Results 1  10
of
12
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 ..."
Abstract

Cited by 41 (9 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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
Advanced Approximation Algorithms (CMU 15854B, Spring 2008) Lecture 19: Sparsest Cut and L1 Embeddings
, 2008
"... We will be studying the Sparsest cut problem in this lecture. In this context we will see how metric methods help in the design of approximation algorithms. We proceed to define the problem and briefly give some motivation for studying the problem. The input to the Sparsest Cut problem is where and ..."
Abstract
 Add to MetaCart
We will be studying the Sparsest cut problem in this lecture. In this context we will see how metric methods help in the design of approximation algorithms. We proceed to define the problem and briefly give some motivation for studying the problem. The input to the Sparsest Cut problem is where and • A weighted graph G = (V, E) with positive edge weights (or costs or capacities, as they are called in this context) ce for every edge e ∈ E. As is usual, n = V . • A set of pairs of vertices {(s1, t1), (s2, t2)...(sk, tk)}, with associated demands Di between si and ti. Given such a graph, we define sparsity of a cut S ⊆ V to be c(S, ¯ S) = D(S, ¯ S) = Φ(S) = c(S, ¯ S)
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 ..."
Abstract
 Add to MetaCart
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
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 ..."
Abstract
 Add to MetaCart
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
2 Local and Almost LinearTime Clustering and Partitioning
, 2009
"... You should probably know that • the first problem set (due October 15) is posted on the class website, and • its hints are also posted there. Also, today in class there was a majority vote for posting problem sets earlier. Professor Kelner will post the problem sets from two years ago, but he reserv ..."
Abstract
 Add to MetaCart
You should probably know that • the first problem set (due October 15) is posted on the class website, and • its hints are also posted there. Also, today in class there was a majority vote for posting problem sets earlier. Professor Kelner will post the problem sets from two years ago, but he reserves the right to add new problems once a problem set has already been posted. Questions from last time. • What is a level set? The level set of a function corresponding to a (fixed) constant c is the set of points in the function’s domain whose image equals c. • What is a good reference on applications of expander graphs? A course taught by Nathan Linial and Avi Wigderson [3]. Plan for today. We use what we proved last time to obtain a local clustering algorithm from a random walk scheme. Then, noting that similar results to the ones proved last time also hold for PageRank, we obtain a second scheme that yields a second, better local clustering algorithm. Finally, we briefly motivate the technique of sparsification, which we will discuss next time.