattices, also takes into account the degeneration of information as it…
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…
Secret sharing is an important building block in cryptography. All explicitly defined secret sharing schemes with known exact complexity bounds are multi-linear, thus are closely related to linear codes. The dual of such a linear scheme, in…
Secret sharing is the art of securely sharing information between more than two people in such a way that its reconstruction requires the collaboration of a certain number of parties. Entanglement-based secret sharing schemes which utilise…
Secret sharing is a cryptographic discipline in which the goal is to distribute information about a secret over a set of participants in such a way that only specific authorized combinations of participants together can reconstruct the…
An important metric of the performance of a quantum secret sharing scheme is its information rate. Beyond the fact that the information rate is upper bounded by one, very little is known in terms of bounds on the information rate of quantum…
We derive a sharp scaling law for deviations of edge-isoperimetric sets in the lattice $\mathbb Z^d$ from the limiting Wulff shape in arbitrary dimensions. As the number $n$ of elements diverges, we prove that the symmetric difference to…
This paper shows that structured transmission schemes are a good choice for secret communication over interference networks with an eavesdropper. Structured transmission is shown to exploit channel asymmetries and thus perform better than…
Let $d$ be an integer greater than $1$, and let $t$ be fixed such that $\frac{1}{d} < t < \frac{1}{d-1}$. We prove that for any $n_0$ chosen sufficiently large depending upon $t$, the $d$-dimensional cubes of sidelength $n^{-t}$ for $n \geq…
In an on-line secret sharing scheme the dealer assigns shares in the order the participants show up, knowing only those qualified subsets whose all members she has seen. We assume that the overall access structure is known and only the…
Denote by Q_d the d-dimensional hypercube. Addressing a recent question we estimate the number of ways the vertex set of Q_d can be partitioned into vertex disjoint smaller cubes. Among other results, we prove that the asymptotic order of…
We give an example of a wide class of problems for which quantum information protocols based on multi-system entanglement can be mapped into much simpler ones involving one system. Secret sharing is a cryptographic primitive which plays a…
For special $d$-dimensional hyperbolic shells $E$ with $ d\geq 5$ we show that the number of lattice points in $E$ intersected with a $d$-dimensional cube $C_r$ of edge length $r$, can be approximated by the volume of $E\cap C_r$, as $r$…
The nearest lattice point problem in $\mathbb{R}^n$ is formulated in a distributed network with $n$ nodes. The objective is to minimize the probability that an incorrect lattice point is found, subject to a constraint on inter-node…
The main problem considered in this paper is construction and theoretical study of efficient $n$-point coverings of a $d$-dimensional cube $[-1,1]^d$. Targeted values of $d$ are between 5 and 50; $n$ can be in hundreds or thousands and the…
We study the effective conductivity $\sigma_e$ for a random wire problem on the $d$-dimensional cubic lattice ${\mathbb Z}^d, d \geq 2$ in the case when random conductivities on bonds are independent identically distributed random…