Related papers: Secret sharing on the $d$-dimensional cube

We consider an online version of the geometric minimum hitting set problem that can be described as a game between an adversary and an algorithm. For some integers $d$ and $N$, let $P$ be the set of points in $(0, N)^d$ with integral…

We establish long-range order for the hard-core model on a finite, regular bipartite graph above a threshold fugacity given in terms of expansion parameters of the graph. The result applies to the $d$-dimensional hypercube graph and, more…

Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…

For integers $1 < k < d-1$ and $r \ge k+2$, we establish new lower bounds on the maximum number of points in $[n]^d$ such that no $r$ lie in a $k$-dimensional affine (or linear) subspace. These bounds improve on earlier results of…

The random-energy model (REM), a solvable spin-glass model, has impacted an incredibly diverse set of problems, from protein folding to combinatorial optimization to many-body localization. Here, we explore a new connection to secret…

We consider the hard-core lattice gas model on Z^d and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds Cd^{-1/3}(log d)^2, the model exhibits multiple hard-core measures, thus improving…

This paper introduces the Symmetric Extensible Quantum Secret Sharing protocol, which is a novel quantum protocol for secret sharing. At its heart, it is an entanglement based protocol that relies on the use of maximally entangled GHZ…

In the $d$-Scattered Set problem we are asked to select at least $k$ vertices of a given graph, so that the distance between any pair is at least $d$. We study the problem's (in-)approximability and offer improvements and extensions of…

We present two experimental schemes to perform continuous variable (2,3) threshold quantum secret sharing on the quadratures amplitudes of bright light beams. Both schemes require a pair of entangled light beams. The first scheme utilizes…

This paper establishes the strict optimality in precision for frequency and distribution estimation under local differential privacy (LDP). We prove that a linear estimator with a symmetric and extremal configuration, and a constant support…

Let $X=X(n,q)$ be the set of $n\times n$ Hermitian matrices over $\mathbb{F}_{q^2}$. It is well known that $X$ gives rise to a metric translation association scheme whose classes are induced by the rank metric. We study $d$-codes in this…

A Lattice is a partially ordered set where both least upper bound and greatest lower bound of any pair of elements are unique and exist within the set. K\"{o}tter and Kschischang proved that codes in the linear lattice can be used for error…

Understanding the composition of final states in $B \to X_c l \nu$ could help to get a feedback on the persisting disagreement between exclusive and inclusive determinations of $V_{cb}$. In particular the series of orbital excitations…

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

In this paper will be presented methodology of encoding information in valuations of discrete lattice with some translational invariant constrains in asymptotically optimal way. The method is based on finding statistical description of such…

This paper presents a recursive computational multi-secret sharing technique that hides k-2 secrets of size b each into n shares of a single secret S of size b, such that any k of the n shares suffice to recreate the secret S as well as all…

Given a positive integer $d$, the d-CUT is the problem of deciding if an undirected graph $G=(V,E)$ has a cut $(A,B)$ such that every vertex in $A$ (resp. $B$) has at most $d$ neighbors in $B$ (resp. $A$). For $d=1$, the problem is referred…

To devise D2D resource allocation algorithms in underlay D2D communications the channel state information (CSI) between the D2D transmitters and the BS and the D2D receiver CSI (DCSI-R) needs to be transmitted to the BS. However, this…

An existence result is presented for the worst-case error of lattice rules for high dimensional integration over the unit cube, in an unanchored weighted space of functions with square-integrable mixed first derivatives. Existing studies…

In the $d$-dimensional cow-path problem, a cow living in $\mathbb{R}^d$ must locate a $(d - 1)$-dimensional hyperplane $H$ whose location is unknown. The only way that the cow can find $H$ is to roam $\mathbb{R}^d$ until it intersects…