Results 1  10
of
14
Mixnetworks with Restricted Routes
 Proceedings of Privacy Enhancing Technologies workshop (PET 2003). SpringerVerlag, LNCS 2760
, 2003
"... We present a mix network topology that is based on sparse expander graphs, with each mix only communicating with a few neighbouring others. We analyse the anonymity such networks provide, and compare it with fully connected mix networks and mix cascades. We prove that such a topology is efficient si ..."
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Cited by 46 (8 self)
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We present a mix network topology that is based on sparse expander graphs, with each mix only communicating with a few neighbouring others. We analyse the anonymity such networks provide, and compare it with fully connected mix networks and mix cascades. We prove that such a topology is efficient since it only requires the route length of messages to be relatively small in comparison with the number of mixes to achieve maximal anonymity. Additionally mixes can resist intersection attacks while their batch size, that is directly linked to the latency of the network, remains constant. A worked example of a network is also presented to illustrate how these results can be applied to create secure mix networks in practise.
An introduction to randomness extractors
"... Abstract. We give an introduction to the area of “randomness extraction” and survey the main concepts of this area: deterministic extractors, seeded extractors and multiple sources extractors. For each one we briefly discuss background, definitions, explicit constructions and applications. 1 ..."
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Cited by 14 (2 self)
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Abstract. We give an introduction to the area of “randomness extraction” and survey the main concepts of this area: deterministic extractors, seeded extractors and multiple sources extractors. For each one we briefly discuss background, definitions, explicit constructions and applications. 1
Eigenvectors of the discrete Laplacian on regular graphs  a statistical approach
, 2008
"... In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical observations, suggesting that the eigenvectors follow a Gaussian distri ..."
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Cited by 11 (2 self)
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In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical observations, suggesting that the eigenvectors follow a Gaussian distribution. Following this assumption, we reconstruct some properties of the nodal structure which were observed in numerical simulations, but were not explained so far [1]. We also show that some statistical properties of the nodal pattern cannot be described in terms of a percolation model, as opposed to the suggested correspondence [2] for eigenvectors of 2 dimensional manifolds.
Eigenvectors of random graphs: Nodal domains
"... We initiate a systematic study of eigenvectors of random graphs. Whereas much is known about eigenvalues of graphs and how they reflect properties of the underlying graph, relatively little is known about the corresponding eigenvectors. Our main focus in this paper is on the nodal domains associated ..."
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Cited by 7 (0 self)
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We initiate a systematic study of eigenvectors of random graphs. Whereas much is known about eigenvalues of graphs and how they reflect properties of the underlying graph, relatively little is known about the corresponding eigenvectors. Our main focus in this paper is on the nodal domains associated with the different eigenfunctions. In the analogous realm of Laplacians of Riemannian manifolds, nodal domains have been the subject of intensive research for well over a hundred years. Graphical nodal domains turn out to have interesting and unexpected properties. Our main theorem asserts that there is a constant c such that for almost every graph G, each eigenfunction of G has at most two large nodal domains, and in addition at most c exceptional vertices outside these primary domains. We also discuss variations of these questions and briefly report on some numerical experiments which, in particular, suggest that almost surely there are just two nodal domains and no exceptional vertices. 1
Regular trees in random regular graphs
, 2008
"... We investigate the size of the embedded regular tree rooted at a vertex in a d regular random graph. We show that almost always, the radius of this tree will be 1 2 log n, where n is the number of vertices in the graph. And we give an asymptotic estimate for Gauss’ Hypergeometric Function. 1 ..."
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Cited by 5 (0 self)
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We investigate the size of the embedded regular tree rooted at a vertex in a d regular random graph. We show that almost always, the radius of this tree will be 1 2 log n, where n is the number of vertices in the graph. And we give an asymptotic estimate for Gauss’ Hypergeometric Function. 1
Data stream algorithms via expander graphs
 In 19th International Symposium on Algorithms and Computation (ISAAC
, 2008
"... Abstract. We present a simple way of designing deterministic algorithms for problems in the data stream model via lossless expander graphs. We illustrate this by considering two problems, namely, ksparsity testing and estimating frequency of items. 1 ..."
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Cited by 4 (0 self)
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Abstract. We present a simple way of designing deterministic algorithms for problems in the data stream model via lossless expander graphs. We illustrate this by considering two problems, namely, ksparsity testing and estimating frequency of items. 1
Hard Metrics From Cayley Graphs Of Abelian Groups
, 2009
"... Hard metrics are the class of extremal metrics with respect to embedding into Euclidean spaces; they incur Ω(log n) multiplicative distortion, which is as large as it can possibly get for any metric space of size n. Besides being very interesting objects akin to expanders and good errorcorrecting ..."
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Cited by 2 (0 self)
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Hard metrics are the class of extremal metrics with respect to embedding into Euclidean spaces; they incur Ω(log n) multiplicative distortion, which is as large as it can possibly get for any metric space of size n. Besides being very interesting objects akin to expanders and good errorcorrecting codes, and having a rich structure, such metrics are important for obtaining lower bounds in combinatorial optimization, e. g., on the value of MinCut/MaxFlow ratio for multicommodity flows. For more than a decade, a single family of hard metrics was known (Linial, London, Rabinovich (Combinatorica 1995) and Aumann, Rabani (SICOMP 1998)). Recently, a different family was found by Khot and Naor (FOCS 2005). In this paper we present a general method of constructing hard metrics. Our results extend to embeddings into negative type metric spaces and into ℓ1.
PublicKey Encryption with Efficient Amortized Updates
"... Abstract. Searching and modifying publickey encrypted data has received a lot of attention in recent literature. In this paper we revisit this important topic and achieve improved amortized bounds including resolving a prominent open question posed by Boneh et al. [3]. First, we consider the follo ..."
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Abstract. Searching and modifying publickey encrypted data has received a lot of attention in recent literature. In this paper we revisit this important topic and achieve improved amortized bounds including resolving a prominent open question posed by Boneh et al. [3]. First, we consider the following much simpler to state problem: A server holds a copy of Alice’s database that has been encrypted under Alice’s public key. Alice would like to allow other users in the system to replace a bit of their choice in the server’s database by communicating directly with the server, despite other users not having Alice’s private key. However, Alice requires that the server should not know which bit was modified. Additionally, she requires that the modification protocol should have “small ” communication complexity (sublinear in the database size). This task is referred to as private database modification, and is a central tool in building a more general protocol for modifying and searching over publickey encrypted data. Boneh et al. [3] first considered
Computational Complexity and Information Asymmetry in Election Audits with LowEntropy Randomness
"... We investigate the security of an election audit using a table of random numbers prepared in advance. We show how this scenario can be modeled using tools from combinatorial graph theory and computational complexity theory, and obtain the following results: (1) A randomly generated table can be used ..."
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We investigate the security of an election audit using a table of random numbers prepared in advance. We show how this scenario can be modeled using tools from combinatorial graph theory and computational complexity theory, and obtain the following results: (1) A randomly generated table can be used to produce a statistically good election audit that requires less randomness to be generated in real time by the auditors. (2) It is likely to be computationally infeasible for an adversary to compute, given a preprepared table of random numbers, how to minimize their chances of detection in an audit. (3) It is computationally infeasible to distinguish a truly random table from a malicious table that has been modified to decrease the probability of detecting cheating in certain precincts. 1