Related papers: Randomness Requirements for Three-Secret Sharing
The purpose of this paper is to introduce the idea of triangular Ramsey numbers and provide values as well as upper and lower bounds for them. To do this, the combinatorial game Mines is introduced; after some necessary theorems about…
In this note we study a problem of fair division in the absence of full information. We give an algorithm which solves the following problem: n $\ge$ 2 persons want to cut a cake into n shares so that each person will get at least 1/n of…
In this paper, we study an asynchronous randomized gossip algorithm under unreliable communication. At each instance, two nodes are selected to meet with a given probability. When nodes meet, two unreliable communication links are…
We introduce a dynamic mechanism design problem in which the designer wants to offer for sale an item to an agent, and another item to the same agent at some point in the future. The agent's joint distribution of valuations for the two…
We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties…
We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfare- and profit-maximizing auctions under this communication restriction. For…
We consider the problem of secure key distribution among $n$ trustful agents: the goal is to distribute an identical random bit-string among the $n$ agents over a noisy channel such that eavesdroppers learn little about it. We study the…
We study the fundamental problem of index coding under an additional privacy constraint that requires each receiver to learn nothing more about the collection of messages beyond its demanded messages from the server and what is available to…
In this paper we extend the notion of {\em locally repairable} codes to {\em secret sharing} schemes. The main problem that we consider is to find optimal ways to distribute shares of a secret among a set of storage-nodes (participants)…
In this paper we introduce a quantum information theoretical model for quantum secret sharing schemes. We show that quantum information theory provides a unifying framework for the study of these schemes. We prove that the information…
In frequently repeated matching scenarios, individuals may require diversification in their choices. Therefore, when faced with a set of potential outcomes, each individual may have an ideal lottery over outcomes that represents their…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…
Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…
Within entanglement theory there are criteria which certify that some quantum states cannot be distilled into pure entanglement. An example is the positive partial transposition criterion. Here we present, for the first time, the analogous…
Two processors output correlated sequences using the help of a coordinator with whom they individually share independent randomness. For the case of unlimited shared randomness, we characterize the rate of communication required from the…
In this expository paper we discuss a relatively new counterfeit coin problem with an unusual goal: maintaining the privacy of, rather than revealing, counterfeit coins in a set of both fake and real coins. We introduce two classes of…
We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study…
A central server needs to perform statistical inference based on samples that are distributed over multiple users who can each send a message of limited length to the center. We study problems of distribution learning and identity testing…
We consider theoretical limits of partial secrecy in a setting where an eavesdropper attempts to causally reconstruct an information sequence with low distortion based on an intercepted transmission and the past of the sequence. The…
Signaling is an important topic in the study of asymmetric information in economic settings. In particular, the transparency of information available to a seller in an auction setting is a question of major interest. We introduce the study…