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Worstcase to averagecase reductions based on Gaussian measures
 SIAM J. on Computing
, 2004
"... We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost linear in the dimension of the lattice. The lattice problems we consider are the shortest vector problem, the shortest indepe ..."
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Cited by 128 (23 self)
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We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost linear in the dimension of the lattice. The lattice problems we consider are the shortest vector problem, the shortest
WorstCase to AverageCase Reductions for Module Lattices
"... Abstract. Most latticebased cryptographic schemes are built upon the assumed hardness of the Short Integer Solution (SIS) and Learning With Errors (LWE) problems. Their efficiencies can be drastically improved by switching the hardness assumptions to the more compact RingSIS and RingLWE problems. ..."
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Cited by 7 (1 self)
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lattices (which themselves generalize arbitrary and ideal lattices). As these new problems enlarge the toolbox of the latticebased cryptographer, they could prove useful for designing new schemes. Importantly, the worstcase to averagecase reductions for the module problems are (qualitatively) sharp
On WorstCase to AverageCase Reductions for NP Problems
 IN PROCEEDINGS OF THE 44TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 2003
"... We show that if an NPcomplete problem has a nonadaptive selfcorrector with respect to a samplable distribution then coNP is contained in AM/poly and the polynomial hierarchy collapses to the third level. Feigenbaum and Fortnow show the same conclusion under the stronger assumption that an NPcompl ..."
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Cited by 61 (6 self)
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complete problem has a nonadaptive random selfreduction. Our result
WorstCase to AverageCase Reductions Revisited
"... Abstract. A fundamental goal of computational complexity (and foundations of cryptography) is to find a polynomialtime samplable distribution (e.g., the uniform distribution) and a language in NTIME(f(n)) for some polynomial function f, such that the language is hard on the average with respect to ..."
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Cited by 5 (0 self)
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worstcase/averagecase connection. In other words, their techniques give a way to bypass the impossibility arguments. By taking a closer look at the proof of [GSTS05], we discover that the worstcase/averagecase connection is proven by a reduction that ”almost ” falls under the category ruled out
On WorstCase to AverageCase Reductions for NP Problems
"... 1. Introduction WorstCase versus AverageCase Complexity A problem in distributional NP [18] is a pair (L, D)where ..."
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1. Introduction WorstCase versus AverageCase Complexity A problem in distributional NP [18] is a pair (L, D)where
WorstCase Optimal and AverageCase Efficient Geometric AdHoc Routing
, 2003
"... In this paper we present GOAFR, a new geometric adhoc routing algorithm combining greedy and face routing. We evaluate this algorithm by both rigorous analysis and comprehensive simulation. GOAFR is the first adhoc algorithm to be both asymptotically optimal and averagecase e#cient. For our simul ..."
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Cited by 245 (11 self)
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In this paper we present GOAFR, a new geometric adhoc routing algorithm combining greedy and face routing. We evaluate this algorithm by both rigorous analysis and comprehensive simulation. GOAFR is the first adhoc algorithm to be both asymptotically optimal and averagecase e#cient. For our
AverageCase Complexity
 in Foundations and Trends in Theoretical Computer Science Volume 2, Issue 1
, 2006
"... We survey the averagecase complexity of problems in NP. We discuss various notions of goodonaverage algorithms, and present completeness results due to Impagliazzo and Levin. Such completeness results establish the fact that if a certain specific (but somewhat artificial) NP problem is easyonav ..."
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Cited by 25 (0 self)
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is of particular interest and that do not yet fit into this theory. A major open question is whether the existence of hardonaverage problems in NP can be based on the P ̸ = NP assumption or on related worstcase assumptions. We review negative results showing that certain proof techniques cannot prove such a
An Averagecase Analysis of the Gaussian Algorithm for Lattice Reduction
, 1996
"... .The Gaussian algorithm for lattice reduction in dimension 2 is analysed under its standard version. It is found that, when applied to random inputs in a continuous model, the complexity is constant on average, the probability distribution decays geometrically, and the dynamics is characterized by a ..."
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Cited by 47 (9 self)
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.The Gaussian algorithm for lattice reduction in dimension 2 is analysed under its standard version. It is found that, when applied to random inputs in a continuous model, the complexity is constant on average, the probability distribution decays geometrically, and the dynamics is characterized
Structural lattice reduction: Generalized worstcase to averagecase reductions. Eprint report 2014/283
, 2014
"... In lattice cryptography, worstcase to averagecase reductions rely on two problems: Ajtai’s SIS and Regev’s LWE, which refer to a very small class of random lattices related to the group G = Znq. We generalize worstcase to averagecase reductions to (almost) all integer lattices, by allowing G to ..."
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Cited by 1 (1 self)
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In lattice cryptography, worstcase to averagecase reductions rely on two problems: Ajtai’s SIS and Regev’s LWE, which refer to a very small class of random lattices related to the group G = Znq. We generalize worstcase to averagecase reductions to (almost) all integer lattices, by allowing G
Q : Worstcase Fair Weighted Fair Queueing
"... The Generalized Processor Sharing (GPS) discipline is proven to have two desirable properties: (a) it can provide an endtoend boundeddelay service to a session whose traffic is constrained by a leaky bucket; (b) it can ensure fair allocation of bandwidth among all backlogged sessions regardless o ..."
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Cited by 361 (11 self)
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The Generalized Processor Sharing (GPS) discipline is proven to have two desirable properties: (a) it can provide an endtoend boundeddelay service to a session whose traffic is constrained by a leaky bucket; (b) it can ensure fair allocation of bandwidth among all backlogged sessions regardless of whether or not their traffic is constrained. The former property is the basis for supporting guaranteed service traffic while the later property is important for supporting besteffort service traffic. Since GPS uses an idealized fluid model which cannot be realized in the real world, various packet approximation algorithms of GPS have been proposed. Among these, Weighted Fair Queueing (WFQ) also known as Packet Generalized Processor Sharing (PGPS) has been considered to be the best one in terms of accuracy. In particular, it has been proven that the delay bound provided by WFQ is within one packet transmission time of that provided by GPS. In this paper, we will show that, contrary to pop...
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