Related papers: Multiple Threshold Schemes Under The Weak Secure C…
We consider a secret-sharing model where a dealer distributes the shares of a secret among a set of participants with the constraint that only predetermined subsets of participants must be able to reconstruct the secret by pooling their…
In 1968, Liu described the problem of securing documents in a shared secret project. In an example, at least six out of eleven participating scientists need to be present to open the lock securing the secret documents. Shamir proposed a…
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…
Suppose that $P$ is a property that may be satisfied by a random code $C \subset \Sigma^n$. For example, for some $p \in (0,1)$, ${P}$ might be the property that there exist three elements of $C$ that lie in some Hamming ball of radius…
Data sharing enables critical advances in many research areas and business applications, but it may lead to inadvertent disclosure of sensitive summary statistics (e.g., means or quantiles). Existing literature only focuses on protecting a…
Multilevel diversity coding is a classical coding model where multiple mutually independent information messages are encoded, such that different reliability requirements can be afforded to different messages. It is well known that {\em…
In secure summation, $K$ users, each holds an input, wish to compute the sum of the inputs at a server without revealing any information about {\em all the inputs} even if the server may collude with {\em an arbitrary subset of users}. In…
A source model of key sharing between three users is considered in which each pair of them wishes to agree on a secret key hidden from the remaining user. There are rate-limited public channels for communications between the users. We give…
The secrecy of a communication system in which both the legitimate receiver and an eavesdropper are allowed some distortion is investigated. The secrecy metric considered is the exponent of the probability that the eavesdropper estimates…
In network communications, information transmission often encounters wiretapping attacks. Secure network coding is introduced to prevent information from being leaked to adversaries. The investigation of performance bounds on the numbers of…
To detect frauds from some internal participants or external attackers, some verifiable threshold quantum secret sharing schemes have been proposed. In this paper, we present a new verifiable threshold structure based on a single qubit…
We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the…
We show strongly secret achievable rate regions for two different wiretap multiple-access channel coding problems. In the first problem, each encoder has a private message and both together have a common message to transmit. The encoders…
We propose a new scheme for sharing symmetric key operations among a set of participants according to a (t,n) threshold access structure. We focus on anonymity properties of this scheme and show that this scheme provides improved values of…
In this paper, we propose a class of threshold secret sharing schemes with repairing function between shares without the help of the dealer, that we called repairable threshold secret sharing schemes. Specifically, if a share fails, such as…
Motivated in part by the problem of secure multicast distributed storage, we analyze secrecy rates for a channel in which two transmitters simultaneously multicast to two receivers in the presence of an eavesdropper. Achievable rates are…
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…
Fundamental results on secret sharing schemes (SSSs) are discussed in the setting where security and share size are measured by (conditional) min-entropies. We first formalize a unified framework of SSSs based on (conditional) R\'enyi…
We study variants of the secretary problem, where $N$, the number of candidates, is a random variable, and the decision maker wants to maximize the probability of success -- picking the largest number among the $N$ candidates -- using only…
A secret sharing scheme is a method to store information securely and reliably. Particularly, in a threshold secret sharing scheme, a secret is encoded into $n$ shares, such that any set of at least $t_1$ shares suffice to decode the…