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Sieving for Shortest Vectors in Ideal Lattices
, 2011
"... Lattice based cryptography is gaining more and more importance in the cryptographic community. It is a common approach to use a special class of lattices, socalled ideal lattices, as the basis of lattice based crypto systems. This speeds up computations and saves storage space for cryptographic ke ..."
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Cited by 5 (0 self)
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counterparts. In this paper we present IdealListSieve, a variant of the ListSieve algorithm, that is a randomized, exponential time sieving algorithm solving the shortest vector problem in lattices. Our variant makes use of the special structure of ideal lattices. We show that it is indeed possible to find a
Sieving for Shortest Vectors in Ideal Lattices: a Practical Perspective
"... Abstract. Latticebased cryptography is a promising candidate for providing cryptographic functions that remain secure in a postquantum era. The security of latticebased schemes relies on the hardness of lattice problems such as the problem of finding short vectors in integral lattices. In this wo ..."
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use ideal lattices, and it is known that sieving algorithms can benefit from their additional algebraic structure. Namely, the list size can be reduced by considering vectors along with all their rotations. We show that
A Sieve Algorithm for the Shortest Lattice Vector Problem
, 2001
"... We present a randomized 2 O(n) time algorithm to compute a shortest nonzero vector in an ndimensional rational lattice. The best known time upper bound for this problem was 2 O(n log n) ..."
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Cited by 212 (3 self)
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We present a randomized 2 O(n) time algorithm to compute a shortest nonzero vector in an ndimensional rational lattice. The best known time upper bound for this problem was 2 O(n log n)
Virtual Time and Global States of Distributed Systems
 PARALLEL AND DISTRIBUTED ALGORITHMS
, 1988
"... A distributed system can be characterized by the fact that the global state is distributed and that a common time base does not exist. However, the notion of time is an important concept in every day life of our decentralized "real world" and helps to solve problems like getting a consiste ..."
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Cited by 741 (6 self)
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consistent population census or determining the potential causality between events. We argue that a linearly ordered structure of time is not (always) adequate for distributed systems and propose a generalized nonstandardmodel of time which consists of vectors of clocks. These clockvectors arepartially
Taming the Underlying Challenges of Reliable Multihop Routing in Sensor Networks
 In SenSys
, 2003
"... The dynamic and lossy nature of wireless communication poses major challenges to reliable, selforganizing multihop networks. These nonideal characteristics are more problematic with the primitive, lowpower radio transceivers found in sensor networks, and raise new issues that routing protocols mu ..."
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Cited by 775 (21 self)
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The dynamic and lossy nature of wireless communication poses major challenges to reliable, selforganizing multihop networks. These nonideal characteristics are more problematic with the primitive, lowpower radio transceivers found in sensor networks, and raise new issues that routing protocols
Mtree: An Efficient Access Method for Similarity Search in Metric Spaces
, 1997
"... A new access meth d, called Mtree, is proposed to organize and search large data sets from a generic "metric space", i.e. whE4 object proximity is only defined by a distance function satisfyingth positivity, symmetry, and triangle inequality postulates. We detail algorith[ for insertion o ..."
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Cited by 652 (38 self)
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are reported, considering as th performance criteria th number of page I/O's and th number of distance computations. Th results demonstratethm th Mtree indeed extendsth domain of applicability beyond th traditional vector spaces, performs reasonably well inhE[94Kv#E44V[vh data spaces, and scales well
Segmentation of brain MR images through a hidden Markov random field model and the expectationmaximization algorithm
 IEEE TRANSACTIONS ON MEDICAL. IMAGING
, 2001
"... The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic limi ..."
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Cited by 619 (14 self)
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The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic
An Architecture for WideArea Multicast Routing
"... Existing multicast routing mechanisms were intended for use within regions where a group is widely represented or bandwidth is universally plentiful. When group members, and senders to those group members, are distributed sparsely across a wide area, these schemes are not efficient; data packets or ..."
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Cited by 529 (22 self)
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Existing multicast routing mechanisms were intended for use within regions where a group is widely represented or bandwidth is universally plentiful. When group members, and senders to those group members, are distributed sparsely across a wide area, these schemes are not efficient; data packets or membership report information are occasionally sent over many links that do not lead to receivers or senders, respectively. Wehave developed a multicast routing architecture that efficiently establishes distribution trees across wide area internets, where many groups will be sparsely represented. Efficiency is measured in terms of the state, control message processing, and data packet processing, required across the entire network in order to deliver data packets to the members of the group. Our Protocol Independent Multicast (PIM) architecture: (a) maintains the traditional IP multicast service model of receiverinitiated membership; (b) can be configured to adapt to different multicast group and network characteristics; (c) is not dependent on a specific unicast routing protocol; and (d) uses softstate mechanisms to adapt to underlying network conditions and group dynamics. The robustness, flexibility, and scaling properties of this architecture make it well suited to large heterogeneous internetworks.
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 548 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
Results 1  10
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131,463