Related papers: Information Rates of Minimal Non-Matroid-Related A…
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…
The secret-key rate measures the rate at which Alice and Bob can extract secret bits from sampling a joint probability distribution, unknown to an eavesdropper Eve. The secret-key rate has been bounded above by the intrinsic information and…
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 consider a distributed multi-user secret sharing (DMUSS) setting in which there is a dealer, $n$ storage nodes, and $m$ secrets. Each user demands a $t$-subset of $m$ secrets. Earlier work in this setting dealt with the case of $t=1$; in…
We study information leakage in secure linear network coding schemes based on nested rank-metric codes. We show that the amount of information leaked to an adversary that observes a subset of network links is characterized by the…
This work investigates the design of sparse secret sharing schemes that encode a sparse private matrix into sparse shares. This investigation is motivated by distributed computing, where the multiplication of sparse and private matrices is…
A key issue in the control of distributed discrete systems modeled as Markov decisions processes, is that often the state of the system is not directly observable at any single location in the system. The participants in the control scheme…
Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered.…
In this work we revisit the fundamental findings by Chen et al. in [5] on general information transfer in linear ramp secret sharing schemes to conclude that their method not only gives a way to establish worst case leakage [5, 25] and best…
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…
This paper establishes the fundamental limits of a multi-access system where multiple users communicate to a legitimate receiver in presence of an external warden. Only a specific subset of the users, called covert users, needs their…
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…
In this paper we consider the problem of extracting secret key from an eavesdropped source $p_{XYZ}$ at a rate given by the conditional mutual information. We investigate this question under three different scenarios: (i) Alice ($X$) and…
The partial information decomposition (PID) is a promising framework for decomposing a joint random variable into the amount of influence each source variable Xi has on a target variable Y, relative to the other sources. For two sources,…
Determining information ratios of access structures is an important problem in secret sharing. Information inequalities and linear rank inequalities play an important role for proving bounds. Characteristic-dependent linear rank…
Splitting a secret s between several participants, we generate (for each value of s) shares for all participants. The goal: authorized groups of participants should be able to reconstruct the secret but forbidden ones get no information…
We study the generation of a secret key of maximum rate by a pair of terminals observing correlated sources and with the means to communicate over a noiseless public com- munication channel. Our main result establishes a structural…
It is well known that networks generated by common mechanisms such as preferential attachment and homophily can disadvantage the minority group by limiting their ability to establish links with the majority group. This has the effect of…
We study the trade-off between communication rate and privacy for distributed batch matrix multiplication of two independent sequences of matrices $\mathbf{A}$ and $\mathbf{B}$ with uniformly distributed entries. In our setting,…