Related papers: A colouring protocol for the generalized Russian c…
In the generalized Russian cards problem, the three players Alice, Bob and Cath draw a,b and c cards, respectively, from a deck of a+b+c cards. Players only know their own cards and what the deck of cards is. Alice and Bob are then required…
We present the first formal mathematical presentation of the generalized Russian cards problem, and provide rigorous security definitions that capture both basic and extended versions of weak and perfect security notions. In the generalized…
In the generalized Russian cards problem, we have a card deck $X$ of $n$ cards and three participants, Alice, Bob, and Cathy, dealt $a$, $b$, and $c$ cards, respectively. Once the cards are dealt, Alice and Bob wish to privately communicate…
The problem of $A$ privately transmitting information to $B$ by a public announcement overheard by an eavesdropper $C$ is considered. To do so by a deterministic protocol, their inputs must be correlated. Dependent inputs are represented…
In the Russian cards problem, Alice, Bob and Cath draw $a$, $b$ and $c$ cards, respectively, from a publicly known deck. Alice and Bob must then communicate their cards to each other without Cath learning who holds a single card. Solutions…
We outline the need for stricter requirements for unconditionally secure cryptographic protocols inspired by the Russian Cards problem. A new requirement CA4 is proposed that checks for bias in single card occurrence in announcements…
Consider three players Alice, Bob and Cath who hold a, b and c cards, respectively, from a deck of d=a+b+c cards. The cards are all different and players only know their own cards. Suppose Alice and Bob wish to communicate their cards to…
We introduce a new variant of graph coloring called correspondence coloring which generalizes list coloring and allows for reductions previously only possible for ordinary coloring. Using this tool, we prove that excluding cycles of lengths…
We deal with a graph colouring problem that arises in quantum information theory. Alice and Bob are each given a $\pm1$-vector of length $k$, and are to respond with $k$ bits. Their responses must be equal if they are given equal inputs,…
Three different quantum cards which are non-orthogonal quantum bits are sent to two different players, Alice and Bob, randomly. Alice receives one of the three cards, and Bob receives the remaining two cards. We find that Bob could know…
We study a general scenario where confidential information is distributed among a group of agents who wish to share it in such a way that the data becomes common knowledge among them but an eavesdropper intercepting their communications…
The graph coloring game is a famous two-player game (re)introduced by Bodlaender in $1991$. Given a graph $G$ and $k \in \mathbb{N}$, Alice and Bob alternately (starting with Alice) color an uncolored vertex with some color in…
Introducing the simplest of all No-Signalling Games: the RGB Game where two verifiers interrogate two provers, Alice and Bob, far enough from each other that communication between them is too slow to be possible. Each prover may be…
We consider a card guessing strategy for a stack of cards with two different types of cards, say $m_1$ cards of type red (heart or diamond) and $m_2$ cards of type black (clubs or spades). Given a deck of $M=m_1+m_2$ cards, we propose a…
We consider a problem, which we call secure grouping, of dividing a number of parties into some subsets (groups) in the following manner: Each party has to know the other members of his/her group, while he/she may not know anything about…
Finding the clique of maximum cardinality in an arbitrary graph is an NP-Hard problem that has many applications, which has motivated studies to solve it exactly despite its difficulty. The great majority of algorithms proposed in the…
The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with problems of algebra, statistical mechanics and planning.…
In this paper it is shown that no public announcement scheme that can be modeled in Dynamic Epistemic Logic (DEL) can solve the Russian Cards Problem (RCP) in one announcement. Since DEL is a general model for any public announcement scheme…
We consider the generic problem of Secure Aggregation of Distributed Information (SADI), where several agents acting as a team have information distributed among them, modeled by means of a publicly known deck of cards distributed among the…
This paper introduces two information-theoretically secure protocols that achieve quantum secure direct communication between Alice and Bob in the first case, and among Alice, Bod and Charlie in the second case. Both protocols use the same…