51 research outputs found

    On Distributed Oblivious Transfer

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    The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at INDOCRYPT 2002This paper is about unconditionally secure distributed protocols for oblivious transfer, as proposed by Naor and Pinkas and generalized by Blundo et al. In this setting a Sender has ζ secrets and a Receiver is interested in one of them. The Sender distributes the information about the secrets to n servers, and a Receiver must contact a threshold of the servers in order to compute the secret. We present a non-existence result and a lower bound for the existence of one-round, threshold, distributed oblivious transfer protocols, generalizing the results of Blundo et al. A threshold based construction implementing 1-out-of-ζ distributed oblivious transfer achieving this lower bound is described. A condition for existence of distributed oblivious transfer schemes based on general access structures is proven. We also present a general access structure protocol implementing 1-out-of-ζ distributed oblivious transfer

    On Unconditionally Secure Distributed Oblivious Transfer.

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    This paper is about the Oblivious Transfer in the distributed model proposed by M. Naor and B. Pinkas. In this setting a Sender has n secrets and a Receiver is interested in one of them. During a set up phase, the Sender gives information about the secrets to m Servers. Afterwards, in a recovering phase, the Receiver can compute the secret she wishes by interacting with any k of them. More precisely, from the answers received she computes the secret in which she is interested but she gets no information on the others and, at the same time, any coalition of k − 1 Servers can neither compute any secret nor figure out which one the Receiver has recovered. We present an analysis and new results holding for this model: lower bounds on the resources required to implement such a scheme (i.e., randomness, memory storage, communication complexity); some impossibility results for one-round distributed oblivi- ous transfer protocols; two polynomial-based constructions implementing 1-out-of-n dis- tributed oblivious transfer, which generalize and strengthen the two constructions for 1-out-of-2 given by Naor and Pinkas; as well as new one-round and two-round distributed oblivious transfer protocols, both for threshold and general access structures on the set of Servers, which are optimal with respect to some of the given bounds. Most of these constructions are basically combinatorial in nature

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    Big Data Processing with Peer-To-Peer Architectures

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    Ph.DDOCTOR OF PHILOSOPH

    27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany

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    Distributed Sparse Computing and Communication for Big Graph Analytics and Deep Learning

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    Sparsity can be found in the underlying structure of many real-world computationally expensive problems including big graph analytics and large scale sparse deep neural networks. In addition, if gracefully investigated, many of these problems contain a broad substratum of parallelism suitable for parallel and distributed executions of sparse computation. However, usually, dense computation is preferred to its sparse alternative as sparse computation is not only hard to parallelize due to the irregular nature of the sparse data, but also complicated to implement in terms of rewriting a dense algorithm into a sparse one. Hence, foolproof sparse computation requires customized data structures to encode the sparsity of the sparse data and new algorithms to mask the complexity of the sparse computation. However, by carefully exploiting the sparse data structures and algorithms, sparse computation can reduce memory consumption, communication volume, and processing power and thus undoubtedly move the scalability boundaries compared to its dense equivalent. In this dissertation, I explain how to use parallel and distributed computing techniques in the presence of sparsity to solve large scientific problems including graph analytics and deep learning. To meet this end goal, I leverage the duality between graph theory and sparse linear algebra primitives, and thus solve graph analytics and deep learning problems with the sparse matrix operations. My contributions are fourfold: (1) design and implementation of a new distributed compressed sparse matrix data structure that reduces both computation and communication volumes and is suitable for sparse matrix-vector and sparse matrix-matrix operations, (2) introducing the new MPI*X parallelism model that deems threads as basic units of computing and communication, (3) optimizing sparse matrix-matrix multiplication by employing different hashing techniques, and (4) proposing the new data-then-model parallelism that mitigates the effect of stragglers in sparse deep learning by combining data and model parallelisms. Altogether, these contributions provide a set of data structures and algorithms to accelerate and scale the sparse computing and communication

    Generalized Zig-zag Functions and Oblivious Transfer Reductions.

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    The Computational Complexity of Some Games and Puzzles With Theoretical Applications

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    The subject of this thesis is the algorithmic properties of one- and two-player games people enjoy playing, such as Sudoku or Chess. Questions asked about puzzles and games in this context are of the following type: can we design efficient computer programs that play optimally given any opponent (for a two-player game), or solve any instance of the puzzle in question? We examine four games and puzzles and show algorithmic as well as intractability results. First, we study the wolf-goat-cabbage puzzle, where a man wants to transport a wolf, a goat, and a cabbage across a river by using a boat that can carry only one item at a time, making sure that no incompatible items are left alone together. We study generalizations of this puzzle, showing a close connection with the Vertex Cover problem that implies NP-hardness as well as inapproximability results. Second, we study the SET game, a card game where the objective is to form sets of cards that match in a certain sense using cards from a special deck. We study single- and multi-round variations of this game and establish interesting con- nections with other classical computational problems, such as Perfect Multi- Dimensional Matching, Set Packing, Independent Edge Dominating Set, and Arc Kayles. We prove algorithmic and hardness results in the classical and the parameterized sense. Third, we study the UNO game, a game of colored numbered cards where players take turns discarding cards that match either in color or in number. We extend results by Demaine et. al. (2010 and 2014) that connected one- and two-player generaliza- tions of the game to Edge Hamiltonian Path and Generalized Geography, proving that a solitaire version parameterized by the number of colors is fixed param- eter tractable and that a k-player generalization for k greater or equal to 3 is PSPACE-hard. Finally, we study the Scrabble game, a word game where players are trying to form words in a crossword fashion by placing letter tiles on a grid board. We prove that a generalized version of Scrabble is PSPACE-hard, answering a question posed by Demaine and Hearn in 2008
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