23,508 research outputs found

    Combinatorial Solutions Providing Improved Security for the Generalized Russian Cards Problem

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    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 Russian cards problem, three players, Alice, Bob, and Cathy, are dealt a deck of nn cards, each given aa, bb, and cc cards, respectively. The goal is for Alice and Bob to learn each other's hands via public communication, without Cathy learning the fate of any particular card. The basic idea is that Alice announces a set of possible hands she might hold, and Bob, using knowledge of his own hand, should be able to learn Alice's cards from this announcement, but Cathy should not. Using a combinatorial approach, we are able to give a nice characterization of informative strategies (i.e., strategies allowing Bob to learn Alice's hand), having optimal communication complexity, namely the set of possible hands Alice announces must be equivalent to a large set of t−(n,a,1)t-(n, a, 1)-designs, where t=a−ct=a-c. We also provide some interesting necessary conditions for certain types of deals to be simultaneously informative and secure. That is, for deals satisfying c=a−dc = a-d for some d≥2d \geq 2, where b≥d−1b \geq d-1 and the strategy is assumed to satisfy a strong version of security (namely perfect (d−1)(d-1)-security), we show that a=d+1a = d+1 and hence c=1c=1. We also give a precise characterization of informative and perfectly (d−1)(d-1)-secure deals of the form (d+1,b,1)(d+1, b, 1) satisfying b≥d−1b \geq d-1 involving d−(n,d+1,1)d-(n, d+1, 1)-designs

    Interaction in Quantum Communication

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    In some scenarios there are ways of conveying information with many fewer, even exponentially fewer, qubits than possible classically. Moreover, some of these methods have a very simple structure--they involve only few message exchanges between the communicating parties. It is therefore natural to ask whether every classical protocol may be transformed to a ``simpler'' quantum protocol--one that has similar efficiency, but uses fewer message exchanges. We show that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity. This, in particular, proves a round hierarchy theorem for quantum communication complexity, and implies, via a simple reduction, an Omega(N^{1/k}) lower bound for k message quantum protocols for Set Disjointness for constant k. Enroute, we prove information-theoretic lemmas, and define a related measure of correlation, the informational distance, that we believe may be of significance in other contexts as well.Comment: 35 pages. Uses IEEEtran.cls, IEEEbib.bst. Submitted to IEEE Transactions on Information Theory. Strengthens results in quant-ph/0005106, quant-ph/0004100 and an earlier version presented in STOC 200

    A secure additive protocol for card players

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    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 each other without Cath learning whether Alice or Bob holds a specific card. Considering the cards as consecutive natural numbers 0,1,..., we investigate general conditions for when Alice or Bob can safely announce the sum of the cards they hold modulo an appropriately chosen integer. We demonstrate that this holds whenever a,b>2 and c=1. Because Cath holds a single card, this also implies that Alice and Bob will learn the card deal from the other player's announcement

    The Road to Quantum Computational Supremacy

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    We present an idiosyncratic view of the race for quantum computational supremacy. Google's approach and IBM challenge are examined. An unexpected side-effect of the race is the significant progress in designing fast classical algorithms. Quantum supremacy, if achieved, won't make classical computing obsolete.Comment: 15 pages, 1 figur

    Special Libraries, January 1958

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    Volume 49, Issue 1https://scholarworks.sjsu.edu/sla_sl_1958/1000/thumbnail.jp

    Secure aggregation of distributed information: How a team of agents can safely share secrets in front of a spy

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    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 agents, so that each of them knows only her cards. The agents have to exchange and aggregate the information about how the cards are distributed among them by means of public announcements over insecure communication channels, intercepted by an adversary "eavesdropper", in such a way that the adversary does not learn who holds any of the cards. We present a combinatorial construction of protocols that provides a direct solution of a class of SADI problems and develop a technique of iterated reduction of SADI problems to smaller ones which are eventually solvable directly. We show that our methods provide a solution to a large class of SADI problems, including all SADI problems with sufficiently large size and sufficiently balanced card distributions

    Special Libraries, October 1960

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    Volume 51, Issue 8https://scholarworks.sjsu.edu/sla_sl_1960/1007/thumbnail.jp

    Special Libraries, October 1960

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    Volume 51, Issue 8https://scholarworks.sjsu.edu/sla_sl_1960/1007/thumbnail.jp
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